Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

Most mathematics assignments consist of a group of problems requiring the same strategy. For example, a lesson on the quadratic formula is typically followed by a block of problems requiring students to use the quadratic formula, which means that students know the appropriate strategy before they read each problem. In an alternative approach,…

This study explored the problem solving experience of pre-service teachers in finding the greatest common factor and the least common multiple using many different approaches. In particular, it examined the effect of pre-service teachers' mathematics content knowledge on how they chose their preferred approach and how they valued the most…

This naturalistic case study investigates the problem posing patterns that emerge as four small groups of 12 year old students in Western Canada work collectively on a structured mathematics task. A method of data analysis is introduced that blurs the data to create transcript "tapestries" providing visual evidence of collective patterns…

The study described herein is part of a larger, inclusive research study exploring the effects of model-eliciting activities (MEAs) of "real-life" situations on the development of students' mathematical creativity. This part aim at revealing students' cognitive abilities that are involved in the creative modeling processes using a…

An historical case is presented in which extra-mathematical certainties lead to invalid mathematics reasonings, and this is compared to a similar case that arose in the area of virtual education. A theoretical-methodological instrument is proposed for analysis of certainties. The article suggests the need for teachers to be aware that certainties…

The article contains the results of the study conducted in order to discover the most effective ways of developing students' programming abilities with the means of non-programming disciplines and activities. The authors observe the learning practices and habits employed by students with highly developed programming abilities and compare these…

The present work studies the influence of leisure activities on the creative intelligence of the students. An experimental pre- and post-test design was carried out with individuals selected in a sampling process. The design identifies the ease of students to place themselves in possible contexts and solve them mathematically through Polya's…

Creative thinking is very important in the modern era so that it should be improved by doing efforts such as making a lesson that train students to pose their own problems. The purposes of this research are (1) to give an initial description of students about mathematical creative thinking level in Problem Posing Model with Lesson Study approach…

The Department of Basic Education in South Africa has identified factorisation as a problem area in Mathematics teaching. Learners in earlier grades are exposed to mathematical tasks, involving concepts, such as factors of integers, fractions, equivalent fractions and prime numbers, that are easier to solve when the divisibility rules are applied.…

5th graders (n=527) were randomly assigned to self-explain worked examples (WE) or solve problems during a yearlong study. WE students learned more algebra skills when given algebra worked examples on an end-of-year transfer measure. Comparing attempts, conceptual, and mechanical correctness by condition, results demonstrated that the condition…

Being part of the German didactic tradition, reflective thinking was first coined by Wilhelm von Humboldt two-century ago. Reflective thinking helps individuals to develop strategies in order to overcome the problems that they encounter. Investigating the reflective thinking skills of students for problem solving is important to identify students…

When implementing large-scale educational computing initiatives (e.g., One Laptop Per Child) it is vital to allocate resources for training, support, and device deployment judiciously. One question that arises is how learners' engagement with online educational resources is affected by receiving a new computer; do the benefits justify the costs?…

With the advent of No Child Left Behind (2002), the academic expectations of students with disabilities have changed. Students with disabilities are now held to the same academic standards as their peers without disabilities. Furthermore, the 2004 provisions in the Individuals With Disabilities Education Improvement Act state that students with…

This study reports findings from a teaching experiment in which 4th grade children engaged in solving multiplication tasks with rectangular arrays in a computer environment. The environment provided flexible task-solving through dynamic virtual manipulatives (VMs) so children could use their existing knowledge of multiplication to complete array…