https://mted.merga.net.au/index.php/mted <p>Mathematics Teacher Education and Development <span style="font-size: 0.875rem;">(MTED) is </span><span style="font-size: 0.875rem;">an official journal of the Mathematics Education Research Group of Australasia, Inc. (MERGA), is an international refereed journal that provides a stimulating collection of articles with a focus on mathematics teacher education. MTED is an open access publication.</span></p> Mathematics Research Group of Australasia en-US Mathematics Teacher Education and Development 1442-3901 https://mted.merga.net.au/index.php/mted/article/view/1341 <p class="MTEDAbstract" style="margin: 24.0pt 36.0pt 24.0pt 36.0pt;">Mathematical games are widely used in primary school classrooms, yet the activities that are labelled as "games" vary considerably in their structure, cognitive demands, and potential to support student reasoning. This conceptual paper offers a typology that distinguishes between pseudo-games, superficial games, gamification, and instructionally rich games. Drawing on examples from classroom practice and research literature, we argue that the presence of choice alone does not define a pedagogically effective game. Instead, instructional value depends on the nature of the choices available and their alignment with key mathematical ideas. We propose three design principles that characterise instructionally rich games, with particular emphasis on the role of strategic reasoning, embedded representations, and opportunities for students to make meaningful mathematical connections. This framework is intended to support teachers, researchers, and designers in critically evaluating and developing mathematical games that move beyond surface-level engagement to promote deep, conceptually grounded learning.</p> James Anthony Russo Toby Russo Copyright (c) 2025 Mathematics Teacher Education and Development 2025-08-05 2025-08-05 27 2 1 1 https://mted.merga.net.au/index.php/mted/article/view/1240 <p class="MTEDAbstract" style="margin: 24.0pt .5in 24.0pt .5in;">This study explores how preservice secondary mathematics teachers comprehend and apply advanced mathematical concepts to the content they will teach in K–12 classrooms. Responding to student inquiries and guided by the <em>Mathematical Education of Teachers II</em> recommendations, an innovative capstone course was developed and integrated into the mathematics education program to bridge the gap between college level mathematics and secondary instruction. The course was designed to foster meaningful mathematical connections through assignments and guided reflection, enhancing preservice teachers’ ability to connect advanced concepts to secondary teaching. Employing a generic qualitative research design with thematic analysis, written reflections from five preservice teachers in their final semester of a teacher preparation program at Northwest Missouri State University were analysed. The purpose of the written reflection was to help these teachers examine their evolving mathematical thinking and instructional planning. The findings indicate that participants transitioned from procedural to conceptual reasoning, developed heightened awareness of mathematical interconnectivity, and gained confidence in designing lessons that integrate advanced mathematics. These results suggest that purposefully designed capstone courses can strengthen preservice teachers' pedagogical effectiveness and promote curricular coherence. Further, it is recommended teacher preparation programs prioritise connecting advanced mathematics to school level instruction.</p> Sara Sony Copyright (c) 2025 Mathematics Teacher Education and Development 2025-09-02 2025-09-02 27 2 2 2