Challenge 5: Role of Mathematical Tools

I have always been a supporter of the use of manipulatives and other concrete tools in mathematics education. However, I realize now that these tools are often overused and misused in the classroom. Students should not be force to use tools or be told to use them in a certain way. Students should be allowed to use these tools in a way that make sense to them. This will promote better problem solving and more creative thinking among our students. Concrete tools are often used to teach students how to do something rather than help them understand concepts. These concepts are the most integral part of math. Students need to be given the chance to figure out what each concrete representation means and stands for in their own way.

Symbols are "tools" in math that communicate ideas. I have learned that there are often misconceptions about the symbols in math. Most often, students learn a definition for each symbol.. This limits what a symbol can communicate. A definition is not the same as learning what concept the symbol stands for. The example of the equal sign in the article is very illuminating. If a student learns that the equal sign means the answer, they will not understand that it has more to do with a relationship between different ideas. Students will become more "symbol literate" if they see the symbols actually used in different ways rather than learning a definition for each symbol.