Although student covariation reasoning has been explored in depth to improve understanding of the correspondence between variables, research has focused on studying existing reasoning about variables in Cartesian representations. The working method had a qualitative approach, with a descriptive exploratory scope, the spontaneous representations…

Teaching is a process for which its plan should contain reflection onto previous experience. With that in mind, teaching situations should be continuously researched and improved in accordance with the research results. Led by this thought and the fact that students are uncritically using visualization to solve mathematical problems, we defined…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Based on our work teaching undergraduate Calculus courses, we offer insight into teaching the chain rule to reduce cognitive load for students. A particularly difficult topic for students to grasp, problems likely arise due to student struggles with the concept of function and, particularly, function composition relative to when they first…

After teaching last 10 years and analyzing student work, I realize that in developmental and Elementary Algebra courses there is a disconnection between the students conceptual understanding in context in contrast to their procedural fluency. In some cases, students can perform the procedure, but do not understand when the procedure is valid. In…

Textbooks, which form the staples of a teacher's set of resources, play a critical role in deciding what and how mathematics is taught in classrooms. However, textbooks do not always present concepts in ways that enhance understanding by students, nor are they always comprehensive in the treatment of a topic. In this exploratory study, we analyse…

Pre-symbolic algebra has been advocated for as a mathematics topic elementary students should experience to better prepare them for middle and high school algebra. However, most elementary pre-service teachers have little to no experience with pre-symbolic algebra. The study reported here analysed the struggles that ten elementary pre-service…

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually…

In this article the authors overview how the recently revised (version 9) Australian Curriculum (Australian Curriculum Assessment and Reporting Authority, 2022) and student difficulties with fractions relate to five developmental Fraction Schemes developed from multiple research projects in the literature. The article shares research findings from…

Schematic chunks denote patterns, schemes, or sophisticated rules and knowledge stored in the long-term memory in the form of chunks. We investigated whether schematic chunking is effective in improving the performance of students with math difficulties (MD) and students at risk of math failure, and how the complexity level of geometry problems…

In this article we examine the nature of inter-semiotic and intermodal construction in the exposition of a solution for a geometry rider. In the tradition of hermeneutic phenomenology, this case study involved an exploration of the oral discourse and visual texts used in a mathematics lesson. This research was intended to contribute to the…

The researchers conducted a qualitative case study to describe the experiences of two seventh grade students with mild intellectual disability as they engaged in mathematics word problems involving proportions. The researchers analyzed student performance in large group settings and with individualized instruction to gain perspective on the…

One of the highest ambitions in educational technology is the move towards personalized learning. To this end, computerized adaptive learning (CAL) systems are developed. A popular method to track the development of student ability and item difficulty, in CAL systems, is the Elo Rating System (ERS). The ERS allows for dynamic model parameters by…

Although teachers are recommended to create a stimulating learning environment in which children can use, perfect, and extend their skills, this is far from easy. In many cases, identifying the optimal difficulty level of learning tasks involves a trial-and-error process during which teachers offer children too difficult tasks, with negative…

Dynamic geometry environment allows us to investigate geometric relationships and problems more efficiently than the pencil-and-paper method. Continuous variation of geometric configurations shows the relationship from different points of view. This paper aims to provide some indications of how a dynamic geometry environment, especially GeoGebra…