Traditional rote learning methods often fail to adequately develop reasoning skills in mathematics, particularly among pre-university students. This study addresses challenges in fostering mathematical reasoning abilities, as evidenced by declining TIMSS results and resistance to pedagogical innovations. My online teaching with GeoGebra (MyOT_G+)…

This paper concerns the design of a specific computer-based educational environment fostering students' shift from argumentation to proof in geometry. In particular, we focus on the language difficulties that such a shift might present and on the need for suitable interventions to overcome them. In this respect, we designed a specific device,…

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are…

In this study we examine the use of cumulative and exploratory talk types in a year 5 computer supported collaborative learning environment. The focus for students in this environment was to participate in mathematical problem solving, with the intention of developing the proficiencies of problem solving and reasoning. Findings suggest that…

We examined whether "discrete trial training" (DTT) could be used to identify learning impairments in mathematical reasoning in boys with fragile X syndrome (FXS). Boys with FXS, aged 10-23 years, and age and IQ-matched controls, were trained to match fractions to pie-charts and pie-charts to decimals either on a computer or with a…

Proving in school geometry is not just about validating the truth of a claim. In the school setting, the main function of the proof is to convince someone that a claim is true by providing an explanation. Students consider proving to be difficult; in fact, they find the very concept of proof demanding. Proving a claim in planar geometry involves…

Mathematics educators frequently extol the virtues of inquiry-based instruction to classroom teachers. Although research suggests that inquiry benefits learners by allowing them to make sense of the mathematics they encounter, particularly through discourse with peers, to assume that all (or even most) teachers successfully create and implement…

Research has shown that affordances of computers may be exploited in the design of mathematical tasks so as to provide interesting and challenging activities. At the same time, opportunities for learning mathematics may be constrained if the design of the task is not appropriate. A tool which allows teachers, researchers and task designers to…

Geometry theorem proving involves skills that are difficult to learn. Instead of working with abstract and complicated representations, students might start with concrete, graphical representations. A proof tree is a graphical representation of a formal proof, with each node representing a proposition or given conditions. A computer-assisted…

This study is part of a large research and development project aimed at observing, describing and analyzing the learning processes of two seventh grade classes during a yearlong beginning algebra course in a computer intensive environment (CIE). The environment includes carefully designed algebra learning materials with a functional approach, and…

In the summer of 2009, a professional development partnership was established between the Peoria Public School District (PPSD), a local education agency (LEA), and Illinois State University (ISU) to improve geometric and trigonometric knowledge and skill for high school mathematics teachers as part of the Illinois Mathematics and Science…

We present results from a study which investigated the influence of dynamic geometry-based activities in the development of proving skills (in geometry) in high-school students (15-16 years of age). After a 12-week course on Cabri and the writing of conjectures and proofs, students were asked to write and prove conjectures based on their…

The objectives of this research were to review existing computer-assisted instruction systems for propositional calculus proofs or elementary logic and to develop an instructional computer program that guides students in the valid construction of propositional calculus proofs. The system is unique in that it provides assistance at each step of the…

This paper provides an historical perspective on the possible roles of cognitive technologies in thinking as "reorganizers" of the mind. It suggests that by understanding the transformational roles of advanced technologies for mathematical thinking, positive contributions can be made to research and practice on the use of computers in…

This paper describes a Personal Intelligent Mentor (PIM) that facilitates metacognitive development in the domain of solving logic word puzzles. Metacognition is an important aspect for critical thinking skills. High school students must develop logical and critical thinking abilities as a prerequisite for higher-level math and computer…