Current research indicates the presence of highly skilled and motivated students with robust computational thinking backgrounds seeking opportunities to leverage their expertise in driving innovation and success in this era. These studies also reveal that students' computational thinking skills vary widely depending on educational resources,…

"Assumptions" play a fundamental role in disciplinary mathematical practice, especially concerning the relativity of truth. However, much is still unclear about ways to help students recognize key aspects of this role. In this paper, we propose a set of principles for task design to introduce students to the role of assumptions in…

This study focused on improving students' learning mathematical of proofs and proving by using combinations of proof strategies that span different levels of understanding of proof structure; we refer to these as 'level-spanning proof-production strategies'. We analysed the level-specific proof-production strategies evident in the lessons and…

To encourage students' self-regulated learning at home, developing skills for textbook use to overcome learning-related impasses is crucial. This study examined the effects of providing mathematics class sessions that combined teacher instruction on appropriate textbook use with peer instruction, aimed at promoting students' spontaneity and…

In this paper, we analyse a grade 8 (age 13-14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in…

A Common Core expectation of high school mathematics students is to analyze functions using different representations. One type of function to be analyzed is piecewise-defined functions. The author has found most approaches to the study of piecewise functions to be abstract, disconnected from any context, and difficult for students to understand.…

An interesting Sangaku problem was chosen and a multidirectional study was performed, which included finding the locus of a circle's center moving while being tangent to two circles. It also included finding the radius of that circle given the datum that it is also tangent to the side of an isosceles triangle. Two different proofs are presented of…

This paper reports on a study conducted within VIDEO-LM (Viewing, Investigating and Discussing Environments of Learning Mathematics), a video-based professional development project for secondary mathematics teachers that aims to enhance reflection on practice. The study explored VIDEO-LM sessions where Israeli teachers watched an 8th grade…

With the proliferation of video-based professional development (PD) courses for mathematics teachers, understanding the role of the facilitators of these courses has become an emerging field of theoretical and empirical study. The purpose of this article is to address some of the challenges and opportunities that facilitation of discussions…

Functions is considered an important mathematical literacy concept within the Organization for Economic Cooperation and Development's (OECD's) Programme for International Student Assessment (PISA), and it has been shown that Japanese junior high school students are experiencing problems understanding functions. This paper examines the difficulty…

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we…

While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the…

This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof--statement, proof, and theory--suggested by…

Inclusive education remains a significant challenge in today's educational landscape, as K-12 classrooms and higher education institutions struggle to meet the diverse needs of all students. To address this pressing issue, "Developing Inclusive Environments in Education: Global Practices and Curricula," led by Kiyoji Koreeda, offers…

From a fallibilist perspective, mathematics gradually develops with problems, conjectures, proofs, and refutations. To attain such authentic mathematical learning, it is important to intentionally treat refutation in mathematics classrooms, such as facing or proposing counterexamples and coping with them. In particular, analysing students'…