Appendix A
A Case for Revisiting Primary Standards in 6 th and 7 th grade classrooms
"It is not enough to know how, we must know why". This quote from a Chinese teacher interviewed by Liping Ma in her book, Knowing and Teaching Mathematics, resonates with me and needs to be a mantra for both elementary and middle school teachers. We have taught a generation of students to calculate, solve and evaluate, but we have not taught them how to think about a problem. It is rare for children to ask themselves, "what makes sense?" This is a difficult skill to teach, but revisiting concepts thought to have been mastered, and having them explain, prove and justify their solutions will go a long way in this direction.
I see 5 th, 6 th and 7 th grade students revisiting addition, subtraction, multiplication and division. I am not advocating that we re-do the same calculation lessons, but instead, open up these concepts through Number Talks, work with number lines and a deeper analysis of place value. In the Great Ideas of Primary Mathematics Seminar I was enrolled in the summer of 2011, we spent quite a bit of time working on place value activities that were quite difficult. If we focus not just on the positional aspect of this concept, but on the powers of ten and expanded notation aspects, we will be deepening our children's content knowledge without re-teaching the same old dusty algorithms.
My unit proposes to teach decimal and fraction precision using the number line. I will take students through a series of lessons that asks them to see the number line not as a place holder for whatever digits they are working with, but as a tool for understanding value of a number through linear measurement. In other words, placing numbers on a line with the distance between them in mind. In writing this curriculum and then teaching it, I must recognize that I am not, by a long shot, the first of their teachers in the 7 school years prior to my class to use number lines for students education. As I teach 7th grade Pre Algebra, it is likely that students have been exposed to, asked to create, even been taught to use number lines as a part of understanding many different mathematical concepts. With this in mind I proposed a process of deconstruction in my prospectus. This seems a bandaid (although an important one) for a more systemic issue: Teachers need to be educated/ re-educated on the potentially powerful uses of the number line and the articulation of these uses across grade levels.
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