As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

Neuropsychological investigations of FMR1 premutation carriers without FXTAS present one domain resulting in contradictory findings, namely that of mathematical skills. One reason for this might be that standard clinical batteries used so far may be inadequate to uncover precise deficits within specific mathematical skills. In fact, these…

In this paper we analyse the introduction of irrational and real numbers in secondary textbooks, and specifically the propositions on how these should be taught, in a sample of Brazilian textbooks used in state schools and approved by the Ministry of Education. The analyses discussed in this paper follow an institutional perspective (using…

Parity helps us determine whether an arithmetic equation is true or false. The current research examines the development of sensitivity to parity cues in multiplication in typically achieving (TA) children (grades 2, 3, 4 and 6) and in children with mathematics learning disabilities (MLD, grades 6 and 8), via a verification task. In TA children…

The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic--operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were…

In this study it is investigated to what extent contextualized and non-contextualized mathematics test items have a differential impact on examinee effort. Mixture item response theory (IRT) models are applied to two subsets of items from a national assessment on mathematics in the second grade of the pre-vocational track in secondary education in…

Children with mild intellectual disabilities (MID) appear to have particular problems in understanding the numerical meaning of Arabic digits. Therefore, we developed and evaluated a numerical domino game that specifically targeted the association between these digits and the numerical magnitudes they represent. Participants were 30 children with…

The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

This study aims to understand the differences in student learning outcomes and classroom behaviour when using the interpersonal computer, personal computer and pen-and-paper to solve arithmetic exercises. In this multi-session experiment, third grade students working on arithmetic exercises from various curricular units were divided into three…

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory,…

Intellectual abilities are consistently found to be associated to child functioning. To date, however, it is unclear how varying intellectual profiles relate to differential aspects of child functioning. We screened 513 fifth-grade children on their intellectual abilities and selected three groups of gifted children, scoring in the top 10%:…

This in-brief technical report documents the results from two different analytic approaches for examining the reliability of the slope for easyCBM® math measures in Grades K-8. Results varied by grade, assessment measure, and the analytic approach. Results patterns are discussed.

In this article, John West explores student misconceptions relating to division. A range of activities that promote the understanding of divisibility rules are provided.

How can a simple dot--the decimal point--be the source of such frustration for students and teachers? As the author worked through her own frustrations, she found that her students seemed to fall into groups in terms of misconceptions that they revealed when talking about and working with decimals. When asking students to illustrate their thinking…