USING CONCEPT MAPS TO ENHANCE CONCEPTUAL UNDERSTANDING: AN ANTHROPOLOGICAL APPROACH TO DIDACTICS
Main Article Content
Abstract
Developing conceptual understanding is essential for strengthening students’ mathematical competence. It enables learners to interpret symbols, recognize relationships among concepts, and apply mathematics effectively. Previous studies have highlighted concept maps as tools for assessing conceptual understanding by examining connections among concepts. Framed by the Anthropological Theory of the Didactic (ATD), particularly the concept of knowledge organization, this study characterizes constraints in students’ personal relationships to the task type “Design a concept map with a central keyword.” An exploratory experiment involving eight Grade 10 students in Ho Chi Minh City combined quantitative and qualitative assessment methods to explain the observed differences. The findings indicate that concept maps have research value and may also serve as a practical pedagogical tool for teachers to observe and support students’ conceptual learning. However, the small sample and specific context limit the generalizability of the findings.
Keywords
Anthropological Theory of the Didactic, concept map, conceptual understanding, mathemat-ics education, praxeology, quantitative and qualitative assessment
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. https://doi.org/10.1007/978-0-387-89194-1_2
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. https://doi.org/10.1007/978-0-387-89194-1_8
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. https://doi.org/10.1007/978-0-387-89194-1_4
Bednarz, N., Dufour-Janvier, B., Poirier, L., & Bacon, L. (1993). Socioconstructivist View-point on the Use of Symbolism in Mathematics Education. The Alberta Journal of Re-search, 39(1), 41–59.
Bessot, A., Comiti, C., Le, T. H. C., & Le, V. T. (2009). Éléments fondamentaux de di-dactique des mathématiques [Fundamental elements of mathematics didactics]. Vi-etnam National University Ho Chi Minh City Publishing House.
Caldwell, W. (2009). Applying Concept Mapping to Algebra I. In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 217–234). Springer, Boston, MA. https://doi.org/10.1007/978-0-387-89194-1_11
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 as-sessment. In 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 con-cepts and motivation to learn chemistry. The Journal of Educational Research, 110(1), 85–97. https://doi.org/10.1080/00220671.2015.1039422
Chevallard, Y. (1991). La transposition didactique: Du savoir savant au savoir enseigné [Didactic transposition: From scholarly knowledge to taught knowledge] (2nd ed.). La Pensée Sauvage.
Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique [The analysis of teaching practices from the anthropological theory of the didactic]. Recherches en Didactique des Mathématiques, 19(2), 221–266. https://revue-rdm.com/1999/l-analyse-des-pratiques/
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 [The anthropological theory of didactic facts in the teaching of cultural and linguistic otherness: An outsider’s perspective]. In J. Aden (Ed.), Création identitaire et altérité en didactique des langues (pp. 17–38). Éditions Le Manuscrit.
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), 111-144. https://doi.org/10.2307/749646
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 math-ematics. In 2013 IEEE Frontiers in Education Conference (FIE) (pp. 1742–1744). IEEE. https://doi.org/10.1109/FIE.2013.6685135
Gelman, R., Cohen, M., & Hartnett, P. (1989). To know mathematics is to go beyond think-ing that “Fractions aren’t numbers”. In C. Maher, G. Goldin, & R. Davis (Eds.), Pro-ceedings of the Eleventh Annual Meeting of the North American Chapter of the Interna-tional Group for the Psychology of Mathematics Education (Vol. 2, pp. 29–67).
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 https://doi.org/10.1007/s10857-023-09577-4
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. https://doi.org/10.1007/s10763-013-9500-2
Kamble, S. K., & Tembe, B. L. (2013). The Effect of Use of Concept Maps on Problem Solv-ing Performance and Attitude in Mechanical Engineering Course. Procedia - Social and Behavioral Sciences, 83, 748–754. https://doi.org/10.1016/j.sbspro.2013.06.141
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. https://doi.org/10.1080/07377363.2014.872011
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. https://doi.org/10.1080/001318800363908
Kurniawan, F., Samsudin, A., Chandra, D. T., Sriwati, E., Zahran, M., Gani, A. W., Rama-dhan, B. P., Aminudin, A. H., & Ramadani, F. (2023). Assessing conceptual under-standing of high school students on transverse and stationary waves through Rasch analysis in Malang. Journal of Physics: Conference Series, 2596(1), 012060. https://doi.org/10.1088/1742-6596/2596/1/012060
Le, T. H. C., & Comiti, C. (2018). Thuyết nhân học trong Didactic Toán [The anthropologi-cal theory of didactics of mathematics]. Ho Chi Minh City University of Education Pub-lishing House.
Mansfield, H., & Happs, J. (1989). Using concept maps to explore students’ understanding in geometry. In G. Vergnaud, J. Rogalski, & M. Artique (Eds.), Proceedings of the 13th Annual Conference of the International Group for the Psychology of Mathematics Edu-cation (Vol. 2, pp. 250–257). PME.
