Great Ideas of Primary Mathematics

Introduction

I have only one short hour a day for math instruction and at third and fourth grade much of the time is used to teach algorithms and solving problems. Admittedly, I often prioritize teaching algorithms and steps so that children have the necessary skills to solve problems so that we can move forward onto new material. Teaching problem solving methods is satisfying. For example, when dealing with subtraction problems, training students to perform the standard right to left algorithm which involves (often blindly) crossing through a place value, reducing values by one, adding dashes to make values ten more and finally arriving at the correct answer feels like success! The success, however, is often disappointing when I ask a student to explain what he or she just did and explain why, he or she has only a shoulder shrug to offer, or a "that's just what you do to get it right" type of reply. The inclusion of place value concepts in the teaching of operations in elementary mathematics education may help students obtain not only a right answer, but also a reason for why the answer is correct. The intent of this unit is to tie the concepts of place value to operational algorithms in order to provide students with a conceptual understanding of addition, subtraction, and multiplication, and not just a procedure.

I teach in a third and fourth grade classroom at Westcott Elementary in Chicago, IL. The students are in my classroom for both third and fourth grade. Westcott consists of ninety-nine percent African-American students. Additionally, one hundred percent are classified as low-income families and qualify for free lunch. The school's population is transient due to housing and income based issues. These two factors also affect attendance and student performance. My students have a fragile concept about the composition of multidigit numbers, and place value concepts in relation to operations. Karen Fuson states, "The evidence indicates that U.S. children do not learn place-value concepts or multi-digit addition and subtraction adequately and even many children who calculate correctly show little understanding of the procedures they are using (1990)." ¹ Fuson's research confirms my students' lack of understanding, but the issue is more widespread than just my classroom.