Chapter 3 Reflection

What are the key ideas presented in chapter 3?

• connecting meanings and relationships to addition, subtraction, multiplication, and division
• addition and subtraction are connected
• subtraction names a missing part
• addition names the whole in parts
• multiplication takes counting in groups, multiplication is repeated addition
• multiplication and division are connected
• division names a missing factor
• models can be used to solve any mathematical problem
• models can be used with any problem or any number size
• you can use models to make number sentences make sense

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

The ideas set a foundation and give a deeper meaning and understanding to teaching numbers and operations. The chapter also metioned that addition is not "put together" and subtraction is not "take away". As a teacher I must remember that children should not have limited definitions or understandings for addition and subtraction because later they will have trouble understanding that addition and subtraction can be used in different forms. Connecting problems to children's lives and keeping the problems in context is very important. The ideas presented in chapter 3 helped open my eyes to new and different ways to solve math problems other than the traditional ways I learned. I must keep in mind that the children do not have the mathematical skills that I have developed, and solving problems in different ways and thinking about different ways to solve problems can help me facilitate students more efficiently. I liked how the text highlighted avoiding key words. When I was in elementary school, I was always taught to look for key words. After reading the explanations as to why key words should be avoided, I now understand why I should not stress using key words. Problem analysis and explanations are very important in mathematical processes. Explanations can be particularly helpful in understanding why a student solved a problem a certain way or how he or she got an answer to a problem.