|Exploring Cognitive and Foundational Processes Underlying Pre-Algebra Among Students With and Without Mathematics Learning Difficulties
|University of Delaware
|Cognition and Student Learning in Special Education [Program Details]
|4 years (07/01/2020 – 06/30/2024)
Previous Award Number: R324A200165
Co-Principal Investigator: Peng, Peng; Smith, Wendy
Purpose: The purpose of this project is to explore the domain-general cognitive and domain-specific foundational processes that underlie pre-algebra. Specifically, the project will (a) identify explicit links among cognitive and foundational processes, and pre-algebra competence among seventh graders with mathematics learning difficulties (MD) versus typically developing students (TYP), (b) explore whether cognitive processes indirectly contribute to pre-algebra competence through foundational mathematics processes for students with MD vs. TYP, and (c) explore factors (i.e., MD severity and comorbidity with reading difficulties) that moderate the relation between the cognitive processes and language, and pre-algebra. The findings of the proposed study will build theoretical foundations for understanding the differentiated role of cognitive and foundational processes that underlie pre-algebra competence. This will advance assessment and instructional practices that account for the weaknesses in those processes for students with MD.
Project Activities: The proposed study takes place over a four-year period, and data will be collected with the first-, second-, and third-year cohorts of seventh graders in years one through three in Nebraska and Texas. In each year of Years 1–3, 82 seventh graders with MD and 82 with TYP will be recruited across the NE and TX sites, yielding a total of 164 students yearly and a total sample size of 492 over three years. Students will be classified as either MD (below the 25th percentile) or TYP (between the 35th and 65th percentile) based on their scores on a universal screener and confirmed by their performance on the previous year's high-stakes, participation in the school's MTSS program, or teacher corroboration. No students will be recruited in Year 4, in which final data cleaning, aggregation, analyses, and dissemination will occur.
Products: The products include an improved theoretical model of the malleable factors that influence pre-algebra competence. The project will also result in peer-reviewed publications and presentations as well as additional dissemination products that reach education stakeholders, such as practitioners and policymakers.
Setting: The research will take place in middle schools in Nebraska and Texas.
Sample: The participants will include 492 seventh grade students, which includes 246 students with MD (performing below the 25th percentile) and 246 TYP students (performing between the 35th and 65th percentile).
Malleable Factors: The study focuses on executive functions (working memory, inhibition, and cognitive flexibility) as malleable cognitive processes, language, and magnitude understanding and arithmetic competence as malleable foundational processes associated with pre-algebra competence.
Research Design and Methods: Researchers will conduct a multi-stage (sites, schools, classrooms, and students) stratified (MD versus TYP) correlational design study where primary data is collected for each cohort of seventh graders with MD or TYP at two time points (fall and spring) in Years 1–3.
Control Condition: There is no control group since an experimental design is not used.
Key Measures: Researchers will use easyCBM Mathematics as a screening measure. Students' cognitive and foundational processes, and pre-algebra competence will be assessed. Cognitive processes will be assessed via working memory (NIH Toolbox- List Sorting Task), cognitive flexibility (NIH Toolbox- Dimensional Change Card Sort Test), and inhibition measures (NIH Toolbox- Flanker) in addition to teachers' behavioral ratings (Behavior Rating Inventory of Executive Function 2). Foundational processes will be assessed via language (Picture Vocabulary subtest of the Woodcock-Munoz Language Survey-III), whole-number and fraction magnitude understanding (Whole-number Lines Estimate and Fraction Number Line), and arithmetic competence (Woodcock Johnson IV Tests of Achievement – Calculation Fluency and AIMSweb: Mathematics Computation) measures. Pre-algebra competence will be assessed using the Iowa Algebra Aptitude Test and the Algebra Foundations measure. In addition, a measure of decoding and comprehension will be used as a moderator (Test of Silent Reading Efficiency and Comprehension).
Data Analytic Strategy: Data will be analyzed using multilevel structural equation modeling. The unique effects of each cognitive and foundational process on students' prealgebra competence will be examined for each subgroup (MD vs. TYP). Spring measures of foundational mathematics processes will serve as mediators of the relation between the cognitive processes and pre-algebra competence for each subgroup (MD vs. TYP). Finally, researchers will use the same multilevel structural equation modeling to conduct moderation analyses limited to students with MD with the moderators (i.e., MD severity and comorbid reading difficulties) as continuous moderating variables.