Mental model (Johnson-Laird, 2001) and probabilistic theories (Oaksford & Chater, 2009) claim to provide distinct explanations of human reasoning. However, the dual strategy model of reasoning suggests that this distinction corresponds to different reasoning strategies, termed "counterexample" and "statistical,"…

In addressing the challenge of fostering functional thinking (FT) in secondary school students, our research centered on the question of how an embodied design can enhance FT's different aspects, including input-output, covariation, and correspondence views. Drawing from embodied cognition theory and focusing on an action- and perception-based…

Background: Research on causal reasoning often uses group-level data analyses that downplay individual differences and simple reasoning problems that are unrepresentative of everyday reasoning. In three empirical studies, we used an individual differences approach to investigate the cognitive processes people used in fault diagnosis, which is a…

Contribution: This research provides insights into the applications of virtual reality (VR) in learning spatial reasoning, which could be utilized and developed in educational frameworks and settings, especially in science, technology, engineering, arts, and mathematics (STEAM), and other aspects. Background: Spatial reasoning and VR are essential…

Mathematical writing is one way for primary students to communicate their mathematical thinking. Research in the field of writing has shown that to become an effective teacher of writing, preservice teachers must have experience engaging in the kinds of writing given to their students. The study reported in this paper explored how 27 preservice…

Generalisation is a skill that enables learners to acquire knowledge in general, and mathematical knowledge in particular. It is a core aspect of algebraic thinking and, in particular, of functional thinking, as a type of algebraic thinking. Introducing primary school children to functional thinking fosters their ability to generalise, explain and…

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…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

Secondary school pupils underachieve in tests in which reasoning abilities are required. Brain-based training of working memory (WM) may improve reasoning abilities. In this study, we use a brain-based training programme based on historical content to enhance reasoning abilities in history courses. In the first experiment, a combined intervention…

Legal reasoning is a type of problem solving, and is situated within thinking skills, one of the six threshold learning outcomes established under the auspices of the Australian Learning and Teaching Council's Bachelor of Laws Learning and Teaching Academic Standards Statement. The threshold learning outcomes define what law graduates are…

Ratio, rate, and proportion are central ideas in the Common Core State Standards (CCSS) for middle-grades mathematics (CCSSI 2010). These ideas closely connect to themes in earlier grades (pattern building, multiplicative reasoning, rational number concepts) and are the foundation for understanding linear functions as well as many high school…

The QEP that was implemented in this study focused on enhancing students' critical thinking skills. A pretest/posttest approach was used to assess students' critical thinking progress in freshman level core English and Math courses. An intervention was performed involving intensive instruction and assignments relating to a set of reasoning…

The purpose of this research study was to learn about students' conceptions concerning the line of best fit just prior to their introduction to the topic. Task-based interviews were conducted with thirty-three students, focused on five tasks that asked them to place the line of best fit on a scatterplot and explain their reasoning throughout the…