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…

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…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

The periodic table is recognized as one of the most powerful tools in science. While it is included in virtually all high school and undergraduate general chemistry curricula, it remains a mystery to many chemistry students who find it impossible to decode. Students are often able to predict periodic trends concerning atomic radius, ionization…

The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students' ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical…

This exploratory study uses the convergent design of mixed methods to integrate adaptive expertise theory to study how individual student participant from graphic design or non-graphic-design majors to solve a novel ideation problem in graphic design. Adaptive expertise includes six dimensions: metacognition, flexibility, dynamic knowledge,…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

Categorization in well-known natural concepts is studied using a special version of the Varying Abstraction Framework (Vanpaemel, W., & Storms, G. (2006). A varying abstraction framework for categorization. Manuscript submitted for publication; Vanpaemel, W., Storms, G., & Ons, B. (2005). A varying abstraction model for categorization. In B. Bara,…

Examines the differences between concrete and abstract concepts and their implications for instructional design and teaching. How specific concepts are stored in and retrieved from memory is described, analogies are discussed as an instructional tool in abstract concept learning, and a possible instructional strategy for teaching abstract concepts…

Specific teaching strategies to help hearing-impaired secondary students comprehend abstract concepts include (1) pinpointing facts and fallacies, (2) organizing information visually, (3) categorizing ideas, and (4) reinforcing new vocabulary and concepts. Figures provide examples of strategy applications. (DB)

The purpose of this study was to: (1) investigate the relationship between the learning approaches of high school students, their prior knowledge, and their attitudes toward chemistry, and their performance on a misconceptions test; and (2) describe and analyze the differences between the responses of students of different learning approaches on…

Four experiments investigated children's ability to notice and remember events in which the acquisition of factual information occurs. Results indicated that children tend to report they have known newly learned information for a long time, suggesting that children have some understanding of knowledge acquisition, but not at the level of adults.…

Examined the nature of perceptual classification in children and young adults. Found that most children attend selectively to one stimulus dimension when making perceptual classification judgments. Suggests that this developmental trend does not appear to be a holistic-to-analytic shift but rather a trend toward greater consistency in following a…

An inquiry attempted to build an agenda for research that would result in a cognitive theory of instruction capable of informing educational practice and extending the limits of knowledge about how people learn and develop. What would such a theory look like, how close are we to having one, and what directions must be followed to further its…