Rationale
I decided to use the number line to teach multiplication and division because there are four units on multiplication and division at my grade level (4 th grade). These units provide a framework for teaching the concepts of multiplication and division and later multi digit multiplication and long division. Currently I use an area model to introduce multiplication. The benefits of teaching two conceptual models of multiplication are 1) It lets kids know that there are more ways of thinking about multiplication, and 2) The number line model extends readily to fractions and signed numbers. Additionally, the number line applies to measurement of time and distance, and geometrical transformations. I will develop interpretations of addition and subtraction using the number line. In this unit, I plan to do that using primarily two digit numbers. I know my students will have prior knowledge about addition and subtraction with regrouping using two and three digit numbers, but I teach a unit specifically about that later in the year, so I can revisit this concept later on.
"I'm terrible at math." "I just don't have a math mind." "I wasn't taught how to do that." That is a familiar chorus many teachers would hear in their classroom on any given day. Now imagine a group of elementary school teachers singing this chorus. Guilty of this faulty thinking myself, I have perpetuated the notion that some people are just "born to do math" and some are not. It is time to let go of this kind of thinking! Most everyone is capable of learning how to think mathematically given the proper circumstances; that includes quality instruction from the earliest years. As Hung-Hsi Wu (2009) states so eloquently, "We want students to be exposed, as early as possible, to the idea that beyond the nuts and bolts of mathematics, there are unifying undercurrents that connect disparate pieces."
Research is beginning to show that one of the reasons for the discrepancy between Asian students and American student's performance in math is due to the lack of mathematical knowledge of teachers, particularly at the elementary school level. One discovery by researcher Liping Ma (1999) is that in China there is a much different approach to understanding mathematics and therefore, in the instruction of mathematics. Even though Chinese teachers are generally less formally educated than their teaching peers in the U.S., they demonstrate a much greater understanding of how math works and why. They also understand the content, the underlying concepts of math in a deep and substantive way.
I use some variations of the number line in my classroom, including line plots and likelihood lines, but after recognizing the importance of the number line in mathematical concepts, I wanted to take a concept I teach and make it better. Knowing that my students will be required to understand symmetry where mathematics is represented geometrically gives me substantial motivation for providing them with this conceptual understanding now. Most importantly, if I understand the "how and the why" of the concepts I teach, then my students will too.
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