This article reports on a study in which third-grade students (8-9 years) were given a degree of agency in conducting chance experiments and representing the outcomes. Students chose their own samples of 12 coloured counters, ensuring all colours were represented. They predicted the outcomes of item selection, tested their predictions, explained…

It's not surprising that rainbows have received a great deal of attention: in textbooks, in magazines, and on the web. They are, after all, beautiful, fascinating, occasionally awe-inspiring, even a little mysterious. They are an almost perfect blend of natural beauty and simple physics. Has everything that can be said about rainbows already been…

This paper focuses on the emergence of abstraction through the use of a new kind of motion detector--WiiGraph--with 11-year-old children. In the selected episodes, the children used this motion detector to create three simultaneous graphs of position vs. time: two graphs for the motion of each hand and a third one corresponding to their…

We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…

This study sets for itself the task of constructing a learning trajectory for the fundamental theorem of calculus (FTC) that takes into account the interaction with an educational digital tool. Students were asked to explain the connections between interactive and multiple-linked representations in an educational digital tool, and to conjecture…

In selecting from a repertoire of traditional kinetics experiments, an instructor often has to choose among having students gain experience with the graphical method, the method of initial rates, or a temperature-dependent experiment in which students construct an Arrhenius plot. This paper presents an environmentally friendly bleaching reaction…

Creating charts and graphs is all about visual abstraction: the process of representing aspects of data with imagery that can be interpreted by the reader. Children may need help making the link between the "real" and the image. This abstraction can be achieved using symbols, size, colour and position. Where the representation is close to what…

The activities described here allow students to explore the concept of diffusion with the use of common equipment such as computers, webcams and analysis software. The procedure includes taking a series of digital pictures of a container of water with a webcam as a dye slowly diffuses. At known time points, measurements of the pixel densities…

The different combinations involved in additive and subtractive colour mixing can often be difficult for students to remember. Using transmission graphs for filters of the primary colours and a numerical scheme to write out the relationships are good exercises in analytical thinking that can help students recall the combinations rather than just…