The present study seeks to explore the mathematical connections that 13-14-year-old secondary school students establish when solving area tasks. Emphasis is placed on different mathematical objects, and the connections between them, that allow students to successfully solve the tasks. The study follows a mixed methodology using qualitative and…

This paper demonstrates that a teachable agent (TA) can play a dual role in an online learning environment (OLE) for learning by teaching--the teachable agent working as a synthetic peer for students to learn by teaching and as an interactive tool for cognitive task analysis when authoring an OLE for learning by teaching. We have developed an OLE…

High school teachers often encounter incorrect solutions from students, especially when teaching combinatorics. This study investigates the ability of prospective mathematics teachers to assess the correctness of solutions to combinatorial problems and to falsify incorrect ones. 39 second-year prospective teachers participated in the experiment,…

The mathematical-related affect research agenda demands studies on the affect-cognition relationship, as well as interventions aimed at improving affective aspects of mathematical learning. The potential of technological environments for promoting cognitive changes in students has been widely informed and there is evidence of their influence in…

As vast amounts of data have become available in business in recent years, the demand for data scientists has been rising. The author of this article provides a tutorial on how one entry-level machine learning competition from Kaggle, an online community for data scientists, can be integrated into an undergraduate econometrics course as an…

This study investigates the utilisation and perceptions of artificial intelligence (AI) applications among mathematics and science teachers in enhancing students' learning experience in mathematics classrooms. One prominent AI application this research seeks to explore, given its recent rise in popularity and usage, is ChatGPT. The study aims to…

Research has shown assistance can provide many benefits to novices lacking the mental models needed for problem solving in a new domain. However, varying approaches to assistance, such as subgoals and next-step hints, have been implemented with mixed results. Next-Step hints are common in data-driven tutors due to their straightforward generation…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

This study aims to explore the validity of measuring joint attention through gaze coordination in computer-supported collaborative learning (CSCL) research. Gaze coordination, aligning visual attention in social contexts, aids comprehension and communication. Many CSCL researchers use gaze coordination to gauge joint attention quantitatively.…

Background: In this cross-national study, Spanish, Finnish, and Swedish middle and high school students' procedural flexibility was examined, with the specific intent of determining whether and how students' equation-solving accuracy and flexibility varied by country, age, and/or academic track. The 791 student participants were asked to solve…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

To live independently, it is critical that students with disabilities maintain the basic mathematical skills they have acquired so they may apply these skills in daily life. To support maintenance of mathematical skills among students with developmental disabilities, the researchers used a multiple probe across participants design to examine the…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

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…

This study aimed to investigate children's potential for reasoning by analogy utilizing a newly-developed computerized dynamic test, and the potential differential influence of executive functions (cognitive flexibility, attention, and planning) on static and dynamic measures of analogical reasoning. Participants included 64 children (mean age =…