Reflective and formative assessments are commonly used in both K-12 and higher education but are less common in university mathematics courses. In fact, much of mathematics education seems to be heavily reliant on summative assessments. In this article, we introduce a formative assessment in the frame of a reflective homework system that can be…

One of our favorite face-to-face teaching frameworks is "Launch, Explore, Summarize" (LES). However, transitioning LES activities to online settings challenged us to reimagine how learning and its interactions could be supported in this new environment. We explore our experience transitioning an LES lesson on the quadrilateral hierarchy…

The pervasive shortage of mathematics teachers in Australia has resulted in a critical reliance on out-of-field (OOF) teaching, significantly impacting student performance. This study shares insights from a scholarly inquiry in progress aiming to map the complex educational ecosystem that perpetuates OOF teaching. This paper examines the…

Charles Sturt University had the motto "For the common good" but listening to the wisdom of the voices of the Wiradjuri Elders, "Yindyamarra Winhanganha" -- the wisdom of knowing how to live well in a world worth living in -- now guides us. We teach and research in mathematics with a deep-seated belief about mathematics and…

Mathematics education researchers (MERs) use practices unique to the mathematics education discipline to conduct their work. MERs' practices, i.e., ways of being, interacting, and operating, define the field of mathematics education, are initially learned in doctoral preparation programs, and are encouraged and sanctioned by conferences and…

Didactic transposition transpose knowledge relatively across various institutions, or the place where knowledges live within. In this study we analyse the position and the role of reduction of fraction arithmetic, specifically on how the piece of knowledge takes account, in the mathematics school textbooks of Japan, Indonesia, and Malaysia. We…

This article shares the learning experienced by my seventh-grade students during a lesson incorporating LEGO robotics into my mathematics class. I provide evidence of my students' learning, which represents how LEGO robotics can benefit students in the mathematics classroom to support engagement and development of understanding.

In this article, the authors present an inquiry activity presented to Year 7 students in a mathematics excellence class at a P-12 school in regional Queensland. Different students solved the activity (comparing the sugar content of fruit) using decimals, percentages, ratio and rates. By asking the students to solve a problem they were much more…

Children start preschool with large individual differences in their early numerical abilities. Little is known about the importance of heterogeneous patterns that exist within these individual differences. A person-centered analytic approach might be helpful to unravel these patterns and the cognitive and environmental factors that are associated…

The purpose of this study was to investigate the effect of incorporating higher order thinking skills (HOTS) in a school-based assessment (SBA) on mathematics achievement among students. A mixed-method case study design was used to assess a sample size of 158 students and three mathematics teachers. The students' proficiency in mathematics was…

Cheating is a common human behavior but few studies have examined its emergence during early childhood. In three preregistered studies, a challenging math test was administered to 5- to 6-year-old children (total N = 500; 255 girls). An answer key was present as children completed the test, but they were instructed to not peek at it. In Study 1,…

Pre-service mathematics teachers (PSTs) enter university with diverse beliefs and understandings of teaching and learning; yet, they may not be aware of how these conceptions are related to their epistemological and efficacy beliefs. This study explored how the mathematical beliefs, mathematics self-efficacy, and mathematics teaching efficacy of…

The growing interest in classroom discourse reflects a wide recognition within the mathematics education community of the critical role of social interactions in the joint construction of mathematics knowledge. An extensive body of empirical and theoretical work has been undertaken in the last two decades to characterise the types of classroom…

Word problems are frequently used in school mathematics to offer students the opportunity to explore mathematical relationships and structure. However, previous studies have reported that word problems are misused or abused in ways that overlook the original intent of exploring mathematical structure and relationship. This study aims to share a…

We discuss and examine a numerical indicator--the individual gain--of students' engagement and mathematical growth in relation to an instructor's course aims and goals. The individual gain statistic assesses the fractional amount an individual student improves initial-test to final-test. We argue that an initial-test score and a final-test score,…