2024-03-29T13:30:37Z
https://hipatiapress.com/hpjournals/index.php/redimat/oai
oai:oai.hipatiapress.com:article/128
2023-09-26T11:39:37Z
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Vol. 1 No. 2 (2012): June ; 105-135
“Nobody Can Sit There”: Two Perspectives on how Mathematics Problems in Context Mediate Group Problem Solving Discussions
Zahner, William C.; Boston University
2012-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/128
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This study examines how a group ofbilingualninth grade algebra students discussed two word problems stated in terms of "real life" contexts. Using a lens of mediated action (Wertsch, 1998), the analysis reveals two distinct ways that the problem contexts influenced the group's mathematical reasoning. In one problem, the problem context afforded particular ways of interpreting the given inscriptions, which had benefits as well as costs. In the other problem, the unfamiliar story and terminology appeared the hinder the group's mathematical reasoning. These two forms of context mediation are discussed in light of current research on the use of real life problems in mathematics education.Keywords: mathematical discussions, mediation, word problems, algebra, group discussions
oai:oai.hipatiapress.com:article/187
2023-09-26T11:39:57Z
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Vol. 1 No. 1 (2012): February; 5-28
Mathematicians, Mathematics Educators and the State of the World
D'Ambrosio, Ubiratán; Pontificia Universidade Catolica de Sao Paulo
2012-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/187
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This paper is, essentially, the transcription of my conference at the conference CIEAEM 63, promoted by the CIEAEM/Commission for the Study and Improvement of Mathematics Teaching, held in Barcelona, Spain, from 24 to 29 July 2011. The main objective of the CIEAEM, since its foundation, in the fifties, has been to analyze the actual conditions and the possibilities for the development of mathematics education in order to improve the quality of teaching mathematics. The annual conferences are the essential means for realizing this goal. The main theme of the annual conference of 2011 was “Facilitating access and participation: Mathematical practices inside and outside the classroom”. I understand access and participation as Social Justice.
oai:oai.hipatiapress.com:article/190
2023-09-26T11:39:57Z
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Vol. 1 No. 1 (2012): February; 57-78
Estudio de las Actitudes Hacia una Postura Sociocultural y Política de la Educación Matemática en Maestros en Formación Inicial
Blanco Alvarez, Hilbert; Docente de la Universidad de Nariño
2012-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/190
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This article presents a study on attitudes towards social, cultural and political posture of mathematics education of 154 students in second year of primary education degree at the Universidad Autónoma de Barcelona. The research was conducted in two phases: the first established common features of a sociocultural and political posture in Mathematics Education starting from comparative analysis of four theories of mathematics education, and a second phase were found consonances and dissonances between attitudes of students and this posture through a closed questionnaire type Likert with two open questions. Finally, it concluded that the attitude towards sociocultural and political posture of mathematics education of participating students is moderately positive.
oai:oai.hipatiapress.com:article/191
2023-09-26T11:39:57Z
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Vol. 1 No. 1 (2012): February; 29-56
Embracing Nepantla: Rethinking "Knowledge" and its Use in Mathematics Teaching
Gutierrez, Rochelle; University of Illinois at Urbana - Champaign
2012-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/191
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Although educational researchers are moving beyond purely psychological and cognitive models of learning to consider the ways in which mathematics teaching might reach a more diverse student population, this work remains in its infancy, and the concept of “knowledge” is rarely questioned. This paper begins with the idea that mathematics education has much to gain from perspectives in Latin@ studies. I draw on the work of Gloria Anzaldúa, specifically her concepts of “conocimiento” and “Nepantla” to bring a more holistic/connected perspective to the “knowledge” teachers may need for teaching and highlight how it might align with broader definitions of mathematics. I also offer examples from a partnership with a Chicago high school to show how pre-service teachers move through cycles of knowledge construction. Implications for teacher education, and teacher recruitment are discussed.
oai:oai.hipatiapress.com:article/193
2023-09-26T11:39:57Z
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Vol. 1 No. 1 (2012): February; 79-92
Mathematics Education and Ethnomathematics. A Connection in Need of Reinforcement.
Palhares, Pedro; University of Minho
2012-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/193
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In this article we analyze Ethnomathematics research in Portugal in the recent past and the way it has been used in Education. We divide our reflection in three main parts. One is about people’s discourse and actions and how to use them to uncover mathematical thinking. The second is about artifacts and how to use them to uncover mathematical thinking. The third is about how to use ethnomathematics research to improve mathematics education. In each of these sections we reflect on some of what has been made and we propose paths we think are worth pursuing.
oai:oai.hipatiapress.com:article/211
2023-09-26T11:39:37Z
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Vol. 1 No. 2 (2012): June ; 159-193
The Use of Concrete Artifacts in Analytic Geometry: the Ellipse Experience
Cortes Zavala, José Carlos; Universidad Michoacana
Soto Rodríguez, Héctor Arturo; Universidad Michoacana
2012-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/211
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The purpose of this article is to provide the results of a research on the use ofspecific artefacts (two different ellipsographs) for the learning of Mathematics,specifically in Analytic Geometry on the topic of Ellipse. It was implementedone activity for each one of the artefact, by means of the use of working sheetsthat guided the students for tem to build the formal concept of Ellipse, answeringto the corresponding questions in each activity as well as manipulating theellipsograph. All with the aim to facilitate to the students the understanding andlearning of the mathematic concepts. Keywords: analytic geometry, ellipsograph, collaborative learning
oai:oai.hipatiapress.com:article/229
2023-09-26T11:38:59Z
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Vol. 1 No. 3 (2012): October; 301-336
Analyzing students’ difficulties in understanding real numbers
Voskoglou, Michael; Professor of Mathematical Sciences
Graduate Technological Educational Institute (T.E.I.)
School of Technological Applications
26334 Patras- Greece
Kosyvas, Georgios D.; Varvakio Pilot Lyceum - Palaio Psychico, 15452 Athens, Greece
2012-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/229
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This article reports on a study of high-school and of technologist students (prospective engineers and economists) understanding of real numbers. Our study was based on written response to a properly designed questionnaire and on interviews taken from students. The quantitative results of our experiment showed an almost complete failure of the technologist students to deal with processes connected to geometric constructions of incommensurable magnitudes. However, this didn’t prevent them in answering satisfactorily the other questions. The superiority of their correct answers with respect to those of high-school students, although the majority of them correspond to mediocre graduates of the secondary education, was evident in most cases. This is a strong indication that the age and the width of mathematical knowledge of the individual play an important role for the better understanding of the real numbers. The results of our experiment suggest also that the ability to transfer in comfort among several representations of real numbers helps students in obtaining a better understanding of them. A theoretical explanation about this is obtained through the adoption of the conceptual framework of dimensions of knowledge, introduced by Tirosh et al. (1998) for studying the comprehension of rational numbers. Following in part the idea of generic decomposition of the APOS analysis (Weller et al. 2009) we suggest a possible order for development of understanding the real numbers by students when teaching them at school. Some questions open to further research are also mentioned at the end of the paper. Keywords: Real, rational, irrational, algebraic and transcendental numbers, fractions, decimals, representations of real numbers.
oai:oai.hipatiapress.com:article/235
2023-09-26T11:39:37Z
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Vol. 1 No. 2 (2012): June ; 136-158
Mathematics Teacher Continuing Education: Fostering the Constitution of a Learning Network
Lobo da Costa, Nielce Meneguelo; UNIBAN BRASIL
Brisola Brito Prado, Maria Elisabette; UNIBAN BRASIL
2012-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/235
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This qualitative study analyzes log entries from a group of elementary school teachers aiming to understand how a collaborative learning network is set up during the continued development actions. The interpretive analysis revealed the following categories: Shared reflection, Learning, Trust, Reflection on practice, Experience Exchanging, Shared Goals and Commitment to the other, which show the features of collaborative work. Categories were analyzed using CHIC software which allowed for the relational analysis among them showing that development under this perspective can favor the practitioner’s professional development by offering him opportunities to experience his role as a learner and a teacher simultaneously. Keywords: Professional development, Collaborative work, Learning networks
oai:oai.hipatiapress.com:article/249
2023-09-26T11:38:08Z
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Vol. 2 No. 3 (2013): October; 316-342
Reconceptualizing Research on Workplace mathematics: Negotiations Grounded in Personal Practical Experiences
Naresh, Nirmala; Miami University
Chahine, Iman; Georgia State University
2013-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/249
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In this paper, we view and describe our transitions through three phases of a reflective cycle as a journey from the past to the future. In the descriptive phase, we delve into our past research experiences and address questions such as: What is the role of mathematics at work? What counts as mathematics in the workplace? Whose perceptions matter - the insiders' (workers') or the outsiders' (researchers')? In doing so, we uncovered additional venues for exploration that called for a new mode of analysis. We transition into a theory-building phase where we share our learning experiences that occurred in-the-moment. We then shift to an action oriented (reflexive) phase during which we construe personal practical theories that enable us to negotiate broader understandings of the role of mathematics at work and identify areas for future inquiry. We document our lived experiences as informed and inspired by our work with two groups of workers - bus conductors and street vendors.
oai:oai.hipatiapress.com:article/254
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Vol. 1 No. 2 (2012): June ; 194-213
How Do Elementary Preservice Teachers Form Beliefs and Attitudes Toward Geometry Learning? Implications for Teacher Preparation Programs
Yang, Kai-Ju; Indiana University Bloomington
2012-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/254
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In my personal interactions with elementary preservice teachers (EPSTs) at a large Midwestern university in United States, many EPSTs held negative beliefs and attitudes about geometry learning. Although finding ways to help EPSTs change their negative beliefs and attitudes is an important issue, it can be best addressed by first investigating how they are formed. This study sought to document how EPSTs’ beliefs about and attitudes toward geometry were formed prior to and during a mathematics and pedagogy course at a large Midwestern university in United States. McLeod’s (1989) theoretical framework of influencing one’s beliefs and attitudes toward specific action events, and objects --- Representation, Discrepancy, and Metacognition --- was used to analyze data from two interviews with each of four EPSTs. The results of the analysis confirmed McLeod’s framework but also identified a fourth factor, understanding, as playing an important role in affecting EPST’s beliefs about and attitudes toward geometry. If in fact we can understand how EPSTs beliefs about and attitudes toward learning geometry are formed, we will be able to find out ways to help EPSTs change negative orientations, which can have positive implications for designing mathematics and pedagogy courses for EPSTs that will better prepare them to be effective mathematics teachers.Keywords: Beliefs, Attitudes, Geometry, Elementary Preservice Teachers.
oai:oai.hipatiapress.com:article/328
2023-09-26T11:38:08Z
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Vol. 2 No. 3 (2013): October; 293-315
Working with Families in Bilingual Mathematics: Supporting a Leadership Space for Latina Mothers
Lopez Leiva, Carlos; University of New Mexico
Torres, Zayoni; The University of Illinois at Chicago
2013-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/328
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This paper analyzes the work developed with a group of Latina mothers in a mathematics afterschool program for a period of 3 ½ years. The analysis of the productive patterns of interaction of this group of mothers with a group of bilingual participants shows that the program’s participation and activity structure closely determines the quality of the mothers’ participation. We present a sequence of attempts developed to alter this structure in order to successfully capitalize on mothers’ leadership roles and knowledge during intergenerational and bilingual mathematical activity. We further discuss key social processes—acknowledging mothers as facilitators, focusing on communication rather than on a specific language, and supporting mathematics performance through social interactions—that opened up a space for Latina mothers’ leadership and dynamic participation during bilingual mathematical activity.
oai:oai.hipatiapress.com:article/379
2023-09-26T11:38:59Z
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Vol. 1 No. 3 (2012): October; 222-245
Understanding of Randomness by Prospective Primary School Teachers
Batanero, Carmen; Universidad de Granada
Gómez, Emilse; Universidad Nacional de Colombia
Serrano, Luis; Universidad de Granada
Contreras, José Miguel; Universidad de Granada
2012-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/379
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Current curricular guidelines for probability at Primary school level imply the need for a specific training of prospective teachers, which should be based on the previous assessment of their training needs. In order to contribute to this need, in this paper we present the analysis of responses by 157 Spanish prospective teachers to an open question, taken from previous research on subjective perception of randomness. The results show a mixture of correct and wrong conceptions, some of which parallel some historical conceptions of randomness. Teachers’ educators could start from these intuitions to help prospective teachers advance to a broader meaning of the concept, adequate for their future teaching responsibility.
oai:oai.hipatiapress.com:article/390
2023-09-26T11:38:59Z
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Vol. 1 No. 3 (2012): October; 278-300
Understanding the practices of mathematics teacher educators who focus on issues of equity
McLeman, Laura; University of MIchigan-Flint
Department of Mathematics
Vomvoridi-Ivanovic, Eugenia; College of Education
Dept of Secondary Education
University of South Florida
2012-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/390
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Most mathematics teacher educators (MTEs) would agree that teachers must be prepared to provide equitable mathematics instruction to all their students. However, to date, there is not a wide database regarding the practice of MTEs who play an integral role in this preparation. In this paper we argue that additional information is needed about the approaches in which MTEs have addressed or incorporated equity as a core part of the preparation of teachers. We further argue for the importance of developing a research agenda that examines the practices of MTEs who teach through a lens of equity, the goal of which would be to build models of professional development that prepare and support other MTEs to develop this specialized knowledge.Keywords: mathematics teacher educators, practice, equity, research
oai:oai.hipatiapress.com:article/414
2023-09-26T11:38:43Z
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Vol. 2 No. 1 (2013): February; 77-99
From human activity to conceptual understanding of a mathematical concept
Jojo, Zingiswa Mybert Monica; Mangosuthu University of Technology
Maharaj, Aneshkumar; University of KwaZulu Natal
Brijlall, Deonarain; University of KwaZulu Natal
2013-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/414
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Abstract:This article reports on a study which investigated first year university engineering students’ construction of the definition of the concept of the chain rule in differential calculus at a University of Technology in South Africa. An APOS (Action-Process-Objects-Schema) approach was used to explore conceptual understanding displayed by students in learning the chain rule in calculus. Structured worksheets based on instruction designed to induce construction of conceptual understanding of the chain rule were used. A number of students used the straight form technique in differentiating complicated tasks while very few used either the link and Leibniz form techniques. In this manner differentiation of each function within the composite function was accomplished. Students either operated in the Inter- or Trans stages of the Triad. It was found that even students who had inadequate understanding of composition of functions, performed well in the application of the chain rule.Keywords: Calculus, chain rule, APOS, Genetic decomposition
oai:oai.hipatiapress.com:article/459
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Vol. 1 No. 3 (2012): October; 246-277
'Being Good' at Maths: Fabricating Gender Subjectivity
Chronaki, Anna; University of Thessaly
Pechtelidis, Yannis; University of Thessaly
2012-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/459
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Current research in mathematics education places emphasis on the analysis of men and women’s accounts about their life trajectories and choices for studying, working and developing a career that involves the learning and teaching of mathematics. Within this realm, the present study aims to highlight how mathematics, gender and subjectivity become interwoven by focusing the analysis on a single case study, that of Irene -a teacher in her early 40s. Based on how she articulates hegemonic discourses and narrates her relation to mathematics from the time she was a schoolgirl up till her recent work as teacher and her endeavours as participant in a professional development teacher training course, we argue how ‘mathematics’ becomes a mythical object for her subjectification. Irene as a female subject appropriates through her narrative the socially, culturally and historically constructed ideals about maths and gender and essentialises mathematical ability. Our study reveals how dominant discourses concerning ‘mathematics’ and ‘gender’ relate closely to subjectivity fabrication.
