Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

Through a series of four papers, this dissertation investigates developmental mathematics students' experiences with relearning, or the experience of learning about content one has already tried to learn in a previous mathematics course. Developmental math courses typically focus on K-12 algebra, and are required for graduation but notorious for…

Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

Conceptual approaches to contemporary physics topics pose many learning challenges. One factor influencing knowledge integration is a student's epistemic framing. Epistemic frames provide a context within which a particular situation is perceived, interpreted, and judged. The objective of this study is to explore secondary students' framings…

The metaphors used by teachers to explain the nature of student learning and student difficulty can reveal a great deal about how teachers conceive the teaching and learning process. This is an important area of research as it can shed light on how they see their role in the learning process and how they should intervene to assist students in…

This article describes students learning to build their own numbering system by recognizing and identifying patterns with interlocking cubes in different place values. The students used the Egyptian hieroglyphic numeral system in conjunction with this activity to connect learning in other subjects. Students used prior knowledge of place value to…

This article reflects on the author's experience of developing a standalone geographies of sport module that is taught using an active blended learning (ABL) approach. The article argues that an ABL pedagogy is an effective way of teaching meaningful sports geography to undergraduate students. It discusses how the approach allows a diverse range…

Literature suggests that "current characterizations of the terms procedural knowledge and conceptual knowledge are limiting and are, in fact, impediments to careful investigation of these constructs" (Star, 2005, p. 405). We examined secondary mathematics teachers' understanding of procedural and conceptual knowledge at superficial and…

Most chemistry students struggle with interpreting and understanding NMR (nuclear magnetic resonance) spectra and the general concepts of NMR spectroscopy. NMR spectroscopy seems to be difficult to both teach and learn. Therefore, the corresponding courses should be investigated in more detail. We conducted a survey with N = 39 German university…

Media resources are a central component of families' learning ecologies in the U.S. At the start of the COVID-19 pandemic, the information ecosystem was flooded with content about the SARS-CoV-2 virus and personal protection measures. However, much of the coverage came through channels for adult audiences, and the 'infodemic' added to the…

A scientific conceptual understanding of photosynthesis and respiration provides an important basis for understanding nature and the regulations of life. Photosynthesis and respiration are complex processes, and learning about them requires a proper understanding of their various aspects, from molecular biology to the ecosystem level. This study…

Children often learn abstract mathematics concepts with concrete manipulatives. The current study compared different ways of using specific manipulatives -- base-ten blocks -- to support children's place value knowledge. Children (N = 112, M age = 6.88 years) engaged in place value learning activities in one of four randomly assigned conditions in…

Empirical evidence is insufficient on the specific roles GIS learning plays in developing students' understanding various spatial concepts. The present study aims to draw attention to common struggles of learning some spatial concepts in geography and offer directions for future research on GIS learning and the development of student spatial…

Programming is becoming increasingly common in mathematics degrees as it is a desirable skill for new graduates. However, research shows that its use is mostly restricted to computational or modelling tasks. This paper reports a study on students' perceptions of and difficulties with Lean, an interactive theorem prover introduced as part of a…

As technology-enhanced children's learning has gained wide attention, programmable robots have been gradually introduced in early childhood education. Hence, it would be valuable to understand how young children perceive robot programming learning. Draw-a-picture technique is an ideal method to elicit ideas, thoughts, and feelings for children…