Cognitive Profiles Associated With Responsiveness to Fraction Intervention

Abstract

This study examined differences in cognitive processing between 4th-grade students who respond adequately, as opposed to inadequately, to intervention on 3 fraction outcomes: number-line estimation, calculation, and word problems. Students were assessed on 7 cognitive processes and on the 3 fraction outcomes. Students were grouped as adequate or inadequate responders, using as the cut-point the control-group mean on pre-to-post improvement on the relevant measure. Between-group differences identified reasoning, concept formation, and listening comprehension related to all 3 fraction outcomes. On the number-line outcome, within-group profile analysis indicated that inadequate responders experienced low reasoning ability relative to their other forms of cognitive processing.

Constructing written arguments to develop fraction knowledge.

“…When examining outcomes using the mean scores at the student level, special education students made significant and meaningful gains and were able to generalize their understanding of fractions on the far learning measure ( g = 1.04) and to demonstrate a gain of 3 correct points on the fractions test compared to at-risk learners. The significant effect evidenced on the far learning measure indicated that when explicit SRSD instruction for argument writing is embedded simultaneously with learning complex mathematical concepts that are scaffolded using multiple representations, this approach to treatment benefits all students and is especially meaningful for students who may exhibit comorbidity with language and mathematics (Korhonen et al, 2012; Krowka & Fuchs, 2017). The significant gains in fraction knowledge for students with LD are also likely, in part, because these students required more time on the learning tasks.…”

“…Further investigations are needed for increasing students' mathematical understanding in which students are provided opportunities, individually and together with peers, to explain and elaborate on their ideas in writing, to recognize patterns and relationships among their ideas, and to make decisions about when to apply what they know to new problems. Even, so, current studies do not address whether explicit teaching of argumentative writing for fraction learning provides a useful approach for children with and at-risk for LD who often exhibit language delays, which exacerbate learning and understanding fractions (Geary, 2004;Korhonen, Linnanmäki, & Aunio, 2012;Krowka & Fuchs, 2017;Vukovic & Lesaux, 2013).…”

“…learning measure indicated that when explicit SRSD instruction for argument writing is embedded simultaneously with learning complex mathematical concepts that are scaffolded using multiple representations, this approach to treatment benefits all students and is especially meaningful for students who may exhibit comorbidity with language and mathematics (Korhonen et al, 2012;Krowka & Fuchs, 2017). The significant gains in fraction knowledge for students with LD are also likely, in part, because these students required more time on the learning tasks.…”

Supporting the Fraction Magnitude Understanding of Students With Significant Behavior Problems

“…An earlier study by Namkung and Fuchs (2016) found that whole number and fraction competence use the same cognitive resources, specifically attentive behavior, processing speed, and nonverbal reasoning. Understanding the underlying cognitive processes and executive functioning skills required to work with fractions is essential, as students with deficits in these areas have been found to be unresponsive to some fraction interventions (Krowka & Fuchs, 2017).…”

“…Understanding the underlying cognitive processes and executive functioning skills required to work with fractions is essential, as students with deficits in these areas have been found to be unresponsive to some fraction interventions (Krowka & Fuchs, 2017).…”