Ariadne is a touch-based program for the learning of homotopies of paths, without the use of formalism, by building mental models. Using Ariadne, the user can construct points, paths by dragging points and homotopies by dragging paths as well as compute winding numbers of paths, all on a variety of surfaces, through touch gestures. Ariadne…

This article highlights the main ideas that underlie the differences in potential pragmatic knowledge constructs students experience when solving problems, between the zone of proximal development (ZPD) and the zone of potential construction (ZPC). This qualitative research is based on a phenomenological approach to finding the meaning of things…

The most important ingredient of the pedagogy for teaching non-majors is getting their engagement. This paper proposes to use gamification to engage non-majors. An innovative game termed as Cover the Hungarian's Zeros is designed to tackle the common weakness of non-majors mathematics in solving the assignment problem using the Hungarian Method.…

Robust knowledge serves as a common instructional target in academic settings. Past research identifying characteristics of experts' knowledge across many domains can help clarify the features of robust knowledge as well as ways of assessing it. We review the expertise literature and identify three key features of robust knowledge (deep,…

Mathematics word-problems continue to be an insurmountable challenge for many middle school students. Educators have used pictorial and schematic illustrations within the classroom to help students visualize these problems. However, the data shows that pictorial representations can be more harmful than helpful in that they only display objects or…

Mike Rose, author of "The Mind at Work," extols both the wholesome, pragmatic qualities of handcraft and the implicit intellectual skills required of its practitioners. His recent article, "Rethinking Remedial Education and the Academic-Vocational Divide," is titled with a call to action; in these few words alone, Rose problematizes the polar…

This paper reports on the findings from individual interviews and focus group discussions involving six teachers implementing the Singapore Mathematics Curriculum (SMC) in the Foundation Phase (Grade R to Grade 3) in a school in South Africa. The interviews presented an opportunity to explore teachers' experiences with their attempts to use the…

Studying physics for nonphysics majors at college level is usually a process of learning new problem-solving skills and sometimes seems a frustrating experience. In an attempt to provide students with more learning resources, online homework was required to supplement the instruction. This study reveals the role of the online homework assignments…

A group theory course for chemists was taught entirely with process oriented guided inquiry learning (POGIL) to facilitate alternative strategies for learning. Students completed a test of one aspect of visuospatial aptitude to determine their individual approaches to solving spatial tasks, and were sorted into groups for analysis on the basis of…

Teachers of gifted students often are challenged to find ways to stimulate critical thinking and problem-solving skills. School chess clubs are one way of meeting that challenge. This article poses how games such as chess affect learning and gifted students. Two detailed strategies for teaching chess to students beginning in kindergarten are…

In 3 experiments, we examined the effects of using concrete and/or abstract visual problem representations during instruction on students' problem-solving practice, near transfer, problem representations, and learning perceptions. In Experiments 1 and 2, novice students learned about electrical circuit analysis with an instructional program that…

The immersive method is a new concept of visual education that is better suited to the needs of students in contemporary post-industrial society. The features of the immersive method are: (1) it emerges from interaction with visual culture; (2) it encourages understanding of contemporary art (as an integral part of visual culture); and (3) it…

Justification is a core mathematics practice. Although the purposes of justification in the mathematician community have been studied extensively, we know relatively little about its role in K-12 classrooms. This paper documents the range of purposes identified by 12 middle grades teachers who were working actively to incorporate justification…

Research has shown that for acquiring problem-solving skills, instruction consisting of studying worked examples is more effective and efficient for novice learners than instruction consisting of problem-solving. This study investigated whether worked examples would also be a useful instructional format for the acquisition of visual perceptual…

Teaching students to use and interpret representations in science is critically important if they are to become scientifically literate and learn how to communicate their understandings and learning in science. This study involved 248 students (119 boys and 129 girls) from 26 grade 6 teachers' classes in nine primary schools in Brisbane,…