We adapt the Lanchester combat model to represent conflict between vampires and humans. It is assumed that vampires attack humans during the hours of darkness whilst humans attack vampires during the hours of light. The right-hand side of the differential equation model therefore depends upon the hour of the day. A key insight is that to answer…

The concept of function is critical in mathematics in general and abstract algebra in particular. We observe, however, that much of the research on functions in abstract algebra (1) reports widespread student difficulties, and (2) focuses on specific types of functions, including binary operation, homomorphism, and isomorphism. Direct, detailed…

Calculus is perhaps the most widely taught and researched upper-secondary/post-secondary mathematics subject the world over. The research literature is amassing greater clarity around students' understandings of calculus, yet calculus instruction tends to be at odds with this literature, maintaining a focus on procedural aspects of the subject.…

In the United States, calls for improved K-12 learning opportunities in mathematics have shifted focus in school district offices from bureaucratic pursuits to instructional improvement efforts. Yet, district leaders often receive little guidance on how to achieve these goals. Further, although widely recognized that content-specificity matters in…

This paper focuses on the definitions and the mis-out and mis-in examples of rational numbers that four prospective elementary teachers presented while working on rational number assignments. The participants were first asked to respond, individually, to an Individual Rational Number Assignment, consisting of items aiming at detecting their…

Collaborative learning is a group learning paradigm in which individuals or students work together to solve problems or complete tasks, exemplifying the essence of collective educational efforts. There are a lot of collaborative learning methods available; however, finding one that is suitable for the complex nature of mathematical problem-solving…

In Chile, mathematics results are insufficient at the school level. To address this problem, the need to rethink teaching has been raised. Evidence indicates that epistemological beliefs are at the basis of pedagogical decisions, and their study has been developed mainly in primary and secondary school teachers. However, scientific evidence is…

The relevance of the published research on the actualization of interdisciplinary integration at mathematics lessons is due to the need for conceptual clarification of what is included in the concept of an academic discipline, and, consequently, interdisciplinary integration. Currently, there is no uniformly consistent interdisciplinary…

Research suggests that troubleshooting activities that require students to reflect on teacher-crafted erroneous examples; i.e., erroneous solutions to problems that correspond to widespread naïve ideas, are beneficial to learning. One possible explanation to these beneficial effects is that troubleshooting activities encourage students to test the…

This paper is part of a broader study which explores South African pre-service teachers' use of the jump strategy on the empty number line for enhancing their confidence to do and teach mental mathematics computation strategies. The focus of this paper is the use of micro-teaching in the form of video recordings by pre-service teachers. Forty…

We examined the characteristics of video annotations frequently discussed during debriefing conversations as part of video-assisted coaching cycles. We also analyzed how mathematics coaches used written annotations to inject ideas into debriefing conversations when supporting teachers to reflect on important classroom events. Coaches and teachers…

This research is based on a bibliometric analysis of publications on math anxiety. It aims to analyze the distribution of the results of publications on math anxiety in the last ten years based on research trends and topics, reputable journals, influential authors, institutions, and productive countries. Scopus was used as a data collection…

The present study aimed to describe teachers' instructional flows when implementing a mathematical problem-posing task using scriptwriting technique. With matchsticks, a growing pattern that increases by a constant unit was created and presented to the teachers as a problem-posing situation. We analyzed the instructional flows in 50 scripts,…

The early years of education are a crucial time to develop a strong foundation of critical mathematical skills. A growing body of research continues to demonstrate that this foundational knowledge can be successfully built through teacher-facilitated, or guided, approaches to play. Despite its benefits, the implementation of guided play is…

In this study, our team observed sixth-grade teachers as they taught fractions to students in their mathematics intervention classes to see whether they were including motivational-supportive messages within the framework of Situated Expectancy-Value Theory. Messages in the intervention lessons and teacher transcripts were explored and analyzed,…