Mathematical competencies of 180 children were examined at 4 points between 2nd and 3rd grades (age range between 7 and 9 years). Children were initially classified into one of 4 groups: math difficulties but normal reading (MD only), math and reading difficulties (MD-RD), reading difficulties but normal math (RD only), and normal achievement in math and reading (NA). The groups did not differ significantly in rate of development. However, at the end of 3rd grade the MD only group performed better than the MD-RD group in problem solving but not in calculation. The NA and RD only groups performed better than the MD-RD group in most areas. Deficiencies in fact mastery and calculation fluency, in particular, are defining features of MD, with or without RD.

The performance of 210 2nd graders in different areas of mathematical cognition was examined. Children were divided into 4 achievement groups: children with difficulties in mathematics but not in reading (MD-only), children with difficulties in both mathematics and reading (MD/RD), children with difficulties in reading but not in mathematics, and children with normal achievement. Although both MD groups performed worse than normally achieving groups in most areas of mathematical cognition, the MD-only group showed an advantage over the MD/RD group in exact calculation of arithmetic combinations and in problem solving. The 2 groups did not differ in approximate arithmetic and understanding of place value and written computation. Children with MD-only seem to be superior to children with MD/RD in areas that may be mediated by language but not in ones that rely on numerical magnitudes, visuospatial processing, and automaticity.

Researchers of mathematics learning disability (MLD) commonly use cutoff scores to determine which participants have MLD. Some researchers apply more restrictive cutoffs than others (e.g., performance below the 10th vs. below the 35th percentile). Different cutoffs may lead to groups of children that differ in their profile of math and related skills, including reading, visual-spatial, and working memory skills. The present study assesses the characteristics of children with MLD based on varying MLD definitions of math performance either below the 10th percentile (n = 22) or between the 11th and 25th percentile (n = 42) on the Test of Early Math Ability, second edition (TEMA-2). Initial starting levels and growth rates for math and related skills were examined in these two MLD groups relative to a comparison group (n = 146) whose TEMA-2 performance exceeded the 25th percentile. Between kindergarten and third grade, differences emerged in the starting level and growth rate, suggesting qualitative differences among the three groups. Despite some similarities, qualitative group differences were also observed in the profiles of math-related skills across groups. These results highlight differences in student characteristics based on the definition of MLD and illustrate the value of examining skill areas associated with math performance in addition to math performance itself.

Children with poor arithmetic fact mastery (n = 45) at the end of third grade were compared to gradelevel peers with good arithmetic fact mastery (n = 60) in competencies related to reading and mathematics. Children were assessed longitudinally across second and third grades. When predictor variables such as IQ were held constant, the poor fact mastery and good fact mastery groups performed at about the same level and progressed at a comparable rate on math story problems and on broad reading achievement. The groups also progressed at a comparable rate on broad math achievement, although children with poor fact mastery performed at a significantly lower level. Children with poor fact mastery showed remarkably little growth on timed number facts during the study period, despite normal growth in other areas of mathematics. Deficits in fact mastery are highly persistent and appear to be independent of reading and language abilities. Keywords Mathematics; Learning disabilities; Cognitive developmentYoung children show uneven patterns of competencies in mathematics. In particular, some children cannot master basic arithmetic facts despite relatively strong problem-solving skills (Hanich, Jordan, Kaplan, & Dick, 2001;Jordan & Hanich, 2000;Jordan & Montani, 1997). Deficits related to mastery, or fast retrieval, of arithmetic facts is a key characteristic of children with mathematics difficulties (MD) who are good readers (Geary, Hamson, & Hoard, 2000Hanich et al., 2001; Jordan, Hanich, & Kaplan, in press). In contrast, children with both MD and reading difficulties (RD) are characterized by weaknesses in problem solving as well as in arithmetic fact mastery.Speed of processing numerical information appears to be a particular problem for children with MD only. Jordan and Montani (1997) presented children with MD only and children with MD/ RD with number facts and math story problems, both in timed and in untimed conditions. All the problems involved addition or subtraction operations. On the timed condition, children were required to answer orally presented problems within 3 s. Relative to children with normal mathematics achievement, children with MD only were strong on untimed conditions but not on timed conditions. When given enough time, MD only children successfully represented the problems and employed verbal counting methods. Children with MD/RD performed worse than normally achieving children on untimed as well as on timed tasks. They inaccurately represented problems and made numerous counting mistakes, even in the absence of time constraints.*Corresponding author. Fax: 1-302-831-0241. njordan@udel.edu (N.C. Jordan). NIH Public Access NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptIt has been suggested that number fact deficits are associated with general weaknesses in processing speed (Bull & Johnston, 1997) and in linguistic processes related to representing phonological information and retrieving information from long-term semantic memory (Ashcraft, 1992;Geary, 1993). If nu...

Based on their performance on a standardized achievement test, second-grade children (N = 49) were classified as having mathematics difficulties with normal reading achievement (MD only), both mathematics and reading difficulties (MD/RD), reading difficulties with normal mathematics achievement (RD only) and normal mathematics and reading achievement (NA). Each child was given a series of tasks so that we might assess their thinking across four areas of mathematics: number facts, story problems, place value, and written calculation. Children with MD/RD performed significantly worse than NA children in most areas of mathematical thinking, whereas children with MD only performed worse than NA children only on complex story problems. The MD-only group outperformed the MD/RD group on story problems and written calculation. No significant differences were found between the RD-only and NA groups on any of the tasks. The results suggested that among children with mathematics difficulties, the MD/RD subgroup is distinct from the MD-only subgroup, with the former being characterized by pervasive deficiencies in mathematical thinking and the latter by more specific deficits in problem solving.