This scholarly inquiry critically examines the pedagogical aspects pertaining to the instruction and acquisition of Abstract Algebra within the realm of University Mathematics Education (UME). Drawing upon multiple lenses, including epistemological, cognitive, phenomenological, and institutional perspectives, this study investigates the formidable…

This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

This study investigates the interplay between student reasoning and instructional strategies in trigonometry education. A qualitative case study was conducted to examine how Grade 10 students employ various reasoning approaches -- deductive, inductive, abductive, analogical, and algorithmic -- when solving trigonometry problems. Each approach…

Inquiry-based learning (IBL) in mathematics is a student-centered approach that encourages exploration, problem-solving, and critical thinking, allowing students to actively engage with mathematical concepts and discover relationships through hands-on activities and collaborative learning. Despite the growing interest in IBL within mathematics…

This article proposes an interconnected framework, "Ways of thinking in STEM-based Problem Solving," which addresses cognitive processes that facilitate learning, problem solving, and interdisciplinary concept development. The framework comprises critical thinking, incorporating critical mathematical modelling and philosophical inquiry,…

Conceptual challenge is often considered a necessary ingredient for promoting deep learning in an inquiry-based environment. However, challenge alone does not support conceptual development. In this paper, we draw on complexity theory as a theoretical lens to explore how a primary teacher facilitated students' conceptual change through repeated…

This paper aims to show how the Logic of Game Theory can facilitate the structuring of games for the learning of mathematical concepts, in a way which is cognitively resonant with students' attitudes and epistemologically sound from the mathematical standpoint. We propose a kind of game, based on an inquiry approach to mathematics, called Digital…

This paper explores the integration of STEM activities in teaching and learning, emphasizing the importance of innovative pedagogical approaches in effectively introducing theoretical concepts, such as variables and functions, and merging them with practical applications. Drawing on existing literature, this study investigates the integration of…

A digital wall is a tool for students to structure and register their online work on mathematical problem-solving activities that involve the coordinated use of digital technologies. How could students use such digital wall to understand mathematical concepts and to develop problem-solving competencies? The aim of this study is to analyze and…

Southern Cross University (SCU) educators and local teachers have developed a five-lesson instructional sequence built around fluke identification as a way of resolving the question: How fast do humpback whales travel up the east coast of Australia?

Inquiry-based instruction is a student-centered approach to teaching that focuses on active learning (Barron and Darling-Hammond 2008) in which students engage with "tasks that promote reasoning and problem solving" (NCTM 2014). Specifically, such tasks encourage a variety of solution strategies and stimulate use of the NCTM Process…

As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own…

In this study, we report on what types of mathematical knowledge for teaching teachers (MKTT) mathematics teacher educators (MTEs) use and develop when they work together and reflect on their teaching in a Community of Practice while helping prospective primary teachers (PTs) generate their own mathematical knowledge for teaching in learning…

Have you ever considered how technology could facilitate reasoning and sense making of systems of linear inequalities? In this article, the authors share how to use Google® Maps® and Desmos to achieve this and provide students with opportunities to access mathematics as they build a more formalized understanding. Using an inquiry-based approach,…

This article offers a description of how empirical experiences through the use of procedural knowledge can serve as the stage for the development of hypothetical concepts using the learning cycle, an inquiry teaching and learning method with a long history in science education. The learning cycle brings a unique epistemology by way of using…