In Pursuit of a Connected Way of Knowing: The Case of one Mathematics Teacher
Keywords:
Quality, Effectiveness, Change, Improvement, Equity, Innovation.Copyright (c) 2015 REICE. Revista Iberoamericana sobre Calidad, Eficacia y Cambio en Educación
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Abstract
In this paper we offer illustrations of a mathematics teacher’s difficulties with content knowledge when trying to find connections between school mathematics and science. The paper is based on a sub-study that is part of a larger Colombian project, PROMESA (Creating Science and Mathematics Connected Learning Experiences that Open Opportunities for the Promotion of Algebraic Reasoning), which incorporated a Professional Learning Programme (PLP) seeking to integrate school science and mathematics teachers into working teams, in order to create science and mathematics connected learning experiences that considered the promotion of algebraic reasoning. The “challenging questions” which emerged for this teacher, during the workshops of the Induction Stage of the PLP, became the driving force for her continued engagement in learning mathematics content in a connected way, as opposed to the compartmentalised content-item thinking she had experienced as a school student. We provide illustrations of first steps in the development of a teacher’s mathematical understanding which can support growth of mathematical knowledge for teaching.
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References
Agudelo-Valderrama, C. y Vergel, R. (2009a). Informe final del Proyecto PROMICE. Promoción de un enfoque interdisciplinario y de resolución de problemas en el inicio del trabajo algebraico escolar: Integrando contextos de ciencias y el uso de tecnología digital. Bogotá: IDEP, Secretaría de Educación Distrital.
Agudelo-Valderrama, C. y Vergel, R. (2009b). La apertura del aula de ciencias para promover el desarrollo del pensamiento algebraico: el caso del profesor Simón, participante del Proyecto PROMICE. En L.F. Acuña y L. Zea (Eds.). Universidad-escuela y producción de conocimiento pedagógico: resultados de la investigación IDEP- Colciencias (pp. 245-258). Bogotá: IDEP.
Ball, D.L., Lubienski, S. y Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. En V. Richardson (Ed.), Handbook of Research on Teaching (pp. 433-456). Nueva York: McMillan.
Barr, G. (1981). Some student ideas on the concept of gradient. Mathematics in School, 10(1), 14-17.
Basista, B. y Mathews, S. (2002). Integrated science and mathematics professional developmnet programs. School Science and Mathematics, 102(7), 359-370.
Birgin, O. (2012). Investigation of eight-grade students’ understanding of slope of the linear function. Bolema, 26(42), 139-162.
Czerniac, C., Weber, W., Sandman, A. y Ahern, J. (1999). A literature review of science and mathematics. Integration, School Science and Mathematics, 99(8), 421-430.
Dawkins, D., Dickerson, D., McKinney, S. y Butler, S. (2008). Teaching density to middle school students: Pre-service science teachers’ content knowledge and pedagogical practices. A Journal of Educational Strategies, Issues and Ideas, 82(1), 21-26.
Department of Education and Early Childhood Development. (2013). Principles of Learning and Teaching P-12. Recuperado de http://www.education.vic.gov.au/
Dole, S., Clarke, D., Wright, T. y Hilton, G. (2009). Developing year 5 students understanding of density: implications for mathematics teaching. En R. Hunter, B. Bicknell y T. Burges (Eds.). Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (pp. 153-160). Palmerston North, NZ: MERGA.
Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: a model. Journal of Education for Teaching, 15(1), 13-33.
Frykholm, J. y Glasson, G. (2005). Connecting science and mathematics instruction: pedagogical context knowledge for teachers. School Science and Mathematics, 105(3), 127-141.
Glaser, B. y Strauss, A. (1967). The discovery of grounded theory. Chicago, IL: Aldine Publishing Co.
Hill, H.C., Ball, D.L. y Schilling, S.G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.
Hill, H.C., y Ball, D.L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330-351.
Lamon, S. (1999). Teaching fractions and ratios for understanding: essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum Associates.
Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
MacGegor, M. y Stacey, K. (1995). The effect of different approaches to algebra on student perceptions of functional relationships. Mathematics Education Research Journal, 7(1), 69-85.
Michelsen, C. (2005). Expanding the domain: variables and functions in an interdisciplinary context between mathematics and physics. En A. Beckmann, C. Michelsen y B. Sriraman (Eds.), Proceedings of the 1st international symposium of mathematics and its connections to the arts and sciences (pp. 201-214). Gmünd: The University of Education.
Michelsen, C. y Sriraman, B. (2009). Does disciplinary instruction raise students’ interest in mathematics and the subjects of the natural sciences? ZDM Mathematics Education, 41(1-2), 231-244.
Ministerio de Educación Nacional. (1998a). Lineamientos curriculares de ciencias naturales y educación ambiental. Bogotá: Magisterio.
Ministerio de Educación Nacional. (1998b). Lineamientos curriculares de matemáticas. Bogotá: Magisterio.
Ministerio de Educación Nacional. (2006). Estándares básicos de competencias en lenguaje, matemáticas, ciencias y ciudadanas. Bogotá: Magisterio.
Moschkovich, J. (1996). Moving up and getting steeper: negotiating shared descriptions of linear graphs. The Journal of the Learning Sciences, 5(3), 239-277.
National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Academy Press.
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: National Academy Press.
National Research Council. (1996). The National Science Education Standards. Washington D.C.: National Academy Press.
Roach, L. (2001). Exploring students’ conceptions of density. Journal of College Science Teaching, 30(6), 386-389.
Sierpinska, A. (1994). Understanding in Mathematics. Londres: The Falmer Press.
Singh, P. (2000). Understanding the concepts of proportion and ratio constructed by two grade six students. Educational Studies in Mathematics, 43(3), 271-292.
Smith, C., Maclin, D., Grosslight, L. y Davis, H. (1997). Teaching for understanding: A study of students’ preinstruction theories of matter and comparison of the effectiveness of two approaches to the teaching about matter and density. Cognition and Instruction, 15(3), 317-393.
Steen, L.A. (1999). Does everybody need to study algebra? In B. Moses (Ed.), Algebraic thinking grades K-12: readings from NCTM's school journal and other publications (pp. 49-51). Reston, VA: NCTM.
Stump, S. (2001). High school precalculus students’ understanding of slope as a measure. School Science and Mathematics, 101(2), 81-89.
Stump, S. (1997). Secondary mathematics teachers’ knowledge of the concept of slope. Comunicación presentada en el The annual meeting of the American educational research association. Chicago, IL: EDRS.
Westbrook, S. (1998). Examining the conceptual organization of students in an integrated algebra and physical science class. School Science and Mathematics, 98(2), 84-92.
Woodbury, S. (1998). Rhetoric, reality, and possibilities: interdisciplinary teaching and secondary mathematics. School Science and Mathematics, 98(6), 303-311.
Yin, R.K. (2003). Case study research: design and methods. Thousand Oaks, CA: Sage Publications, Inc.
Zaslavsky, O., Sela, H. y Leron, U. (2002). Being sloppy about slope: the effect of changing the scale. Educational Studies in Mathematics, 49(1), 119-140.
Zohar, A. (2006). Connected knowledge in science and mathematics education. International Journal of Science Education, 28(13), 1579-1599.