oai:oai.hipatiapress.com:article/467
2023-09-26T11:38:08Z
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Vol. 2 No. 3 (2013): October; 343-357
Agents of Change in Promoting Reflective Abstraction: A Quasi-Experimental, Study on Limits in College Calculus
Cappetta, Robert W.; College of DuPage
Zollman, Alan; Northern Illinois University
2013-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/467
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We measured student performance on the concept of limit by promoting reflection through four agents of change: instructor, peer, curriculum and individual. It is based on Piaget’s four constructs of reflective abstraction: interiorization, coordination, encapsulation, and generalization, and includes the notion of reversal, as refined into a construct by Dubinsky. Our quasi-experimental study examined the performance of two sections of first-semester calculus students at a midwestern community college. Scores by students in the experimental section were significantly higher than scores by students in the control traditional section on a posttest of limits. A deeper examination of a three-tiered subgroup showed the reflective abstraction section had moderate effect size on mathematical knowledge and strategic knowledge and a large effect size on explanation.
oai:oai.hipatiapress.com:article/487
2023-09-26T11:38:26Z
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Vol. 2 No. 2 (2013): June ; 242-267
Elementary Student' Spontaneous Metacognitive Functions in Different Types of Mathematical Problems
Mokos, Evagelos; UNIVERSITY OF THE AEGEAN, GREECE
Kafoussi, Sonia; UNIVERSITY OF THE AEGEAN.GREECE
2013-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/487
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Metacognition is the mind's ability to monitor and control itself or, in other words, the ability to know about our knowing (Dunlosky & Bjork, 2008). In mathematics education, the importance of the investigation of students' metacognition during their mathematical activity is focused on the aerea of mathematical problem solving. This study investigates the spontaneous emergence of the metacognitive functions of control and monitoring during the solving of different types of mathematical problems with fifth grade students. We used the "think aloud"method on a group of ten year old students and the resulys showed that metacognitive strategies were used by the students so as the the metacognitive functions of control and monitoring to be achieved.
oai:oai.hipatiapress.com:article/494
2023-09-26T11:38:43Z
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Vol. 2 No. 1 (2013): February; 100-153
Early childhood mathematics education: research, curriculum and educational practice
Alsina, Angel; Universidad de Girona
2013-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/494
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This article reviews data obtained through research into early childhood mathematics education in Spain. It analyses the current curricular directions in mathematics education with early learners. It also provides an overview of mathematical practices in early childhood education classrooms to analyse the commonalities and differences between research, curriculum and educational practice. A review of the research presented at SEIEM symposia from 1997 until 2012 demonstrates: a) very little research has been done, a trend that is repeated in other areas, such as the JCR-Social Sciences Edition or the PME; b) the first steps have been taken to create a more and more cohesive body of research, although until now there has not been enough data to outline the curricular directions; and c) some discrepancies still exist between the mathematical practices in early childhood education classrooms and the official guidelines.
oai:oai.hipatiapress.com:article/525
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Vol. 2 No. 1 (2013): February; 45-76
Agency as Inference: Toward a Critical Theory of Knowledge Objectification
Gutiérrez, José Francisco; University of California at Berkeley
2013-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/525
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This article evaluates the plausibility of synthesizing theory of knowledge objectification (Radford, 2003) with equity research on mathematics education. I suggest the cognitive phenomenon of mathematical inference as a promising locus for investigating the types of agency that equity-driven scholars often care for. In particular, I conceptualize students’ appropriation of cultural artifacts (e.g., algebraic symbols and forms) as semiotic means of objectifying their pre-symbolic inferences as conditional on their agency to carefully and incrementally construct personal meaning for these artifacts. To empirically ground this emerging approach, this study focuses on algebraic generalization (as a type of mathematical inference) and applies Radford’s framework to video data of two iterations of an instructional intervention conducted in a high school program for academically at-risk youth. I analyze and compare students’ acts of appropriation/objectification during whole-class conversations centered on pattern-finding tasks, in relation to the instructional mode adopted for each of the iterations—“direct instruction” vs. “inquiry-based.” The analysis shows that the implementation involving inquiry-based instruction enabled more equitable access to opportunities for agency-as-mathematical inference, whereas the implementation involving direct-instruction was ostensibly more productive. Implications for future equity research involving cognition-and-instruction analyses are discussed.
oai:oai.hipatiapress.com:article/528
2023-09-26T11:38:26Z
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Vol. 2 No. 2 (2013): June ; 183-208
Un origen matemático vs. dos orígenes fenomenológicos: la significación del movimiento de objetos respecto del punto (0,0)
Miranda, Isaias; National Institute Politechich
Radford, Luis; Laurentian University
Guzmán, José; Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional
2013-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/528
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En este artículo se analiza la evolución de las formas de significar, en estudiantes de grado 10, el origen de coordenadas de una gráfica d vs. t que informa sobre el movimiento simultáneo de dos objetos. Esta evolución es analizada a través de la teoría de la objetivación, la cual describe el saber como una forma codificada de acción y reflexión, y el aprendizaje como una transformación del sujeto que resulta de la toma de conciencia de la lógica histórico-cultural que subyace al saber. Desde el punto de vista metodológico, el aprendizaje se investiga como serie de procesos de objetivación; es decir, procesos sociales de toma de conciencia crítica en los que intervienen diferentes medios semióticos puestos en juego por los estudiantes (lenguaje, gestos, símbolos, artefactos, etc.). Los resultados indican la densidad epistemológica del concepto de origen cartesiano, así como las dificultades que implica la toma de conciencia sobre la importancia del punto (0,0) en la descripción del movimiento. Dicha toma de conciencia se caracteriza por un constante refinamiento de dotación de significados durante la interacción sucedida entre los estudiantes, el profesor y el problema a resolver.
oai:oai.hipatiapress.com:article/535
2023-09-26T11:38:26Z
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Vol. 2 No. 2 (2013): June ; 209-241
The Impact of Early Algebra: Results from a Longitudinal Intervention
Brizuela, Barbara M; Tufts University
Martinez, Mara V; University of Illinois-Chicago
Cayton-Hodges, Gabrielle A; Educational Testing Service
2013-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/535
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In this paper, we provide evidence of the impact of early algebra (EA) over time. We document this impact in the following ways: (a) by showing the performance over time of an experimental group of 15 children on an algebra assessment, from 3rd to 5th grade; and (b) by showing how the performance on an algebra assessment of children from an experimental group differs from the performance of a group of comparison students from their same elementary school who did not receive EA instruction from 3rd to 5th grade. We compared students’ scores through comparisons of means, correspondence factorial analyses, and hierarchical analyses. Our results highlight the positive impact of an early access to algebra, indicating that this early access is associated, when we compare 3rd graders to 5th graders, with increased scores on items that involve inequalities and graphs. When comparing experimental to comparison-group students we find increased scores on items that involve variables, functional relations, intra-mathematical contexts, tables, and algebraic expressions. The study adds to a body of literature that has been arguing for EA as well as a need to thread algebra throughout the mathematics curriculum, starting in the earliest grades.
oai:oai.hipatiapress.com:article/570
2023-09-26T11:38:43Z
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Vol. 2 No. 1 (2013): February; 7-44
Three Key Concepts of the Theory of Objectification: Knowledge, Knowing, and Learning
Radford, Luis; Université Laurentienne
2013-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/570
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In this article I sketch three key concepts of a cultural-historical theory of mathematics teaching and learning—the theory of objectification. The concepts are: knowledge, knowing and learning. The philosophical underpinning of the theory revolves around the work of Georg W. F. Hegel and its further development in the philosophical works of K. Marx and the dialectic tradition (including Vygotsky and Leont’ev). Knowledge, I argue, is movement. More specifically, knowledge is a historically and culturally codified fluid form of thinking and doing. Knowledge is pure possibility and can only acquire reality through activity—the activity that mediates knowledge and knowing. The inherent mediated nature of knowing requires learning, which I theorize as social, sensuous and material processes of objectification. The ideas are illustrated through a detailed classroom example with 9-10-year-old students.
oai:oai.hipatiapress.com:article/594
2023-09-26T11:37:53Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/594
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Vol. 3 No. 1 (2014): February; 54-73
An APOS analysis of natural science students’ understanding of integration
Maharaj, Aneshkumar; University of KwaZulu-Natal
2014-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/594
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This article reports on a study which used the APOS (action-process-object-schema) Theory framework and a classification of errors toinvestigate university students’ understanding of the integration concept and its applications. Research was done at the Westville Campus of the University of KwaZulu-Natal in South Africa. The relevant rules for finding antiderivatives, the link between derivatives and antiderivatives, interpreting a definite integral as area under the relevant curve and their context-based applications were taught to undergraduate science students. This paper reports on the analysis of two students’ responses to questions on integrals and their applications. The findings of this study suggest that those students had difficulty in applying the rules for integrals and their applications, and this was possibly the result of them not having appropriate mental structures at the process, object and schema levels.
oai:oai.hipatiapress.com:article/616
2023-09-26T11:38:08Z
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2023-09-26T11:38:08Z
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Vol. 2 No. 3 (2013): October; 274-292
Caminando “Sobre el Suelo Árido” en el Análisis del Discurso del Modelaje Matemático Escolar
Knijnik, Gelsa; Universidade do Vale do Rio dos Sinos
Quartieri, Marli Teresinha; UNIVATES
2013-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/616
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Este artículo examina enunciados relativos a la noción de interés que constituyen el discurso sobre el Modelaje Matemático Escolar (MME), específicamente en la Enseñanza Primaria y Enseñanza Secundaria en Brasil. El enfoque teórico se basa en las teorizaciones de M. Foucault. El material de investigación abarca el conjunto de disertaciones sobre el Modelaje Matemático Escolar realizadas de 1987 a 2009 en Brasil. El ejercicio analítico que se realizó sobre el material de investigación ha producido los siguientes resultados: a) el uso del MME requiere tomar el proceso pedagógico como punto de partida para despertar el interés del alumno; b) el uso del MME hace que el alumno se interese y, por consiguiente, corresponsabilice de su aprendizaje; c) el uso del MME suscita el interés del alumno por la matemática escolar. La discusión de esos enunciados ha posibilitado concluir que la libertad que se concede al alumno para elegir los temas de su interés puede entenderse como una forma que tiene el profesor de conducir la conducta del estudiante.
oai:oai.hipatiapress.com:article/631
2023-09-26T11:38:26Z
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Vol. 2 No. 2 (2013): June ; 161-182
Enseñar matemáticas en la sociedad de mañana: alegato a favor de un contraparadigma emergente
Chevallard, Yves; Aix-Marseille Université, France
2013-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/631
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El análisis histórico de la enseñanza de las matemáticas en secundaria muestra cómo se han ido sucediendo en el tiempo diferentes paradigmas escolares. En este trabajo se describe y se analiza un nuevo paradigma didáctico, todavía en su infancia, el paradigma del “cuestionamiento del mundo”, que se basa principalmente en cuatro conceptos interrelacionados, el de la indagación y el de ser “herbartiano”, “procognitivo”, y “exotérico”. La ambición del autor es mostrar, aunque sea de manera sucinta, cómo la actual crisis en la educación matemática se podría con suerte resolver según estas líneas, descartando el recurso a estrategias que solo buscan poner parches al viejo paradigma, todavía dominante, “de la visita de las obras”.
oai:oai.hipatiapress.com:article/637
2023-09-26T11:37:53Z
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Vol. 3 No. 1 (2014): February; 30-53
Algebra and Proof in High School: The Case of Algebraic Proof as Discovery
Martinez, Mara Vanina; University of Illinois - Chicago
2014-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/637
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In the United States, students’ learning experiences around proof is generally concentrated in the domain of high school geometry with a focus on its verification function. Thus, providing students with a limited conception of what proof entails and the role that it plays in performing mathematics. Moreover, there is a lack of U.S.-based studies addressing how to integrate proof into other mathematical domains within the high school curriculum. In this paper, the author reports results from an interview at the end of a teaching experiment which was designed to integrate algebra and proof into the high school curriculum. Algebraic proof was envisioned as the vehicle that would provide high school students the opportunity to learn about proof in a context other than geometry. Results indicate that most students were able to produce an algebraic proof involving variables and a parameter and its multiples. In doing so, students experienced the discovery function of proof.
oai:oai.hipatiapress.com:article/640
2023-09-26T11:37:53Z
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Vol. 3 No. 1 (2014): February; 7-29
Horizon Content Knowledge: shaping MKT for a continuous mathematical education
Figueiras, Lourdes; Universitat Autònoma de Barcelona
2014-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/640
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Mathematics learning is a continuous process in which students face some abrupt episodes involving many changes of different natures. This work is focused on one of those episodes, transition from primary to secondary school, and targets teachers and their mathematical knowledge. By characterising the mathematical knowledge that teachers of mathematics need to smooth transition processes, we aim to highlight teachers’ impact in the continuity of mathematics education. The concept of Mathematical Knowledge for Teaching (MKT) developed by Ball among others (Ball, Thames & Phelps, 2008) and, within this framework, the construct Horizon Content Knowledge (HCK) emerge as our theoretical response to the knowledge needed for teaching mathematics in a continuous way, particularly relevant during transition to secondary school. The enrichment of the idea of HCK and the characterisation of its expression in the teaching practice intends to develop a theoretical tool to approach transition from teachers’ mathematical knowledge perspective.
