Understanding part-whole relations is crucial in early mathematics education. However, both analogue and digital learning environments often lack systematic approaches to foster part-whole understanding. With the rising popularity of educational apps, it is essential to evaluate how they implement learning of part-whole relations. Accordingly,…

Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential.…

This research explores two methods through which ten preservice math teachers develop an understanding of trigonometric values. Using the unit circle, preservice math teachers engage in knowledge-building activities such as paper folding and GeoGebra application. Grounded in Altman and Kidron's 2016 didactical design research, this study examines…

Purpose: The purpose of this study is to develop a game-based mobile application to help learners practice mathematical patterns and structures. Method: The study followed a mixed-method research design and prototyping methodology to guide the study in developing the mobile application. An instrument based on the Octalysis framework was developed…

Simulation is an effective tool for analyzing probability models as well as for facilitating understanding of concepts in probability and statistics. Unfortunately, implementing a simulation from scratch often requires users to think about programming issues that are not relevant to the simulation itself. We have developed a Python package called…

The present study contributes to knowledge about how to design tasks that benefit from dynamic software in math education, comparing practice performance and learning outcomes among 129 students practicing on two different task designs using GeoGebra. The task designs differed with respect to the presence or absence of guidelines on how to solve…

Digital pedagogical skills are essential for teachers dedicated to the ethical and effective use of digital resourcesin blended learning, artificial learning, teaching, communication, collaboration, evaluation, and problem-solving in the era of digitalization. A variety of competency frameworks have been developed for teachers and learners by…

The Google Chrome browser, widely available on computers today, has a variety of free and low-cost apps and extensions that can benefit all students in inclusive classroom settings. Using apps and extensions readily available for the Google Chrome browser, teachers have access to assistive tools that can be useful learning supports for students…

Information competency is one of the essential qualities of a person living in the information age. It includes skills in information handling in both educational domains and the outside world, as well as readiness and capability to use modern information and communication technologies when involved in various types of information activities.…

Researchers have generated a powerful framework that identifies three aspects of noticing students' mathematical thinking: attending to, interpreting, and deciding how to respond to student thinking. Previous research has tended to focus on evaluating how "well" teachers engaged in noticing, and how "well" they connected the…

The 1998 paper by Martin Mühlenbrock, Frank Tewissen, and myself introduced a multi-agent architecture and a component engineering approach for building open distributed learning environments to support group learning in different types of classroom settings. It took up prior work on "multiple student modeling" as a method to configure…

Latent variable models, such as the popular Knowledge Tracing method, are often used to enable adaptive tutoring systems to personalize education. However, finding optimal model parameters is usually a difficult non-convex optimization problem when considering latent variable models. Prior work has reported that latent variable models obtained…

Digital content is increasingly present in U.S. K-12 classrooms, with a current push by federal officials to increase the rate at which digital textbooks are adopted. While some teachers' use of electronic resources involves locating activities and lessons from various internet sites, textbook and educational software companies have begun to…

Critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities and corresponding implementation guidelines were identified in this study. Based on the identified features and guidelines, a multimedia computer-assisted instruction program, "Math Explorer", which delivers…

With the world moving rapidly into digital media and information, the ways in which learning activities in mathematics can be created and delivered are changing. However, to get the best results from the integration of ICTs in education, any application's design and development needs to be based on pedagogically appropriate principles, in terms of…