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. https://doi.org/10.15804/tner.2019.55.1.05
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 Re-search, 89(6), 351–363. https://doi.org/10.1080/00220671.1996.9941339
Novak, J. D., & Cañas, A. J. (2009). The Development and Evolution of the Concept Map-ping Tool Leading to a New Model for Mathematics Education. In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 3–16). Springer. https://doi.org/10.1007/978-0-387-89194-1_1
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. https://doi.org/10.2105/AJPH.2023.307449
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual under-standing and procedural skill in mathematics: An iterative process. Journal of Educa-tional Psychology, 93(2), 346–362. https://doi.org/10.1037//0022-0663.93.2.346
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson Education.
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. https://doi.org/10.1007/978-0-387-89194-1_8
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. https://doi.org/10.1007/978-0-387-89194-1_4
Bednarz, N., Dufour-Janvier, B., Poirier, L., & Bacon, L. (1993). Socioconstructivist View-point on the Use of Symbolism in Mathematics Education. The Alberta Journal of Re-search, 39(1), 41–59.
Bessot, A., Comiti, C., Le, T. H. C., & Le, V. T. (2009). Éléments fondamentaux de di-dactique des mathématiques [Fundamental elements of mathematics didactics]. Vi-etnam National University Ho Chi Minh City Publishing House.
Caldwell, W. (2009). Applying Concept Mapping to Algebra I. In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 217–234). Springer, Boston, MA. https://doi.org/10.1007/978-0-387-89194-1_11
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 as-sessment. In 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 con-cepts and motivation to learn chemistry. The Journal of Educational Research, 110(1), 85–97. https://doi.org/10.1080/00220671.2015.1039422
Chevallard, Y. (1991). La transposition didactique: Du savoir savant au savoir enseigné [Didactic transposition: From scholarly knowledge to taught knowledge] (2nd ed.). La Pensée Sauvage.
Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique [The analysis of teaching practices from the anthropological theory of the didactic]. Recherches en Didactique des Mathématiques, 19(2), 221–266. https://revue-rdm.com/1999/l-analyse-des-pratiques/
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 [The anthropological theory of didactic facts in the teaching of cultural and linguistic otherness: An outsider’s perspective]. In J. Aden (Ed.), Création identitaire et altérité en didactique des langues (pp. 17–38). Éditions Le Manuscrit.
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), 111-144. https://doi.org/10.2307/749646
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 math-ematics. In 2013 IEEE Frontiers in Education Conference (FIE) (pp. 1742–1744). IEEE. https://doi.org/10.1109/FIE.2013.6685135
Gelman, R., Cohen, M., & Hartnett, P. (1989). To know mathematics is to go beyond think-ing that “Fractions aren’t numbers”. In C. Maher, G. Goldin, & R. Davis (Eds.), Pro-ceedings of the Eleventh Annual Meeting of the North American Chapter of the Interna-tional Group for the Psychology of Mathematics Education (Vol. 2, pp. 29–67).
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 https://doi.org/10.1007/s10857-023-09577-4
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. https://doi.org/10.1007/s10763-013-9500-2
Kamble, S. K., & Tembe, B. L. (2013). The Effect of Use of Concept Maps on Problem Solv-ing Performance and Attitude in Mechanical Engineering Course. Procedia - Social and Behavioral Sciences, 83, 748–754. https://doi.org/10.1016/j.sbspro.2013.06.141
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. https://doi.org/10.1080/07377363.2014.872011
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. https://doi.org/10.1080/001318800363908
Kurniawan, F., Samsudin, A., Chandra, D. T., Sriwati, E., Zahran, M., Gani, A. W., Rama-dhan, B. P., Aminudin, A. H., & Ramadani, F. (2023). Assessing conceptual under-standing of high school students on transverse and stationary waves through Rasch analysis in Malang. Journal of Physics: Conference Series, 2596(1), 012060. https://doi.org/10.1088/1742-6596/2596/1/012060
Le, T. H. C., & Comiti, C. (2018). Thuyết nhân học trong Didactic Toán [The anthropologi-cal theory of didactics of mathematics]. Ho Chi Minh City University of Education Pub-lishing House.
Mansfield, H., & Happs, J. (1989). Using concept maps to explore students’ understanding in geometry. In G. Vergnaud, J. Rogalski, & M. Artique (Eds.), Proceedings of the 13th Annual Conference of the International Group for the Psychology of Mathematics Edu-cation (Vol. 2, pp. 250–257). PME.
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. https://doi.org/10.15804/tner.2019.55.1.05
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 Re-search, 89(6), 351–363. https://doi.org/10.1080/00220671.1996.9941339
Novak, J. D., & Cañas, A. J. (2009). The Development and Evolution of the Concept Map-ping Tool Leading to a New Model for Mathematics Education. In K. Afamasaga-Fuata’i (Ed.), Concept Mapping in Mathematics (pp. 3–16). Springer. https://doi.org/10.1007/978-0-387-89194-1_1
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. https://doi.org/10.2105/AJPH.2023.307449
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual under-standing and procedural skill in mathematics: An iterative process. Journal of Educa-tional Psychology, 93(2), 346–362. https://doi.org/10.1037//0022-0663.93.2.346
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson Education.
White, R. T., & Gunstone, R. (2014). Probing understanding. Routledge, Taylor & Francis Group.