A Mixture Modeling Approach to Profile Individuals' Math Learning Ability

• In Event: 61.083 - Working Memory and Learning Disabilities

Abstract

Objective
This investigation examined the occurrence of discrete latent classes in the math problem-solving continuum. Identifying latent subpopulations will help in understanding obstacles faced by individuals underachieving in math. Constructs related to math problem solving were used to better understand subgroups—specifically with deficits—in math problem solving distribution.

Theoretical Framework
Academic performance has been traditionally conceptualized as a continuum. However, subgroups are used to describe students’ academic performance. Individuals with learning disabilities are at risk for deficits that inhibit typical academic performance (Swanson, & Beebe-Frankenberger, 2004). Research has revealed four subgroups on the continuum of math problem solving (Geary, 2013), representing high achievers, typical achievers, low achievers (LA), and those with math learning difficulties (MLD); an ideal conceptualization for statistical techniques that test for the existence of latent subgroups (Collins & Lanza, 2010).
Research has identified constructs related to math problem solving showing the existence of subgroups (Geary 2013). Individuals with MLD have deficits in general domains related to working memory. Specific domains such as speed, inhibition, understanding numeracy, fluid intelligence, reading, word problem solving, and math calculation, for instance, are constructs in which MLD groups underperform. LA students’ deficits are less severe, while typical and high achieving children have no deficit or excel. Improved understanding of cognitive constructs that are related to math problem solving processes will better inform our understanding of the subgroups profiles.

Method
Elementary school children from multiple ethnicities and ranging from 6-10 years (Mage =7.97, SDage =0.57) were the target sample from four public schools in a Southwest region of the United States (N=312). The constructs used were created using two or more measures. The following constructs were assessed: Reading, Math Calculation, Inhibition, Naming Speed, Visual Spatial Sketch (WM), Executive Function (WM), Phonological loop (WM), Problem Solving, Word Problem Solving, Comprehensive Math Ability Test, Numeracy, and Fluid Intelligence.

Results
The twelve latent variables were dichotomized at the 25th percentile cutoff (z-score of -.66) (Fletcher et al., 1989; Geary, 2013; Siegel & Ryan, 1989). A latent class analysis (LCA) tested six latent groups. The adjusted BIC indicated that five-latent classes were the ideal model. Class 5 (MLD—16%) had the most difficulties. Identified deficits were reading, math calculation, VSSP, phonological loop, problem solving, word problem solving, numeracy, and fluid intelligence (range 0.99-0.00). Class 4 (low numeracy—26%) had the least number of deficits (range 0.03-0.40). Class 3 (42%) was a typical achieving group that is at risk for deficit with estimation (range 0.00 – 0.53). Class 2 (9%) was a low achieving group with deficits in verbal and visual areas. Finally, the LA group (class 1—9%) had deficits in naming speed (range 0.00 – 0.92).

Implications
Findings identified five subclasses of profiles on cognitive measures of math performance. Latent classes on math ability emerged corroborating the notion that subgroups exist within math ability continuum. Findings argue for the current classification model of math difficulties suggesting that subgroups of individuals should be used to highlight the challenges that low performing students may have in math problem solving.

Authors

• Andres Olide, University of California - Riverside

• H. Lee Swanson, University of California - Riverside