Thinking in Patterns to Solve Multiplication, Division, and Fraction Problems in Second Grade

Abstract

Experts think in patterns and structures using the specific “language” of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve addition and subtraction, a pilot curriculum using an Asian model of base-10 counting was introduced in kindergarten and first grade. Children in the pilot program, like their Asian counterparts, did not appear to have any difficulty with the concept of place value. They also did not have significant difficulties with single- and double-digit addition and subtraction as is often the case with American students (Stokes, 2010, 2013, 2014a, 2014b). To continue the pattern-based process in second grade, a Multi-Operation Chart was designed to make the relationships between multiplication, division and fractions clear. Testing at the end of the school year showed that students not only met, but exceeded the Standards set by the Common Core standards for second grade. Medians and modes for correct single- and double-digit multiplication, single-digit division and fractions were 100%. Educational implications are offered and discussed.