oai:oai.hipatiapress.com:article/690
2023-09-26T11:37:35Z
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Vol. 3 No. 2 (2014): June ; 151-168
Observatório da Educação: an investigation of Teacher Professional Development of Mathematics Teachers
Garcia Silva, Angélica da Fontoura; Universidade Bandeirante Anhanguera UNIBAN
Campos, Tania Maria Mendonça; Universidade Bandeirante Anhanguera UNIBAN
Pietropaolo, Ruy Cesar; Universidade Bandeirante Anhanguera UNIBAN
2014-06-20
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/690
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This paper aims to present the results of an investigation regarding the professional development of teachers who worked in the early years of basic education. The qualitative research involved teachers who participated in the Observatório da Educação project (MEC/CAPES). Because of the data amount, we choose to present the data analysis based on the work of only one teacher, who is considered as a legitimate representative of the whole group. All data were collected through direct observations, recordings, questionnaires, interviews and reflective relatorios on the implementation of the activities to their students. Data analysis was based on Ponte, Garcia, Shulman and Serrazina studies, researchers that study the development and professional knowledge or reflection. This study reveals that the experiences during the training process favored the redefinition process of mathematical content and teaching beyond reflection on practice.
oai:oai.hipatiapress.com:article/696
2023-09-26T11:37:53Z
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Vol. 3 No. 1 (2014): February; 74-102
A Case Study on Pre-Service Teacher Students’ Interaction with Graphical Artefacts
Olande, Oduor; Mittuniversitetet
2014-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/696
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This study reports from a pre-service teacher’s online learning and assessment activity on determining variability of two graphical artefacts. Using a critical-analytical perspective to data, the present study indicate that the prospective teachers surveyed showed awareness of relevant subject specific operators and methods however, these seem not be well coordinated and were submerged in forms of expressions characterized by intuitive methods and everyday language. Significantly the prospective teachers seemed to substitute statistical and mathematical methods with explanatory metaphors which while providing room for deeper subject specific engagement were however, only used superficially. Their reliance on everyday forms of expression and visual perception is perceive as a factor that might have hampered their effective choice and application of relevant subject specific tools and forms of expression. This observation puts to task the role of informal methods in statistics education.
oai:oai.hipatiapress.com:article/763
2023-09-26T11:37:35Z
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Vol. 3 No. 2 (2014): June ; 168-185
Students’ Equation Understanding and Solving in Iran
Barahmand, Ali; Department of Mathematics, Science and Research Branch, Islamic Azad University, Theran, Iran
Shahvarani, Ahmad; Department of Mathematics, Science and Research Branch, Islamic Azad University, Theran, Iran
2014-06-20
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/763
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The purpose of the present article is to investigate how 15 year old Iranian students interpret the concept of equation, its solution, and studying the relation between the students’ equation understanding and solving. Data from two equation-solving exercises are reported. Data analysis shows that there is a significant relationship between understanding and solving equation. The results indicate that students’ understanding of equation has, basically, been shaped by their experiences in arithmetic and students usually have not any perception of equations and real world problems. Moreover, the study shows that students rarely paid any attention to the equality sign and the use of operators in both sides of the equation.
oai:oai.hipatiapress.com:article/806
2023-09-26T11:37:18Z
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2023-09-26T11:37:18Z
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Vol. 3 No. 3 (2014): October; 253-275
Trayectorias iniciales de formación de profesores. El caso de las transformaciones geométricas
Thaqi, Xhevdet; University Teacher of Mathematics
Gimenez, Joaquim; University Teacher at University of Barcelona
2014-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/806
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Se desarrolla un estudio empírico con los estudiantes para futuros profesores de primaria en dos contextos diferentes, en España y Kosovo.It is significant to note that, even though, the opportunity sample used in this study comprised students from diverse parts of the world, the notion of culture, as it is used in this paper, does not have direct implications to geographical locations from which the learners come. Se ha empleado una práctica didáctica sobre aprender a enseñar las transformaciones geométricas en educación primaria para Iemployed active interviewing to construct narratives with learners about their experience of learning in a British university.construir narrativas de los estudiantes sobre su experiencia de aprender a enseñar las transformaciones geométricas.The interviews were conducted with the assumption that all processes of knowing are socially constituted. Hence, the context, culture as well as the relationship between the researcher and respondents during the interview conversation was supposed to shape the meanings constructed.The study revealed that there are diverse cultural scripts for learning in different cultures. The notion of cultural scripts reflects the generalized action knowledge which informs how people make sense of situations and which also guides their action in particular contexts. El estudio reveló que existen diversas escrituras culturales para el aprender a enseñar las transformaciones geométricas en los dos grupos de participantes de la investigación.
oai:oai.hipatiapress.com:article/850
2023-09-26T11:37:35Z
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Vol. 3 No. 2 (2014): June ; 121-150
Predictors of Achievement When Virtual Manipulatives are Used for Mathematics Instruction
Moyer-Packenham, Patricia S.; Utah State University
Baker, Joseph; Stanford University
Westenskow, Arla; Utah State University
Anderson, Katie L.; Utah State University
Shumway, Jessica F.; Utah State University
Jordan, Kerry E.; Utah State University
2014-06-20
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/850
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The purpose of this study was to determine variables that predict performance when virtual manipulatives are used for mathematics instruction. This study included the following quasi-experimental design features: 1) a large number of students (N=350); 2) within-class random-assignment to treatment groups; 3) retention effects measured by post-test and delayed post-test; 4) fidelity of instructional treatments documented through observations; and, 5) instrument development for the unit of study. This design was used to determine variables that predict student performance on tests of fraction knowledge for third- and fourth-grade students in two treatment groups: classroom instruction using texts and physical manipulatives (CI), and computer lab instruction using virtual fraction applets (VM). The Pre-test, Post-test 1, and Post-test 2 measured learning and retention of fraction concepts. Observation ethograms documented representation use. The results revealed that fewer demographic predictors of student performance (e.g., socio-economic status, English language learner status, and gender) exist during fraction instruction when virtual manipulatives were used. When instructors used virtual manipulatives, there was an equalizing effect on achievement in third and fourth grade classrooms, in that fewer demographic factors were influential for VM groups compared to CI groups.
oai:oai.hipatiapress.com:article/859
2023-09-26T11:37:18Z
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2023-09-26T11:37:18Z
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Vol. 3 No. 3 (2014): October; 220-252
De la Aritmética al Álgebra: Números Triangulares, tecnología y ACODESA
Cortés, José Carlos; Universidad Michoacana, México
Hitt, Fernando; Université du Québec à Montreal
Saboya, Mireille; Université du Québec à Montreal
2014-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/859
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El propósito de este documento es el de abordar la articulación entre la aritmética y el álgebra. La literatura habla del pensamiento aritmético o algebraico, sin mencionar la importancia de un pensamiento aritmético- algebraico previo al algebraico. A través de actividades diseñadas para tal efecto, proponemos un acercamiento aritmético y visual, con la intención de promover procesos de visualización matemática, que a su vez, constituirán estructuras cognitivas sobre el control que ejercen los alumnos en la resolución de una tarea matemática. Nuestro diseño está ligado a un marco teórico sobre la acción, en un aprendizaje en colaboración (ACODESA) y uso de tecnología en el aula de Matemáticas. En este estudio, presentaremos nuestro proyecto de investigación entre Québec y México, pero nos restringiremos a los resultados obtenidos con la población mexicana en relación con los números poligonales en la escuela secundaria.
oai:oai.hipatiapress.com:article/921
2023-09-26T11:37:35Z
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Vol. 3 No. 2 (2014): June ; 110-120
The Use of the History of Mathematics in the Teaching of Preservice Teachers
Galante, Dianna; Governors State University
2014-06-20
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/921
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Many scholars have written about using the history of mathematics in the teaching of preservice mathematics teachers. For this study, preservice mathematics teachers developed an electronic journal of reflections based on presentations in the history of mathematics in a secondary mathematics education course. The main purpose of the Mathematics History Journal was to help measure the mathematics content knowledge and pedagogical content knowledge of the preservice mathematics teachers for accreditation purposes. Results of the study indicated that by allowing preservice teachers to investigate and present topics in the history of mathematics, preservice teachers believed they strengthened their mathematics content knowledge and were introduced to a new avenue for teaching secondary students about mathematics.Keywords: History, Preservice Teachers, Secondary Mathematics, Teacher Knowledge
oai:oai.hipatiapress.com:article/958
2023-09-26T11:37:18Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/958
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Vol. 3 No. 3 (2014): October; 192-219
Pre-service Teachers’ Common Content Knowledge Regarding the Arithmetic Mean
de Haro, Juan Jesús Ortiz; Universidad de Granada, Granada, spain
Moll, Vicenç Font; Universidad de Barcelona, Barcelona, Spain
2014-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/958
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The main goal of this study is to determine the common content knowledge of a group of pre-service primary teachers regarding the arithmetic mean. The cognitive configuration tool proposed by the Onto-semiotic Approach of Cognition and Mathematics Instruction shows that the arithmetic mean can have a variety of meanings, and the application of this tool here revealed significant difficulties related to the students’ understanding of this mathematical object and some of its properties. This article concludes with some educational implications for teacher training in the field of statistics.
oai:oai.hipatiapress.com:article/1110
2023-09-26T11:36:47Z
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2023-09-26T11:36:47Z
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Vol. 4 No. 2 (2015): June ; 179-194
Students’ Recognition of Function Transformations’ Themes Associated with the Algebraic Representation
Daher, Wajeeh M.; Al-Qasemi Academic College of Education & An-Najah National University
Anabousi, Ahlam A.; Al-Qasemi Academic College of Education & Tel-Aviv University
2015-06-23
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1110
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The topic of function transformations is a difficult mathematical topic for school and college students. On the other hand, GeoGebra is a new technological tool for mathematics teaching and learning, so we wanted to experiment with this new tool in teaching non-basic function transformations to middle school students. Specifically, we wanted to examine how students conceive function transformations after working with GeoGebra, when this conceiving relates to the algebraic representation. The research participants were 19 ninth grade high achieving students who learned, with the help of GeoGebra translations, reflection and stretch. During their learning, the participants worked with transformations on the absolute function, the cubic function, and the quartic function. After they finished the transformation unit, the participants solved mathematics problems by means of function transformations. This research is interested in the participants’ solution of problems that included two non-basic functions: the absolute value of the quadratic function and the rationale function. The research findings show that the participants were generally able to solve successfully mathematical problems, by means of transformations on new and non-basic functions. Furthermore, the participants encountered difficulties in working with translations. These difficulties were due to the special algebraic form of the functions. We recommend that mathematics teachers expose middle school students to transformations on different types of non-basic function during learning this mathematical topic. Future researches could examine the impact of activities that include such functions and that are GeoGebra based on students’ conceptions and behavior when performing translations is involved.
oai:oai.hipatiapress.com:article/1140
2023-09-26T11:37:18Z
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Vol. 3 No. 3 (2014): October; 276-293
Students' Misconceptions About Hypothesis Test
Krishnan, Saras; Universiti Malaya
Idris, Noraini; Universiti Malaya
2014-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1140
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Students’ misconceptions about hypothesis test have been discussed for decades by many researchers in the developed countries. However, documented studies in the non-developed countries are lacking. The purpose of this study is to fill the gap by identifying misconceptions about hypothesis test made by students in the higher education institutions in a developing country. Descriptive analysis namely percentages and pie charts have been used to analyze students’ responses to open-ended items. The misconceptions identified in this study are similar to those discussed in earlier literature implying that students in different educational settings are prone to similar misconceptions about hypothesis test.
oai:oai.hipatiapress.com:article/1141
2023-09-26T11:37:02Z
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Vol. 4 No. 1 (2015): February; 6-29
Inventing (in) early geometry, or How creativity inheres in the doing of mathematics
Maheux, Jean-Francois; UQAM
Roth, Wolf-Michael; University of Victoria
2015-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1141
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Inventing is fundamental to mathematical activity, should one be a professional mathematician or a primary school student. Research on mathematical creativity generally is organized along three axes according to its focus on the final product, the overall process, or the individual person. Through these conceptualizations, however, research rarely considers how mathematical actions themselves are fundamentally creative. In an action-oriented perspective, every single act is recognized as creative, whereas discovery and invention emerge as the result of the incoming of the unexpected qua unexpected—which can take place at any moment in the most mundane, everyday action. In this article, we conceptualize mathematical actions as inherently creative of the activity within which professional mathematicians and primary school students experience (some) mathematics for a first time. To make our case, we develop the microanalysis of an exemplary episode of third-grade geometry (age 8-9 years) in which two children and an adult work with a tangram set. Our analysis characterizes inventing (in) geometry as a serendipitous, open-ended experience of working with traces in the receiving and the offering of something novel. In concluding, we propose considering that inventing in early geometry is also inventing geometry itself: an inventing-in-the-act which also result in being invented as a (professional or school) geometer
oai:oai.hipatiapress.com:article/1193
2023-09-26T11:37:02Z
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Vol. 4 No. 1 (2015): February; 80-98
Polynomial functions resulting from the multiplication of curves in the framework of the Research and Study Paths
Llanos, Viviana Carolina; Núcleo de Investigación en Educación en Ciencia y Tecnología (NIECyT)
Facultad de Ciencias Exactas. Universidad Nacional del Centro de la Provincia de Buenos Aires (UNCPBA).
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
Otero, Maria Rita; Núcleo de Investigación en Educación en Ciencia y Tecnología (NIECyT)
Facultad de Ciencias Exactas. Universidad Nacional del Centro de la Provincia de Buenos Aires (UNCPBA).
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
Colombo Rojas, Emmanuel; Núcleo de Investigación en Educación en Ciencia y Tecnología (NIECyT)
Facultad de Ciencias Exactas. Universidad Nacional del Centro de la Provincia de Buenos Aires (UNCPBA).
