Exploring what it means to know and do Mathematics

Chapter 2

What does it mean to learn mathematics? The answer lies in learning theory and research on how people learn. The two most commonly used theories by researchers in mathematics education are:

• Constructivism theory - rooted in Jean Piaget's work, which was developed in the 1930s.
• Sociocultural theory - the work of Lev Vygotsky, emerged in the 1920s and 1930s.

It is explained that making connections between mathematics concepts are connecting blue dots (ideas we already have) to red dot (emerging idea). Whatever existing ideas (blue dots) are used in the construction will be connected to the new idea (red dot) because those were the ideas that gave meaning to it.

Multiplying, dividing, adding, subtracting, fractions, decimals, ratio, algebra are some troublesome equations to solve without calculator. To solve those equations, I was taught to use either workings or diagrams/models. To solve multiplication and division, I had to memorise the times-table. To solve algebra equations, I was taught to memorise formula. I was taught specifically on how to solve problems; neither promoting thinking nor engaging in productive struggle. Strangely, I understood those concepts, and surprisingly, I did rather well. Its just that exploring problems and understanding mathematical ideas wasn't the way I was taught to do mathematics.

Reading this chapter was interesting as it was a total contrast of how mathematics was taught to me. It mentioned about providing opportunities to talk about Mathematics, providing opportunities for reflective thought, encourage multiple approaches, consider solutions of others, scaffolding new content, engaging students in productive struggle and treat errors as opportunities for learning. This chapter is a whole new learning point of teaching and understanding mathematics concepts. "This shift in practice, away from the teacher telling one way to do the problem, establishes a classroom culture where ideas are valued. This approach values the uniqueness of each individual." (Van de Walle, J.)

Van de Walle, J. Elementary and middle school mathematics: Teaching developmentally (8th Edition). New York: Longman. ISBN: 9780132879040