A STUDY OF CONCEPTUAL UNDERSTANDING THROUGH CONCEPT MAPS BASED ON THE ANTHROPOLOGICAL THEORY OF DIDACTICS
Main Article Content
Abstract
The development of conceptual understanding in mathematics is essential for enhancing students’ mathematical competence. This understanding helps learners grasp the meaning of symbols, the relationships between concepts, and facilitates the application of mathematics in learning and communication. Modern educational theories emphasize the importance of conceptual understanding as an educational competency across many countries. Concept maps are used as a tool to assess conceptual understanding. Numerous studies have demonstrated that students' conceptual understanding can be measured through connections, specifically the degree of linkage among concepts represented on a concept map. Anchored within the theoretical framework of the Anthropological Theory of Didactics, this study employs the concept of Praxéologie to describe the constraints in students’ personal relationships with the task type “Design a concept map with a central keyword”. The quantitative assessment method of a concept map showed that Map A was more effective than Map B. When combined with qualitative evaluation methods, this approach partially explains the reasons behind this difference.
Keywords
Anthropological Theory of the Didactic, Praxéologie, Conceptual understanding, Concept map.
Article Details
References
Afamasaga-Fuata’i, K. (2009a). Analysing the “Measurement” Strand Using Concept Maps and Vee Diagrams. In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 19–46). Springer US.
Afamasaga-Fuata’i, K. (2009b). Concept Mapping a Teaching Sequence and Lesson Plan for “Derivatives.” In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 149–169). Springer US.
Afamasaga-Fuata’i, K. (2009c). Using Concept Maps and Vee Diagrams to Analyse the “Fractions” Strand in Primary Mathematics. In K. Afamasaga-Fuata’i(Ed.), Concept Mapping in Mathematics(pp.59-86). Springer US.
Bednarz, N., Dufour-Janvier, B., Poirier, L., & Bacon, L. (1993). Socioconstructivist Viewpoint on the Use of Symbolism in Mathematics Education. The Alberta Journal of Research, 39(1), 41–59.
Bessot, A., Comiti, C., Châu, L. T. H., & Tiến, L. V. (2009). Những yếu tố cơ bản của Didactic Toán (Éléments fondamentaux de didactique des mathématiques). NXB Đại học Quốc gia TP. Hồ Chí Minh.
Caldwell, W. (2009). Applying Concept Mapping to Algebra I. In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 217–234). Springer US.
Cañas, A. J., Novak, J. D., & Vanhear, J. (2012). Freedom vs. Restriction of content and structure during concept mapping-Possibilities and limitations for construction and assessment. Concept maps: Theory, methodology, technology. Proceedings of the Fifth International Conference on Concept Mapping (pp. 247-257).
Cetin-Dindar, A., & Geban, O. (2017). Conceptual understanding of acids and bases concepts and motivation to learn chemistry. The Journal of Educational Research, 110(1), 85–97.
Chevallard, Y. (1991). La transposition didactique: Du savoir savant au savoir enseigné (2. éd). La Pensée Sauvage.
Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches En Didactique Des Mathématiques, 19(2), 221–266.
Chevallard, Y. (2006). La théorie anthropologique des faits didactiques devant l’enseignement de l’altérité culturelle et linguistique. Le point de vue d’un outsider. Construction identitaire et altérité : Créations curriculaires et didactique des langues, Université de Cergy-Pontoise.
Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational Number Project Curriculum. Journal for Research in Mathematics Education, 33(2), 111.
Curriculum Planning and Development Division - Ministry of Education Singapore. (2012). Mathematics Syllabus Primary One to Six.
De Zeeuw, A., Craig, T., & You, H. S. (2013). Assessing conceptual understanding in mathematics. 1742–1744.
Gelman, R., Cohen, M., & Hartnett, P. (1989). To know mathematics is to go beyond thinking that “Fractions aren’t numbers.” Proceedings of the Eleventh Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education, 2, 29–68.
Hoffmann, A., & Even, R. (2024). What do mathematicians wish to teach teachers about the discipline of mathematics? Journal of Mathematics Teacher Education, 27(3), 479–497.
Jin, H., & Wong, K. Y. (2011). Assessing Conceptual Understanding in Mathematics with Concept Mapping. In B. Kaur & K. Y. Wong, Assessment in the Mathematics Classroom (pp. 67–90). World scientific.
