Teaching with analogies is an important pedagogy that helps learners construct abstract conceptions through reasoning with something familiar. Heat concepts were chosen for this study because they have an intangible nature and involve complex mechanisms that often challenge school-aged learners. Learning this kind of complex concept with analogies…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students' conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools…

Analytical questions are the types of questions that can lead students to gain an understanding of a concept and explore reasoning. This research is a descriptive, qualitative study investigating the emergence of analytical questions and their interaction patterns in group discussions facilitated by a scientific approach to learning. The subjects…

Historical reasoning, as a disciplinary literacy, aims to develop higher-order thinking in addition to depth of historical knowledge beyond the textbook and memorization of facts. It teaches students to use information across multiple sources to contextualize and corroborate historical accounts, constructing an informed yet critical interpretation…

For several decades, there has been a push to advance students' knowledge and abilities in science, technology, engineering, and mathematics (STEM). One capacity that has been linked positively to STEM achievement is relational reasoning, which involves identifying associations between objects, ideas, and situations. Yet, few studies have examined…

An important goal in school algebra is to help students notice the covariational nature of functional relationships, how the values of variables change in relation to each other. This study explored 102 Year 7 (12 to 13-year-old) students' covariational reasoning with their constructed graphs for figural growing patterns they had generalised. A…

This paper describes the design of an instrument to assess secondary school students' proficiency in structure-property reasoning (SPR). Design criteria for the instrument required that it should be based on a comprehensive model for structure-property reasoning, assess both reproductive and productive use of structure-property reasoning, be…

Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics…

BrainPOP Science is a research-based program that has been shown to be effective in improving and quickly developing students' scientific reasoning skills. This white paper presents a comprehensive case study conducted in school districts in the Southeastern United States. BrainPOP Science is one of the leading supplemental middle school programs.…

Fluid intelligence and conscientiousness are important predictors of students' academic performance and competence gains. Although their individual contributions have been widely acknowledged, less is known about their potential interplay. Do students profit disproportionately from being both smart and conscientious? We addressed this question…

Classroom dialogues have special educational value because they allow students to engage critically but constructively with each other's ideas, solve scientific problems jointly and develop their scientific understanding. The present study focuses on how groups of twelfth-grade high school and university students communicate and co-operate through…

Adaptive reasoning is one of five components students use to develop mathematical expertise and become mathematically proficient. When students adapt their reasoning they are logically thinking about the mathematical relationships between concepts and adapting their thinking to solve problems. Three Act Math Tasks are popular math problems used in…

We report on findings from two one-on-one teaching experiments with prospective middle school teachers (PTs). The focus of each teaching experiment was on identifying and explicating the mental processes and types of intermediate, supporting reasoning that each PT used in their development of combinatorial reasoning. The teaching experiments were…

This paper focuses on the analysis of Bebras Challenge tasks to find Informatics tasks that develop abstract thinking. Our study seeks to find which Bebras tasks develop abstraction and in what way. We analysed hundreds of tasks from the Czech contest to identify those tasks requiring participants to abstract directly or use abstract structures.…