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…

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…

Background/purpose: Learning mathematics often presents challenges for students, particularly in problem-solving and establishing mathematical connections. Self-regulated learning allows students to direct, adjust, and control their learning processes. This approach is essential in encouraging students to manage their learning strategies…

Research has shown that teaching mathematics through problem posing, or problem-posing based learning (P-PBL), is a student-centered instructional approach that can improve students' cognitive and affective aspects of learning. However, since textbooks continue to include very few opportunities for problem posing, researchers have been working to…

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,…

Many of today's educators learned math in elementary and secondary schools with approaches very different from those outlined in the current standards, and it is difficult to teach for proficiencies educators have not yet developed in themselves. How can teachers find time for this kind of professional learning with all the other responsibilities…

Background/purpose: This study investigates the probabilistic thinking process in solving probability problems by prospective mathematics teachers with a field-independent cognitive style. The objective is to explore how individuals with this cognitive style approach problem-solving based on the three stages of Polya's framework: understanding the…

Background: Educational technologies typically provide teachers with analytics regarding student proficiency, but few digital tools provide teachers with process-based information about students' variable problem-solving strategies as they solve problems. Utilising design thinking and co-designing with teachers can provide insight to researchers…

The invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on…

Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…

This classroom-based action research investigates the impact of teaching problem-solving heuristics on preservice teachers' mathematical creativity, self-efficacy, and problem-solving beliefs. The study was conducted with seven preservice teachers at a state university in the Philippines, using a Plan-Do-Study-Act (PDSA) cycle. Participants were…

Students often instrumentally use variables and unknowns without considering the variational thinking behind them. Using parameters to modify the coefficients or unknowns in equations or systems of linear equations (without altering their structure) involves consciously incorporating variational thinking into problem-solving. We will test the…

The integration of artificial intelligence (AI) into mathematical problem-solving has shown significant potential to enhance student learning and performance. However, while AI tools offer numerous benefits, they are prone to occasional conceptual and arithmetic errors that can mislead users and obscure understanding. This research examines such…

This study explores gender-based differences in sixth-grade students' potential for mathematical creativity through the interrelated processes of problem solving (PS) and problem posing (PP), grounded in a multidimensional framework of creativity--encompassing fluency, flexibility, and originality. A total of 346 sixth graders from public schools…

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…