|Title:||Arithmetic Practice that Promotes Conceptual Understanding and Computational Fluency|
|Principal Investigator:||McNeil, Nicole||Awardee:||University of Notre Dame|
|Program:||Cognition and Student Learning [Program Details]|
|Award Period:||4 years||Award Amount:||$761,425|
|Type:||Development and Innovation||Award Number:||R305B070297|
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.
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.
Related IES Projects: Improving Children's Understanding of Mathematical Equivalence (R305A110198)
Journal article, monograph, or newsletter
Brown, M.C., McNeil, N.M., and Glenberg, A.M. (2009). Using Concreteness in Education: Real Problems, Potential Solutions. Child Development Perspectives, 3(3): 160–164.
Knuth, E.J., Alibali, M.W., Hattikudur, S., McNeil, N.M., and Stephens, A.C. (2008). The Importance of Equal Sign Understanding in the Middle Grades. Mathematics Teaching in the Middle School, 13(9): 514–520.
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.
McNeil, N.M., and Uttal, D.H. (2009). Rethinking the use of Concrete Materials in Learning: Perspectives From Development and Education. Child Development Perspectives, 3(3): 137–139.
McNeil, N.M., Chesney, D.L., Matthews, P.G., Fyfe, E.R., Petersen, L.A., and Dunwiddie, A.E. (2012). It Pays to be Organized: Organizing Arithmetic Practice Around Equivalent Values Facilitates Understanding of Math Equivalence. Journal of Educational Psychology, 104(4): 1109–1121.
McNeil, N.M., Fuhs, M.W., Keultjes, M.C., and Gibson, M.H. (2011). Influences of Problem Format and SES on Preschoolers' Understanding of Approximate Addition. Cognitive Development, 26(1): 57–71.
McNeil, N.M., Fyfe, E.R., Petersen, L.A., Dunwiddie, A.E., and Brletic-Shipley, H. (2011). Benefits of Practicing 4 = 2 + 2: Nontraditional Problem Formats Facilitate Children's Understanding of Mathematical Equivalence. Child Development, 82(5): 1620–1633.
McNeil, N.M., Rittle-Johnson, B., Hattikudur, S., and Petersen, L.A. (2010). Continuity in Representation Between Children and Adults: Arithmetic Knowledge Hinders Undergraduates' Algebraic Problem Solving. Journal of Cognition and Development, 11(4): 437–457.
Keultjes, M.C., Gibson, M.H., and McNeil, N.M. (2009). Children's Understanding of Approximate Arithmetic Depends on Problem Format. In N.A. Taatgen and H. Van Rijn (Eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society (pp. 329–334). Austin, TX: Cognitive Science Society.
Petersen, L.A., Heil, J.K., McNeil, N.M., and Haeffel, G.J. (2010). Learning From Errors in Game-Based Versus Formal Mathematics Contexts. In S. Ohlsson and R. Catrambone (Eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society (pp. 2578–2582). Austin, TX: Cognitive Science Society.