This article highlights the importance of re-defining units unconventionally with fractions. We provide three examples of tasks Grade 5 students engaged in; we highlight the creative ways that they flexibly re-defined units and engaged deeply with fractions. We offer suggestions for supporting unconventional units for promoting conceptual…

This study established whether 12 South African secondary school physics students had incorrect conceptions of basic magnetism and if they had, to what extent they consistently applied such conceptions. Different scenarios in the form of thought experiments were presented in a clinical interview approach. A complex systems perspective underpinned…

The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children's understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also…

Spatial reasoning, the ability to mentally represent and transform objects and their relations, is considered so closely connected to mathematics that there is no longer a question of whether the two are related. Instead, there remains debate about how to answer the question of why. This paper explores the way the two fields of mathematics…

Suzuki-Miyaura coupling reactions are well-known among the most versatile catalytic C-C bond formation reactions. Two different routes of C-C bond Suzuki-Miyaura coupling reactions for the undergraduate organic chemistry laboratory courses have been designed and explained. A two-step reaction involving a catalyst preparation as the first step and…

This article examines whether geography can provide the powerful knowledge that is a key element of a Future 3 curriculum, and an important component of the GeoCapabilities Project's proposals for the teaching of geography. Powerful knowledge is knowledge that gives students the intellectual ability to analyse, explain, predict, evaluate and think…

Within a study of student reasoning in abstract algebra, we encountered the claim "division and multiplication are the same operation." What might prompt a student to make this claim? What kind of influence might believing it have on their mathematical development? We explored the philosophical roots of "sameness" claims to…

Binary operations are one of the fundamental structures underlying our number and algebraic systems. Yet, researchers have often left their role implicit as they model student understanding of abstract structures. In this paper, we directly analyze students' perceptions of the general binary operation via a two-phase study consisting of task-based…

A bouncing rubber ball under a motion sensor is a classic of introductory physics labs. It is often used to measure the acceleration due to gravity, and can also demonstrate conservation of energy. By observing that the ball rises to a lower height upon each bounce, posing the question "What is the main source of energy loss?" and…

The use of cartoons, songs, and quotes can be a useful way to engage students in discussion and learning key concepts about quantifying the uncertainty in statistical estimates.

Variation and variability are key concepts in K-16 statistics education. Prior research has investigated students' reasoning about variability in different contexts. However, there is a lack of research on students' development of understanding of variability when comparing distributions in bar graphs, dot plots, and histograms as they took an…

We previously proposed a hypothetical learning progression around the disciplinary core idea of the Solar System and its formation as a first step in a research program to begin to fill this gap and address questions of student learning in this domain. In this study, we evaluate the effectiveness of two dimensions within the learning progression,…

Using a qualitative analysis of school artifacts, this article analyzes the documentary record of one Christian school system's experience with technological change. It focuses on documentary evidence for how the concept of Christian discernment was deployed to situate new technologies within a Christian discourse. The idea of discernment shifted…

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…

Teaching with analogies is an important pedagogy that helps learners construct abstract conceptions through reasoning with something familiar. Heat concepts were chosen for this study because they have an intangible nature and involve complex mechanisms that often challenge school-aged learners. Learning this kind of complex concept with analogies…