Teacher gestures support mathematics learning and promote student collaboration. Aligned with speech, gestures can help students to notice the important visual information of geometry tasks. However, students' visual attention to the teacher's gestural cues during collaborative problem solving remains a largely unexplored field in mathematics…

Promoting mathematical creativity is an important aim of mathematics education, which may be promoted by engaging students with open-ended tasks. Most studies of students' creativity have investigated the creativity of students working individually. This study concerns the mathematical creativity of students working as individuals as compared with…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

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…

Eye tracking is getting increasingly popular in mathematics education research. Studies predominantly rely on the so-called eye-mind hypothesis (EMH), which posits that what persons fixate on closely relates to what they process. Given that the EMH was developed in reading research, we see the risk that implicit assumptions are tacitly adopted in…

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students' ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were…

Although mathematical practice has traditionally valued two distinct kinds of mathematical work--referred to by Gowers (2000) as theory building and problem solving--activity in classrooms appears to be organized largely around the latter, rather than the former. This study takes up the question of whether there is a customary role for theory…

We explored transformations that teachers made to modify geometry proof problems into investigation problems and analyzed how these transformations differ in teachers who use a dynamic geometry environment (DGE) in their classes and those who do not. We devised a framework for the analysis of problem transformations and types of teacher-generated…

In the field of human cognition, language plays a special role that is connected directly to thinking and mental development (e.g., Vygotsky, "1938"). Thanks to "verbal thought", language allows humans to go beyond the limits of immediately perceived information, to form concepts and solve complex problems (Luria, "1975"). So, it appears language…

Our main goal in this study is to exemplify that a meticulous design can lead pre-service teachers to engage in productive unguided peer argumentation. By productivity, we mean here a shift from reasoning based on intuitions to reasoning moved by logical necessity. As a subsidiary goal, we aimed at identifying the kinds of reasoning processes…

Reports on a study in which three 3rd grade students were presented with the volume of cuboids. Examines the problem solving actions students demonstrate and analyzes students' strategies and solutions. Explores the connection between spatial structuring and the use of numerical operation. Considers perseverance and control emerging when solving…

Contains an analysis of the activities of 12-year-old students solving problems of polygonal tilings and presents two categories of the thinking processes of these students: instantaneous thinking resulting in perceptions of simple structures and discursive thinking appearing in drawing activities and arguments of proofs. (13 references)…

Reports, in French, an investigation on the use of graphic representations in problem-solving tasks of the type in Spanish Mathematical Olympiads. Analysis showed that the choice and interpretation of the first graphic representation played a decisive role in the discovery of the solution. (34 references) (Author/MKR)

Discusses some aspects of the defining process in geometrical context in the reference frame of the theory of "figural concepts." Presents analysis of some examples taken from a teaching experiment at the sixth-grade level. Contains 30 references. (Author/ASK)