Journal of Learning Disabilities

This article highlights key findings from the small body of research on mathematics difficulties (MD) relevant to early identification and early intervention. The research demonstrates that (a) for many children, mathematics difficulties are not stable over time; (b) the presence of reading difficulties seems related to slower progress in many aspects of mathematics; (c) almost all students with MD demonstrate problems with accurate and automatic retrieval of basic arithmetic combinations, such as 6 + 3. The following measures appear to be valid and reliable indicators of potential MD in kindergartners: (a) magnitude comparison (i.e., knowing which digit in a pair is larger), (b) sophistication of counting strategies, (c) fluent identification of numbers, and (d) working memory (as evidenced by reverse digit span). These are discussed in terms of the components of number sense. Implications for early intervention strategies are explored.

Gersten, Jordan, and Flojo (in this issue) provide the beginnings of an essential bridge between basic research on mathematical disabilities (MD) in young children and the application of this research for the early identification and remediation of these forms of learning disability. As they acknowledge, the field of MD is in the early stages of development, and thus recommendations regarding identification measures and remedial techniques must be considered preliminary. I discuss the importance of maintaining a tight link between theoretical and empirical research on children's developing numerical, arithmetical, and mathematical competencies and future research on learning disabilities in mathematics. This link will provide the foundation for transforming experimental procedures into assessment measures, understanding the cognitive strengths and weaknesses of children with these forms of learning disability, and developing remedial approaches based on the pattern of cognitive strengths and weaknesses for individual children.

This commentary addresses issues concerning (a) the measurement of numbers, letters, and words versus cognitive processes in early screening batteries, and (b) comorbid associations of reading, math, and attention disorders. Based on reading prediction studies, assessments that include numbers should be most predictive of math outcomes. However, given the comorbid association of reading, math, and attention disorders, measures sensitive to reading and attention difficulties may be necessary in early screening batteries for math disabilities.

Gersten, Jordan, and Flojo (in this series) review their research on math difficulties, with an emphasis on applying current knowledge to inform practices of early identification and intervention. On a practical level, educators are in dire need of empirically based screening and intervention tools. From a scientific perspective, it is important to recognize the need to clearly define what we seek to identify and remediate, and to acknowledge that we are currently far from achieving this goal despite recent advances in the field. Among the studies reviewed by Gersten et al., as well as other studies by several other researchers, there is much variability in how mathematics difficulties are defined and measured, and even in the terms used to refer to them. I address the degree of consensus and controversy currently characterizing the state of math learning disabilities research, with an emphasis on the usefulness of a developmental perspective in appraising this young field.

Drawing on various approaches to the study of mathematics learning, Gersten, Jordan, and Flojo (in this issue) explore the implications of this research for identifying children at risk for developing mathematical disabilities. One of the key topics Gersten et al. consider in their review is that of “number sense.” I expand on their preliminary effort by examining in detail the diverse set of components purported to be encompassed by this construct. My analysis reveals some major differences between the ways in which number sense is defined in the mathematical cognition literature and its definition in the literature in mathematics education. I also present recent empirical evidence and theoretical perspectives bearing on the importance of measuring the speed of making magnitude comparisons. Finally, I discuss how differing conceptions of number sense inform the issue of whether and to what extent it may be teachable.

Gersten, Jordan, and Flojo (in this issue) have written an elegant summary of the research on early identification and interventions for students with mathematical difficulties. The general constructs of arithmetic combinations, counting strategies, and number sense encapsulate elemental components of early math learning and suggest approaches to remediation. Recent changes in the Individuals with Disabilities Education Act may enhance opportunities for researchers, practitioners, and young learners to benefit from this knowledge.

The purpose of this study was to examine the reliability and validity of curriculum-based measures as indicator of growth in content-area learning. Participants were 58 students in 2 seventh-grade social studies classes. CBM measures were student- and administrator-read vocabulary-matching probes. Criterion measures were performance on a knowledge test, the social studies subtest of the Iowa Test of Basic Skills (ITBS), and student grades. Both the student- and examiner-read measures reflected change in performance; however, only the student-read measure resulted in interindividual differences in growth rates. Significant relations were found between the growth rates generated by the student-read vocabulary measure and student course grades, ITBS scores, and growth on the knowledge test. These results support the validity of a vocabulary-matching measure as an indicator of student learning in the content areas. The results are discussed in terms of the use of CBM as a system for monitoring performance and evaluating interventions for students with learning disabilities in content-area classrooms.

In this quasi-experimental study, which is part of a series of investigations on supplemental reading tutoring variations, the relative effectiveness of more intense decoding instruction or text reading practice was examined. Fifty-seven first-grade students scoring in the lowest quartile for reading skills received either classroom reading instruction or one of two treatments: tutoring in word study with text reading practice, or word study tutoring alone. Individual instruction was provided by trained paraprofessional tutors. At the end of first grade, treatment students significantly outperformed their nontutored peers on measures of reading accuracy, reading comprehension, reading efficiency, passage reading fluency, and spelling. Differential treatment effects on passage reading fluency are examined, taking into consideration pretest skill levels and text reading practice characteristics.