Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term…

The use of visual metaphors has received growing attention in recent years, but their widespread use is not without certain challenges. The most common critique of visual metaphors in teaching indicates that they can be misleading as the meaning attributed by the recipient can be far apart from the intended one. This can make learning less…

This analytic paper explores the challenges that undergraduate students face in understanding introductory physics concepts on circular and rotational motion. Challenges are drawn from researchers' own experiences and from the research literature. An innovative method is proposed that combines practical work, PhET simulations, and a systematic…

We report here on students' views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we…

In recent years computer algebra systems (CAS) have become an integrated part of the upper secondary school mathematics program. Despite the many positive possibilities of CAS, there also seems to be a flip side of the coin in relation to actual difficulties in learning mathematics, not least because a strong dependence on CAS for mathematical…

This article explores the use of pre-recorded video mini-lectures to support and enhance traditional face-to-face lectures for undergraduate students. Mini-lectures guide students through key concepts so that they can understand and assimilate key content before attending lectures.

Any meaningful initiative to improve the teaching and learning in introductory control systems courses needs a clear test of student conceptual understanding to determine the effectiveness of proposed methods and activities. The authors propose a control systems concept inventory. Development of the inventory was collaborative and iterative. The…

Due to the complexity of the legal domain, reasoning about law cases is a very complex skill. For novices in law school, legal reasoning is even more complex because they have not yet acquired the conceptual knowledge needed for distilling the relevant information from cases, determining applicable rules, and searching for rules and exceptions in…

The persistence of students' misconceptions about motion illustrates the enormous difficulty that teachers face in their attempts to overcome these with traditional physics instruction. An understanding of students' ideas about motion and ways to incorporate them into successful instructional approaches can be obtained from an analysis of…

Using the US national sample from the Third International Mathematics and Science Study (TIMSS) and the Rasch modeling method, this study identified the conceptual progression sequence of various matter concept aspects, and compared students' latent abilities against the sequence. We found that the four matter aspects, i.e. conservation, physical…