Math Thinking Skills

It is obvious that a good majority of Indonesian science and math teachers are not used to and do not practice and develop math thinking skills. I roughly estimate about 75% of these teachers teach their students math and physics using formulaic approach, where math and physics problems are understood and solved using standard formulas given in classroom.

One can only blame Department of National Education (DepDikNas) for this bad teaching strategy. It does not produce tough students who have abiding interests in rigorous, consistent thinking. It only creates students who are lazy in thinking through problems; these students do not have disciplined, supple mind.

I am of the opinion that the mess Indonesia now experiences - corruption, bad infrastructure planning and network - is partially caused by state planners who are not rigorous and thorough in their planning deliberations.

It would be good if someone could share with me data that link bad infrastructure planning and execution with poor math teaching. The connection for me is obvious. These state planners are normally economists and engineers. They took math in high schools and universities, but they never learned it rigorously enough so that math thinking skills are never embedded in their thinking.

What are math thinking skills? They are learned when one solves math problems. Math problems are normally goal-oriented. To prove a theorem, or to show using algebraic manipulations a math formula. The way this goal-oriented problem is solved is, however, equally important.

Math thinking skills involve the following activities. One cannot use circular argument to get an answer. One must map the problem in terms of what variables he can manipulate and what the constraints are. One needs to know how to construct the answer based on previously available theorems and results. One must be diligent and careful to not make algebraic mistakes - mixing negative and positive signs, or forgetting a term in an equation, for example. One must be able to map a broad strategy to attack the problem; in fact, this broad strategy has to be available first before making a first step. A lot of thinking goes into getting this broad strategy. All these skills are practiced constantly when solving math problems.

When one spends enough time solving math problems, one develops an understanding of a standard for himself how a problem - any problem - is solved. One is not happy if a problem is not solved completely. One becomes an independent thinker since he applies his own thinking and standard.

A lot of Indonesians are not taking seriously what lacks in Indonesia's education system. At their own perils.