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IES Grant

Title: Integrating Conceptual Foundations in Mathematics through the Application of Principles of Perceptual Learning
Center: NCER Year: 2006
Principal Investigator: Kellman, Philip Awardee: University of California, Los Angeles
Program: Cognition and Student Learning      [Program Details]
Award Period: 3 years Award Amount: $1,500,000
Type: Development and Innovation Award Number: R305H060070

Purpose: The objective of this project is to help students in Grades 3–8 develop an integrated mathematical knowledge base in which the domains of measurement and fractions are meaningfully connected to each other and to core concepts of multiplication, division, ratio, and proportion. This interrelated set of mathematical concepts has been selected because it is central to the mathematical standards identified for these grades (NCTM, 2000); it provides essential foundations for higher math learning; expert understanding is characterized by dense connections across these topics; and there is convincing evidence that too few children in U.S. schools are reliably achieving this integrated knowledge base.

Project Activities: The researchers will develop a series of interventions that introduce an instructional innovation in mathematics teaching based on cognitive research: namely, perceptual learning, defined as "changes in the pick-up of information as a result of experience or practice." Recent research supports the claim that perceptual learning is especially effective in leading students to extract structural invariance across contextual variation, and to improve fluency, thus accelerating the development of expertise. The researchers will apply well-established principles of perceptual learning and recent research on perceptual learning in mathematics to improve students' math learning via computer-based learning modules coordinated with other modes of instruction.

Products: The products from this study include a series of mathematics curriculum units consisting of a set of interactive classroom lessons with accompanying computer-based Perceptual Learning Modules for supplementary use in Grades 3–8; and published reports.

Setting: The schools are located in California and in Pennsylvania.

Population: The schools include culturally diverse student bodies with substantial numbers of children from low and moderate income families. The intervention will focus on students in Grades 3–8.

Intervention: The researchers will develop a series of interventions that introduce an instructional innovation in mathematics teaching based on cognitive research: namely, perceptual learning, defined as "changes in the pick-up of information as a result of experience or practice." The researchers will develop and evaluate approximately six units of instructional materials that combine computer-based Perceptual Learning Modules, diagnostic assessments, benchmark lessons and investigations, and resources for teachers. The units are designed as supplemental materials to the classroom curriculum across several grade levels, and could be used flexibly in various combinations. Each unit includes a set of classroom lessons that introduces essential ideas (with teaching resources such as overhead transparencies and student pages included). These lessons connect to carefully targeted hands-on investigations in which students work in small groups engaging in quantitative reasoning to solve problems in measurement and fractions. Students also work individually on the corresponding computer-based Perceptual Learning Modules, which are aimed at achieving fluency in recognizing and discriminating key structures and relationships.

Research Design and Methods: Experimental studies will be conducted. Following pretest assessments, students will be assigned randomly to treatment and control conditions. Students assigned to perceptual learning treatment conditions will typically participate in two to six sessions working with a given Perceptual Learning Module. Following the instructional phase, immediate and delayed posttests are administered.

Control Condition: Students in the control condition will receive the existing mathematics curriculum in the school.

Key Measures: The researchers will rely primarily on three kinds of data to evaluate learning: (1) accuracy and speed (reaction time) data collected via the Perceptual Learning Modules, (2) diagnostic items derived from the research literature; and (3) items derived from standardized tests, such as NAEP items.

Data Analytic Strategy: The Perceptual Learning Modules software will allow individual learning profiles to be examined in detail (e.g., analyzing the shape of the learning curves for plateaus, inflection points, steady progress, and so forth). The researchers will also be able to compare characteristics of students who show strong, moderate, or weak learning gains. Within-subject analyses will allow them to systematically compare performance on different subtypes of items. Standard multivariate statistical methods (such as ANOVA) will allow them to look for main effects as well as interactions among factors, for both between-subject and within-subject variables.

Related IES Projects: Perceptual Learning Technology in Mathematics Education: Efficacy and Replication (R305A120288) and Perceptual and Adaptive Learning Technologies: Developing Products to Improve Algebra Learning



Kellman, P.J., and Massey, C.M. (2013). Perceptual Learning, Cognition, and Expertise. (1st ed.). San Diego: Elsevier Academic Press.

Book chapter

Massey, C.M., Kellman, P.J., Roth, Z., and Burke, T. (2011). Perceptual Learning and Adaptive Learning Technology: Developing New Approaches to Mathematics Learning in the Classroom. In N.L. Stein, and S. Raudenbush (Eds.), Developmental and Learning Sciences go to School: Implications for Education (pp. 235–250). New York: Taylor and Francis.

Journal article, monograph, or newsletter

Kellman, P.J., and Garrigan, P.B. (2009). Perceptual Learning and Human Expertise. Physics of Life Reviews, 6(2): 53–84.

Kellman, P.J., Massey, C.M., and Son, J. (2010). Perceptual Learning Modules in Mathematics: Enhancing Students' Pattern Recognition, Structure Extraction, and Fluency. Topics in Cognitive Science, Special Issue on Perceptual Learning, 2(2): 285–305.

Kellman, P.J., Massey, C.M., Roth, Z., Burke, T., Zucker, J., Saw, A., Aguero, K.E., and Wise, J.A. (2008). Perceptual Learning and the Technology of Expertise: Studies in Fraction Learning and Algebra. Learning Technologies and Cognition: Special Issue of Pragmatics and Cognition, 16(2): 356–405.


Mettler, E., and Kellman, P.J. (2009). Unconscious and Abstract Perceptual Learning of Hidden Patterns. In Proceedings of the 2009 Meeting of the Vision Sciences Society.

Son, J., Massey, C., Roth, Z., Longmire, W., Burke, T., Zucker, J., and Kellman, P. (2008). Perceptual Learning in Mathematics Education-Abstract. In B.C. Love, K. McRae, and V.M. Sloutsky (Eds.), Proceedings of the 30th Annual Conference of the Cognitive Science Society (pp. 2366). Austin, TX: Cognitive Science Society.