Proposition Debate

Write a short essay (no more than two pages) taking either the "pro" or "con" position on the following proposition:

Proposition: Problem solving can not be a central part of the mathematics curriculum in the secondary school because it takes too much time. There is too much other material in the curriculum that must be covered.

Note: Neither "pro" nor "con" is assumed to be "correct." I will "grade" this on the strength of the argument you make, which ever direction you take.

Problem solving is a very enriching method of learning mathematics. It allows students to investigate what is going on in a problem and gives them the opportunity figure out why this is happening and to predict future outcomes. Some students may excel at learning mathematics through problem solving, but many will struggle because they cannot see what is actually happening.

In response to the proposition stated above, I would have to disagree. If the students have enough background knowledge on a subject, letting them do problem solving can be very beneficial for them. They will get to explore things that they would not normally be able to explore with regular classroom teaching. Problem solving also makes them think about what they are doing instead of just matching the problem with a formula they memorized. Through problem solving, students discover new things on their own. This is very important because they feel that they have accomplished something. When one accomplishes things by oneself, it makes one feel good.

Problem solving as the only means of learning mathematics I do not feel is a very good idea. I feel this way because without knowing some of the background mathematics beforehand one will more-or-less have to derive it all themselves. This leads to students getting stuck on figuring out where to go next with the problem. Not being able to figure out where to go next then leads to students feeling like they cannot do the mathematics involved.

Problem solving has its place in the mathematics classroom, but the students need enough background information beforehand so that they can have a chance at solving the problem.

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