In their recent article on teachers' proportional reasoning, Copur-Gencturk et al. (2022) draw attention to a type of strategy that they call "relative", lodged right between additive and multiplicative thinking. This strategy raised interest in our research team, as it aligned well and helped give stronger meaning to some strategies…

The use of analogies is a well-known teaching strategy to bridge unfamiliar and familiar concepts. However, analogies may become ineffective if the familiar concept is not familiar anymore. For example, this may occur when we describe rotational sense as clockwise and counterclockwise, assuming students know how to read a clock with hour and…

Mark Creager noticed that how we teach students to reason mathematically may be counter-productive to our teaching goals. Sometimes a linear approach, focusing on sub-processes leading to a proof works well. But not always. Students should be made aware that reasoning is not always a straight forward process, but one filled with false starts and…

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 algebraic structure is one of the axiomatic mathematical materials that consists of definitions and theorems. Learning algebraic structure will facilitate the development of logical reasoning, hence facilitating the study of other aspects of axiomatic mathematics. Even with this, several researchers say a lack of algebraic structure sense is a…

In this paper, we seek to evaluate the extent to which students can follow a deductive reasoning chain when it is presented to them. A great deal of instruction in introductory physics courses is centered on presenting students with a logical argument that starts from first principles and systematically leads to a particular conclusion. This…

Due to growing interest in twenty-first-century skills, and critical thinking as a key element, logical reasoning is gaining increasing attention in mathematics curricula in secondary education. In this study, we report on an analysis of video recordings of student discussions in one class of seven students who were taught with a specially…

Drawing on prior research on indirect proof, this paper reports on a series of exploratory studies that examine the extent to which findings on students' ways of reasoning about contradiction and contraposition characterize students' views of indirect existence proofs. Specifically, Study 1 documents students' comparative selections and selection…

Analogical reasoning is a basic learning mechanism. Analogy in teaching science is a very popular pedagogical approach in many countries. The use of analogy is not recognized as one of the formal teaching learning strategies to facilitate students' science learning in Bangladesh. In secondary science teaching, teachers' unconscious and…

At the onset of the coronavirus disease (COVID-19) global pandemic, our interdisciplinary team hypothesized that a mathematical misconception--whole number bias (WNB)--contributed to beliefs that COVID-19 was less fatal than the flu. We created a brief online educational intervention for adults, leveraging evidence-based cognitive science…

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

Teachers readily welcome instructional materials that situate mathematics in the real world because they provide the relevance of mathematics to students who genuinely seek the answer to the question, "When are we ever going to use math in real life?" Although using the real world as a motivational hook is often effective for engagement,…

If an organic chemistry student explains that she represents a mechanistic step because ''it's a productive part of the mechanism,'' what meaning could the professor teaching the class attribute to this statement, what is actually communicated, and what does it mean for the student? The professor might think that the explanation is based on…

The labels used to describe patterns and relations can influence children's relational reasoning. In this study, 62 preschoolers (M[subscript age] = 4.4 years) solved and described eight pattern abstraction problems (i.e., recreated the relation in a model pattern using novel materials). Some children were exposed to concrete labels (e.g.,…

The role of analogies and metaphors has played a significant part in the work on teaching and learning science. This commentary discusses three papers from this current issue that cover a wide range of studies in the spirit of conceptual metaphors--ranging from a study somewhat similar to "classical" conceptual change, to a teacher…