Transfer is not static but a dynamic process of learning. In this article, the concept of transfer and the implications of its study are reconsidered from the theoretical basis of the complex dynamic system approach. We describe "transfer" as an emergent process that implies not a copy of knowledge applied to a new situation, but a new…

Several teaching moves have been suggested to support young children's simple addition and subtraction performance, including use of a number path, directly modeling addition and subtraction, using mathematical symbols, and modifying problem difficulty. In the present study, teacher-researchers implemented an early arithmetic activity, "Big…

Reaction mechanisms commonly used in organic chemistry are a great challenge for students in terms of understanding the representation and inferring the appropriate chemical concepts. In order to support the process of identifying and selecting chemical concepts, purposefully designed case comparisons are widely used. While these tasks place great…

Current understanding of the development of quantity representations is based primarily on performance in the number-line task. We posit that the data from number-line tasks reflect the observer's underlying representation of quantity, together with the cognitive strategies and skills required to equate line length and quantity. Here, we specify a…

Introduction: The purpose of the study was to investigate the effect of task format on pre-service mathematics teachers' creative problem-posing performance. Methods: In this quantitative study, a figural and a written pattern related to daily life with the same mathematical structure were presented to participants and they were asked to write as…

This study explores the effect of self-regulated learning support on learners' cognitive load and problem-solving performance, considering cases from well-structured to ill-structured tasks in a computer programing course. Sixty-seven undergraduate students in a computer programing fundamentals course were randomly assigned into one of two groups:…

This quasi-experimental research aimed to describe the syllabus design process using the "backward design model" and its features to determine the teacher candidates' perceptions of its application in the English Skills Development course. To achieve these objectives, the syllabus based on the BDM was designed before starting the course;…

In computer-supported collaborative learning research, studies examining the combined effects of individual level, group level and within-group differences level measures on individual achievement are scarce. The current study addressed this by examining whether individual, group and within-group differences regarding engagement and prior…

Collaborative problem-solving (CPS) engages students in solving ill-structured problems, creating group knowledge, and developing self-regulation and collaboration skills. Different scaffoldings, such as minimal-guided, task-oriented, and idea-oriented, can be used to facilitate students' CPS activities, but their effects have not been…

Though the United States maintains a great presence in our global economy, our country is still lagging behind many others in terms of achievement in mathematics. Developing the ability to think creatively and communicate effectively is paramount to ensuring our students are prepared for the competitiveness of the 21st century world. Rich…

Where do novel ideas come from? What mental processes facilitate them? The disinhibition hypothesis suggests creative cognition can be assisted by reducing cognitive inhibition of ideas, facilitating looser associative thoughts to bond with one another to produce novel concepts. Past exploration of the disinhibition hypothesis has been drawn from…

The More A-More B intuitive rule has become a research hotspot in the field of mathematical education in recent years. The intuitive rule of More A-More B is often reflected in students' responses to comparison tasks. In such tasks, students are asked to compare 2 objects that differ in a certain salient quantity A (where A[subscript 1] >…

Three mathematics education researchers discuss their findings on the use of diagrams in math instruction for English language learners. The authors show how diagrams can help students who are English learners better develop mathematical thinking and communicate their mathematical understanding.

This study explored how approximating the practice of mathematicians by communally negotiating the standards for proof mediates middle grade students' abilities to collaboratively construct mathematical arguments. Forty-seven eighth-grade students engaged in an instructional sequence wherein they, along with the instructors, negotiated communal…

This article provides information to educational leaders about how to address the challenge of supporting students who are emergent multilingual--i.e., those identified as English Learners (ELs) by their schools--in middle grades mathematics classes. The ideas in this article draw on research and collaborations with hundreds of teachers across the…