Arithmetic fact mastery in young children: A longitudinal investigation

Abstract

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...

Remediating Computational Deficits at Third Grade: A Randomized Field Trial

“…As might be expected, therefore, some previous work suggests that students with concurrent difficulty in math and reading experience more pervasive difficulties, including more severe mathematics deficits in procedural computation (e.g., Jordan & Hanich, 2000), simple word problems (e.g., Hanich, Jordan, Kaplan, & Dick, 2001;Jordan & Hanich, 2000), and complex forms of mathematical problem solving . By contrast, other work (e.g., Jordan, Hanich, & Kaplan, 2003;Landerl, Began, & Butterworth, 2004) shows that students with mathematics disabilities, with and without concurrent reading difficulty, experience comparable mathematics deficits.Most recently, Cirino, Ewing-Cobbs, assessed 291 third and fourth graders whom the researchers classified as having math disabilities, reading disabilities, math and reading disabilities, or normal achievement. Students were assessed on computerized measures of cognitive arithmetic, addition, subtraction, and estimation.…”

Nature and origins of mathematics difficulties in very preterm children: a different etiology than developmental dyscalculia

“…Alongside these, a number of specific mathematics processes are also related to achievement (9), including basic counting skills (10), the ability to apply efficient strategies (11), the accuracy and speed of retrieval of basic number facts (12), and the conceptual understanding of mathematics (9).…”

Development of Number Line Representations in Children With Mathematical Learning Disability

“…Children with MLD have deficits in a wide range of basic mathematical domains, including a delayed understanding of counting concepts (Geary, Bow-Thomas, & Yao, 1992), difficulties remembering arithmetic facts (Geary, 1993;Jordan, Hanich, & Kaplan, 2003;Jordan & Montani, 1997), and poor conceptual knowledge of rational numbers (Mazzocco & Devlin, in press). The delayed learning of LA children, in contrast, may center on basic numerical representations, including the number line (Geary et al, 2007).…”