The Importance of Using Contexts in Learning Mathematics

In recent years, many mathematicians argued whether mathematics teaching and learning should begin with contexts or not. In 2007 in California, some people claimed that a mathematical approach that focused on number sense using contexts will be a detrimental to children (Sowder, 2007). Some researchers also showed that abstract examples were more advantageous for students (Kaminski, Sloutsky & Heckler, 2008; Kaminski & Sloutsky, 2012). They stated that concrete instantiations prone to distract students’ concentration in doing transfer task. This lead teachers begin to doubt the importance of involving contexts in teaching learning activity. The role of contexts in the classroom is questioned. How important contexts are in learning mathematics, this paper will discuss this questions.

In the past, people tend to see students as an empty vessel and ready to be filled with knowledge. However, they come to classroom bringing a lot of daily experiences. On the other hand, mathematics is abstract and difficult for students to learn. To help them understand it, teachers use models to make it familiar or concrete. Familiar models for them are everyday-life experiences known as contexts (Gravemeijer, 2011). In realistic mathematics education, students construct mathematics by mathematizing these contexts through concrete examples. Contexts make mathematics become meaningful for them (Freudenthal, 2002). As a result, students will easily understand and build concepts of mathematics.

Concrete examples are also the source of concept construction and the zone of application (Leen Streefland, 1991). The source of concept construction means mathematical concepts are originally maintained on daily life problems and students learn it informally. If this source of concept are brought up in a classroom, children will understand it easily. A research by Carraher et al (1985) showed that those who have difficulties in doing computation at school are able to do it when buying or selling at the market. Contexts are not only helping children build their mathematics but also as the zone of application. The benefit is students will have many experiences of the application of mathematics in their daily life.

In some research, contexts successfully support students in understanding mathematics under right circumstances (Brown, McNeil & Glenberg, 2009). De Bock et al also provided evidences on his research that those who learn mathematics with concrete models did transfer task better than abstract learners (De bock, Deprez, Van Dooren, Roelens & Verschaffel, 2011). They conclude that students can reach a higher level of abstraction than those generic group. This proves that the use of contexts in mathematics classroom are crucial for students.

Reference

Sowder, Judith. (2007). What are the “Math Wars” in California All About? Reason and Perspective. Mathematically Sane.

Kaminski, J. A., Sloutski, V. M., & Heckler, A. F. (2008). The Advantage of Abstract Examples in Learning Math. Science.

Kaminski, J. A., & Sloutski, V. M. (2012). Children’s Acquisition of Fraction Knowledge from Concrete versus Generic Instantiations. Cognitive Science Society.

Gravemeijer, Koeno. (2011). How Concrete is Concrete?. IndoMS. J.M.E

Freudenthal, H. (2002). Revisiting Mathematics Education. Kluwer Academic Publishers.

Leen Streefland. (1991). Fractions in Realistic Mathematics Education: A paradigm of Developmental Research. Kluwer Academic Publishers.

Carraher, T., Carraher, D. & Schliemann, A. (1985). Mathematics in the streets and in schools. British Journal of Developmental psychology.

Brown, M. C., McNeil, N. M., & Glenberg, A. M. (2009). Using Concreteness in Education: Real Problems, Potential Solutions. Child Development Perspectives.

De Bock, D., Deprez, J., Van Dooren, W., Roelens, M., & Verschaffel, L. (2011). Abstract or Concrete Examples in Learning Mathematics? A Replication and Elaboration of Kaminski, Sloutsky, and Heckler’s Study. Journal for Research in Mathematics Education