Jin, H., & Wong, K. Y. (2015). Mapping conceptual understanding of algebraic concepts: an exploratory investigation involving grade 8 chinese students. International Journal of Science and Mathematics Education, 13(3), 683–703.
Kamble, S. K., & Tembe, B. L. (2013). The Effect of Use of Concept Maps on Problem Solving Performance and Attitude in Mechanical Engineering Course. Procedia - Social and Behavioral Sciences, 83, 748–754.
Kinchin, I. M. (2014). Concept Mapping as a Learning Tool in Higher Education: A Critical Analysis of Recent Reviews. The Journal of Continuing Higher Education, 62(1), 39–49.
Kinchin, I. M., Hay, D. B., & Adams, A. (2000). How a qualitative approach to concept map analysis can be used to aid learning by illustrating patterns of conceptual development. Educational Research, 42(1), 43–57.
Kurniawan, F., Samsudin, A., Chandra, D. T., Sriwati, E., Zahran, M., Gani, A. W., Ramadhan, B. P., Aminudin, A. H., & Ramadani, F. (2023). Assessing conceptual understanding of high school students on transverse and stationary waves through Rasch analysis in Malang. Journal of Physics: Conference Series, 2596(1), 012060.
Châu, L. T. H. & Comiti, C. (2018). Thuyết nhân học trong Didactic Toán. NXB Đại học Sư phạm TP. Hồ Chí Minh.
Mansfield, H., & Happs, J. (1989). Using concept maps to explore students’ understanding in geometry. Proceedings of the 13th Conference of the International Group for Psychology of Mathematics Education, 2, 250–257.
Mansfield, H., & Happs, J. (1991). Concept Maps. Australian Mathematics Teacher, 47(3), 30–33.
Nasution, N. (2019). Effect of Case Study and Concept Map on Critical Thinking Skills and Dispositions in Indonesian College Students. The New Educational Review, 55(1), 64–76.
NCTM (Ed.). (2000). Principles and standards for school mathematics. NCTM.
Niemi, D. (1996). Assessing Conceptual Understanding in Mathematics: Representations, Problem Solutions, Justifications, and Explanations. The Journal of Educational Research, 89(6), 351–363.
Novak, J. D., & Cañas, A. J. (2009). The Development and Evolution of the Concept Mapping Tool Leading to a New Model for Mathematics Education. In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 3–16). Springer US.
Novak, J. D., & Gowin, D. B. (1984). Learning how to learn. Cambridge University Press.
Nykiforuk, C. I. J., Belon, A. P., & Scott, L. K. A. (2024). Untangling Concepts of Financial Circumstances for Public Health Professionals and Scholars: A Glossary and Concept Map. American Journal of Public Health, 114(1), 79–89.
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and middle school mathematics teaching developmentally (Tenth edition / Global edition).
White, R. T., & Gunstone, R. (2014). Probing understanding. Routledge, Taylor & Francis Group.
Afamasaga-Fuata’i, K. (2009b). Concept Mapping a Teaching Sequence and Lesson Plan for “Derivatives.” In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 149–169). Springer US.
Afamasaga-Fuata’i, K. (2009c). Using Concept Maps and Vee Diagrams to Analyse the “Fractions” Strand in Primary Mathematics. In K. Afamasaga-Fuata’i(Ed.), Concept Mapping in Mathematics(pp.59-86). Springer US.
Bednarz, N., Dufour-Janvier, B., Poirier, L., & Bacon, L. (1993). Socioconstructivist Viewpoint on the Use of Symbolism in Mathematics Education. The Alberta Journal of Research, 39(1), 41–59.
Bessot, A., Comiti, C., Châu, L. T. H., & Tiến, L. V. (2009). Những yếu tố cơ bản của Didactic Toán (Éléments fondamentaux de didactique des mathématiques). NXB Đại học Quốc gia TP. Hồ Chí Minh.
Caldwell, W. (2009). Applying Concept Mapping to Algebra I. In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 217–234). Springer US.
Cañas, A. J., Novak, J. D., & Vanhear, J. (2012). Freedom vs. Restriction of content and structure during concept mapping-Possibilities and limitations for construction and assessment. Concept maps: Theory, methodology, technology. Proceedings of the Fifth International Conference on Concept Mapping (pp. 247-257).
Cetin-Dindar, A., & Geban, O. (2017). Conceptual understanding of acids and bases concepts and motivation to learn chemistry. The Journal of Educational Research, 110(1), 85–97.
