Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two…

A recent review of research on virtual manipulatives (VMs), defined as technology-based interactive representations of mathematical ideas (Moyer-Packenham, & Bolyard, 2016), suggests strengths relative to other instructional tools in supporting student learning of mathematics (Moyer-Packenham & Westenskow, 2013). Researchers have…

National assessments suggest that many students do not display proficiency with fractions. Considering that time and materials are precious resources, many educators are looking to use technology to provide supplemental instruction with low demand on the instructor. The current study utilized a multiple-baseline design to examine the effects of…

The proliferation of computers, tablets, and internet access has brought the use of virtual manipulatives into the majority of classrooms in the developed world. In responding to the needs of today's students, many of whom are adept at accessing and manipulating technology devices, virtual manipulatives provide a variety of classroom…

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,…

In this article, I use the Vygotskian concept of the Zone of Proximal Development (ZPD) to examine the learning experience of two grade seven pupils as they attempted to solve an addition of fractions problem using fraction strips. The aim is to highlight how tools can facilitate the enactment of a ZPD, within which the tool provides the guidance.…

The aim of this research is to examine digital learning materials designed by pre-service mathematics teachers with GeoGebra software through rubrics. This research was conducted using the integrative mixed method design, which allows the use of qualitative and quantitative methods together or sequentially. The study group of the research consists…

It seems that calculators continue to be misunderstood as devices solely for calculation, although the likely contributions to learning mathematics with modern calculators arise from other characteristics. A four-part model to understand the educational significance of calculators underpins this paper. Each of the four components (representation,…

Manipulatives are a common tool in mathematics teaching and learning, including for students with disabilities. The most common manipulatives are concrete manipulatives, yet app-based manipulatives are a viable age-appropriate option for secondary students with disabilities. Through an adapted alternating treatment design with three middle school…

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,…

The gold standard for identifying more effective pedagogical approaches is to perform an experiment. Unfortunately, frequently a hypothesized alternate way of teaching does not yield an improved effect. Given the expense and logistics of each experiment, and the enormous space of potential ways to improve teaching, it would be highly preferable if…

This paper explores the use of animations as an approximation of practice to provide a transformational technology experience for elementary mathematics preservice teachers. Preservice teachers in mathematics methods courses at six universities (n = 126) engaged in a practice of decomposing and approximating components of a fraction lesson. Data…

This paper explores the use of animations as an approximation of practice to provide a transformational technology experience for elementary mathematics preservice teachers. Preservice teachers in mathematics methods courses at six universities (n = 126) engaged in a practice of decomposing and approximating components of a fraction lesson. Data…

The purpose of this study is to explore how different game designs support students' learning and enjoyment of fractions, specifically, early learning of equivalence and ordering. Two sets of games were contrasted, one that was characterized as "exploratory and implicit," and a second that was characterized as "directive and…

The purpose of this study was to explore the relationship between instructional modality used for teaching fractions and third- and fourth-grade students' responses and strategies to open-response fraction items. The participants were 155 third-grade and 200 fourth-grade students from 17 public school classrooms. Students within each class were…