Horizon Content Knowledge: shaping MKT for a continuous mathematical education
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Abstract
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.
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References
Abellanas, M. (2006-2007) Envolvente convexa, triangulación de Delaunay y diagrama de Voronoi: tres estructuras geométricas en una, con muchas aplicaciones. Un paseo por la Geometría,(paper). http://divulgamat.ehu.es/weborriak/TestuakOnLine/06-07/PG-06-07-Abellanas.pdf
Google Scholar CrossrefAkos, P., & Galassi, J. P. (2004). Middle and high school transitions as viewed by students, parents, and teachers. Professional School Counseling, 7(4), 212–221.
Google Scholar CrossrefAkos, P., Queen, J.A., & Lineberry, C. (2005) Promoting a successful transition to middle school. Larchmont, NY: Eye on Education.
Google Scholar CrossrefAlspaugh, J.W., & Harting, R.D. (1997) Effects of team teaching on the transition to middle school. ERS Spectrum, 15 (1), 9-14.
Google Scholar CrossrefAlspaugh, J.W., & Harting, R.D. (1998) Interdisciplinary team teaching versus departmentalization in middle schools. Research in Middle Level Education Quarterly, 21(4), 31-42.
Google Scholar CrossrefAnderman, E.M., & Midgley, C. (2004) Changes in self-reported academic cheating across the transition from middle school to high school. Contemporary Educational Psychology, 29(4), 499-517.
Google Scholar CrossrefBall, D.L., & Hill, H. (2009). R and D: The curious - and crucial - case of mathematical knowledge for teaching. Phi Delta Kappan, 91(2), 68-71.
Google Scholar CrossrefBall, D.L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59 (5), 389-407.
Google Scholar CrossrefBenitez, D.T. Morningstar, M.E., & Frey, B.B. (2009) A multistate survey of special education teachers’ perceptions of their transition competencies. Career development for exceptional individuals, 32(1), 6-16.
Google Scholar CrossrefBerthelot, R. & Salin, M.H (2000-2001) L’enseignement de la géométrie au début du collège. Comment concevoir le passage de la géométrie de constat à la géométrie déductive? Petit x, 56, 5-34.
Google Scholar CrossrefBoulton-Lewis, G.; Cooper, T.; Atweh, B.; Pillay, H.; Wilss, L.; Mutch, S. (1997). Transition from arithmetic to algebra: A cognitive perspective. 21st Annual Conference of the International Group for Psychology of Mathematics Education (Vol. 2, 178-185). Lahiti, Finland.
Google Scholar CrossrefBoulton-Lewis, G.; Cooper, T.; Atweh, B.; Pillay, H.; Wilss, L. (1998). Arithmetic, pre algebra and algebra: A model of transition. Mathematics Education Research Group of Australasia, Gold Coast.
Google Scholar CrossrefBraund, M. (2002) Smoothing the transfer from Key Stage 2 to Key Stage 3. Education in Science, 197, 28-29.
Google Scholar CrossrefCoad, J.; Jones, K. (1999). Curriculum continuity in mathematics: a case study of the transition from primary to secondary school. University of Southampton, Southampton: Center for Research in Mathematics Education.
Google Scholar CrossrefCooper, T.; Boulton-Lewis, G.; Atweh, B.; Pillay, H.; Wilss, L.; Mutch, S. (1997). Transition from arithmetic to algebra: Initial understanding of equals, operation and variables. 21st Annual Conference of the International Group for Psychology of Mathematics Education (Vol. 2,. 82-89). Lahiti, Finland.
Google Scholar CrossrefDing, C.S. (2008) Variations in academic performance trajectories during high school transition: exploring change profiles via multidimensional scaling growth profile analysis. Educational Research and Evaluation, 14(4), 305-319.
Google Scholar CrossrefFerguson, P.D.; Fraser, B.J. (1998) Student gender, school size and changing perceptions of science learning environment during transition from primary to secondary school. Research in Science Education, 28(4), 387-397.
Google Scholar CrossrefFlores, A. (2002). Geometric Representations in the Transition from Arithmetic to Algebra. In Fernando Hitt (Ed), Representations and Mathematics Visualization. (pp. 9-29). México, DF. Departamento de Matemática Educativa del Cinvestav-IPN.
Google Scholar CrossrefFraser, B.J. (1998) Classroom Environment Instruments: Development, Validity and Applications. Learning Environments Research, 1(1), 7-33.
Google Scholar CrossrefGallardo, A. (2002) The extension of the natural number domain to the integers in the transition from arithmetic to algebra. Educational Studies in Mathematics, 49, 171-192.
Google Scholar CrossrefGentle-Genitty, C. (2009) Best practice program for low- income african-american students transitioning from middle to high school. Children and schools, 31(2), 109-117.
Google Scholar CrossrefGonzales, F.E.; Ruiz Lopez, F. (2003) Las centenas cuadriculadas: un material matemáticamente potente para ilustrar el tránsito de la aritmética al álgebra. SUMA: Revista sobre la enseñanza y el aprendizaje de las matemáticas, 42, 47-59.
