This study reviews the literature on error patterns in mathematics among students with mathematics difficulty. We analyzed and synthesized the findings from 17 studies, focusing on the characteristics of error analysis studies, the mathematics topics examined, and the specific error patterns identified. The results revealed the following: (a) the…

Through a constructivist teaching experiment, we studied how a 6th-grade student (Adam, pseudonym) struggling in mathematics may reorganize his available additive scheme (count-up-to) into a more advanced scheme involving the decomposition of composite units (break-apart-make-ten, or BAMT). First, we posed a task that led us to infer Adam was yet…

Counting is foundational to success with mathematics. In this synthesis, we analyzed 17 studies about counting-focused interventions for preschool and kindergarten students with mathematics difficulty or at-risk of mathematics difficulty. All interventions addressed several components of counting, including stable order, one-to-one correspondence,…

This article investigates how students with mathematical difficulties (MD) differ from typically developing (TD) students in enumeration processes of small sets of objects (of 1 up to 9 dots). We present a study with 20 fifth-grade students of which ten were found to have MD in initial diagnostics. The students were supposed to exactly enumerate…

Assessment data from the United States and international reports of student achievement indicate that upper elementary students are failing to meet basic levels of proficiency in fractions and writing, and that this is particularly prevalent with students with or at-risk for learning disabilities in mathematics. Proficiency with fractions has been…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…

The purpose of this study was to assess the relative contribution of teacher and tutor ratings of inattentive behavior in two different instructional settings in predicting students' performance on fraction concepts and whole-number calculations. Classroom teachers rated each student's attentive behavior in a whole-class setting and tutors rated…

The purpose of this study was to determine the effects of an early numeracy preventative Tier 2 intervention on the mathematics performance of first-grade students with mathematics difficulties. Researchers used a pretest-posttest control group design with randomized assignment of 139 students to the Tier 2 treatment condition and 65 students to…

339 children aged 6 and 7 at Oxford primary schools took part in a study of arithmetic. 204 of the children had been selected by their teachers as having mathematical difficulties and the other 135 children were unselected. They were assigned to an Addition Performance Level on the basis of a calculation pretest, and then given Dowker's (1998)…

The mathematical performance of 182 third and fourth graders in 8 different areas of mathematics was examined. The children belonged to 4 achievement groups: children with mathematic difficulties (MD only), children with both mathematic and reading difficulties (MD-RD), children with reading difficulties (RD only), and normally achieving children…

This longitudinal study investigated the academic and cognitive characteristics of persistent mathematics difficulty (MD-p) from first to fourth grade. Ninety-nine children were retrospectively categorized into one of three groups: MD-p, transient mathematics difficulty (MD-t), or typically developing. MD-p was defined as persistently low…

Magnitude comparison, calculation verification, and short-term memory span experiments were conducted as a means of investigating number processing in 17 deaf college students with academic weaknesses. Deaf students' level of accuracy did not differ from that shown by their hearing peers; however, mean response times of deaf students were greater…

Demonstrates the consequences of teaching rules without understanding using examples from two 3rd grade children. Suggests alternative instructional strategies. (KHR)

Standards in numeracy are a constant concern to educational policy-makers. However, why are differences in arithmetical performance so marked? In "Individual Differences in Arithmetic", Ann Dowker seeks to provide a better understanding of why these differences in ability exist, encouraging a more informed approach to tackling numeracy…