Purpose: Algebra is widely regarded as a "gatekeeper" to future educational and employment opportunities. Unfortunately, there are growing concerns about children's poor performance and inadequate understandings of fundamental concepts in algebra, such as mathematical equivalence. In response to these concerns, many mathematics educators have called for algebra to be treated as a K-12 strand. They argue that teachers should focus on fundamental algebraic concepts, even at the elementary school level. However, some educators worry that such an emphasis on concepts forces teachers and students to neglect repeated practice with "basic" skills and computations. The purpose of this project is to develop and evaluate an approach to arithmetic practice that promotes computational fluency and conceptual understanding.

Project Activities: Approximately 480 second-grade children will participate in this study. In Studies 1-3, traditional arithmetic practice problems will be modified to promote understanding of math equivalence while improving computational fluency. The successful modifications will be incorporated into arithmetic practice workbooks. In Study 4, the researchers will conduct an initial evaluation in second grade classrooms to compare the effect of using the experimental workbooks to an existing arithmetic practice workbook. The end product should be an effective, affordable intervention that is easy to administer in schools, after-school programs, and homes.

Products: Products from this study include arithmetic practice workbooks for primary grade students that can be used in classrooms and at home. Published reports on the development and evaluation of this arithmetic intervention will also be prepared.

Structured Abstract

Purpose: The purpose of this project is to develop and evaluate an approach to arithmetic practice for primary grade students that promotes computational fluency and conceptual understanding.

Setting: Studies 1-3 will take place with second-grade students in Indiana. Study 4 will take place in public and private schools in North Carolina, Indiana, and Illinois.

Population: Approximately 480 second-grade children will participate in this study. Approximately 50 percent will be from families with low SES. Several of the participating schools serve poor urban communities.

Intervention: In Studies 1-3, traditional arithmetic practice problems will be modified to promote understanding of math equivalence while improving computational fluency. Modifications that are found to improve student learning will be incorporated into arithmetic practice workbooks. These experimental workbooks will be used in classrooms and compared to an existing arithmetic practice workbook (control) in Study 4. The end product should be an effective, affordable intervention that is easy to administer in schools, after-school programs, and homes.

Research Design and Methods: Four experimental studies (three lab-based, one classroom-based) will be conducted to develop a form of arithmetic practice that is more effective than traditional practice in promoting understanding of math equivalence while improving computational fluency. In both laboratory and classroom-based experiments, children will be randomly assigned to conditions. In the classroom-based experiment, children will be assessed immediately following the intervention, as well as at a one-year follow-up.

Control Condition: Children in the control condition will receive traditional arithmetic practice. They will receive the same amount of practice as students in the experimental conditions.

Key Measures: Children will complete both standardized and experimenter-developed measures of understanding of math equivalence and computational fluency. The standardized measure of arithmetic computation to be used is the Math Computation section of Level 8 of the Iowa Test of Basic Skills (ITBS). In addition, students will complete a paper-and-pencil assessment of arithmetic skill. Experimenter developed measures are being used to determine students' understanding of math equivalence, and include measures of equation-solving performance, equation encoding, and equal sign understanding.

Data Analytic Strategy: Analysis of variance techniques will be used for continuous outcomes to evaluate the performance of children who receive the experimental and control interventions. Logistic regression will be used for categorical outcomes.

Publications from ths Project:

McNeil, N.M. (2008). Limitations to Teaching Children 2 + 2 = 4: Typical Arithmetic Problems Can Hinder Learning of Mathematical Equivalence. Child Development, 79 (5): 1524–1537.