To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

Children need support in the early elementary grades to construct a deep, formal understanding of foundational prealgebraic concepts. In this article, the authors share recommendations for teaching one such foundational concept--mathematical equivalence. First, they define mathematical equivalence and discuss research supporting the benefits of…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Even in primary school, mathematics achievement depends upon the efficiency of cognitive, metacognitive and self-regulatory processes. Thus, for pupils to carry out a computation, such as a written calculation, metacognitive mechanisms play a crucial role, since children must employ self-regulation to assess the precision of their own thinking and…

This article describes a follow-up analysis of findings from a randomized study that tested the efficacy of a blended version of Enhanced Anchored Instruction (EAI) designed to improve both the computation and problem-solving performances of middle school students with disabilities. The goals of the secondary analysis were to track overall error…

Aims: Through this qualitative approach we intent to investigate the existence of patterns in errors that children with Down's syndrome make while counting. Study Design: The current study can be described as descriptive correlational, while we are also trying to extract data through qualitative analysis. Place and Duration of Study: In the…

Students with emotional and behavioral disorders (E/BD) display severe social and academic deficits that can adversely affect their academic performance in mathematics and result in higher rates of failure throughout their schooling compared to other students with disabilities (U.S. Department of Education, 2005; Webber & Plotts, 2008).…

This paper presents a computer based diagnostic tool developed to facilitate the learning process. The developed tool is capable of generating possible error syndromes associated with the answers received. The developed tool simulates the error pattern of the test results and then accordingly models the action plan to help in children's learning…

An analysis of the 1990 National Assessment of Educational Progress (NAEP) found that only 46 percent of all high school seniors demonstrated success with a grasp of decimals, percentages, fractions and simple algebra. This article investigates error patterns that emerge as students attempt to answer questions involving the ability to apply…

An approach to teaching factors and terms is offered that builds directly on students' knowledge of arithmetic. Errors arising from factor and term confusions are noted, followed by the pedagogical strategy of exploration, invention, and discovery. (MNS)

A nine-step model is presented for diagnosing and correcting computation errors in arithmetic. The model, which lends itself to curriculum-based assessment and instruction, involves such steps as identifying error patterns, interviewing the student, and selecting the appropriate corrective strategy. (JDD)

Outlined are the weaknesses of traditional, norm-referenced tests which fail to help in making instructional decisions. Presented is a step-by-step series of operations for analyzing and categorizing arithmetic errors, for selecting corrective strategies, and for applying peer-referenced standards to judge the performance of special needs…

Diagnostic interviews were conducted with third graders to determine why they made mistakes on sixteen arithmetical tasks. A modified version of the Newman method of analyzing errors is discussed and applied to these interviews. (MP)

The nature of arithmetic disabilities in children is discussed first in this review. Then research studies are reported, classified by cognitive and neuropsychological studies and social competency studies. Finally, suggestions for remediation are provided. (MNS)

The objective of this paper is to explain the need for and defend the sufficiency of the child's-play method of teaching the place value notation concept to preschool and elementary school children. Discussion first illustrates error patterns of school children in the use and interpretation of place value notation, arguing that the errors reflect…