Skip Navigation
Funding Opportunities | Search Funded Research Grants and Contracts

IES Grant

Title: Cognitive Support for Learning Fractional Magnitudes
Center: NCER Year: 2016
Principal Investigator: Opfer, John Awardee: Ohio State University
Program: Cognition and Student Learning      [Program Details]
Award Period: 4 years (7/1/20166/30/2020) Award Amount: $1,399,542
Type: Exploration Award Number: R305A160295
Description:

Co-Principal Investigator: Clarissa Thompson (Kent State University)

Purpose: The purpose of this project is to explore the relationship between cognitive supports (i.e., supports to facilitate student thinking and reasoning) for mathematical comparisons and students' learning of fractional magnitudes, with a particular focus on students with low executive functioning (EF) skills. Understanding fractional magnitudes is a skill that is correlated with later math achievement as well as important real-world outcomes. Students with low EF skills are typically at high risk for poor math learning, and these students may benefit disproportionally from cognitive supports for mathematical comparisons.

Project Activities: The research team will conduct one study each year of the grant. The studies conducted in Years 1-3 will independently examine three cognitive supports for learning fractional magnitudes. The study conducted in Year 4 will examine whether a combination of cognitive supports can improve students' ability to learn fractional magnitudes. All four studies have a similar experimental design: random assignment to training condition, pretest/training/immediate posttest/delayed posttest, and testing of trained and untrained items.

Products: The products include preliminary evidence of potentially promising cognitive supports for improving students' learning of fractional magnitudes and peer reviewed publications.

Structured Abstract

Setting: This project will take place in participating elementary schools in urban and suburban areas of Ohio.

Sample: Each year, participants will include approximately 150 students from third through fifth grade, with an equal number from each grade.

Intervention: Due to the exploratory nature of this project, there is no intervention. The malleable factors studied are different cognitive supports for facilitating mathematical comparisons in the context of learning fractional magnitudes.

Research Design and Methods: The research team will conduct four studies that explore the relationship between cognitive supports for mathematical comparisons and students' learning of fractional magnitudes. The research team will conduct one study each year of the grant. The first three studies, to be conducted in Years 1-3, will independently examine three cognitive supports for learning fractional magnitudes: (1) progressive alignment (spatially aligning number-line problems that are coded with a superficial feature, such as color, to identify the magnitude of the fraction); (2) relational language (language that highlights part-to-whole relations); and (3) familiar analogical sources (e.g., providing students with a whole number line as an analogical source to aid in understanding of fractions). The fourth study, to be conducted in Year 4, will examine whether a combination of cognitive supports can improve students' ability to learn fractional magnitudes. In all studies, students will be randomly assigned to one of two conditions. Additionally, all studies take place across four sessions and have the same procedures. The research team will administer fractional magnitude pre-tests to students in the first session, training on fractional magnitudes in the second session, an immediate posttest occurring within one day of training in the third session, and a delayed posttest occurring one month after training in the fourth session. The type of training a student receives depends on the experimental condition to which he or she was assigned.

Control Condition: For all studies, the comparison group receives training on fractional magnitudes that does not include the cognitive support (or combination of supports) that is the focus of the study.

Key Measures: Researchers will assess participants' knowledge of fractional magnitudes using four tests: a fraction-to-position number-line task, a position-to-fraction number-line task, a fraction comparison task, and a fraction categorization task. The research team will also collect students' performance on the mathematics section of the Partnership for Assessment of Readiness for College and Careers (PARCC) assessment. They will assess students' EF skills using tasks from the National Institutes of Health Toolbox.

Data Analytic Strategy: The research team will use hierarchical linear modeling to examine differences in post-test scores and learning gains across experimental conditions and interactions among variables.

Publications

Book chapter

Opfer, J.E., Kim, D., and Qin, J. (in press). How Does the "Learning Gap" Open? A Cognitive Theory of Nation Effects On Mathematics Proficiency. Development of Mathematical Cognition: Language and Culture, Volume IV.

Schneider, M., Thompson, C. A., and Rittle-Johnson, B. (2017). Associations of Magnitude Comparison and Number Line Estimation With Mathematical Competence: A Comparative Review. In P. Lemaire (Ed.), Cognitive Development from a Strategy Perspective: A Festschrift for Robert S. Siegler.

Sidney, P. G., Thompson, C. A., and Opfer, J. E. (in press). Development of Fraction Understanding. Cambridge University Handbook on Cognition and Education..

Journal article, monograph, or newsletter

Kim, D. and Opfer, J.E. (2017). A Unified Framework for Bounded and Unbounded Numerical Estimation. Developmental Psychology, 53(6): 1088–1097.

Sidney, P. G., Thompson, C. A., Matthews, P. G., and Hubbard, E. M. (2017). From Continuous Magnitudes to Symbolic Numbers: The Centrality of Ratio. Brain and Behavioral Sciences, 40.


Back