Google Scholar CrossrefGueudet, G. (2008) Investigating the secondary-tertiary transition. Educational Studies in Mathematics, 67(3), 237-254.
Google Scholar CrossrefGuzmán, M.; Hodgson, B.; Robert, A.; Villani, V. (1998). Difficulties in the passage from secondary to tertiary education. Documenta Mathematica Journal, III, 747-762.
Google Scholar CrossrefHerlihy, C. (2007). Toward ensuring a smooth transition into high school. Washington DC: National High School Center.
Google Scholar CrossrefHill, H.C.; Rowan, B.; Ball, D.L. (2005) Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42 (2), 371-406.
Google Scholar CrossrefHill, H. C.; Blunk, M.; Charalambous, C.; Lewis, J.; Phelps, G.; Sleep, L.; Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511.
Google Scholar CrossrefHill M.; Graham C.; Caulfield C.; Ross N.; & Shelton A. (2007) Inter-ethnic relations among children at school: the perspectives of young people in Scotland. European Journal of Education, 42, 2, 267-279.
Google Scholar CrossrefHoller, E.W. (2008) Welcome to Clipper Camp! Principal Leadership Journal, 8 (8), 28-31.
Google Scholar CrossrefJourdan, N.; Cretchley, P.; Passmore, T. (2007) Secondary-Terciary transition: what Mathematics skills can and should we expect this decade? In: 30th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA30), 2-6 July, Hobart, Australia.
Google Scholar CrossrefKajander, A., Lovric, M. (2005) Transition from secondary to terciary mathematics: McMaster University experience. International Journal of Mathematical Education in Science and Technology, 36 (2-3), 149-160.
Google Scholar CrossrefKnight, P., Huggins, M. (1997) Curriculum Continuity and Transfer from Primary to Secondary School: the Case of History. Educational Studies, 23(3), 333-348.
Google Scholar CrossrefLewbel, S., Haskins, A., Spradling, N., Thompson, S. C. (1996) Practitioners Respond. Middle School Journal, 28(1), 21-23.
Google Scholar CrossrefLucey, H., Reay, D. (2002) Carrying the Beacon of Excellence: Social Class Differentiation and Anxiety at a Time of Transition. Journal of Education Policy, 17(3), 321-336.
Google Scholar CrossrefMcGee, C., Ward, R., Gibbons, J; Harlow, A. (2004) Transition to Secondary School: A Literature Review. Hamilton: The University of Waikato.
Google Scholar CrossrefNew Zealand Ministry of Education (2008) Students’ Transition from Primary to Secondary Schooling.
Google Scholar CrossrefNoyes, A. (2006) School transfer and the diffraction of learning trajectories. Research papers in Education, 21(1), 43-62.
Google Scholar CrossrefPujol, R. (2006) Diagnóstico sobre la disposición del alumnado para aprender matemáticas a través de la resolución de problemas. PhD Thesis. Universitat Autònoma de Barcelona.
Google Scholar CrossrefQueen, J. A. (2002) Student Transitions From Middle to High School: Improving Achievement and Creating a Safer Environment. Larchmont, NY: Eye On Education.
Google Scholar CrossrefRice, J.K. (1997) Explaining the negative impact of the transition from middle to high school on student performance in mathematics and science: an examination of school discontinuity and student background variables. Paper presented at the annual meeting of the American Education Research Association Annual Conference, Chicago, IL.
Google Scholar CrossrefRowland, T.; Huckstep P.; Thwaites, A. (2005) Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education 8(3), 255-281.
Google Scholar CrossrefSdrolias, K.A.; Triandafillidis, T.A. (2008) The transition to secondary school geometry: can there be a “chain of school mathematics”? Educational Studies in Mathematics, 67(2), 159-169.
Google Scholar CrossrefShulman, L.S. (1986) Those who understand: knowledge groth in teaching. Educational Researcher, 15(2) 4-14.
Google Scholar CrossrefSimpson M., Goulder, J. (1998) Promoting Continuity and Progression: Implementing the 5-14 Development Programme in Secondary School Mathematics and English Language Departments. Scottish Educational Review, 30(1), 15-28.
Google Scholar CrossrefZanobini, M.; Usai, C. (2002) Domain-specific Self-concept and Achievement Motivation in the Transition from Primary to Low Middle School. Educational Psychology, 22 (2), 203-217.
Google Scholar CrossrefZeedyk, M. S.; Gallacher, J.; Henderson, M.; Hope, G.; Husband, B.; Lindsay, K. (2003). Negotiating the transition from primary to secondary school: Perceptions of pupils, parents, and teachers. School Psychology International, 24(1), 67–79.
Google Scholar CrossrefZhang, D.; Ivester, J.; Katsiyamis, A. (2005) Teachers’ view of transition services: results from a statewide survey in South Carolina. Education and Training in Developmental Disabilities, 40(4), 360-367.
Google Scholar CrossrefDownloads
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