Development of Mathematics Learning Model Concept-Based Understanding

Mohamad Rif’at, Sudiansyah Sudiansyah


This research is the development of a mathematical learning model based on conceptual understanding. The main research problem: How to develop students' current understanding which tends to turn from factual and procedural knowledge to conceptual knowledge? The purpose of the research is to build and develop the emergence of students' conceptual knowledge, as well as to identify and analyze the lecturer's conceptual knowledge. Data were collected through direct observation in the classroom while learning was taking place in the Mathematics Education Study Program. Observations in three different classes, namely Algebra Class, Calculus Class, and Geometry Class. The display and class discussion were recorded by the researcher, especially on some of the problems that arose. Then the researcher developed a discussion through conceptual questions, which aimed to build conceptual knowledge and simultaneously develop prior knowledge from educators and students. The data recording mechanism is from the classroom so that in the first stage, researchers get a class model in learning or teaching mathematics. From the initial model, the researcher and the class developed conceptual thinking of the problem or problem solving as a form of testing the validity of the model. Testing is carried out primarily to avoid factual and procedural knowledge. The results of this study are the identification of mathematical knowledge in learning and can be known how to work and the way the class thinks as a whole. Overall, an analysis of the concept-based learning model is generated.


factual knowledge; procedural knowledge; conceptual knowledge; mathematics learning; math learning model

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Anderson, et al. (2001). A Taxonomy for Learning, Teaching, and Assessing: A Revisiopn of Bloom’s Taxonomy of Educational Objectives. New York: David Mckay Company, Inc.

Ausubel, D.P. (1968). Educational psychology: A cognitive view. New York: Holt, Reinhart, and Winston.

Campbell, J.R., Voelkl, K.E., & Donahue, P.L. (2000). NAEP 1996 trends in academic progress (NCES 97–985r). Washington, DC: National Center for Education Statistics. Available: [July 10, 2001].

Davis, Leslie L. (1984). Clothing and Human Behavior. Research journal of Family & Consumer Sciences, 12 (3), 325-339

Donovan, M.S., Bransford, J.D., & Pellegrino, J.W. (Eds.). (1999). How people learn: Bridging research and practice. Washington, DC: National Academy Press. Available: [July 10, 2001].

Hiebert, J., & Carpenter, T.P. (1992). Learning and teaching with understanding. In D. A.Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York: Macmillan.

Maher, C.A., & Martino, A.M. (1996). The development of the idea of mathematical proof: A 5-year case study. Journal for Research in Mathematics Education, 27, 194–214.

Mayer, R.E., & Hegarty, M. (1996). The process of understanding mathematical problems. In R.J.Sternberg & T.Ben-Zee (Eds.), The nature of mathematical thinking (Studies in Mathematical Thinking and Learning Series, pp. 29–53). Mahwah, NJ: Erlbaum.

Mazur, E. (2012). A visit to Harvard and Exeter: problem solving done right. ~ thoughts on education by Grant Wiggins. Tersedia: [25 Mei 2017].

Meir Ben-Hur. (2006). Methematics Instruction: Building Strong Foundation for Reasoning and Problem Solving. Virginia: Association for Supervision and Curriculum Development.

Minsky, M. (1975). A Framework for Representing Knowledge. USA: Mc Graw Hill.

Nunes, T. (1992). Cognitive invariants and cultural variation in mathematical concepts. International Journal of Behavioral Development, 15, 433–453.

Rif’at, M. (2009). Pendidikan Matematika dari Perspektif Mengajar dan Belajar. Pontianak: Romeo Mitra Grafika.

Rittle-Johnson, B., & Alibali, M.W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91, 175– 189.

Schoenfeld, A.H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20, 338–355

Skemp, Richard R. (1971). The psychology of learning mathematics. Harmoodsworth: Penguin Books.

Skemp, Richard R. (1987). Intelligence, learning, and action. New York: Wiley.

Steele, C.M., & Aronson, J. (1995). Stereotype threat and the intellectual test performance of African-Americans. Journal of Personality and Social Psychology, 69, 797–811.

Tarigan, E. et al. (2020). Development of Students Work Sheet Based on Realistic Mathematic Approach with Ethnomatematic nuanced to Improve Critical Thinking of 4th Grade Students in Primary School (SD Negeri 091358 Haranggaol, Haranggaol Horisan Sub-District). Budapest International Research and Critics in Linguistics and Education (BirLE) Journal. P. 133-143.


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