2015-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1193
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This paper presents the results of a research which proposes the introduction of the teaching by Research and Study Paths (RSPs) into Argentinean secondary schools within the frame of the Anthropologic Theory of Didactics (ATD). The paths begin with the study of Q0: How to operate with any curves knowing only its graphic representation and the unit of the axes?, which was implemented for two consecutive years by 14-17 year-old students. The results of part of the paths that allows the study of the polynomial functions in the frame of RPS are hereby described. These results justify the introduction of a new pedagogy into schools as proposed by Yves Chevallard in order to study Mathematics in conventional courses of Secondary Education schools in Argentina. The scopes relative to the attitudes of the students which are necessary to face a questions-based education are outlined in this work.
oai:oai.hipatiapress.com:article/1195
2023-09-26T11:37:02Z
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Vol. 4 No. 1 (2015): February; 52-79
Examining the Impact of a Videocase-based Mathematics Methods Course on Secondary Preservice Teachers’ Skills at Analyzing Students’ Strategies
Martinez, Mara Vanina; University of Illinois - Chicago
Castro Superfine, Alison; University of Illinois-Chicago
Carlton, Theresa; University of Illinois-Chicago
Dasgupta, Chandan; University of Illinois-Chicago
2015-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1195
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This paper focuses on results from a study conducted with two cohorts of preservice teachers (PSTs) in a videocase-based mathematics methods course at a large midwestern university in the US. The motivation for this study was to look beyond whether or not PSTs pay attention to mathematical thinking of students, as shown by previous studies when engaging with video, and, in turn, characterize at a more specific level areas in which PSTs’ responses change. Our findings show that regarding PSTs anticipation of strategies, both cohorts showed a significant increase in the overall number of strategies PSTs were able to anticipate, and a significant increase in the mathematical depth of the anticipated strategies. However, there was no change in terms of PSTs identification and description of high school students’ strategies as displayed in video given that both cohorts of PSTs performed equally proficient at both pre- and post- tests.
oai:oai.hipatiapress.com:article/1332
2023-09-26T11:36:31Z
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Vol. 4 No. 3 (2015): October; 259-270
Fostering Students’ Statistical Literacy Through Significant Learning Experience
Krishnan, Saras; INTI International University
2015-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1332
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A major objective of statistics education is to develop students’ statistical literacy that enables them to be educated users of data in context. Teaching statistics in today’s educational settings is not an easy feat because teachers have a huge task in keeping up with the demands of the new generation of learners. The present day students have higher expectations in terms of classroom pedagogy particularly in the use of creative and engaging methods to create a significant learning experience for them. This paper discusses how students’ statistical literacy can be fostered by creating a more integrated statistics course using the Fink’s Taxonomy of Significant Learning.
oai:oai.hipatiapress.com:article/1355
2023-09-26T11:37:02Z
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Vol. 4 No. 1 (2015): February; 30-51
Mathematizing Perceptions: Preservice Teachers’ Use of Mathematics to Investigate Their Relationship with the Community
Simic-Muller, Ksenija; Professor
2015-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1355
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Preservice teachers often hold deficit views about the students they will teach and their communities. These limiting beliefs can result in lower expectations of and poor outcomes for the students, and need to be addressed in all areas of teacher education, including mathematics courses. In particular, mathematics content courses for preservice teachers offer numerous opportunities for investigating social justice issues and challenging preservice teachers’ beliefs. The assignment described in this manuscript provides an example of the work that can take place in mathematics content courses for preservice K-8 teachers. As part of the assignment, preservice teachers used mathematics to investigate negative perceptions that their campus community has of the surrounding neighborhood. They wrote reflections and created mathematical arguments about household income, poverty rates, educational attainment, crime, and diversity in the neighborhood. Through working on the assignment many preservice teachers began to question their stereotypes about the community. Because of the preservice teacher interest in the topic, and because some problematic beliefs were displayed in the reflections, there is a need for similar assignments in this and other courses, in order to help preservice teachers see the strengths of diverse communities, instead of just their shortcomings.
oai:oai.hipatiapress.com:article/1386
2023-09-26T11:36:47Z
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Vol. 4 No. 2 (2015): June ; 106-131
El problema didáctico del álgebra elemental: Un análisis macro-ecológico desde la teoría antropológica de lo didáctico
Munzón, Noemí Ruiz; Universitat Pompeu Fabra-Tecnocampus
Bosch, Marianna; Universitat Ramon Llull
Gascón, Josep; Universitat Autònoma de Barcelona
2015-06-23
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1386
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We present a global, synthetic and updated vision of the contributions made by the anthropological theory of the didactic to the problem of teaching elementary algebra. We start by summarising the first results obtained by Yves Chevallard in the 80s that have marked the trend of research on elementary algebra in the anthropological approach. A reference epistemological model of elementary algebra is then proposed. This model provides a new interpretation of the role of elementary algebra in current school mathematics and guides the study of its ecology, that is, the constraints which partially explain the current situation and the conditions that could modify it in a given direction.
oai:oai.hipatiapress.com:article/1398
2023-09-26T11:36:47Z
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Vol. 4 No. 2 (2015): June ; 161-178
Creencias de profesores y estudiantes de profesor de educación primaria y secundaria sobre los problemas de matemáticas
Giné de Lera, Celia; Universitat Autònoma de Barcelona
Deulofeu Piquet, Jordi; Universitat Autòmoma de Barcelona
2015-06-23
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1398
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Las creencias que tienen los alumnos de las matemáticas como disciplina, su finalidad en la enseñanza, el significado y sentido de los problemas, etc., dependen en gran medida de las propias creencias de los profesores, que son transmitidas, consciente o inconscientemente, a los alumnos mediante todo aquello que dicen y hacen en el aula. Por otro lado, la resolución de problemas constituye uno de los ejes principales en la enseñanza de las matemáticas, y es una de las herramientas que ayudan a dar sentido a esta ciencia. En este artículo nos proponemos caracterizar y comparar las creencias de los profesores y estudiantes de profesor de matemáticas de primaria y de secundaria sobre el objeto problema de matemáticas.La investigación utiliza una metodología esencialmente cualitativa, mediante la cual se analizan definiciones de problema de matemáticas y ejemplos de problema y de ejercicio obtenidas mediante un cuestionario pasado a cada una de las cuatro muestras del estudio. El análisis realizado nos ha permitido caracterizar las creencias de cada muestra y constatar que hay diferencias relevantes entre ellas.
oai:oai.hipatiapress.com:article/1422
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Vol. 4 No. 2 (2015): June ; 132-160
Modeling Metacognition: Making Thinking Visible in a Content Course for Teachers
Conrady, Kansas; University of Oklahoma
2015-06-23
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1422
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Helping students develop their ability to use the mathematical practices relies on their awareness of and ability to share their thinking to be used as part of classroom instruction. This type of instruction tends to be different from most teachers mathematics learning experiences thus requiring teachers to rethink what it means to teach mathematics without a model for reference. This preservice geometry content course was designed specifically for future elementary teachers with the intent of modeling effective non-traditional methods of instruction. Unfortunately, analysis of classroom observations suggested that even in this carefully designed inquiry-based course, there is a lack of cognitive and metacognitive thoughts being made visible for use as part of instruction. Content courses, such as this one, are the final opportunities to help students learn mathematics content in an environment supported by positive research findings, thus teacher education is missing an opportunity to provide a potentially powerful learning experience for future teachers.
oai:oai.hipatiapress.com:article/1469
2023-09-26T11:36:19Z
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Vol. 5 No. 1 (2016): February; 56-73
How can I help my students with learning disabilities in Mathematics?
Jiménez-Fernández, Gracia; University of Granada
2016-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1469
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Learning Disabilities in Mathematics (LDM) or dyscalculia are a frequent and disruptive problem within schools. Nevertheless, this problem has received little attention from researchers and practitioners, if compared with the number of studies published on disabilities in reading. Therefore, teachers do not have enough guidance to help children overcome their difficulties. Consequently, educators, practitioners and teachers are in need ofsome guidelines which help them choose teaching methods that are adapted for children with LDM. This paper proposes an interventional framework for improving skills in children who show problems in learning basic mathematics. Concretely, it suggests some guidelines which are focused on number sense and problem solving, two of the most important mathematical areas.
oai:oai.hipatiapress.com:article/1517
2023-09-26T11:36:31Z
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Vol. 4 No. 3 (2015): October; 234-259
School Socio-Cultural Identity and Perceived Parental Involvement About Mathematics Learning in Greece
Moutsios-Rentzos, Andreas; University of the Aegean
Chaviaris, Petros
Kafoussi, Sonia; University of the Aegean
2015-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1517
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In this quantitative study we investigated the primary school students’ perceived parental involvement in mathematics with respect to different school socio-cultural identity as identified by the students’ ethnicity. 493 students attending the two last grades of three primary schools participated in the study. The role of the students’ grade and gender, as well as the mother/father contrast were also considered in the analyses. The findings of the study revealed both inter-school and intra-school divergences and convergences, thus suggesting the complex links between school identity and perceived parental involvement. More specifically, according to our results, the ‘multi-cultural’ seems to be linked with a more stable perceived parental involvement across different year groups and calendar years. The pedagogical implication of the findings are discussed.
oai:oai.hipatiapress.com:article/1519
2023-09-26T11:36:31Z
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Vol. 4 No. 3 (2015): October; 271-287
The Effect of using Teams Games Tournaments (TGT) Cooperative Technique for Learning Mathematics in secondary schools of Bangladesh
Salam, Abdus; Institute of Education and Research, University of Dhaka,
Hossain, Anwar; University of Chittagong
Rahman, Shahidur; Interactive Computer Learning Club, University of Dhaka
2015-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1519
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Abstract Games-based learning has captured the interest of educationalists and industrialists who seek to reveal the characteristics of computer games as they are perceived by some to be a potentially effective approach for teaching and learning. Despite this interest in using games-based learning, there is a dearth of studies context of gaming and education in third world countries. This study investigated the effects of game playing on performance and attitudes of students towards mathematics of Grade VIII. The study was undergone by implementing TGT technique for the experimental group and typical lecture-based approach for the control group. A same achievement test was employed as in both pretest and posttest, an inventory of attitudes towards mathematics were applied for the pretest and posttest on TGT experimental and control group, an attitude scale on computer games was employed for the TGT experimental group, a semi-structured interview for teacher and an FGD guideline for students were applied to serving the purpose of research objectives. After three-weeks of intervention, it had been found out that TGT experimental group students had achieved a significant learning outcome than lecture based control group students. Attitude towards mathematics were differed to a certain positive extent on TGT experimental group. On the basis of findings of this study, some recommendations were made to overcome the barriers of integrating web-based game playing in a classroom.
oai:oai.hipatiapress.com:article/1568
2023-09-26T11:36:31Z
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Vol. 4 No. 3 (2015): October; 202-233
Análisis de la complejidad cognitiva en la lectura y escritura de expresiones simbólicas matemáticas
Distéfano, Maria Laura; Facultad de Ingeniería, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, Mar del Plata, Argentina
Pochulu, Marcel David; Instituto Académico Pedagógico de Ciencias Básicas y Aplicadas, Universidad Nacional de Villa María, Arturo Jauretche 1555, Villa María, Argentina
Font, Vicenç; Universitat de Barcelona, Facultat d’Educació, Departament de Didà ctica de les Ciències Experimentals i la Matemà tica, Passeig de la Vall d'Hebrón, 171, 08035 Barcelona
2015-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1568
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Este artículo está centrado en un análisis de las actividades cognitivas involucradas en la lectura y escritura de expresiones simbólicas, como parte del proceso de significación de símbolos matemáticos. Particularmente, se ha puesto el foco en algunos símbolos que son de uso exclusivo en el ámbito matemático y a cuyo uso se enfrentan los estudiantes que ingresan a carreras universitarias que contienen Matemática en su plan de estudios. Para caracterizar la actividad matemática realizada al usar estos símbolos se diseñó un instrumento ad hoc. Se presenta un análisis sobre distintos ítems del instrumento que da cuenta de la complejidad cognitiva que poseen las tareas de lectura y escritura de expresiones simbólicas que involucran los símbolos en estudio. Para el análisis de las respuestas se utilizaron herramientas proporcionadas por el Enfoque Ontosemiótico (EOS). En particular se utilizaron las funciones semióticas y las configuraciones de objetos primarios. La combinación de estas herramientas pone de manifiesto la multiplicidad de procesos involucrados en las tareas de lectura y escritura de expresiones simbólicas, como así también la trama de vinculaciones necesarias para otorgar significado, evidenciando la complejidad cognitiva que la manipulación de símbolos matemáticos posee.
oai:oai.hipatiapress.com:article/1753
2023-09-26T11:36:05Z
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Vol. 5 No. 2 (2016): June ; 158-179
The direction and autonomy of interdisciplinary study and research paths in teacher education
Rasmussen, Klaus; University of Copenhagen & Metropolitan University College
2016-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1753
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This paper presents a case study of didactic infrastructures to direct Study and Research Paths (SRP) in teacher education within the context of interdisciplinary inquiry. The disciplines of school mathematics and school biology, and their didactics, are made to interconnect through the investigation of a generating question concerning the illness diabetes. The resulting interdisciplinary knowledge as evidenced through students written diaries is analysed using the Anthropologic Theory of the Didactic and shows the challenge of combining two disciplines and their didactics at the same time. Two particular forms of didactic infrastructure to guide the self-sustained process of SRP are proposed and scrutinized: Selective picking and Side questions. Selective picking is shown to be a promising, yet indirect, infrastructure to steer the SRP without taking away the desired autonomy of the students. Side questions, initially proposed by Ives Chevallard, are considered in light of the case, and a number of suggestions for their characteristics and use are put forward.
oai:oai.hipatiapress.com:article/1809
2023-09-26T11:36:19Z
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Vol. 5 No. 1 (2016): February; 28-55
Creatividad matemática: Momentos de insight en estudiantes de 4º de ESO
Sánchez, Francisco; Universitat de Barcelona
Fiol, Maria Lluïsa; Universitat Autònoma de Barcelona
2016-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1809
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Las investigaciones en creatividad matemática son escasas en comparación con otros ámbitos de la educación matemática, debido a que en general se presentan los desarrollos y resultados formales pero se dice muy poco acerca de los procesos creativos matemáticos que los han generado.La resolución de problemas geométricos tradicionalmente llamados de Insight, constituye uno de los ejes principales que puede ayudar a los estudiantes a desarrollar y fomentar su potencial creativo en el aprendizaje de las matemáticas. En este artículo nos proponemos identificar, describir y caracterizar las evidencias que promueven momentos de Insight en un grupo de estudiantes de 4º de ESO. Utilizamos inicialmente una metodología cuantitativa y posteriormente una cualitativa. Esta metodología cualitativa utiliza el análisis de las resoluciones de 3 problemas geométricos potencialmente de Insight perceptivo, las contestaciones del cuestionario de respuestas y las explicaciones dadas en la entrevista semiestructurada. El análisis nos ha permitido identificar y caracterizar evidencias explicitadas y no explicitadas en la ocurrencia del Insight. Otorgamos un papel especialmente relevante por un lado, a la celeridad en que se produce la ocurrencia súbita del Insight y por otro a la componente emocionalmente positiva que determina la vivencia afectiva de su experiencia.
oai:oai.hipatiapress.com:article/1823
2023-09-26T11:36:19Z
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Vol. 5 No. 1 (2016): February; 7-27
Contextualizing mathematics related affect: Significance of students’ individual and social level affect in Finland and Chile
Tuohilampi, Laura; University of Helsinki
2016-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1823
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Mathematics related affect turn from positive to negative during comprehensive school years worldwide. There is a clear need to find solutions to the problem. However, some gaps and problems appear in the methodologies and the common approaches used in the field. This article discusses five studies addressing affective development, challenges some of the methods and approaches to measure the development and presents some possibilities to make a change in such a development. The frameworks of the studies, as well as their methods, data and results are briefly presented. Based on the studies, we confirmed several dilemmas concerning affect research and the significance of mathematics-related affect across two cultures. We identified the cultural meaning of different affective levels, and elaborated the social comparison the students live through their school years. As a conclusion, we formulated several suggestions to take into account in future studies. What counts especially is the need to be culturally sensitive in the affect domain.
