Many mathematics educators believe that it is insufficient for students' knowledge of the division of fractions to be limited to the invert-and-multiply algorithm, arguing that students' learning of mathematics must go beyond rote memorization of procedures. Teachers ought to carefully consider what students need to learn beyond the algorithmic…

Assessment is a common task in education that has many varied purposes. One of these is the use of assessment data to make decisions about instructional planning. This article presents a framework for how to use assessment data to plan instruction. It also provides some background on terminology of assessment for instructional planning,…

This paper discusses results from a design research in line with Realistic Mathematics Education (RME). Daily cycles of design, classroom experiments, and retrospective analysis are enacted in five days of working about division by fractions. Data consists of episodes of video classroom discussions, and samples of students' work. The focus of…

Background: In the debate on inclusive education, students without special educational needs (SEN) are an important topic. However, there is a lot unknown about differences between these typical students in inclusive and non-inclusive classes. For example, the neutral results that are often found in earlier research could be caused by positive…

In this article, the author presents a six by six array in which individuals can obtain 182 in total even if they use a different set of numbers. The author then explain why this is possible. The author uses the k-translation of a sequence for this equation. (Contains 8 figures, 2 tables and 6 footnotes.)

Most high school mathematics teachers completed a mathematics history course in college, and many of them likely found it intriguing. Unfortunately, very few of them find the time to allow much, if any, mathematics history to trickle into their instruction. However, if mathematics history is taught effectively, students can see the connections…

Memorizing the basic number combinations, such as 9 + 7 = 16 and 16 - 9 = 7, is a punishing and insurmountable task for children with difficulties learning mathematics. Two perspectives on such learning lead to different conclusions about the primary source of this key learning difficulty. According to the conventional wisdom (the Passive Storage…

Looking away from an interlocutor's face during demanding cognitive activity can help adults and children answer challenging mental arithmetic and verbal-reasoning questions (Glenberg, Schroeder, & Robertson, 1998; Phelps, Doherty-Sneddon, & Warnock, 2006). While such "gaze aversion" (GA) is used far less by 5-year-old school children, its use…

The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…

There exists a substantial number of studies that have identified a subset of low-achieving mathematics students who do not develop a reliance on retrieval for simple addition but who continue to use a counting strategy to solve these problems. There are few studies, however, that have focused on how retrieval of simple addition facts may be…

Introduction: Moved by our interest in the curricular proposal of integrating algebraic thinking in elementary mathematics, we analyse the understanding of number sentences of a group of elementary students and its evolution when working on solving open and true/false number sentences. Method: We developed a teaching experiment with a group of…

Background: Working memory is linked to learning outcomes and there is emerging evidence that training working memory can yield gains in working memory and fluid intelligence. Aims: The aim of the present study was to investigate whether interactive working memory training would transfer to acquired cognitive skills, such as vocabulary and…

The purpose of this technical report is to describe a research study exploring students' cognitive processing while solving problems related to division of fractions. Four students were interviewed using verbal protocol techniques with the intention of better understanding their cognitive processing when dividing fractions. Information gained from…

The manipulation of numbers required during calculation is known to rely on working memory (WM) resources. Here, we investigated the respective contributions of verbal and/or spatial WM manipulation brain networks during the addition of four numbers performed by adults, using functional magnetic resonance imaging (fMRI). Both manipulation and…

This article reports on 20 children's learning in arithmetic after teaching was adjusted to their conceptual development. The report covers periods from three months up to three terms in an ongoing intervention study of teachers and children in schools for the intellectually disabled and of remedial teaching in regular schools. The researcher…