Unitizing, a cognitive support for number sense, describes how students conceptualize quantities in terms of units. Given the importance of this skill, a formative assessment tool was developed for array multiplication problems, including arrays that model the distributive property found in typical classroom curricula. Video of 77 fourth grade…

The purpose of the study was to explore the cognitive profiles associated with inadequate responsiveness to fractions intervention on 3 fractions outcomes (calculations, ordering, and word problems). At the start of 3rd grade, 2 cohorts of students (N = 124) identified at the start of intervention as at-risk for mathematics difficulties were…

Constraint satisfaction problems are a powerful way to abstract and represent academic and real-world problems from both artificial intelligence and operations research. A constraint satisfaction problem is typically addressed by a sequential constraint solver running on a single processor. Rather than construct a new, parallel solver, this work…

The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational…

This research focused on performance indicators for elementary and middle school students. Performance indicators are factors that could hinder or enhance early childhood education. For instance, poverty affects a child's development and educational outcomes beginning in the formative years, both directly and indirectly through mediated,…

After multiple reviews of the literature, which documented that multiple cognitive processes may be involved in mathematics ability and disability, Geary (1993) proposed a model that included three subtypes of math disability: Semantic, Procedural, and Visuospatial. A review of the extant literature produced three studies that examined Geary's…

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given tau greater than 0, the free plate eigenvalues omega and eigenfunctions upsilon are determined by the equation Delta Delta upsilon - tau Delta upsilon = omega upsilon together with…

Students with specific learning disabilities (SLD) tend to have difficulty with reasoning and communication across many mathematical domains. The purpose of this study was, through open response questions, to examine the mathematics reasoning performance of 4 th grade students with SLD. Using the learner centered principles outlined by the…

Interest in students who exhibit characteristics with difficulties in learning can be traced as far back as 1800. In order to better understand the complexities and causes of learning disabilities, many researchers (Bannatyne, 1968, 1974; Rugal, 1974) have investigated ways to better identify learners who struggle with academics. A strong argument…