oai:oai.hipatiapress.com:article/1854
2023-09-26T11:35:51Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1854
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Vol. 5 No. 3 (2016): October; 287-323
Estadios de Comprensión de la Noción Matemática de Límite Finito desde el Punto de Vista Histórico
Medrano, Iván; Universidad de Los Lagos
Pino-Fan, Luis Roberto; Universidad de Los Lagos
2016-10-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1854
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En este trabajo se presenta una investigación sobre la génesis y la evolución de la noción de límite finito. Para tal propósito realizamos un estudio de tipo histórico-documental, en el cual se consideraron elementos relacionados con la estructuración conceptual de dicha noción: los números reales, el infinito, la noción de aproximación, el continuo geométrico y el continuo numérico. Para este estudio se considera como punto de inicio el trabajo de los griegos, específicamente el desarrollo y uso del método de exhaución, continuando con la introducción de los indivisibles por Viéte y Cavallieri y la producción matemática generada en los inicios del cálculo diferencial por Newton y Leibnitz, finalizando con las etapas de formalización del límite y sus generalizaciones métricas y topológicas en el análisis estándar. Como resultado de nuestra investigación se distinguen siete estadios de comprensión del objeto matemático límite.
oai:oai.hipatiapress.com:article/1902
2023-09-26T11:36:05Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1902
2023-09-26T11:36:05Z
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Vol. 5 No. 2 (2016): June ; 135-157
Interpretación de resúmenes estadísticos por futuros profesores de educación secundaria
Gea, María M.; Universidad de Granada
Batanero, Carmen
Fernándes, Jose Antonio; Universidad de Minho
Arteaga, Pedro; Universidad de Granada
2016-06-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1902
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El objetivo de este trabajo fue evaluar la interpretación de resúmenes estadísticos que realizan los futuros profesores de Educación Secundaria y Bachillerato. La evaluación se lleva a cabo analizando las respuestas de una muestra de 65 estudiantes del Máster de Formación del Profesorado, especialidad de Matemáticas, a dos tareas. En la primera se les pide interpretar la media, mediana, moda, mínimo, máximo, cuartiles y desviación típica de una distribución de datos y en la segunda, elegir un promedio representativo utilizando los anteriores estadísticos y un gráfico de caja y bigotes de la misma distribución. Las interpretaciones de los estadísticos, el promedio representativo elegido y el modo en que se justifica la elección fueron generalmente correctos, obteniéndose mejores resultados que en investigaciones previas con estudiantes y futuros profesores de educación primaria. Sin embargo, se observan conflictos sobre el significado de los estadísticos interpretados, que se deberían superar para lograr una buena labor docente de estos futuros profesores.
oai:oai.hipatiapress.com:article/1910
2023-09-26T11:35:36Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1910
2023-09-26T11:35:36Z
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Vol. 6 No. 1 (2017): February; 56-84
Establishing profiles on the use of number sense
Bruno, Alicia; La Laguna University
Almeida, Rut; University of La Laguna
2017-02-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1910
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Number sense includes the ability to use numbers and operations in a flexible and reasonable way. This work presents a case study on the use of number sense by eighth grade students (13-14 years old). We analyse individual interviews of eleven students that include number tasks that can be solved using strategies associated with number sense. By studying the strategies used by the students to answer the questions, we establish four profiles based on their preference for using number sense strategies, rules or algorithms, or on their lack of knowledge of basic number concepts.
oai:oai.hipatiapress.com:article/1935
2023-09-26T11:35:36Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1935
2023-09-26T11:35:36Z
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Vol. 6 No. 1 (2017): February; 85-111
Una aproximación a la medida de actitudes hacia las matemáticas mediante la lógica fuzzy
Boigues, Francisco J.; Universitat Politècnica de València
Estruch, Vicente D.; Universitat Politècnica de València
Vidal, Anna; Universitat Politècnica de València
Llinares, Salvador; Universidad de Alicante
2017-02-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1935
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Este estudio analiza las creencias y actitudes de estudiantes de ingeniería y de ciencias a través de una metodología basada en la lógica fuzzy. La lógica fuzzy proporciona una forma de valorar las actitudes de los estudiantes hacia las matemáticas que permite considerar la relatividad de sus posiciones y las relaciones estructurales en el dominio afectivo. Los resultados muestran, que los estudiantes de ingeniería les gustan más las matemáticas, presentan mayor autoestima matemática y creen que las matemáticas son importantes de un modo significativamente mayor que los estudiantes de ciencias. No obstante, todos son conscientes de su responsabilidad en el aprendizaje de las matemáticas, y coinciden en valorar el papel del profesor, aunque no se considere un elemento influyente a nivel emocional
oai:oai.hipatiapress.com:article/1955
2023-09-26T11:36:19Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1955
2023-09-26T11:36:19Z
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Vol. 5 No. 1 (2016): February; 74-103
Estudio de caso sobre el anális didáctico realizado en un trabajo final de un máster para profesores de matemáticas en servicio
Breda, Adriana
Lima, Valderez Marina do Rosário
2016-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1955
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Este artículo tiene como objetivo investigar las características del análisis didáctico realizado por profesores del Mestrado Profissional em Matemática em Rede Nacional (PROFMAT), para justificar que sus propuestas didácticas son innovadoras y representan una mejora con relación a la enseñanza de las matemáticas que se realiza habitualmente. Para ello se presenta un estudio de caso de un profesor que ha planificado e implementado una propuesta didáctica innovadora. La primera conclusión es que el análisis didáctico realizado por este profesor se basa en el uso implícito de algunos de los componentes y descriptores de la idoneidad didáctica propuestos por el Enfoque Ontosemiótico de la Cognición e Instrucción Matemática. Se concluye también que, aunque la justificación que realiza el profesor estudiado evidencia el uso implícito de algunos de estos componentes y descriptores, no llega a ser una reflexión bien estructurada ni demasiado elaborada.
oai:oai.hipatiapress.com:article/1981
2023-09-26T11:34:59Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1981
2023-09-26T11:34:59Z
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Vol. 6 No. 2 (2017): June ; 164-191
Niveles de Algebrización de la Actividad Matemática Escolar: Análisis de Libros de Texto y Dificultades de los Estudiantes
Castro, Walter F.; Universidad de Antioquia, Medellin, Colombia
Martínez-Escobar, John D.; Colegio Montessori, Medellín
Pino-Fan, Luis R.; Universidad de Los Lagos
2017-06-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1981
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La introducción del razonamiento algebraico elemental desde los primeros niveles educativos es un tema que se ha propuesto desde hace casi dos décadas como resultado de diversas investigaciones. Dicha introducción en el currículo escolar se encuentra con diferentes obstáculos. Este documento contrasta niveles de algebrización tanto en las tareas propuestas en una colección de cinco libros de texto, usados en la primaria, como con los desempeños de niños cuando resuelven tareas algebraicas propuestas en tal colección. Los resultados obtenidos señalan que, si bien los niveles son útiles para asignar grados de algebrización a las tareas propuestas en la colección, y predicen cierta actividad algebraica desarrollada por los niños, la variedad de tareas en los textos y las prácticas que podrían realizar los niños son muy amplias y los criterios no dan cuenta de ellas.
oai:oai.hipatiapress.com:article/1984
2023-09-26T11:35:51Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1984
2023-09-26T11:35:51Z
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Vol. 5 No. 3 (2016): October; 235-262
Evaluación de Conocimientos Didáctico - Matemáticos sobre Visualización de Objetos Tridimensionales en Futuros Profesores de Educación Primaria
Godino, Juan D.; Universidad de Granada
Gonzato, Margherita; Universidad de Granada
Contreras, Ángel; Universidad de Jaén
Estepa, Antonio; Univesrsidad de Jaén
Díaz-Batanero, Carmen; Univesrsidad de Huelva
2016-10-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1984
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El desarrollo de las habilidades de visualización espacial es un objetivo del currículo de matemáticas para la educación primaria y, en consecuencia, los profesores de este nivel educativo deben estar capacitados para diseñar y gestionar tareas instruccionales relacionadas con el tema. La finalidad de esta investigación es evaluar los conocimientos didáctico - matemáticos sobre visualización de objetos tridimensionales en una muestra de futuros profesores de educación primaria. Para ello se analizan las respuestas de 464 estudiantes del grado de Magisterio en las universidades de Granada y Jaén a un cuestionario construido con este propósito. El cuestionario está formado por 10 ítems que evalúan los conocimientos común y ampliado sobre la visualización de objetos tridimensionales y 15 que evalúan conocimientos especializados de dicho contenido relacionados con la enseñanza y aprendizaje del mismo en la educación primaria. El contenido geométrico evaluado incluye tareas sobre reconocimiento de vistas, interpretación del sistema diédrico, desarrollos, secciones de un objeto y cuerpos revolución.El análisis cuantitativo de las respuestas permite informar sobre las características psicométricas del instrumento (fiabilidad y estructura factorial) y realizar un estudio comparativo de los conocimientos de los estudiantes según universidades, género y contenidos geométricos de los ítems. Los resultados muestran un bajo nivel de conocimiento geométrico, que sugiere la necesidad de diseñar acciones formativas específicas sobre estos contenidos en los actuales planes de formación de maestros. La inclusión como anexo del cuestionario construido permitirá realizar replicaciones de esta investigación en otros contextos y usar los ítems como reactivos para promover el desarrollo de los conocimientos sobre visualización de objetos tridimensionales y de la enseñanza del tema. Una mejora del estudio, en su faceta evaluativa, sería incluir una muestra más amplia de universidades, controlando explícitamente la distribución aleatoria y representativa de las muestras seleccionadas. Así mismo, el cuestionario se puede ampliar para contemplar aspectos relativos a las facetas afectiva, mediacional y curricular del conocimiento didáctico - matemático.
oai:oai.hipatiapress.com:article/1987
2023-09-26T11:36:05Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1987
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Vol. 5 No. 2 (2016): June ; 180-204
Research Findings' Impact on the Representation of Proportional Reasoning in Swedish Mathematics Textbooks
Ahl, Linda Marie; Kriminalvarden
2016-06-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/1987
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This article investigates the impact of research findings on the representation of proportional reasoning in two commonly used Swedish mathematics textbook series for grades 7-9. A research-based framework that identifies five learning goals for understanding of proportional reasoning was used to analyse the textbooks. The results brought to surface a gap between research findings of important issues to address and the actual design of mathematics textbooks. Both textbook series make use of an effective range of representations. Besides that, the analysis shows low impact from research findings concerning the importance of given opportunities to compare and contrast additive and multiplicative situations, identify multiplicative structures and proportional thinking, make use of meaningful symbolic representations, and connect and relate fraction knowledge. The main conclusion is that there are possibilities for improvement in textbook design in relation to understanding proportional reasoning.
oai:oai.hipatiapress.com:article/2013
2023-09-26T11:35:51Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2013
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Vol. 5 No. 3 (2016): October; 263-286
The Didactical Contract Surrounding CAS when Changing Teachers in the Classroom
Jankvist, Uffe Thomas; Aarhus University
Misfeldt, Morten; Aalborg University
Marcussen, Anders; Falkornergaardens Gymnasium
2016-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2013
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The article discusses three empirical examples of Computer Algebra System (CAS) use in Danish upper secondary school mathematics class with a recent change of teacher. All examples lead to didactical problems surrounding the situation and unclear expectations between teacher and students, involving loss of students’ mathematical skills and confidence, loss of global mathematical perspective, and the students losing sight of the mathematical objects in question. The article is the result of collaboration between two mathematics education researchers and an upper secondary school mathematics teacher, who experienced severe difficulties when taking over a class from another teacher. CAS was experienced as a crucial part of and reason for these difficulties. As a means for investigating the potential reasons behind the difficulties, a selection of constructs from the Theory of Didactical Situations (TDS) is applied. In particular, it is observed that unclear contractual relations about the role of CAS bring with them misguided winning strategies and metacognitive shifts, eventually causing the students to ‘lose the game’.
oai:oai.hipatiapress.com:article/2015
2023-09-26T11:35:36Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2015
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Vol. 6 No. 1 (2017): February; 7-32
Geometry Students’ Arguments About a 1-Point Perspective Drawing
DeJarnette, Anna F.; University of Cincinnati
Gonzalez, Gloriana; University of Illinois
2017-02-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2015
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The practice of formulating and justifying claims is a fundamental aspect of doing mathematics, and in geometry, students’ use of diagrams is integral to how they establish arguments. We applied Toulmin’s model to examine 23 geometry students’ arguments about figures included in a 1-point perspective drawing. We asked how students’ arguments drew upon their knowledge of 1-point perspective and their use of the diagram provided with the problem. Students warranted their claims based upon their knowledge of perspective, both in an artistic context as well as from experiences in everyday life. Students engaged in multiple apprehensions of the diagram, including using the given features, adding features, or measuring components, to justify claims about the figures. This study illustrates the importance of students’ prior knowledge of a context for formulating arguments, as well as how that prior knowledge is integrated with students’ use of a geometric diagram.
oai:oai.hipatiapress.com:article/2016
2023-09-26T11:34:27Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2016
2023-09-26T11:34:27Z
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Vol. 7 No. 1 (2018): February; 69-92
Desarrollo profesional de profesores de matemáticas en la modalidad en línea y a distancia. El caso de un curso para el diseño de actividades didácticas
Romo Vázquez, Avenilde; Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada del Instituto Politécnico Nacional (CICATA-IPN)
Covián Chávez, Olda Nadinne; Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada del Instituto Politécnico Nacional (CICATA-IPN)
2018-02-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2016
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En este artículo se presenta una Unidad de Enseñanza (UE) de un programa de desarrollo profesional de profesores de matemáticas en ejercicio en la modalidad en línea y a distancia, del CICATA-IPN, México. El objetivo de la UE es proveer de herramientas teóricas y metodológicas a los profesores para el diseño de actividades didácticas, que involucren contextos de la vida y contextos escolares. Elementos teóricos y metodológicos de la Teoría Antropológica de lo Didáctico (TAD) así como los principios de eficacia de los programas en línea y a distancia propuestos por Scott y Scott (2010) son considerados tanto para el diseño de la UE como para analizar los diseños didácticos elaborados por los profesores. Uno de los principales resultados es que las tareas propuestas en los diseños involucran técnicas y justificaciones, matemáticas y prácticas, las cuales modifican principalmente el rol de los profesores y estudiantes en la resolución de las actividades.
