This article assesses how people reason with categories whose features are related in causal cycles. Whereas models based on causal graphical models (CGMs) have enjoyed success modeling category-based judgments as well as a number of other cognitive phenomena, CGMs are only able to represent causal structures that are acyclic. A number of new…

In this paper, we contend that what to teach about scientific reasoning has been bedeviled by a lack of clarity about the construct. Drawing on the insights emerging from a cognitive history of science, we argue for a conception of scientific reasoning based on six "styles of scientific reasoning." Each "style" requires its own…

This article describes how to play two abstract strategy board games: (1) "Blokus" which uses polyominoes--plane geometric figures formed by joining one or more equal squares edge to edge; and (2) "Gemblo" which uses translucent, colored pieces, each of which is made up of one to five hexagons.

After describing Wittgenstein's notion of "certainty", in this article I provide four arguments to demonstrate that no certainty can be acquired at will. Specifically, I argue that, in order to assimilate a certainty, it is irrelevant whether the individual concerned (1) has found a ground that seemingly justifies that certainty; (2) has…

To contribute to the sparse educational research on student understanding of eigenspace, we investigated how students reason about linear combinations of eigenvectors. We present results from student reasoning on two written multiple-choice questions with open-ended justifications involving linear combinations of eigenvectors in which the…

The main aim of the present investigation was to examine conditional reasoning skills in college students whose educational past had emphasized verbatim learning. A successive independent-samples design was utilized to explore the effects of instruction that explicitly targeted critical thinking principles in either freshman students or…

One of the challenges that commencing university students in computing degree programs face is the difficulty in engaging with the abstract and complicated theories in the computing discipline. In particular, it is hard for beginner computer architecture students to visualise the link between the theory of digital logic and the behaviour of the…

Complex thinking is a desired competency in 21st-century university students, so technology-based teaching and learning strategies must be carefully considered when training them in complex reasoning skills. This systematic review aims to map research on the use of teaching and learning strategies supported by technology to enhance complex…

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…

In 'Against Stored Abstractions,' Ambridge uses neural and computational evidence to make his case against abstract representations. He argues that storing only exemplars is more parsimonious -- why bother with abstraction when exemplar models with on-the-fly calculation can do everything abstracting models can and more -- and implies that his…

Students in the elementary grades often experience difficulty setting up and solving word problems. Using an equation to represent the structure of the problem serves as an effective tool for solving word problems, but students may require specific pre-algebraic reasoning instruction about the equal sign as a relational symbol to set up and solve…

A national survey of social work educators teaching in CSWE-accredited social work education programs in the United States was conducted to explore their perceptions about integrating social justice content into their teaching. A content analysis of written commentary provided by 139 educators revealed four key areas relevant to their efforts: (a)…

Research on mathematical modeling is growing rapidly in the field of mathematics education, and there are numerous benefits of engaging students in modeling activities. However, mathematical modeling is still marginalized in mathematics instruction. In order to understand the challenges and obstacles secondary teachers face to incorporate modeling…

The derivative framework described by Zandieh (2000) has been an important tool in calculus education research, and many researchers have revisited the framework to elaborate on it, extend it, or refine certain aspects of it. We continue this process by using the framework to put forward a suggestion on what might constitute a "target…

Recent discussions of leadership paradoxes have suggested that managers who can hold seemingly opposed, yet interrelated perspectives, are more adaptive and effective. One such paradox that has received relatively little attention is the "Stockdale Paradox," named after Admiral James Stockdale, an American naval officer who was held…