Chevallard, Y. (1991). La transposition didactique: Du savoir savant au savoir enseigné (2. éd). La Pensée Sauvage.
Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches En Didactique Des Mathématiques, 19(2), 221–266.
Chevallard, Y. (2006). La théorie anthropologique des faits didactiques devant l’enseignement de l’altérité culturelle et linguistique. Le point de vue d’un outsider. Construction identitaire et altérité : Créations curriculaires et didactique des langues, Université de Cergy-Pontoise.
Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational Number Project Curriculum. Journal for Research in Mathematics Education, 33(2), 111.
Curriculum Planning and Development Division - Ministry of Education Singapore. (2012). Mathematics Syllabus Primary One to Six.
De Zeeuw, A., Craig, T., & You, H. S. (2013). Assessing conceptual understanding in mathematics. 1742–1744.
Gelman, R., Cohen, M., & Hartnett, P. (1989). To know mathematics is to go beyond thinking that “Fractions aren’t numbers.” Proceedings of the Eleventh Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education, 2, 29–68.
Hoffmann, A., & Even, R. (2024). What do mathematicians wish to teach teachers about the discipline of mathematics? Journal of Mathematics Teacher Education, 27(3), 479–497.
Jin, H., & Wong, K. Y. (2011). Assessing Conceptual Understanding in Mathematics with Concept Mapping. In B. Kaur & K. Y. Wong, Assessment in the Mathematics Classroom (pp. 67–90). World scientific.
Jin, H., & Wong, K. Y. (2015). Mapping conceptual understanding of algebraic concepts: an exploratory investigation involving grade 8 chinese students. International Journal of Science and Mathematics Education, 13(3), 683–703.
Kamble, S. K., & Tembe, B. L. (2013). The Effect of Use of Concept Maps on Problem Solving Performance and Attitude in Mechanical Engineering Course. Procedia - Social and Behavioral Sciences, 83, 748–754.
Kinchin, I. M. (2014). Concept Mapping as a Learning Tool in Higher Education: A Critical Analysis of Recent Reviews. The Journal of Continuing Higher Education, 62(1), 39–49.
Kinchin, I. M., Hay, D. B., & Adams, A. (2000). How a qualitative approach to concept map analysis can be used to aid learning by illustrating patterns of conceptual development. Educational Research, 42(1), 43–57.
Kurniawan, F., Samsudin, A., Chandra, D. T., Sriwati, E., Zahran, M., Gani, A. W., Ramadhan, B. P., Aminudin, A. H., & Ramadani, F. (2023). Assessing conceptual understanding of high school students on transverse and stationary waves through Rasch analysis in Malang. Journal of Physics: Conference Series, 2596(1), 012060.
Châu, L. T. H. & Comiti, C. (2018). Thuyết nhân học trong Didactic Toán. NXB Đại học Sư phạm TP. Hồ Chí Minh.
Mansfield, H., & Happs, J. (1989). Using concept maps to explore students’ understanding in geometry. Proceedings of the 13th Conference of the International Group for Psychology of Mathematics Education, 2, 250–257.
Mansfield, H., & Happs, J. (1991). Concept Maps. Australian Mathematics Teacher, 47(3), 30–33.
Nasution, N. (2019). Effect of Case Study and Concept Map on Critical Thinking Skills and Dispositions in Indonesian College Students. The New Educational Review, 55(1), 64–76.
NCTM (Ed.). (2000). Principles and standards for school mathematics. NCTM.
Niemi, D. (1996). Assessing Conceptual Understanding in Mathematics: Representations, Problem Solutions, Justifications, and Explanations. The Journal of Educational Research, 89(6), 351–363.
Novak, J. D., & Cañas, A. J. (2009). The Development and Evolution of the Concept Mapping Tool Leading to a New Model for Mathematics Education. In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 3–16). Springer US.
Novak, J. D., & Gowin, D. B. (1984). Learning how to learn. Cambridge University Press.
Nykiforuk, C. I. J., Belon, A. P., & Scott, L. K. A. (2024). Untangling Concepts of Financial Circumstances for Public Health Professionals and Scholars: A Glossary and Concept Map. American Journal of Public Health, 114(1), 79–89.
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and middle school mathematics teaching developmentally (Tenth edition / Global edition).
White, R. T., & Gunstone, R. (2014). Probing understanding. Routledge, Taylor & Francis Group.