oai:oai.hipatiapress.com:article/2059
2023-09-26T11:35:36Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2059
2023-09-26T11:35:36Z
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Vol. 6 No. 1 (2017): February; 33-55
La enseñanza del número en la escuela infantil: un estudio exploratorio del logos de la profesión
Lendínez Muñoz, Elena María; Universidad de Jaén
García García, Francisco Javier; Universidad de Jaén
Sierra Delgado, Tomás Ángel; Universidad Complutense de Madrid
2017-02-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2059
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En este trabajo confluyen dos problemáticas de investigación. Por un lado, la de enseñanza con sentido de los conocimientos matemáticos. Por otro, la de la caracterización del equipamiento praxeológico de la profesión docente. Presentamos algunos resultados de un estudio exploratorio que pretende identificar aspectos importantes del equipamiento praxeológico de la profesión de Maestro/a de Educación Infantil sobre la enseñanza del número (cardinal) y la numeración, tomando como referencia un modelo epistemológico sobre el número y la numeración en el contexto de las magnitudes discretas y su medida. Para ello, se ha diseñado un cuestionario, que ha sido administrado a una muestra de 103 docentes. Los resultados sugieren dificultades para interpretar una actividad matemática que parta de tareas centradas en la construcción de las cantidades de magnitud, y que dé lugar a un proceso de ampliación praxeológica. Consideramos este estudio realizado como el primer paso de un análisis profundo y necesario que nos permita seguir ahondando en el logos matemático-didáctico de la profesión.
oai:oai.hipatiapress.com:article/2078
2023-09-26T11:34:44Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2078
2023-09-26T11:34:44Z
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Vol. 6 No. 3 (2017): October; 307-330
Mathematical practice in textbooks analysis: Praxeological reference models, the case of proportion
Wijayanti, Dyana; 1. Sultan Agung Islamic University2. University of Copenhagen
Winslow, Carl; University of Copenhagen
2017-10-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2078
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We present a new method in textbook analysis, based on so-called praxeological reference models focused on specific content at task level. This method implies that the mathematical contents of a textbook (or textbook part) is analyzed in terms of the tasks and techniques which are exposed to or demanded from readers; this can then be interpreted and complemented by a discussion of the discursive and theoretical level of the text. The praxeological reference model is formed by the analyst to categorize various elements of the text, in particular the tasks and techniques which it explains or requires from readers. We demonstrate the methodological features of this approach by analyzing examples and exercises in three Indonesian textbooks, focusing on the chapters dealing with arithmetic proportion (defined theoretically by the model). We also illustrate how this rigorous analysis can be used to provide a quantitative “profile” of textbooks within a topic.
oai:oai.hipatiapress.com:article/2093
2023-09-26T11:36:05Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2093
2023-09-26T11:36:05Z
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Vol. 5 No. 2 (2016): June ; 112-134
Evaluating mathematics teachers' professional development motivations and needs
Caddle, Mary C.; Department of Education, Tufts University
Bautista, Alfredo; National Institute of Education, Nanyang Technological University
Brizuela, Bárbara M.; Department of Education, Tufts University
Sharpe, Sheree T.; Department of Mathematics & Statistics, University of New Hampshire
2016-06-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2093
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While there is widespread agreement that one-size-fits-all professional development (PD) initiatives have limited potential to foster teacher learning, much existing PD is still designed without attention to teachers’ motivations and needs. This paper shows that the strengths and weaknesses of middle school mathematics teachers that engage in PD may significantly vary. We present three representative cases that illustrate this diversity. The cases were selected from a cohort of 54 grades 5-9 mathematics teachers in the northeastern United States. The results show that: 1) these three teachers dramatically differed in their motivations and self-perceived needs regarding mathematical content, classroom instruction, and student thinking; 2) their perceptions were closely aligned with the results of our own assessments; and 3) the motivations and needs of these three teachers reflected the general trends identified in the cohort of 54 teachers. We conclude that “giving teachers voice” is essential when designing and implementing PD.
oai:oai.hipatiapress.com:article/2116
2023-09-26T11:34:44Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2116
2023-09-26T11:34:44Z
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Vol. 6 No. 3 (2017): October; 283-306
Razón de ser del cálculo diferencial elemental en la transición entre la enseñanza secundaria y la universitaria
Lucas, Catarina O.; Instituto Politécnico do Porto
Gascón Pérez, Josep; Universitat Autònoma de Barcelona
Fonseca Bon, Cecilio; Universidad de Vigo
2017-10-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2116
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En este trabajo se estudia el fenómeno didáctico de la falta de visibilidad e irrelevancia de la modelización funcional (MF) en la transición entre la enseñanza secundaria y la universitaria, relacionándolo con la razón de ser «oficial» que los documentos curriculares asignan actualmente al cálculo diferencial elemental (CDE). En base al análisis de la transposición didáctica del CDE, proponemos los criterios generales que deberá cumplir un modelo epistemológico de referencia que redefina la MF y asigne al CDE una razón de ser alternativa a la oficial que sea más acorde con el papel que este desempeña en la actividad científica.PALABRAS CLAVE: Modelización funcional, cálculo diferencial elemental, modelo epistemológico de referencia, razón de ser.
oai:oai.hipatiapress.com:article/2191
2023-09-26T11:34:27Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2191
2023-09-26T11:34:27Z
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Vol. 7 No. 1 (2018): February; 38-68
Evaluación por competencias en la aplicación de un modelo semipresencial a las matemáticas de titulaciones técnicas universitarias
Fernández Oliveras, Paz; UNIVERSIDAD DE GRANADA
Rodriguez Ponce, Maria del Carmen; Centro de Estudios Matemáticos (CEMAT), Instituto Superior Politécnico “José Antonio Echeverría” (CUJAE), Cuba
Oliveras Contreras, María Luisa; universidad de Granada
2018-02-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2191
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Este trabajo presenta la adaptación a la modalidad semipresencial de la evaluación por competencias para las asignaturas de matemáticas de enseñanzas técnicas universitarias. Las actividades incluidas en la propuesta forman parte de los recursos para la evaluación, contribuyendo cada una de ellas a la adquisición de una o varias competencias de tipo específico, e incluso considerando su contribución a la adquisición de las competencias de tipo transversal. Se incluye el modelo de evaluación propuesto y los primeros resultados de su aplicación. Concluimos que el método de evaluación diseñado es totalmente coherente con el modelo, confiriéndole una rigurosa validez interna y su validación por expertos garantiza una alta fiabilidad de los resultados de su aplicación. Además la evaluación por competencias es muy valiosa para los profesores de Matemáticas de titulaciones técnicas.
oai:oai.hipatiapress.com:article/2227
2023-09-26T11:35:51Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2227
2023-09-26T11:35:51Z
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Vol. 5 No. 3 (2016): October; 212-234
Investigating Pedagogical Content Knowledge-in-Action
Taylan, Rukiye Didem; MEF University
da Ponte, João Pedro; University of Lisbon
2016-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2227
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Abstract: This paper investigates the pedagogical content knowledge (PCK) of a teacher educator who teaches 5th-grade mathematics in a school in the context of a university-school partnership project. PCK is analyzed in a qualitative way through video-taped classroom episodes with focus on interactions between the teacher and the students as well as the teacher’s reflections and pedagogical reasoning on the interactions. The analyses indicate examples of PCK development during teaching, especially refinement in the domain of knowledge of instructional strategies and representations. This knowledge improved as a result of reflection on student questioning and analysis of students’ misconceptions. Different roles of being teacher, teacher educator, and researcher afforded opportunities to gain insights on how to develop knowledge required for teaching and analyze it in order to facilitate future teachers’ learning.
oai:oai.hipatiapress.com:article/2228
2023-09-26T11:34:59Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2228
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Vol. 6 No. 2 (2017): June ; 192-220
Desarrollo de un modelo praxeológico de referencia en torno a lugares geométricos
Quijano, María de la Trinidad; UNRN
Corica, Ana Rosa; CONICET- NIECYT- UNCPBA
2017-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2228
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En este trabajo discutimos resultados de una investigación sobre la enseñanza de lugares geométricos en la escuela secundaria. Diversos investigadores ponen de manifiesto la pérdida de presencia de la geometría en el aula de matemática y el estudio con poco sentido de lo que se propone. Asimismo, en la enseñanza actual el estudio de la geometría se centra casi exclusivamente en la geometría euclidiana. A partir de la Teoría Antropológica de lo Didáctico, diseñamos y describimos un Modelo Praxeológico de Referencia en relación a lugares geométricos desde la geometría euclidiana. También realizamos un análisis de los alcances y limitaciones de este modelo cuando se estudian los lugares geométricos en la geometría no euclidiana del Taxista. Consideramos que abordar los lugares geométricos también desde esta geometría puede dar lugar a un estudio más amplio de la matemática en el aula. Si bien es un primer acercamiento a la problemática, este estudio permite dar cuenta, al menos teóricamente, que la coexistencia de estas geometrías sería posible al enseñar lugares geométricos en la escuela secundaria. Éste es el inicio de una investigación que podría enriquecer, ampliar y dar otro sentido al estudio de la geometría en la escuela.
oai:oai.hipatiapress.com:article/2262
2023-09-26T11:34:44Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2262
2023-09-26T11:34:44Z
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Vol. 6 No. 3 (2017): October; 256-282
La Base de Orientación en la Resolución de Problemas: “cuando me Bloqueo o me Equivoco”
Villalonga Pons, Joana; Departament de Didàctica de la Matemàtica i de les Ciències Experimentals. Universitat Autònoma de Barcelona (UAB)
Deulofeu Piquet, Jordi; Departament de Didàctica de la Matemàtica i de les Ciències Experimentals. Universitat Autònoma de Barcelona (UAB)
2017-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2262
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Ante los indicios de que el uso de una adecuada base orientación contribuye en la adquisición de la competencia de resolución de problemas, con el presente artículo se pretende examinar parte de aquellos indicios que contribuyen a dicha afirmación al tiempo que profundizar en su interpretación. Para ello se consideran las resoluciones de un problema matemático utilizando una base de orientación por alumnos de entre 11 y 13 años de edad. El estudio se centra en explorar cómo la dimensión dedicada al atasco, que comprende el común error y el temido bloqueo, se ve reflejada en las resoluciones de los alumnos. El análisis llevado a cabo confirma la importancia de la dimensión dedicada al atasco en la base de orientación y su implicación tanto en el proceso de aprendizaje de los alumnos como en la práctica de los docentes. Entretanto, se obtiene una clasificación de las distintas situaciones de atasco y su vinculación con las nueve dimensiones de la base de orientación utilizada.
oai:oai.hipatiapress.com:article/2343
2023-09-26T11:33:54Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2343
2023-09-26T11:33:54Z
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Vol. 7 No. 3 (2018): October; 280-310
Análisis de argumentos producidos por alumnos de bachillerato al resolver problemas de geometría
Larios Osorio, Víctor; Universidad Autónoma de Querétaro
Arellano Camacho, Claudia; Colegio de Bachilleres del Estado de Querétaro
González González, Noraísa; Escuela Secundaria “Mariano Matamoros”, USEBEQ
2018-10-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2343
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En este trabajo se describen los resultados de una investigación sobre la producción de argumentos de estudiantes de bachillerato para validar el proceso de solución de un problemas geométricos. Aprovechando herramientas metodológicas como el modelo de Toulmin y la noción de esquema de demostración se estudiaron y categorizaron los argumentos de los alumnos. Se muestra cómo algunos aspectos, como el tipo de problema, influye en el tipo de argumento que proporcionan los alumnos y cómo el uso del modelo de Toulmin puede ayudar a categorizar los esquemas utilizados por los alumnos. También se presentan conclusiones sobre una posible jerarquía en los esquemas de demostración y cómo el paso por ellos no es un proceso discreto, sino continuo.
oai:oai.hipatiapress.com:article/2380
2023-09-26T11:33:39Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2380
2023-09-26T11:33:39Z
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Vol. 8 No. 1 (2019): February; 76-105
Estudio de las interacciones de alumnado bilingüe paquistaní en la resolución de problemas matemáticos en el aula de secundaria
Lodhi, Atif; UNIVERSIDAD DE BARCELONA
Sala, Núria Rosich; PROFESSORA
FACULTAT DE FORMACIÓ DEL PROFESSORAT
Riveros, Beatriz Cantero; UNIVERSIDADE AUTONOMA BARCELONA
2019-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2380
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El trabajo que presentamos intenta ser una respuesta a si el uso de diferentes lenguas por parte del alumnado inmigrante de origen paquistaní escolarizado en España (Cataluña), facilita o no el trabajo de la resolución de problemas matemáticos de forma cooperativa. Dicho estudio se ha centrado en un taller matemático sobre la resolución de diferentes tipologías de problemas que versan sobre ecuaciones. El análisis de las interacciones del trabajo cooperativo ha mostrado que los alumnos utilizan distintas lenguas cuando resuelven los problemas, dependiendo de sus conocimientos matemáticos previos según la lengua en que los habían aprendido. Los resultados también han puesto en evidencia que cuando estos alumnos trabajan por parejas del mismo país de procedencia, muchas veces efectúan el llamado “code switching”, es decir, delante de dudas e interpelaciones durante la conversación, estos tienden a comunicarse en la lengua del país de acogida pero introducen palabras de la lengua del país de procedencia con la finalidad de facilitar la comunicación de la información. Hemos observado además, que las tipologías de las interacciones más usadas por el grupo de alumnas, han sido las de tipo cooperativo y aclaratorio (pregunta respuesta), con el propósito de esclarecer el enunciado del problema y que les permita su planteamiento.
oai:oai.hipatiapress.com:article/2391
2023-09-26T11:34:59Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2391
2023-09-26T11:34:59Z
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Vol. 6 No. 2 (2017): June ; 118-135
The symbolic world of mathematics
Lingefjärd, Thomas; University of Gothenburg
Farahani, Djamshid; University of Gothenburg
2017-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2391
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In understanding upper secondary school students’ interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in symbolic representations of different phenomena. Two theoretical perspectives have been used to conduct the analysis: Tall and Vinner's theoretical perspectives on learning and Gray’s & Talls’s theory of three mathematical worlds. The findings provide evidence that a detailed analyse of student’s utterances show difference in quality related to student’s interpretations of a distance-time relation. The qualities were related to student’s concept images of functions and derivatives.
oai:oai.hipatiapress.com:article/2396
2023-09-26T11:33:39Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2396
2023-09-26T11:33:39Z
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Vol. 8 No. 1 (2019): February; 53-75
Pedagogical design capacity of lower-secondary mathematics teacher and her interaction with curriculum resources
Jukic Matic, Ljerka; University of Osijek, Department of Mathematics
2019-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2396
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Various curriculum resources emerged in the last decades, but the textbook still remains the most used teaching and learning resource in mathematics classrooms. In this paper, we use a case study to analyze teaching practice of one math teacher. The aim of the study is to examine how math teacher interacts with the textbook and teacher guide, especially when teacher offloads on those resources, adapts them or improvises in the classroom. The study was conducted using lessons observations and semi-structured interviews. The results showed that teacher does not favour particular type of resource mobilization. Her interaction with resources can be characterized as a dynamic interplay, where type of resource mobilization exchange between the lessons and within a lesson as well. Moreover, teacher’s mobilization of textbook and teacher guide depends on teacher’s goals and assessment of the most pedagogically beneficial instruction for students.
