Evidence in South Africa of poor performance on word problems points to particular challenges among learners relating to difficulties with, on the one hand, making sense of mathematical word problems and, on the other, moving beyond inefficient counting based calculation methods. While many studies in mathematics education in South Africa have…

Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…

Despite problem posing's prominence in mathematics education research, its implementation in classrooms is limited. Therefore, teacher educators should incorporate problem posing tasks into preparation programs to help prospective teachers gain confidence in their abilities. One approach to teaching problem posing includes providing examples. The…

Mathematical writing is one way for primary students to communicate their mathematical thinking. Research in the field of writing has shown that to become an effective teacher of writing, preservice teachers must have experience engaging in the kinds of writing given to their students. The study reported in this paper explored how 27 preservice…

Suppose that there is an inexhaustible supply of $3 and $5 vouchers from the local supermarket. They may only be exchanged for items that cost an exact number of dollars made up from any combination of the vouchers. What is the highest amount not able to be obtained? This is an interesting problem in mathematical thinking and logic requiring only…

Focusing on students with mild disabilities, this study aimed to examine the effect of STAR problem solving strategy on their a) solving change problems involving one-step addition and subtraction, b) maintaining their acquisition of solving change problems involving one-step addition and subtraction after 1, 3, and 5 weeks, c) generalizing their…

In this study we investigated the development of 245 kindergarteners' mathematics problem solving (MPS) at two time points within 7 months using a cognitive diagnostic test, which measured three cognitive components (mathematical knowledge and skills, semantic understanding, and quantitative reasoning) with eleven cognitive attributes. The effects…

Assessing student learning traditionally involves determining whether students can solve a certain percentage of problems correctly, under the assumption that this achievement indicates they have the knowledge and understanding they need to progress to new topics. This article explores what teachers can learn from looking closely at student…

This paper examines a problem described as widespread and long-standing in mathematics education: supporting pupils into multiplicative reasoning, a form of reasoning that has been noted as central to large tracts of secondary mathematics and beyond. Also noted, however, is a persistent perception of multiplicative situations only in terms of…

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth…

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

According to numerous studies (Barrouillet & Camos 2002; Brousseau 1988; Chevallard 1988; Riley et al. 1984; Schubauer-Leoni & Ntamakiliro, "Revue Des Sciences de L'éducation," 20(1): 87-113, 1994; Vergnaud 1982; Xin, "The Journal of Educational Research," 100(6):347-360, 2007), a combination of many factors, including…

A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof…

Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…

Many general and special education teachers teach mathematics word problems by defining problems as a single operation and linking key words to specific operations. Unfortunately, teaching students to approach word problems in these ways discourages mathematical reasoning and frequently produces incorrect answers. This article lists eight common…