As adults, I believe, we are more close minded about academic subjects such as math. We have an understanding of how to do specific types of math and it comes naturally to us. This causes the mistakes children make to sometimes seem odd to an adult or a teacher. Even though this is may be true, it is important to realize that these mistakes can be little lessons (Eggleton and Moldavan, 2001). These errors are typically logical and can be used as a way to explore mathematical concepts. For example, until reading DMI: Building a System of Tens I had never seen a child write 10095 for 195. To an adult this answer may seem completely wrong, but when thinking about it in a child’s point of view the answer begins to seem more logical. The child knows the number 100 and the number 95 and therefore puts the two numbers together to create 195. This answer tells a teacher a lot about the student. For example, this particular student does not have an understanding for place value.
From the case studies I have also noticed that sometimes it is hard to completely understand the logic behind a child’s thinking. Children may not be able to explain their understanding completely and therefore the teacher is also likely not to completely understand their thinking. I believe that children come up with their own insights into mathematical thinking through experience and exploration. It is therefore the teachers job to nourish this for all the students in his or her classroom.
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As I was reading your post I somewhat thought about our reading for Language Arts this week that discussed student responses. Although the article talked about students' answers to questions pertaining to literature, some of these ideas may carry over to math. Some students may solve a math problem and when you ask them to explain their reasoning, they may come across as fuzzy thinkers, politicians, and so on. I think it is important to create an environment in math where students are comfortable and confident in expressing their logic. This will be very helpful to both teacher's and students when addressing mistakes and learning from them.
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