oai:oai.hipatiapress.com:article/2415
2023-09-26T11:34:59Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2415
2023-09-26T11:34:59Z
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Vol. 6 No. 2 (2017): June ; 136-163
Análisis de las actividades propuestas por un libro de texto: el caso de la medida
Mengual, Elena; Universitat Autònoma de Barcelona
Gorgorió, Núria; Universitat Autònoma de Barcelona
Albarracín, Lluís; Universitat Autònoma de Barcelona
2017-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2415
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En este artículo estudiamos la propuesta de enseñanza de la medida presente en los libros de texto de matemáticas de la etapa de Educación Primaria (6-12 años) de una de las editoriales más utilizadas en España. Realizamos un análisis cualitativo de las actividades de medida que estructuran la propuesta didáctica del libro. El análisis se basa en una jerarquización de tareas matemáticas que nos permite caracterizar los contenidos de medida que se trabajan. Los resultados muestran un predominio de tareas de tipo aritmético en las actividades de medida que dejan en un segundo término los aspectos conceptuales y procedimentales propios de este contenido. El estudio propone un método para el análisis de los libros de texto extrapolable para analizar las propuestas de otras editoriales o materiales de aula.
oai:oai.hipatiapress.com:article/2463
2023-09-26T11:33:54Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2463
2023-09-26T11:33:54Z
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Vol. 7 No. 3 (2018): October; 251-279
Análisis epistémico y cognitivo de una tarea de visualización en el espacio bidimensional
Blanco, Teresa F.; Santiago of Compostela University
Godino, Juan D.; Granada university
Diego-Mantecón, Jose; Universidad de Cantabria
2018-10-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2463
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En este artículo se presentan los tipos de objetos y procesos puestos en juego por un sujeto ideal en la resolución de una tarea de visualización relacionada con las simetrías en el plano. En el marco del enfoque ontosemiótico del conocimiento y la instrucción matemática esto equivale a elaborar la configuración epistémica asociada a la resolución de dicha tarea. Esta configuración se usará como referencia para analizar las configuraciones cognitivas de una muestra de 400 futuros profesores de Educación Primaria y formular hipótesis sobre conflictos semióticos potenciales. Dichas configuraciones, epistémica y cognitivas, se realizan aplicando las categorías de objetos primarios y secundarios que propone el enfoque ontosemiótico. La metodología de la investigación tiene un doble componente cualitativo y cuantitativo, describiéndose como de tipo mixto. Los resultados muestran que estos estudiantes tienen dificultades en la aplicación de habilidades de visualización para descomponer y recomponer figuras, así como en el reconocimiento de la simetría como movimiento en contextos no habituales. El marco teórico empleado aporta una herramienta eficaz que lleva hacia la necesidad de plantear acciones formativas que inicialmente se dirijan hacia aspectos del conocimiento del contenido del profesor, y considerar acciones que complementen su formación didáctica.
oai:oai.hipatiapress.com:article/2497
2023-09-26T11:34:27Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2497
2023-09-26T11:34:27Z
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Vol. 7 No. 1 (2018): February; 93-103
Incentivizing with Bonus in a College Statistics Course
Ingalls, Victoria; Tiffin Unniversity
2018-02-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2497
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Many studies have argued the negative effects of external rewards on internal motivation while others assert that external motivation does not necessarily undermine intrinsic motivation. At a private university, students were given the option to earn bonus points for achieving mastery in the online homework systems associated with Statistics and Pre-Calculus courses. The results showed a significant difference in online homework grades and final exam scores, dependent upon when the incentive was given. The findings of this research suggest that college students thrive when incentivized. When compared to the students who were not incentivized, the incentivized group had a statistically significantly higher mean for both online homework scores and final exam scores. Many of the incentivized students chose to take the opportunity to earn the bonus points to increase the final semester grade, which apparently also helped to increase the content knowledge necessary for the final exam.
oai:oai.hipatiapress.com:article/2503
2023-09-26T11:33:25Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2503
2023-09-26T11:33:25Z
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Vol. 8 No. 2 (2019): June ; 112-138
Language practices in the maths clasroom, an experience online teaching development for teachers of mathematics
Romo Vázquez, Avenilde; Instituto Politécnico Nacional de México
Hache, Christophe; Université Paris Diderot: Paris, Île-de-France, Francia
2019-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2503
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This article describes the constituent link between language and thought, and therefore the importance of language in learning phenomena. The linguistic practices of mathematicians are specific. In class, students learn at the same time mathematical notions and results, and the way in which they are spoken of. We describe here a teaching development unit proposed in the master of Mathematics Education at Polytechnic National Institute, aiming to provide teachers with tools of analysis, as well as examples of tools to work with students.
oai:oai.hipatiapress.com:article/2516
2023-09-26T11:34:10Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2516
2023-09-26T11:34:10Z
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Vol. 7 No. 2 (2018): June ; 111-133
Desarrollando la competencia de reflexión didáctico-matemática en un curso de posgrado mediante la discusión de la idoneidad didáctica de una experiencia de enseñanza
Beltrán-Pellicer, Pablo; Universidad de Zaragoza
Giacomone, Belén; Universidad de Granada
2018-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2516
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En este artículo se describe el diseño, implementación y evaluación de una intervención formativa en un curso virtual de posgrado de Didáctica de la Matemática orientado al desarrollo profesional de investigadores y profesores. El objetivo del diseño es iniciar a los participantes en el desarrollo de la competencia de reflexión sobre la práctica docente, aplicando la noción de idoneidad didáctica como herramienta teórica y metodológica. La metodología de investigación es cualitativa, exploratoria e interpretativa. Los resultados destacan la importancia de reflexionar de manera profesional y el hecho de ser competente en el uso de herramientas que la faciliten.
oai:oai.hipatiapress.com:article/2541
2023-09-26T11:33:09Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2541
2023-09-26T11:33:09Z
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Vol. 8 No. 3 (2019): October; 293-311
Shortcomings of the ‘approaches to learning’ framework in the context of undergraduate mathematics
Darlington, Ellie
2019-10-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2541
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Students’ approaches to learning are heavily researched in higher education, and are of particular concern in the field of mathematics where many students have been found to struggle with the transition to university mathematics. This article outlines a mixed methods study which sought to describe undergraduate mathematicians’ approaches to learning using the deep-surface-strategic ‘trichotomy’ using the Approaches and Study Skills Inventory for Students with 414 mathematics students and semi-structured interviews with a subset of 13 at a leading British university. Analysis found that neither the ‘approaches to learning’ framework nor the inventory can effectively describe students’ study practices, and conceal important elements of how students learn advanced mathematics for examinations. Therefore, it is important that educators do not try to oversimplify students’ methods using quantitative questionnaires but do seek to support those who would otherwise rely solely on memorisation as a means of passing high-stakes examinations.
oai:oai.hipatiapress.com:article/2559
2023-09-26T11:34:10Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2559
2023-09-26T11:34:10Z
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Vol. 7 No. 2 (2018): June ; 134-161
Enseñanza de Geometría Sintética a Futuros Profesores. El caso de la Universidad Nacional de Rosario
Schaefer, Lucía Inés; Facultad de Ciencias Exactas, Ingeniería y Agrimensura - Universidad Nacional de Rosario
Sgreccia, Natalia Fátima; Facultad de Ciencias Exactas, Ingeniería y Agrimensura - Universidad Nacional de Rosario
2018-06-24
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2559
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El presente artículo tiene como objetivo general conocer acerca de la promoción de construcción de conocimientos relativos a Geometría Sintética en la formación inicial de profesores en Matemática. Se espera identificar, describir y conceptualizar las prácticas de enseñanza llevadas a cabo en el primer año del Profesorado en Matemática de la Universidad Nacional de Rosario (Argentina). Se toma como referencia el conocimiento matemático para la enseñanza(MKT) del grupo Michigan. La investigación tiene un enfoque cualitativo y es de tipo empírica, en su contexto natural y con alcance descriptivo. Las categorías de análisis se corresponden con los seis subdominios del MKT. Entre las técnicas de recolección de información se encuentra la observación de clases y para su procesamiento se aplica el análisis de contenido, a partir de reconocer regularidades en los registros. Entre los principales hallazgos se encuentra la importancia otorgada por el docente a la construcción de los conceptos por parte de los estudiantes utilizando distintas estrategias. Se concluye que si bien el docente realiza un acercamiento a la versión escolar de los contenidos, no lo hace de forma explícita a los futuros profesores.
oai:oai.hipatiapress.com:article/2575
2023-09-26T11:34:10Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2575
2023-09-26T11:34:10Z
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Vol. 7 No. 2 (2018): June ; 162-194
Uncovering the Relation between CK and PCK: An Investigation of Preservice Elementary Mathematics Teachers’ Algebra Teaching Knowledge
Güler, Mustafa
Çelik, Derya
2018-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2575
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This article discuss the algebra teaching knowledge of preservice elementary mathematics teachers in the context of CK and PCK as well as the relationship between them. The study was conducted with 101 preservice teachers sampled from a state university in Turkey. Rasch analysis was used to interpret the data. The results revealed that preservice teachers performed at mid-level for both CK and PCK tests. It was also found that there was significant correlation between the CK and PCK test scores. Weaknesses of the preservice teachers in terms of knowledge of the learner component of PCK, in comparison with presentation of content, were identified.
oai:oai.hipatiapress.com:article/2612
2023-09-26T11:34:44Z
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Vol. 6 No. 3 (2017): October; 228-255
Using a New Schema Approach with Primary At-Risk Students in Word Problem Solving
Amiripour, Parvaneh; Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran
Dossey, John Arthur; Illinois State University--Emeritus Professor
Shahvarani, Ahmad; Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran
2017-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2612
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This comparative study of two approaches contrasts a schema-based approach to represent a solution approach to solving whole number contextual problems for Grades 2 and 3 with the traditional textbook approach. The participants are 9 to 11-year-old Afghani refugee students enrolled in non-public schools administered by NGO organization in Iran. The subjects have difficulty with grade-level mathematics and have been retained in grade at least one year. Subjects were randomly selected from four classrooms in two schools. The schema-based experimental approach is called the Problem Patterns (PP) approach. Students receiving this instructional approach were taught to break problems into data, units, and desired solution, removing irrelevant information, and make a solution model with manipulatives. Control students followed the traditional classroom approach. All classes were taught by the first researcher. Evaluation results showed the PP students had higher achievement and growth scores than the control students. The results also showed the schema building portion of instruction contributed most to the differences in performance of the experimental groups’ students.
oai:oai.hipatiapress.com:article/2707
2023-09-26T11:34:27Z
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https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2707
2023-09-26T11:34:27Z
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Vol. 7 No. 1 (2018): February; 7-37
Teachers’ Perception of Social Justice in Mathematics Classrooms
Panthi, Ram Krishna; Mahendra Ratna Campus, Tahachal, Tribhuvan University
Luitel, Bal Chandra; Kathmandu University School of Education
Belbase, Shashidhar; University College, Zayed University
2018-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2707
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The purpose of this study was to explore mathematics teachers’ perception of social justice in mathematics classrooms. We applied interpretive qualitative method for data collection, analysis, and interpretation through iterative process. We administered in-depth semi-structured interviews to capture the perceptions of three mathematics teachers about social justice in mathematics classroom at three public secondary schools in Kathmandu. We carried out multiple layers of thematic analysis and interpretation of the narratives from the interview data. Altogether five themes on perception of social justice emerged from the analysis of the data. These themes were associated with - equality, equity, fairness, social process, and caring students. Implications of the study have been discussed at the end.
oai:oai.hipatiapress.com:article/2727
2023-09-26T11:33:54Z
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2023-09-26T11:33:54Z
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Vol. 7 No. 3 (2018): October; 311-332
Mathematics History and Cognitive Values on a Didactic Sequence: Teaching Trigonometry
Sampaio Figueiredo, Helenara Regina; Universidade Norte do Paraná
Batista, Irinéa de Lourdes; Universidade Estadual de Londrina
2018-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2727
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This article summarizes the preparation and the results of a study, which aimed to evaluate the effectiveness of historical-philosophical approach in teaching trigonometry in association with the detection of cognitive values, as presented by Lacey. On this association lies the theoretical innovation of the work. To conduct the survey, we organized the activities in sequence as proposed by the Didactic Engineering, based on the history of trigonometry. The study was carried out with high school students of a public school in Londrina and it had a qualitative nature. We have concluded that the approach based on historical perspective with the observation of cognitive values expressed by the mathematics showed being effective for the learning of the Trigonometry and its incorporation into the student's knowledge.
oai:oai.hipatiapress.com:article/2762
2023-09-26T11:34:10Z
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2023-09-26T11:34:10Z
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Vol. 7 No. 2 (2018): June
The Exponential Function Meaning on Mathematical Modeling Activities: A Semiotic Approach
Pessoa da Silva, Karina Alessandra; Universidade Tecnológica Federal do Paraná
Werle de Almeida, Lourdes Maria
2018-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2762
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In this article we present a reflection on the meaning attribution to the mathematical object exponential function that emerges from two mathematical modelling activities. The analysis we present are based on the theoretical assumptions of mathematical modelling and Peirce's semiotics. We analyze the interpretant signs produced by a student in two activities developed in two different educational contexts: a undergraduate degree in Mathematics course and a post-graduation course in Mathematics Education. The analysis indicates that the meaning of the mathematical object and the systems of practices and contexts of use are nested. The interpretant signs in each situation correspond to the interpretive effect that a sign produces in the interpreter's mind. The meaning attribution seems to be aligned with the pragmatism characterized by Peirce in semiotics. The meaning for the exponential function is justified by its use in practical situations that enable the production of specific interpretants signs in each situation.
oai:oai.hipatiapress.com:article/2822
2023-09-26T11:33:39Z
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2023-09-26T11:33:39Z
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Vol. 8 No. 1 (2019): February; 6-29
Students´ reasoning on multiplication in primary school classroom context
Kaufmann, Odd Tore; Østfold University College
2019-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2822
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This article investigates how students in third grade discuss and reason on multiplication when they first encounter that concept in the classroom context. By analysing the data from 24 classrooms focused on teaching and learning multiplication, the article aims at contributing to the research and conceptualisations about students´ reasoning and strategy use in multiplication. The analysis shows that some of the features within previous research are helpful in characterizing the students´ reasoning about multiplication. However, the data material also reveals new aspects of students´ reasoning multiplication in classroom settings. One aspect is how students reason about different characteristics of multiplication, and reason about the concept of multiplication in a more general way. They put it in a broader context by going beyond the actual example in which the activity takes place. The students have moved away from the actual example, shifting their attention towards a focus on mathematical relationships. Another aspect is how a strong emphasis on using addition when they work with multiplication, by for instance that some students may begin to use different sub-totals, can cause tensions in the discussions between the teacher and students. Results are discussed in relation to previous studies of students´ multiplicative reasoning and implications for practice are elaborated upon.
oai:oai.hipatiapress.com:article/2847
2023-09-26T11:33:39Z
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Vol. 8 No. 1 (2019): February; 30-52
Realimentación y comentarios escritos de tutores: ¿cómo los entienden los profesores de matemáticas en formación?
