Reflection Question: Week 4

What are the key ideas presented in chapter 3?

Chapter 3 presented a range of important ideas that contribute to developing meaning for operations and solving story problems. Meanings, interpretations, and relationships to the four operations of addition, subtraction, mulitiplication, and division are each presented throughout chapter 3 and connected to help children establish an understanding of how they can use such operations in real-world settings. One important concept presented is that both addition and subtraction are connected. Another key idea within chapter 3 is that both addition and subtraction involve an action. One is a joining action of putting together where as the other is a separting action or taking away. Subtraction is the operation that names a missing part and addition is the operation that names the whole in terms of the parts. Important ideas regarding multiplication that were presented throughout the chapter include: multiplication involves counting groups of like size and figuring out how many are in all or the process of mulitplicative thinking, multiplication and division are connected/related. Division names a missing factor. In addition, models can be used to solve problems for all operations. They are also used to help figure out the operation involved in a problem despite number size and can be used to help number sentences have meaning.


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

The key ideas presented throughout the chapter help to establish meaning and purpose behind how to teach numbers and operations effectively to students. It is very important that as a teacher, I look at more than just the answer a student gets but instead, look at the techniques the child used to solve the problem. I should show students how operations are connected and help students develop the strategies needed to work through a problem and give it meaning. I realize that it is important to pay attention to how a student works through a problem or the strategies used so that it will give me the information that I need to understand their number development and the strategies being used. I also realize from the ideas presented that it is essential to pay attention to how a child solves a problem or the methods being used. This will help me grasp and understand as to what numbers should be used in problems for the next day.

From the points established throughout the chapter, I have become more aware of the connection and meaning between specific operations. I have also learned that it is important to encourage the use of problem analysis and avoid the use of key words such as "altogether" and "fewer" whem dealing with adddition or subtraction. Being able to provide good explanations behind specific mathematical operations is essential in the learning process. Rather than simply looking at specific "key terms" used throughout a problem, it is important to actually break the problem down and figure it out mathematically. This will help the child become more aware of how he/she was able to solve the problem and help give meaning to how the answer was found.