This is the question that I proposed to my teacher in one of my course. In the discussion, we discussed about the percentage and its relationship with decimal, fractions, ratio and proportion. I argue that we have all been taught about percents and other topics of mathematics in the traditional way, with an emphasis on learning the correct calculation procedures, and very little or not on understanding. Still we all understand what percentages, fractions and decimals are and how they are related. So why should we change the way these topics are taught? Or in any case, why should we not teach the calculation procedures first and let understanding develop later? These questions are the paraphrased ones done by my teacher.
It is an issue that we should discuss, because we hear this argument quite often. Then, my teacher proposed his own question relating to my own question: what arguments do we have for wanting to change the way mathematics is taught traditionally? What data could be used to argue against teaching the procedures, in stead of teaching for understanding?
Mathematics as a human activity
I try to give an answer to my own question, why should we change the way these topics are taught? In my perspectives, I think we have to change the way mathematics has been taught because when we teach students in the traditional way of teaching, I can be really sure that they will not make sense of what they have been learned. Moreover, as Freudenthal said in his wonderful book, Revisiting Mathematics Education, mathematics is a human activity and therefore it must be connected to reality, stay close to children and be relevant to society in order to be of human value. So, in this sense, the focal point is not mathematics as a ready-made subject full of procedures, formulas or whatsoever. Instead, the focal point is on the activity. Education should gives students a guided opportunity to reinvent the mathematics.
why should we not teach the calculation procedures first and let understanding develop later?
I think, if we do it in this way, students will not develop their understanding of mathematics. Instead, what they get from this way of teaching is that they know the procedures and formulas but they do not know how to use it in their life. It can be seen from the test such as PISA or TIMSS, that many Indonesian students fail to answer questions that dealing with complex situations and asking for advance mathematical thinking and reasoning. Even, I argue that students will not develop their understanding after they know the procedures and formulas. It is because, they will always looking for the formulas and procedures when they want to solve the problems.
what arguments do we have for wanting to change the way mathematics is taught traditionally? What data could be used to argue against teaching the procedures, in stead of teaching for understanding?
As Freudenthal said that learning processes, or at least part of them, can be more essential than their products (Cited from Revisiting Mathematics Education book). The focus of the teaching of mathematics is the process of learning it, not the product. In RME, the use of context is very important. In contrast with the traditional way of teaching, RME use the context problem both as a source of learning and to apply mathematical concepts. The students, in RME class, can develop mathematical tools and understanding while working on context problems. In the first time, they develop strategies or models that are closely related to the context. Later on, certain aspects of the context situation can become more general which means that the context can get more or less the character of a model and as such can give support for solving other but related problems (http://www.fisme.science.uu.nl/en/rme/