Transitioning from material to theoretical geometry is often considered a significant challenge in compulsory education. Over the last twenty years, research rooted in the Theory of Didactical Situations (TDS) has explored how material geometry can support the teaching and learning of theoretical geometry, promoting continuity in teaching. These…

Algebra is critical in shaping future mathematics success and is integral to the K-12 curriculum. Despite its inclusion, a common challenge arises as students' progress to higher grades without a solid foundation, resulting in challenging learning experiences. This action research study focuses on the algebraic learning experience of a Grade 7…

Understanding part-whole relations is crucial in early mathematics education. However, both analogue and digital learning environments often lack systematic approaches to foster part-whole understanding. With the rising popularity of educational apps, it is essential to evaluate how they implement learning of part-whole relations. Accordingly,…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

Mathematics vocabulary plays a crucial role in students' mathematics learning. However, students, particularly those with learning disabilities (LDs), encounter challenges in understanding and grasping mathematical terms. This challenge becomes more evident as students progress into the elementary and secondary grades, where mathematics vocabulary…

Non-digital games are a tool that can help children to build and improve problem solving skills in early mathematics learning. Teachers need to design a learning activity using non-digital games taken account problem solving skills in the learning activities. However, the application of problemsolving skills in early mathematics learning…

The Reading and Appreciating Mathematical Proofs (RAMP) project seeks to provide novel resources for teaching undergraduate introduction to proof courses centered around reading activities. These reading activities include (1) reading rich proofs to learn new mathematics through proofs as well as to learn how to read proofs for understanding and…

This paper reports on the development of complex unfamiliar mathematics questions using conventional mathematics questions. The autoethnographic research data included retrospective reflections of two educators and review of literature. Data analysis resulted in a three-phase development process: identifying conventional questions and subject…

The implementation of large-scale intervention and development projects is often problematic, and the impacts of such projects usually fall somewhat short of what was expected. Additionally, the rationalities of intervention projects are not carried over into classroom teaching as directly as expected. This problem is generally known, but…

The author has been influenced throughout his time in mathematics education by the work of Caleb Gattegno. Gattegno made extensive use of the word awareness whereas much educational literature from a psychological perspective talks about memory (for example, Justicia-Galiano, MartÌn-Puga, Linares & Pelegrina, 2017). This has, amongst other…

This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative…

Within the commognitive perspective, ritual and explorative routines are used in a very particular way to distinguish students' routines according to whether they are driven by social reward or by generating a substantiated narrative. Explorative routines in this theorisation may refer not to inquiry-based activity but to the result of a student's…

At the beginning of the 21st century, "number sense" was listed as one of the core words in the mathematics curriculum of compulsory education in China, and it has now become one of the core competencies of primary school mathematics. It is necessary to determine the development of number sense of first-grade primary school students (6-7…

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning…