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Article Excerpt
Abstract. Difficulties with college algebra can be the gatekeeper for earning a degree. Students struggle with algebra for many reasons. The focus of study was to examine students struggling with entry-level algebra courses and differentiate between those who were identified as having a mathematics disability and those who were not. Variables related to working memory, math fluency, nonverbal/visual reasoning, attention, and reading were analyzed using a MANOVA and separate ANOVAs. Significant differences were found on all but attention, supporting the findings of research on students in elementary and secondary education. Implications include a focus on techniques that help to remediate these specific deficits.
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By understanding students struggling with mathematics at the postsecondary level, professionals can offer better assistance both during and before college and can help identify appropriate remediation techniques. Approximately 5-6% of students have significant difficulty in mathematics (Fleischner & Manheimer, 1997), and many struggling students are not identified as requiring special services for math during secondary school. It is becoming increasingly evident that students need help understanding mathematics, especially with the world rapidly evolving scientifically and mathematically. Many college students encounter mathematics difficulties, which can eventually act as a gatekeeper to earning a college degree.
Little research has been published on college students experiencing mathematics difficulties compared to elementary and secondary students having difficulties with mathematics (Strawser & Miller, 2001; Zawaisa & Gerber, 1993). This is especially the case for instructional or remediation interventions. Consequently, researchers often present results involving elementary and secondary students as part of their literature reviews, generalizing this information to students at the college level. Because enrollment in postsecondary settings by students with documented learning difficulties is increasing, researchers must begin to focus on the needs of this population of students (Mercer, 1997).
STUDENTS WITH MATHEMATICS DISABILITY
Research on students with mathematics disabilities often consists of comparisons with other disabilities. That is, students with reading disabilities (RD), disorders of written expression (WD), and mathematics disabilities (MD) and combined reading/mathematics disorders (RD/MD) are compared and contrasted between and among disability groups to establish shared and disparate attributes (Benton, 2001; Greene, 2001; Rourke, 1993; Shafrir & Siegel, 1994). Commonly, these studies focus on elementary and secondary students, highlighting the need for research at the postsecondary level.
Normally achieving (NA) students often make up a fourth group in such comparisons. From the comparisons made, several sources of individual differences can be extracted, including deficiencies in (a) reading ability, (b) nonverbal/visual skills, (c) working memory, (d) poor math fluency, and (e) attention and/or hyperactivity.
Reading Comprehension and MD
Fleischner and Manheimer (1997) identified two primary reasons why students struggle with mathematics. First, some students exhibit difficulty in reading comprehension. Comprehension difficulties seem to exacerbate difficulties in mathematics, especially for solving word or story problems. Examining NA students and students with MD, RD, and MD/RD, Jordan and Hanich (2000) demonstrated that when asked to solve four types of problems (number facts, story problems, place value, and written calculation), the students with MD/RD performed significantly lower than NA students. Further, the students with MD only performed lower on complex story problems compared to the NA students. Students with RD performed similarly to the NA students. Overall, students with MD/RD and MD significantly underperformed the students with RD and NA students on mathematics-related tasks.
Nonverbal Reasoning and MD
Fleischner and Manheimer (1997) also asserted that some students exhibit difficulties in nonverbal reasoning and/or primary mathematics knowledge. Rourke and his colleagues (Rourke, 1993; Rourke & Del Dotto, 1994; Rourke & Fuerst, 1996) have made significant contributions to the field of learning disabilities by studying nonverbal learning disability and its relationship to reading and mathematics disorders from a neurological perspective.
Rourke (1993) summarized several of these studies conducted with children with learning disabilities (LD) using a variety of assessment measures, including the Wechsler Intelligence Scale for Children (WISC) and Woodcock-Johnson Tests of Achievement (WJ). Among the three main clinical groups, Rourke and his colleagues identified differences between students with RD and MD, noting that students with RD typically have verbal deficits whereas students with MD typically have nonverbal deficits, as measured by the discrepancy between VIQ and PIQ measures on the WISC. "Older group [RD] children exhibit normal levels of performance on visual-spatial-organizational, psychomotor, and tactile-perceptual tasks; group [MD] children have outstanding difficulties on such tasks" (p. 220).
Additional findings were presented by Rourke and Fuerst (1996) and Rourke and Del Dotto (1994). For specifics on the range of studies that make up the preceding three studies, the interested reader is referred to Rourke and colleagues' publications on students with RD and MD. Rourke originally referred to MD as MD, but later changed to NLD (nonverbal learning disabilities). For the purposes of this article, Rourke's NLD group is referred to by his initial identification of MD.
According to Silver, Pennett, Black, Fair, and Balise (1999), visuo-spatial deficits may be the core deficit for students with isolated mathematics disorders, yet subtype stability is poorer for the arithmetic-only group. In a literature review, Jordan (1995) found three subtypes of mathematics disabilities, including one identified as having visuo-spatial deficits, similar to the nonverbal deficit discussed by Rourke.
Geary (1993) examined visuo-spatial deficits as one of three core difficulties (along with semantic memory and procedural deficiencies) experienced by students with calculation difficulties. Cirino, Morris, and Morris (2002) further explored Geary's theory on a sample of college students using a comprehensive battery of assessment instruments, Wechsler Adult Intelligence Scale-Revised and Woodcock-Johnson Tests of Achievement-Revised, along with a variety of other neuropsychological instruments. They determined that visuo-spatial deficits did not contribute to the calculation difficulties experienced by this sample. However, they did find evidence that Geary's other two categories of deficiency--semantic memory deficits and procedural deficits--contributed to the calculation difficulties of college students.
Working Memory, Math Fluency, and MD
Geary (1993) described semantic memory...
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