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IES Grant

Title: Opening the Door to Algebra: Does Improving Facets of Fraction Knowledge Impact Algebra Learning?
Center: NCER Year: 2017
Principal Investigator: Booth, Julie Awardee: Temple University
Program: Cognition and Student Learning      [Program Details]
Award Period: 3 years (07/01/2017 – 06/30/2020) Award Amount: $1,301,369
Type: Exploration Award Number: R305A170226
Description:

Co-Principal Investigator: Kristie Newton

Purpose: The purpose of the proposed project is to develop a better understanding of whether, when, and how improving fraction knowledge yields improvements in algebra learning. Specifically, the research team will (1) explore the extent to which improving fraction knowledge improves algebra readiness and learning for middle school students and preservice teachers learning algebra and (2) examine the independent contributions of fraction magnitude and fraction computation knowledge for improving algebra performance.  This project will contribute significantly to the goal of helping all students achieve in algebra, which is considered to be a gatekeeper for success in all science, technology, engineering, and math (STEM) domains.

Project Activities: Two sets of studies will be conducted with middle school students and undergraduate students studying early childhood education. The first set of studies will take place in Year 1 to examine how fraction knowledge is related to improvements in various facets of algebra readiness and learning. In Years 2 and 3, the research team will conduct the second set of studies at each grade level to understand the independent contributions of fraction computation and fraction magnitude on algebra performance.

Products: Researchers will produce evidence of the relationship between fraction knowledge and algebra learning as well as peer-reviewed publications.

Structured Abstract

Setting: Participating middle schools are located in urban and suburban areas in Pennsylvania. Research will also take place in undergraduate early childhood education classrooms.

Sample: In Year 1, 315 sixth- through eighth-grade students (105 from each grade) and 105 undergraduate students studying early childhood education will participate. In Year 2, approximately 300 eight-grade students and 300 undergraduate students studying early childhood education will participate. In Year 3, approximately 300 sixth-grade students and 300 seventh-grade students will participate.

Intervention: Due to the exploratory nature of this project, there is no intervention. The malleable factor of interest is fraction knowledge, specifically fraction magnitude and fraction computation knowledge. Results from this project will have direct implications for what types of fraction interventions should be further developed, when fraction knowledge can be remediated, and how fraction content might be better incorporated into algebra courses.

Research Design and Methods: The research team will conduct two sets of studies with middle school students and undergraduate students studying early childhood education. The first set of studies will take place in Year 1. For these studies, the research team will assess participating students' fraction and algebra knowledge at the beginning and end of the term to examine how fraction knowledge is related to improvements in various facets of algebra readiness and performance. In Years 2 and 3, the research team will conduct the second set of studies at each grade level. Each study will use a quasi-experimental design with student-level random assignment to condition to understand the independent contributions of fraction computation and fraction magnitude on algebra readiness and performance. For these studies, first, all students will take fraction and algebra pretests. Next, they will receive business-as-usual instruction on fraction arithmetic and will be given practice worksheets (varying by condition) to complete. At the completion of the unit as well as at the end of the term, students will take fraction and algebra posttests.

Control Condition: The first set of studies does not have a control condition due to the nature of the design. For the second set of studies, students at each grade level will be randomly assigned to one of three worksheet conditions: practice with fraction computation examples, practice with fraction computation and fraction magnitude examples, or practice only. For the first two conditions, practice will include correct and incorrect examples intended to highlight particular types of fractions knowledge (fraction computation or both fraction magnitude and fraction computation respectively).  In the practice-only control condition, students will be given fraction problems to solve on their own.

Key Measures: Key measures include a researcher-developed assessment of fraction magnitudes, Comparing Fractions items from the 2010 Fraction Battery, a researcher-developed assessment of fraction arithmetic, researcher-developed assessments of algebra knowledge, and researcher-developed assessments of general mathematics competence (adapted for each grade level). Additionally practice worksheets used in the second set of studies will be coded for completion, correctness, and types of errors.

Data Analytic Strategy: For the first set of studies, the research team will analyze the data with a series of multiple regression analyses at each grade level. For the second set of studies, the research team will analyze the data using a series of repeated measures analyses of variance and multiple mediated regression models.


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