Abstract

This literature review focuses on two-digit subtraction with regrouping. Many students struggle with this concept and place value is a major stumbling block for students trying to master subtraction. This paper will also show that delaying the introduction to the traditional algorithm and allowing students to use their invented strategies as well as paying attention to the concrete-representational-abstract instructional sequence help students overcome the obstacles to learning subtraction computations. In addition, studies by Ma, Chick, Pham, and Baker show that teacher content knowledge also effects how students learn two-digit subtraction.

Subtraction with Regrouping

Introduction

Research shows that many students struggle with learning subtraction with regrouping. This difficulty typically arises because the students do not understand the concept of place value in addition to composing and decomposing numbers. This document examines the importance of place value understanding, the use of invented strategies and the utilization of concrete-representational-abstract (CRA) instructional sequence as well as the traditional subtraction strategy. This literature review also discusses how teacher content knowledge impacts student learning of subtraction with regrouping. The Importance of Place Value

Developing students’ place value understanding for whole numbers begins in Kindergarten and continues to build through second grade. In grade two, according to the 2006 Curriculum Focal Points, students develop an understanding of the base-ten numeration system and place value-concepts, in addition to developing fluency with efficient procedures for multi-digit addition and subtraction (p. 14). As a part of this place value development, students begin to work at composing and decomposing numbers in a wide variety of ways as they solve subtraction problems with two-digit numbers. Most textbooks for grades one to five separate chapters on place value from chapters on computational strategies. Van de Walle, Karp, and Bay-Williams (2010) report it is not necessary to complete the development of numeration concepts before exploring computations with two- and three-digit numbers. They suggest that, “When such problems arise in interesting contexts, students can often invent ways to solve them that incorporate and deepen their understanding of place value, especially when students have the opportunities to discuss and explain their invented strategies and approaches” (p. 82). Invented strategies are computational strategies that do not involve counting by ones or the use of manipulatives. Invented Strategies

Students pull on their understanding of number concepts and in particular place value when they are encourage to invent subtraction strategies that involve taking apart and combining numbers in a wide variety of ways. Written records should be encouraged as strategies develop and these records of thinking should be shared with other students. All the invented strategies should be explored and experimented with by others; however, students should not be permitted to use any strategy without having an understanding of the strategy. Invented strategies often become mental methods after ideas have been explored, used, and understood. Van de Walle et al (2010) give several positive benefits of allowing students to develop and use invented strategies: “1) Students make fewer errors. 2) Less re-teaching is required. 3) Students develop number sense. 4) Invented strategies are the basis for mental computations and estimation. 5) Flexible methods are often faster than the traditional algorithms. 6) Algorithm invention is itself a significantly important process of “doing mathematics” (p. 216). Evidence of the usefulness of using invented strategies can be seen in classrooms situations.

Whitenack, Knipping, Novinger, and Underwood (2001) illustrate Van de Walle et al...