Chapter 3: Developing Meaning for the Operations and solving Story Problems

Chapter 3 focuses on the four operations-addition, subtraction, multiplication, and division. The main idea of this chapter is that the four operations are very connected and should not be taught as separate ideas.

This chapter talks about the traditional definitions of the operations. It stresses that teachers should not teach that the operations have these definitions because they are too strict and limited. Instead, addition and subtraction problems should be taught according to the four structures. The four structures are join, separate, part-part-whole and compare. If these structures are used over the traditional "put together" or "take away" methods, the children will have more fluency within their mathematical reasoning. This is important to remember when introducing the symbols to children as well. Children should know that the equal sign is not just a symbol for the answer. The should realize that it means that the things on each side are the same. The minus sign should be seen as minus or subtract and not as take away. The children should learn the cumulative property and the zero property with addition. The cumulative property can be taught by pairing problems with the same addends in different orders.

The same concepts hold true for multiplication and division. There are structures for these problems. Two of these structures are equal groups and multiplicative comparison. The multiplication and division properties can be very helpful for students. Again, the name of the property is not as important as the concepts themselves.

In teaching mathematics, Model based problems are good for teaching the four operations. I will use model-based problems in my classroom. I will also use story problems that are meaningful for the children. For example, I will use the students names and experiences that they can relate to. I could use their recent field trip to find the mice on main in a story problem to help the children anchor their learning to a meaningful experience. Also, as the text stresses, I will stay away from the key word methods. These can be confusing and lead a student to use the wrong operations. The students should have to explain how they solved problems and got their answers. This will make their learning more meaningful.