Chapter 3 Reflections

What are the key ideas presented in Chapter 3?

• The key ideas presented in Chapter 3 had to do with how math problems are approached.
• Children should not learn the term addition as "joining" or "putting together" because this will limit their understanding of the concept.
• In "story problems" children often focus on getting the answer in the way that the teacher wants; in context problems, students can see how math applies to the real world.
• Contextual problems and models are the two main tools that teachers use to help students understand addition and subtraction.
• Models can be used for problem solving, even when there is no context involved.
• Multiplication and division should be combined as soon as possible so students see how they are related.
• Solving problems should be a means to helping students learn.

How do these ideas inform your understanding of teaching numbers and operations?

I thought it was interesting that the one of the problems presented in the chapter sounded like addition but was solved through subtraction, and another problem that sounded like subtraction was solved through addition. Students that are taught concrete ideas of what addition and subtraction are may be limited in their ability to solve math problems in the future. Therefore, I have learned that children should not be told how to solve a math problem; instead, they should use methods that they can understand. If math problems are worked out using manipulatives and real life examples, students may find more purpose in mathematics. Students should be able to use the method they understand best when solving problems.

I have also learned that teaching numbers and operations should not be taught with the sole intention of finding the answer. Children should see that math is useful and applies to everyday situations. If students see how they can apply math to everyday life, they will likely be more interested in the subject.