The English National Curriculum Programmes of Study emphasise the importance of knowledge, understanding and skills, and teachers are well versed in structuring learning in those terms. Research outcomes into how long-term memory is stored and retrieved provide support for structuring learning in this way. Four further messages are added to the…

Imagine high school students glued to computer screens--not playing video games but applying their mathematical knowledge of functions to the design of three-dimensional sculptures. Imagine these students engaging in rich discourse as they transform functions of their choosing to design unique creations. Now, imagine these students using…

The implementation of the distance learning and e-learning in technical disciplines (like Mechanical and Electrical Engineering) is still far behind the grown practice in narrative disciplines (like Economy, management, etc.). This comes out from the fact that education in technical disciplines inevitably involves laboratory exercises and this…

The idea of using a dice game to simulate radioactive decay is not new. However, modern pedagogy encourages, if not requires, us to provide multiple representations and visualizations for our students. The advantage of interactive engagement methods also has been made clear. Here we describe a highly visual and interactive use of dice to develop…

Of the eight practices of science identified in "A Framework for K-12 Science Education" (NRC 2012), helping students develop and use models has been identified by many as an anchor (Schwarz and Passmore 2012; Windschitl 2012). In instruction, disciplinary core ideas, crosscutting concepts, and scientific practices can be meaningfully…

Interactive teaching with larger groups of students can be a challenge, but the use of mobile electronic devices by students (smartphones, tablets, laptops) can be used to improve classroom interaction. We have examined several types of tasks that can be electronically enacted in classes and practical courses using these devices: multiple choice…

Developing "Thinking and Understanding in Young Children" presents a comprehensive and accessible overview of contemporary theory and research about young children's developing thinking and understanding. Throughout this second edition, the ideas and theories presented are enlivened by transcripts of children's activities and conversations taken…

A fundamental component of mathematical learning is spatial visualization. To improve their spatial visualization skills, students should be given opportunities to work with two- and three-dimensional objects. The authors describe two activities that use tetrahedra nested within cubes to help improve students' visualization of two- and…

Since Java applets seem to be on the retreat in web application, other approaches for displaying interactive mathematics in the web browser are needed. One such alternative could be our open-source project JSXGraph. It is a cross-browser library for displaying interactive geometry, function plotting, graphs, and data visualization in a web…

Drawing on cartography, urban design and visual data modelling, we consider how people navigate, or fail to navigate, the mental, physical and social spaces of knowledge communities. Cartographically inspired critical thinking offers opportunities to re-examine the assumptions and formal maps of post-secondary institutions, visualizing…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

It is well documented that many successful individuals are challenged by cognitive-based disabilities that impact their performance in school and on tests. While commonly believed to be related mostly to the constructs of processing speed or reading fluency, there are other aspects of cognition that affect how an individual interacts with the…

The increasing popularity of R is leading to an increase in its use in undergraduate courses at universities (R Development Core Team 2008). One of the strengths of R is the flexible graphics provided in its "base" package. However, students often run up against its limitations, or they find the amount of effort to create an interesting plot may…

Visualization of mathematical relationships enables students to formulate conjectures as well as to search for mathematical arguments to support these conjectures. In this project students are asked to discover the sufficient and necessary condition so that two circles form the circumscribed and inscribed circle of a triangle and investigate how…

Solid modeling is widely used as a teaching tool in summer activities with high school students. The addition of motion analysis allows concepts from statics and dynamics to be introduced to students in both qualitative and quantitative ways. Two sets of solid modeling projects--carnival rides and Rube Goldberg machines--are shown to allow the…