Manipulative-based instructional sequences have proven to be successful with students with disabilities. However, instruction must not only support the acquisition of conceptual and procedural knowledge but also build on students' strengths. This article describes how teachers can use manipulative-based instructional sequences to support the…

There is a growing perception that computational thinking can be developed in unplugged environments. A recent trend among these unplugged approaches is the use of tabletop games. While there are many commercial tabletop games on the market that are promoted as teaching computer science and/or computational skills, little is known about how these…

Incorporating visual representations, rather than strictly relying on symbolic representations, is a research-based strategy for supporting fraction learning. However, students must also make transitions between visual and symbolic fraction representations to apply the conceptual understanding they gained from visual representations to symbolic…

The mechanisms of dissemination of the counting frames in the teaching of mathematics in Spain during the nineteenth century are studied. José Mariano Vallejo and Pablo Montesino proposed them in order to facilitate an arithmetic initiation based on intuition, following Pestalozzi's proposals. The diffusion channels considered were pedagogical…

Researchers determined virtual manipulatives, on their own or as part of an instructional sequence, to be an evidence-based practice for students with intellectual and developmental disabilities (IDD; Long et al., 2022). Yet, the majority of research looking at virtual manipulative-based instructional sequences involves the phases learned in a…

This qualitative case study aims to address the ways that pre-service mathematics teachers (PSTs) used a rope in a daylong research meeting for cognitive development of children's understanding of counting numbers in Tanzanian elementary schools. Three university mathematics pre-service teachers volunteered participating in this study. Collective…

This study was an investigation of the use of manipulative materials in the mathematics classroom. The researcher guided students to create paper triangles, which were then used as a manipulative to calculate the sum of the interior angles of a triangle. On pre- and post-measures of quantitative data, although the data indicated a positive…

This study investigates the integration of computational thinking (CT) into early elementary literacy, focusing on kindergarten to second grade students, using multiple representations to understand their ideas of CT. Through clinical task-based interviews with 12 students, we found that concrete manipulatives, pictorial/graphical representations,…

The natural experiment proposed in this article extracts three stories from boxes of "100 paper clips". The activity requires students to apply three lessons from inferential statistics, starting with a hypothesis test and including confidence intervals as well as tolerance intervals.

This article focuses specifically on the inclusion of meaningful (but potentially messy) real-world mathematics tasks in the middle school classroom. Real-world tasks provide students with learning opportunities allowing mathematics to be used to understand the world, strengthen mathematical knowledge, and offer opportunities for students to use…

Manfred Hauben proposes an approach to teaching non-transitive relationships between 'paradoxical' dice using simple statistical graphics. This method usefully supplements traditional approaches of conditional probability calculations and trees, and students are thereby better able to see what is going on and the mechanism of these relationships.

This article reflects critically on the guidance offered to South African teachers in two canonical texts: the Curriculum and Assessment Policy Statements (CAPS) and Mathematics teaching and learning framework for South Africa: Teaching mathematics for understanding (TMU). I make explicit my philosophical orientation, and how 'teaching mathematics…

Manipulatives have been found to be effective in increasing mathematics achievement when they are put to good use (Canny, 1984; Clements & Battista, 1990; Clements, 1999; Sowell, 1989; Suydam, 1984), but their use in mathematics instruction is not clear and it is often debated to be effective (Ball, 1992; McNeil & Jarvin, 2007). The…

Learning to compute with fractions is a major challenge for many students and especially for students with disabilities (SWD). Phase 1 of this study employed a randomized pretest-posttest comparison design to test the effects of two versions of formative assessment combined with an instructional program called Fractions at Work. In one condition,…

Learning to compute with fractions is a major challenge for many students and especially for students with disabilities (SWD). Phase 1 of this study employed a randomized pretest-posttest comparison design to test the effects of two versions of formative assessment combined with an instructional program called Fractions at Work. In one condition,…