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…

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…

Providing realistic solutions for word problems proves to be challenging. A possible explanation is the influence of individual's expectations and beliefs about word problems. This explanation was tested in the present study in an out-of-school context. Specifically, the study assessed effects of (1) prompting participants to make realistic…

This case study used individual interviews to investigate graduate students' sensemaking in upper-level electrostatics in the context of problems that can be efficiently solved for the electric potential using Laplace's equation. Although there are many technical mathematical issues involved in solving Laplace's equation, the focus of this…

This inquiry-based lesson about the coastline paradox fosters belonging, curiosity, and authentic mathematical thinking as students explore and construct knowledge together.

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…

In "Test-Specific Thinking," the authors provide recommended practices, methods, and means for educators to implement structural schemas into teaching, helping students better prepare for tests and formulate stronger responses to certain question frames. Armed with a better understanding of how tests are designed, teachers will increase…

This qualitative empirical study uses interview data from 16 secondary school students in Austria, who experienced lessons in Critical Mathematics Education (CME), to understand how students perceive a CME approach. Despite the long theoretical tradition and the existence of practical reports from the teacher perspectives, there is a lack of…

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…

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,…