To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…

This study investigated the effect of a paper folding activity prepared to develop the sixth-grade students' concept definitions and images of parallelism and perpendicularity concepts. The study also examined how the concept definition and images changed after the paper folding activity. A combination of quantitative and qualitative methods was…

An alternating treatments design was used to analyze the effects of concrete and virtual manipulatives on the duration and number of correctly solved linear equations by three middle school students with cognitive disabilities. Participants physically manipulated algebra tiles to solve an equation during the concrete manipulative condition. During…

Digital instructional tools, such as virtual manipulatives, have been widely adopted as an enhanced approach to inquiry-based learning. However, the optimal ratio of mobile devices to students in instructional settings remain controversial. This research introduced a counterbalanced quasi-experiment to compare the learning performance and…

Physical and virtual labs have unique capabilities that can influence how students learn from them. The purpose of this study was to examine the effect of physical and virtual manipulatives on students' learning of heat and temperature and to examine the influence of various combinations of physical and virtual manipulatives. A total of 205…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…

In science classrooms, technology affordance varies depending on device-student ratios (DSR) and the ways virtual manipulatives on mobile devices are used. Additionally, external scripts (ES) are widely used to promote effective group interaction in collaborative learning. Therefore, this research explored the influence of DSR and ES on…

The virtual-representational-abstract (VRA) instructional sequence presents as a viable mathematics intervention for students with disabilities, including students with autism spectrum disorder (ASD). Yet, to date, all research has been conducted face-to-face with students. However, virtual manipulatives provide an opportunity for educators to…

In this synthesis, we analyzed 10 prealgebraic reasoning interventions for students with mathematics difficulty (MD) in Grades 6 through 8. All interventions focused on one or more prealgebraic concepts including integer operations, algebraic expressions and equations, and functions. Of the 10 intervention studies, six employed single-case design…

In this study, effects of 2 physical manipulative instructions on students' geometrical knowledge acquisition were compared. Geometry topics' presentation was conducted via using physical manipulative and the practice stage in two different forms: (1) practice consisting of problems supported with explicit metacognitive questions and (2) practice…

This paper offers insight into teachers' perspectives on the role of manipulatives in the mathematics classroom on either side of the primary to post-primary transition (sixth class teachers in Irish primary schools and first year mathematics teachers in post-primary schools) to examine if discontinuities exist around their usage. The transition…

Design research was conducted to investigate the development of dynamic conceptions of area. Students used simple physical instruments, squeegees, and paint, to generate rectangular areas continuously as a sweeping motion of one length through another. Then, they dissected the resulting swept space into discrete units of measure by coordinating…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

This exploratory study attempts to determine problem solving steps in block based programming environments. The study was carried out throughout one term within Code.org. Participants were 15 6th grade secondary school students enrolled in an IT course at a public secondary school. Observations, screenshots and interviews were analyzed together to…

In this article, an activity designed and implemented to improve both procedural knowledge and conceptual knowledge of multiplication is introduced. The students were physically and mentally active while exploring a multiplication method developed by the Russian peasants. They not only explained why and how the method works, but also extended the…