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# Treating Children as Mathematicians (page 4)

By Pearson Allyn Bacon Prentice Hall
Updated on Jul 20, 2010

### Mathematicians get satisfaction from the problem-solving process and take pride in their solutions.

Children will understand mathematical concepts and procedures more thoroughly if they are allowed to use their own thinking processes to explore mathematics (Kamii, Lewis, & Jones, 1993). It allows them to make connections to prior knowledge and real life experiences. In the process of discussing and comparing the different methods they use to reach solutions, children strengthen their understanding of both concepts and procedures.

At the end of the lesson in the Japanese classroom the students discussed the days’ problem with the teacher. They asked if the procedures they learned could be applied to other similar situations. The teacher replied by asking them to think about it and try some alternatives at home that evening, and they would discuss them in class the next day. In essence, the students developed their own homework and were excited by both the process and the content of the days’ work. They demonstrated a sense of great accomplishment.

Children can get very excited about a mathematics problem and take pleasure in the process of problem solving. If children are allowed to think for themselves and discuss and defend their ideas, mathematics becomes just as fun as trying to solve a video game or diligently working to put a puzzle together.

### Mathematicians use unsuccessful attempts as stepping-stones to solutions.

If we really want children to be treated as mathematicians, we need to encourage them to realize that they may have to try many different approaches, some unsuccessfully, before they reach a solution. We need to place an emphasis on the valuable mathematical thinking going on in the child’s mind rather than on the production of a correct answer. It should be emphasized and modeled to children that unsuccessful attempts and errors can be stepping-stones to solutions.

In the U.S. classroom, students did not have time to go through this process. They were given one chance to get the solution right and the thinking behind incorrect solutions was never discussed or examined. Incorrect attempts at providing an answer would often silence a student’s participation in the lesson. The Japanese lesson, by contrast, was designed in such a way that students could experiment with different solutions and then discuss them with other students or with their teacher. They were given time to use different methods and prove their answers to themselves and others.

Negative responses to answers can have disastrous consequences for the way children interact with mathematics. Math anxiety can develop if failure leads to shame or if students perceive too high a risk factor (Burns, 1998; Kitchens, 1995; Stuart, 2000). Math should be presented as a process where wrong answers are a natural and recurring element, not an end point. Instead of getting a problem “wrong,” children should understand progress is being made towards a correct solution, and they should be encouraged to continue working (Verzosa, 2001; Third International Mathematics and Science Study, 1997).