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…

Reduction is a problem-solving strategy, relevant to various areas of computer science, and strongly connected to abstraction: a reductive solution necessitates establishing a connection among problems that may seem totally disconnected at first sight, and abstracts the solution to the reduced-to problem by encapsulating it as a black box. The…

Many under-prepared university students do not know how to study (Martin and Arendale 1993) because they have not yet developed the abstract reasoning skills that allow them to learn new ideas simply by reading a text or listening to a lecture. This article draws from selected findings from a PhD study currently being undertaken at a university in…

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,…

Between 1985 and 1988 eight colleges implemented a "Thinking Across the Curriculum" program and a procedure for assessing the impact of the program on the cognitive development and thinking skills of students. One hundred and twenty faculty members participated in the project and approximately 1,800 students studied in courses developed…