Technology provides the means to create useful learning and practice environments for learners. Well-designed cognitive tutor systems, for example, can provide appropriate learning environments that feature cognitive supports (ie, scaffolding) for students to increase their procedural knowledge. The purpose of this study was to conduct a series of…

This study explored the quality of arguments used by first-year engineering university students enrolled in a traditional physics course dealing with electromagnetic induction and related problem solving where they had to assess whether the electromagnetic induction phenomenon would occur. Their conclusions were analyzed for the relevance of the…

Sometimes Computer Algebra Systems (CAS) offer an answer that is somewhat different from the answer that is probably expected by the student or teacher. These (somewhat unexpected) answers could serve as a catalyst for rich mathematical discussion. In this study, over 120 equations from school mathematics were solved using 8 different CAS. Many…

Students learning to separate variables in order to solve a differential equation have multiple ways of correctly doing so. The procedures involved in "separation" include "division" or "multiplication" after properly "grouping" terms in an equation, "moving" terms (again, at times grouped) from…

Knowledge-based environmental education has been consistently found to be limited in its effectiveness due to its small and indirect role in promoting sustainable behavior, while focusing on the impact of social context has been found to be more conceptually relevant. Transformative learning theory is positioned to be foundational to environmental…

The Monty Hall dilemma (MHD) is a counterintuitive probability problem in which participants often use misleading heuristics, such as the equiprobability bias. Finding the optimal solution to the MHD requires inhibition of these heuristics. In the current study, we investigated the relation between participants' equiprobability bias and their MHD…

Since 1950, the Prisoner's Dilemma has intrigued economists and amused fans of mathematics. It presents a situation in which two players acting to their own advantage do not do as well together as two players whose actions oppose their individual interests--hence, the dilemma. Variations of the Prisoner's Dilemma have appeared in diverse…

Students with mathematics difficulty demonstrate lower mathematics performance than typical-performing peers. One contributing factor to lower mathematics performance may be misunderstanding of mathematics symbols. In several studies related to the equal sign (=), students who received explicit instruction on the relational definition (i.e.,…

The Indian National Curriculum Framework has as one of its objectives the development of mathematical thinking and problem solving ability. However, recent studies conducted in Indian metros have expressed concern about students' mathematics learning. Except in some private coaching academies, regular classroom teaching does not include problem…

In this paper we propose an approach to organizing Adaptive Problem-Based Learning (PBL) leading to the development of Higher-Order Thinking (HOT) skills and collaborative skills in students. Adaptability of PBL is expressed by changes in fixed instructor assessments caused by the dynamics of developing HOT skills needed for problem solving,…

Students at a large urban community college enrolled in seven classes of an experimental remedial algebra programme, which integrated study skills instruction and collaborative problem solving. A control group of seven classes was taught in a traditional lecture format without study skills instruction. Student performance in the course was…

This article reports on a longitudinal observation study about students' development in their use of procedures to calculate instantaneous rate of change. Different procedures for solving tasks on rate of change are taught in mathematics and physics classes, and together they form a repertoire. Our study took an actor-oriented perspective, which…

Purpose: The purpose of this paper is to discuss the current context, scope and problems in the provision of work-integrated learning (WIL) in legal education and how the adoption transformative pedagogies in WIL which is offered in legal education can foster personal and social transformation in addition to enhancing lawyering skills. The paper…

In this article, Scott Smith presents an innocent problem (Problem 12 of the May 2001 Calendar from "Mathematics Teacher" ("MT" May 2001, vol. 94, no. 5, p. 384) that was transformed by several timely "what if?" questions into a rewarding investigation of some interesting mathematics. These investigations led to two…

Recent studies reveal that children can solve proportional reasoning problems presented with continuous amounts that enable intuitive strategies by around 6 years of age but have difficulties with problems presented with discrete units that tend to elicit explicit count-and-match strategies until at least 10 years of age. The current study tests…