The presented paper is devoted to the new teaching model of congruences of computer science students within the subject of discrete mathematics at universities. The main goal was to create a new model of teaching congruences on the basis of their connection with Diophantine equations and subsequently to verify the effectiveness and efficiency of…

In this article, we use a case study to explore the views of first-year university students on the differences between mathematics at school and at university, and on the changes to their study methods as they make the transition to university mathematics. We also consider their views on the differences and affordances of tasks that they encounter…

This article explains how explorations into the quadratic formula can offer students opportunities to learn about the structure of algebraic expressions. In this article, the author leverages the graphical interpretation of the quadratic formula and describes an activity in which students derive the quadratic formula by quantifying the symmetry of…

Using Cultural-Historical Activity Theory, we analyze lecturers' views on the aims and teaching practices of mathematical modelling (MM) education in Norway and England. We aim to expose the tensions that exist within the activity of teaching MM at university, such as those between multiple, sometimes competing, aims for teaching MM, or between…

This article investigates how the recent implementation of programming in school mathematics interacts with algebraic thinking and learning. Based on Duval's theory of semiotic representations, we analyze in what ways syntax and semantics of programming languages are aligned with or divert from corresponding algebraic symbolism. Three examples of…

Young children's symbolic magnitude understanding, or knowledge of how written numerals and number words can be ordered and compared, is thought to play an important role in their mathematical development. There is consistent evidence that symbolic magnitude skills predict mathematical achievement in later childhood and adulthood. Yet less is…

Responding constructively to unexpected events during a lesson is a particularly challenging facet of teaching. This study aimed to investigate how a secondary school mathematics teacher responded to learners' unexpected or unplanned offers in the teaching of algebra. A total of three sequential lessons were video recorded and the quality of the…

In order to enhance students learning environments, mathematics lecturers need to prepare suitable materials in their lessons. So improving the materials in textbooks based on learning theories is so important to enhance the ability of students in mathematics learning through problem solving activities. The purpose of this qualitative case study…

Solving problems involving absolute value is one of the hardest topics for students learning in elementary algebra course. This is an important topic in student's mathematics life since absolute value functions are important example of a function which is continuous on the real line but not differentiable at the origin. A deep understanding of…

This research shares progressions in thinking about equations and the equal sign observed in ten students who took part in an early algebra classroom intervention across Kindergarten and first grade. We report on data from task-based interviews conducted prior to the intervention and at the conclusion of each school year that elicited students'…

This paper reports on one aspect of a bigger project: teachers' design of instructional materials. We found a number of design moves used by the teachers in our study. In this paper, we report three of them: Making things explicit, making connections, and resequencing practice examples. [This paper is the fourth in a symposium of four papers. For…

Research has shown the majority of students who have completed a university calculus course reason about the definite integral primarily in terms of prototypical imagery or in purely algorithmic and non-quantitative ways. This dissertation draws on the framework of Emergent Quantitative Models to identify how calculus students might develop a…

This dissertation study investigated the efficacy of a multi-component intervention package delivered via an online learning tool on math fluency for prerequisite algebra skills for three 6th-grade students. Students were referred by their math teacher due to concerns with academic performance. Target skills were individualized for each student…

This single case study investigated the implementation of a modularized mathematics course designed to eliminate the usage of remedial mathematics courses from post-secondary mathematics curricula. The literature review revealed that introductory college level mathematics success and student retention rates in post-secondary schools was…

The purpose of this case study was to examine one school district's 8th grade mathematics teachers' perceptions, analysis of, and use of their own students' formative interim data. Research has shown that teachers have difficulty with data literacy, and are not getting the trainings they need. Unfortunately, this may arise from the fact that a…