This research article is about "Introducing a Supportive Framework to Address Students' Misconceptions and Difficulties in Learning Mathematical proof techniques (MPT): A Case of Debark University". This study aims to develop, introduce, and implement a supportive framework to overcome students' misconceptions and difficulties in MPT.…

This dissertation examines the development of combinatorial reasoning in high school students through an in-depth analysis of a problem-solving session involving the Pizza Problem. The study, part of the long-term Rutgers-Kenilworth longitudinal research project, focuses on four 11th-grade students as they explore and connect concepts related to…

Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural…

Various solving strategies in probability of events could complicate the students in choosing the best strategy in problem solutions. This research was carried out to identify the favourite solving strategies used by college students to solve probability and event problems. As a preliminary of a case study, only three students were selected as…

For over a decade, Which One Doesn't Belong? (WODB; Danielson, 2016) has been a beloved classroom routine that invites students to engage in mathematical decision-making and justification. In the WODB routine, four related figures are shown to students, and they are asked to decide which of them doesn't belong with the other three. The beauty of…

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

Do you work tirelessly to make your math lessons meaningful, challenging, accessible, and engaging? Do you spend hours you don't have searching for, adapting, and creating tasks to provide rich experiences for your students that supplement your mathematics curriculum? Help has arrived! "Classroom Ready-Rich Math Tasks for Grades 2-3"…

Do you work tirelessly to make your math lessons meaningful, challenging, accessible, and engaging? Do you spend hours you don't have searching for, adapting, and creating tasks to provide rich experiences for your students that supplement your mathematics curriculum? Help has arrived! "Classroom Ready-Rich Math Tasks for Grades 4-5"…

The National Council of Teachers of Mathematics's "Principles to Actions" (NCTM, 2014) cites posing purposeful questions and eliciting and using evidence of student thinking as effective mathematics teaching practices. Interviewing students creates opportunities for teachers to develop these practices. Through interviewing, they can try…

Mathematical reasoning, which plays a critical role in students' capacity to make sense of mathematics, is now emphasised more strongly in various curricula internationally. However, reasoning is sometimes difficult for teachers to recognise, let alone teach. This case study considers video of one teacher's implementation of a problem-solving…

This paper presents a novel figure for teaching multiple geometric proofs of the Pythagorean theorem. Because it consists only of congruent given right triangles, the figure can be constructed using a template of the given right triangle or, if available, a computer program. Within the figure, called a Pythagorean multi-proof square, there are…

The aim of this study is to develop a descriptive framework for teacher educators to assist teachers to plan and realize modelling implementations in their classrooms and for researchers to describe and analyse how modelling is implemented. The planning process and implementations of 12 middle and high school mathematics teachers who conducted…

This study posits mathematics as a fundamental methodological framework for navigating the complexities of multidisciplinary research. It argues that the increasing prevalence of real-world problems demands the integration of knowledge from diverse scientific fields, where mathematics, particularly through the method of analysis and synthesis,…

Windmill images and shapes have a long history in geometry and can be found in problems in different mathematical contexts. In this paper, we share and discuss various problems involving windmill shapes and solutions from geometry, algebra, to elementary number theory. These problems can be used, separately or together, for students to explore…

This article discusses a set of tasks that introduce dilations using nonstandard figures, incorporating snippets of classroom conversations as students try to make sense of the specified tasks, to show how they progress in their understanding. The authors provide a theoretical foundation for the tasks and discuss the pedagogical implications for…