Conjecturing has been considered to inspire the need for proof, enhance the understanding of proofs, and construct a valid proof. This study describes students' processes of formulating a Euclidean geometry conjecture in the form of a conditional statement through constructing a geometric figure and using measuring and dragging modalities of a…

The purpose of this work was to explore how elementary pre-service' teachers (PSTs) responded to a volume task that asked for a coordination of changes in one dimension with changes in volume. We carried out both written pre-assessments and follow-up interviews with seventeen PSTs, focused on exploring volume content knowledge. Our findings…

Students' issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students' outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads…

Given the centrality of angle in mathematics curricula and scarcity of research in this area, we investigated 64 PTs' assimilatory domains of angularity by analyzing the angles they indicated when presented with four segments mutually sharing an endpoint. In both interview and written settings, we found PTs were more likely to recognize convex…

The purpose of this study was to analyze the prompts that preservice secondary mathematics teachers used for the acquisition of mathematics knowledge in dynamic geometry environment tasks. The participants, four preservice secondary mathematics teachers who were enrolled in a computer-supported mathematics education course, designed a dynamic…

We examined high school geometry students' written work on four proof tasks where they posed a conjecture, drafted an argument, provided written critiques, then revised their argument based on peer feedback. Students' written work across the tasks was analyzed to determine whether the instructional sequence supported them in improving their…

A digital wall is a tool for students to structure and register their online work on mathematical problem-solving activities that involve the coordinated use of digital technologies. How could students use such digital wall to understand mathematical concepts and to develop problem-solving competencies? The aim of this study is to analyze and…

This study explores the progression from student justification to generalization in the course of example-based reasoning. Data was collected through group interviews with high school students who were working collaboratively on a task of determining connections between perimeter and area of tile shaped patterns. The task called for making and…

A theoretical model describing young students' (Grades 1-3) functional-thinking modes was formulated and validated empirically (n = 345), hypothesizing that young students' functional-thinking modes consist of recursive patterning, covariational thinking, correspondence-particular, and correspondence-general factors. Data analysis suggested that…

This study explored prospective middle school mathematics teachers' developing understanding of geometric transformations through designing and implementing an instructional unit in a technology supported classroom environment. The instructional unit including seven activities was developed by considering past research on learners' pre-existing…

This paper focuses on pre-service mathematics teachers' geometrical construction processes while using a duo of artefacts, namely the paper-and-pencil environment (PPE) and a dynamic geometry system (DGS). The participants of this case study were two pre-service mathematics teachers, who had limited DGS experiences in solving geometry tasks. The…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

Technical Graphics is one of the technology subjects taught at Junior Certificate level in post- primary schools in Ireland. The Junior Certificate examination is held at the end of the Junior Cycle in post-primary schools, which caters for students aged from 12 to 15 years. As a teacher of Technical Graphics for the past seven years, I have…

Awareness of one's own strengths and weaknesses during visualisation is often initiated by the imagination -- the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West…

This paper attempted to make explicit some of the underlying characteristics of spatial visualisation using the concept of area of composite shapes. By engaging students with metric-free tasks, we identify the type of perceptual and visual/spatial manoeuvres that they deploy in such situations. Interview data collected from three students in Grade…