While there are many documented approaches to using technological tools to support collaboration in remote environments, studies related to proof-based courses are overwhelmingly situated in the context of geometry. This study uses instrumental genesis theory to study how students in an introduction to proofs course operationalize the…

This study focused on investigating the ability of 58 pre-service mathematics teachers (PSMTs) to construct-evaluate-refine mathematical conjectures and proofs. The PSMTs enrolled in a three-credit mathematics education course that offered various opportunities to engage with mathematical activities including constructing-evaluating-refining…

Unprecedented investments are being made in mathematics tutoring interventions for K-12 students, but results from these interventions are not always promising. Traditional online or distance math tutoring can treat learning as disembodied, and not give learners access to embodied resources like gestures, movements, and actions. Virtual Reality…

I explore students' discourses in small groups working on mathematical problems using GeoGebra, focusing on the Cartesian connection between algebra and geometry. Specifically, the interest lies in what is internally persuasive for students in upper-secondary school (11th grade) with histories of low attainment. Three problem-solving episodes are…

This article is part of a wider research project that has the educational goal of supporting students in the production of conjectures, arguments and proofs, as well as promoting a move from the production of arguments expressed in colloquial registers to arguments expressed in literate registers. In this regard, we Giovannina Albano, Umberto…

Findings synthesized across five empirical laboratory- and classroom-based studies of high school and college students engaged in geometric reasoning and proof production during single- and multi-session investigations (346 participants overall) are presented. The findings converge on several design principles for computer technologies to support…

In this article, we report how a geometric task based on the ACODESA methodology (collaborative learning, scientific debate and self-reflection) promotes the reformulation of the students' validations and allows revealing the students' aims in each of the stages of the methodology. To do so, we present the case of a team and, particularly, one of…

Planning a mathematics lesson plan is a complex process. Its quality contributes to the effectiveness of mathematics instruction. Given this significance, improving prospective mathematics teachers' lesson planning ability is essential for teacher preparation programs to produce effective teachers. This study examines how a lesson study within a…

National Council of Teachers of Mathematics' (NCTM's) "Principles to Actions: Ensuring Mathematical Success for All" outlines eight teaching practices for effective teaching and learning of mathematics (NCTM 2014). One of the teaching practices, "elicit and use evidence of student thinking," states, "Effective teaching of…

The Hidden Village (THV) is a motion-capture video game for investigating how physical movements foster mathematical thinking and proof practices based on principles of embodied cognition. Analysis of the interactions of students in an all-Limited English Proficiency Title 1 high school geometry classroom revealed ways simulated enactment and…

The purposes of this research were to know the validity, practicality, and effectivity of geometrical learning material based on the constructivism to Increase students' mathematic reasoning ability and increasing students' mathematic reasoning ability by using learning material at the grade VIII of SMP Negeri 3 Padangsidimpuan. Type of the…

Meaningful learning of formal mathematics in regular classrooms remains a problem in mathematics education. Research shows that instructional approaches in which students work collaboratively on tasks that are tailored to problem solving and reflection can improve students' learning in experimental classrooms. However, these sequences involve…

Sorting shapes and solving riddles develop and advance children's geometric thinking and understanding while promoting mathematical communication, cooperative learning, and numerous representations. This article presents a brief summary of how children develop an understanding of the properties of geometric shapes as well as a description of the…

A geometry textbook or mathematics journal that prints all the work that mathematicians use as they generate proofs of mathematical results would be rare indeed. The false starts, the tentative conjectures, and the arguments that led nowhere--these are conveniently omitted; only the final successful product is presented to the world. To students…

This article describes one classroom activity in which the author simulates the Newtonian gravity, and employs the Euclidean Geometry with the use of new technologies (NT). The prerequisites for this activity were some knowledge of the formulae for a particle free fall in Physics and most certainly, a good understanding of the notion of similarity…