Gómez, Pedro; Universidad de los Andes
2019-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/2847
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En este artículo, presentamos algunos resultados de un estudio en torno a la comunicación entre tutores y grupos de profesores de matemáticas en un programa de formación de posgrado. Realizamos un análisis interpretativo de las discusiones de dos grupos de profesores luego de recibir los comentarios escritos de sus tu-tores a sus producciones escritas. Explicamos los resultados más relevantes de este estudio con base en cómo los grupos de profesores entendieron y abordaron los comentarios de sus tutores. Constatamos que los grupos no siempre entienden los comentarios con el mismo significado con que sus tutores los formulan y logramos identificar algunas razones por las cuales esto ocurre.
oai:oai.hipatiapress.com:article/3065
2023-09-26T11:33:09Z
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2023-09-26T11:33:09Z
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Vol. 8 No. 3 (2019): October; 312-338
Evaluating the Effects of Professional Development on Urban Mathematics Teachers TPACK Using Confidence Intervals
Young, Jamaal Rashad; University of North Texas
Young, Jemimah; University of North Texas
Hamilton, Christina; Texas A&M Central Texas
Pratt, Sarah Smitherman; University of North Texas
2019-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3065
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The purpose of this study was to use meta-analytic thinking to evaluate the results of a three-week professional development on mathematics teachers’ technological pedagogical content knowledge (TPACK). The study aims to elucidate the necessity of technology professional development activities to support mathematics teaching and learning in urban schools. This study utilizes mean difference confidence intervals as measures of the effectiveness of a professional development intervention in an urban school district in the U.S. This article presents a practical application of meta-analytic thinking to better contextualize the results through direct comparisons to similar studies. The results of this study suggest that the professional development increased mathematics teachers’ perceptions of their pedagogical knowledge, technological knowledge, pedagogical content knowledge, and technological content knowledge. The study results indicate that despite smaller overall effect sizes the results observed in this urban intervention were not statistically significantly different from most prior research in this area. Because of the chosen research approach, the research results have practical as well as empirical implications for the development and delivery of professional development in urban schools. This article contributes to the literature by providing a contextualized assessment of PD effects and by placing these effects in a broader scholarly context.
oai:oai.hipatiapress.com:article/3068
2023-09-26T11:32:54Z
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2023-09-26T11:32:54Z
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Vol. 9 No. 1 (2020): February; 88-115
El applet como un recurso para la reflexión en la resolución de problemas geométricos
Mayo Juárez, Clara; DEPARTAMENTO DE MATEMÁTICA
EDUCATIVA CENTRO DE INVESTIGACIÓN Y DE ESTUDIOS AVANZADOS DEL INSTITUTO POLITÉCNICO
NACIONAL
Xolocotzin Eligio, Ulises; DEPARTAMENTO DE MATEMÁTICA
EDUCATIVA CENTRO DE INVESTIGACIÓN Y DE ESTUDIOS AVANZADOS DEL INSTITUTO POLITÉCNICO
NACIONAL
2020-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3068
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Este artículo utiliza una aproximación documental para explorar las maneras en las que un applet podría facilitar la reflexión acerca del uso de recursos matemáticos como conceptos y teoremas, durante la resolución de problemas geométricos no rutinarios. Se presenta un estudio cualitativo que investigó las maneras en que un applet diseñado en Geogebra ayudaba a que una pareja de futuros profesores de educación Secundaria reflexionara sobre su uso de ciertos recursos matemáticos involucrados en el problema planteado, tales como el teorema de Pitágoras para triángulos rectángulos, un ángulo, la bisectriz, el área de un círculo, un segmento. El estudio tuvo dos etapas: la primera consistió en resolver el problema, planteado por el investigador, en papel-y-lápiz y la segunda, en resolver el mismo problema apoyándose en un applet. La videograbación de estas etapas fue triangulada con una entrevista semi-estructurada. El análisis de estos datos mostró la presencia de los 2 procesos inmersos en la génesis documental: instrumentalización e instrumentación, en este último proceso se aprecia el surgimiento de la reflexión en los estudiantes cuando está presente el applet.
oai:oai.hipatiapress.com:article/3112
2023-09-26T11:33:25Z
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2023-09-26T11:33:25Z
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Vol. 8 No. 2 (2019): June ; 139-165
Discurso docente y prácticas matemáticas democráticas en la clase de matemáticas
Vanegas Muñoz, Yuly Marsela; Universitat Autònoma de Barcelona
D'Ambrosio, Ubiratan; Universidade de São Paulo
Giménez Rodríguez, Joaquin; Universitat de Barcelona
2019-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3112
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En este artículo presentamos una caracterización de prácticas matemáticas, que denominamos democráticas, teniendo en cuenta el análisis de debates que se han producido en el desarrollo de una unidad didáctica de álgebra con estudiantes de 12-13 años de edad. Se reflexiona sobre el papel del docente en cada debate y se caracterizan los tipos de prácticas en distintos momentos. Partimos de la perspectiva educativa democrática propuesta por D'Ambrosio y la integramos con la perspectiva de construcción colaborativa de significados. Nuestro análisis muestra que las actuaciones del profesor y los estudiantes en una experiencia de participación deliberativa matemática posibilitan negociar exitosamente significados matemáticos.
oai:oai.hipatiapress.com:article/3274
2023-09-26T11:33:54Z
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2023-09-26T11:33:54Z
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Vol. 7 No. 3 (2018): October; 226-250
Latinx Bilingual Students' Perseverance on a Mathematical Task: A Rehumanizing Perspective
Morales, Hector; Northeastern Illinois University
DiNapoli, Joseph; Montclair State University
2018-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3274
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We draw on a rehumanizing perspective that covets a student-centered viewpoint around the discipline of mathematics. For Latinx bilinguals, we posit that a translanguaging practice is a vital option by which collective perseverance during problem solving can be sustained and leveraged for meaningful learning. This study explores and examines the collaborative efforts of a group of Latinx twelfth-grade students persevering to make meaning of an exponential relationship. We employed a discursive thematic analysis of this groups’ ongoing engagement with a challenging mathematical task, paying specific attention to the ways in which these bilingual students encountered and overcame mathematical obstacles and setbacks. Our findings suggest that Latinx bilingual students can spontaneously and dialogically leverage communicative resources to help persevere with in-the-moment obstacles and build mathematical understandings. We argue for the development of more explicit translanguaging support systems in mathematics classrooms to privilege the viewpoint and experiences of the student, and the ways in which they develop mathematical understandings.
oai:oai.hipatiapress.com:article/3315
2023-09-26T11:33:09Z
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2023-09-26T11:33:09Z
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Vol. 8 No. 3 (2019): October; 232-266
CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks
Jankvist, Uffe Thomas; Aarhus University
Misfeldt, Morten; Aalborg University
2019-10-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3315
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This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are identified in ten different textbooks. The CAS based proofs in these textbooks are of three types: complete outsourcing of the proof to CAS; partial outsourcing of the proof to CAS; and additional verification of the proof’ correctness by CAS. Analyses of examples of each of these types are provided. The analyses draw on theoretical constructs related to both proofs and proving (e.g. proof schemes) and to use of digital technologies in mathematics education (lever potential, blackboxing, instrumental genesis). In particular, the analyses make use of a distinction between epistemic, pragmatic and justificational mediations. Results suggest both potential problems with using CAS as an integrated part of deductive mathematical proofs in textbooks, since it appears to promote undesired proof schemes with the students, and difficulties with understanding these problems using the constructs of epistemic and pragmatic mediations that are often adopted in the literature regarding CAS use in mathematics teaching and learning.
oai:oai.hipatiapress.com:article/3353
2023-09-26T11:32:54Z
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2023-09-26T11:32:54Z
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Vol. 9 No. 1 (2020): February; 62-87
Investigating Preservice Mathematics Teachers’ Pedagogical Content Knowledge through Microteaching
Kula Ünver, Semiha
Özgür, Zekiye
Bukova Güzel, Esra; Dokuz Eylül University
2020-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3353
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The purpose of this study was to investigate how pre-service mathematics teachers’ pedagogical content knowledge was reflected in their microteaching. Twenty preservice secondary mathematics teachers participated in the study. The participants formed groups of two, three or four people of their choice, resulting in six groups in total. Each group designed and conducted a microteaching on a topic of their choice. The videotapes of the groups’ microteaching and their lesson plans constituted the data set for the study. We analyzed the data per the components of the pedagogical content knowledge framework outlined by various researchers. We found that the preservice mathematics teachers in general were knowledgeable about different instructional strategies and the curriculum about the topic of their microteaching, but their knowledge of learners was relatively poor. Implications for teacher education are discussed.
oai:oai.hipatiapress.com:article/3432
2023-09-26T11:32:54Z
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2023-09-26T11:32:54Z
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Vol. 9 No. 1 (2020): February; 30-61
4th and 5th grade students’ structuring of 2D rectangular arrays
Ribeiro, Sara Cristina
Palhares, Pedro
2020-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3432
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In this article we examine 4th and 5th grade Portuguese students’ performance on problems of structuring 2D rectangular arrays of squares, which was analyzed and categorized into the five levels of sophistication described by Battista, Clements, Arnoff, Battista, and Borrow (1998). In general, the results suggest that students in the higher grade exhibit higher levels of sophistication. Nevertheless, several students from both grades could not perceive the structure in rows and columns of such rectangular arrays; their spatial structuring of such arrays was still inadequate. The result for their learning may be even worse if we think that for students in these grades, many textbooks display rectangular arrays as the representation to teach area measurement.
oai:oai.hipatiapress.com:article/3618
2023-09-26T11:33:25Z
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2023-09-26T11:33:25Z
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Vol. 8 No. 2 (2019): June ; 193-225
Formación de Profesores de Matemática en servicio: la organización de una enseñanza basada en preguntas.
Otero, Maria Rita; UNICEN - CONICET
Llanos, Viviana Carolina; UNICEN - CONICET
2019-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3618
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Durante un curso on-line de Didáctica de las Matemáticas, realizado por N=31 profesores en servicio, se analiza cómo ellos estudian una pregunta que podría engendrar un Recorrido de estudio e Investigación (REI). Los profesores investigaron la pregunta de manera individual y grupal, y luego se les propuso organizar una posible enseñanza adaptada a una institución conocida por ellos, basada en la pregunta. Los textos escritos producidos por los profesores se analizan empleando dos tipos de técnicas: una cualitativa y otra basada en métodos estadísticos lexicométricos. Los resultados describen las dificultades de los profesores en servicio para organizar una enseñanza conforme al paradigma de la investigación y el cuestionamiento del mundo.
oai:oai.hipatiapress.com:article/3627
2023-09-26T11:31:49Z
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Vol. 10 No. 2 (2021): June ; 152-174
Mathematics Teacher Education in Turkey through the Lens of International TEDS-M Study
Ertaş, Güneş; Boğaziçi University
Aslan-Tutak, Fatma; Boğaziçi University
2021-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3627
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This paper is a part of a broader study which aims to investigate mathematics teacher candidates' mathematical knowledge for teaching (MKT) by using the Turkish translated versions of TEDS-M (Teacher Education and Development Study in Mathematics) Primary and Secondary Released Items. The sample of the study comprised freshman (first year) and senior (fourth and fifth year) students from primary and secondary mathematics teacher education programs. Firstly, this study aimed to examine differences in MKT of teacher candidates at the beginning and at the end of their undergraduate education. For both departments, senior students had statistically significant higher scores than freshman students. Secondly, this study also aimed to examine participating Turkish preservice mathematics teachers’ mathematical knowledge for teaching by using international results of TEDS-M Study. Participating senior preservice teachers’ correct response percentages were higher than international average in all domains except “data” in primary level, and “data”, “mathematical modelling” and “symmetry” in secondary level. The common content domains where primary and secondary preservice teachers’ percentages were lower than international average is “data”. In this paper, these areas will be examined within the context of Turkish education.
oai:oai.hipatiapress.com:article/3638
2023-09-26T11:31:49Z
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Vol. 10 No. 2 (2021): June ; 175-212
Investigation of pre-service elementary mathematics teachers’ understanding on solids
Karakus, Fatih; Afyon Kocatepe University
Erşen, Zeynep Bahar
2021-06-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3638
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The aim of the present study is to determine the elementary pre-service mathematics teachers’ understanding on solids. For this purpose, pre-service teachers’ definitions and drawings of these objects were examined. Qualitative research method was used. A written questionnaire consisting of sixteen open-ended and multiple-choice questions was conducted with 127 elementary pre-service mathematics teachers chosen by convenience sample which is one of non-random sampling method. The collected qualitative data were analyzed by both descriptive and content analysis. The results revealed that pre-service teachers made insufficient connections among cylinder, prism, cone and pyramid. So, it can be said that their understanding about solids was weak and procedural.
oai:oai.hipatiapress.com:article/3667
2023-09-26T11:31:03Z
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2023-09-26T11:31:03Z
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Vol. 11 No. 1 (2022): February; 86-112
Are 9th Grade Students Ready to Engage in the Theoretical Discursive Process in Geometry?
Karpuz, Yavuz; Recep Tayyip Erdogan University
Güven, Bülent; Karadeniz Technical University
2022-02-24
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url:https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3667
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This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval’s Cognitive Model. The sample of the study was comprised of 51 newly-enrolled 9thgrade students between the ages of 14 and 15, who had not received any prior geometry instruction. These 51 students were posed two open-ended questions that would enable them to make a transition between perceptual and discursive apprehension. The qualitative data obtained from the open-ended questions were classified into three categories, and clinical interviews were held with three students from each category. According to the findings obtained from the study, many of the students could not display the necessary behaviors for theoretical discursive process. Students were mostly unsuccessful in converting discursive information into perceptual information, in writing discursive information based on perceptual information, and making inferences based on discursive information. These findings indicate that recent graduates of secondary school are not ready enough to directly engage in theoretical discursive process and, thus, they could experience difficulties in such high order skills as providing proof requiring the theoretical discursive process.
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