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…

In this paper we develop a case for introducing a new teaching tool to undergraduate mathematics. Lean is an interactive theorem prover that instantly checks the correctness of every step and provides immediate feedback. Teaching with Lean might present a challenge, in that students must write their proofs in a formal way using a specific syntax.…

In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors,…

In this qualitative multiple-case study, three teachers' understanding of holistic education philosophy was explored through their enacted instructional practices in mathematics classrooms in a holistic school in India. Drawing upon the ethnographic methodology, the data collected include interviews and conversations, classroom observations, and…

Recent literature underlines the increasing use of online platforms in learning undergraduate mathematics, where students refer to these as supplementary resources to develop their mathematical understanding. Through an intrinsic case study, we focus on a highly viewed YouTube learning resource for learning derivative. The selected case is from…

This research aims to improve the numeracy abilities of secondary students after using the Labirin: the board game and students' perceptions of mathematics learning using the game. This empirical study research used a one-group pretest posttest design. The research population is all grade-8 students in one of the Islamic public secondary schools…

Mathematical problem posing, generally defined as the process of interpreting given situations and formulating meaningful mathematical problems, is academically important, and thus several interventions have been used to enhance this competence among students and teachers. Yet little is known about the interventions' various components and their…

Mathematical beliefs and metacognitive knowledge play significant roles in solving mathematical problems; thus, this study aims to investigate the influence of middle school students' beliefs on their metacognitive knowledge when solving geometry problems. This study utilizes both quantitative and qualitative research methods. A linear regression…

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…

A socioeconomic status (SES)-related achievement gap in mathematics emerges in children from many countries before school entry, persists in primary school, and imposes challenges for education systems worldwide. In response, the United Nations' sustainable development goals include universal access to quality preschool education to support…

Students' proficiency in the language of instruction is essential for their mathematical learning. Accordingly, language-responsive instruction, which includes adapting teaching material to students' language needs, is thought to promote mathematical learning, particularly for students with lower levels of proficiency in the language of…

In our action research projects as teacher educators, we focus on broadening preservice teachers' understandings about language diversity in mathematics classrooms, away from just improving students' fluency in the language of instruction. To undertake these projects, we developed a flexible analytical tool, for identifying those pedagogical…

High-quality instruction in preschool is important for children's mathematical development. To date, the domain-specific elements constituting mathematics instruction quality and the factors associated with this quality are hardly studied, resulting in serious gaps in our insights into the topic. We aimed to address this gap by investigating (a)…

Proof comprehension is an important skill for students to develop in their proof-based courses, yet students are rarely afforded opportunities to develop this skill. In this paper, we describe two implementations of an activity structure that was developed to give students the opportunity to engage with complex proofs and to develop their proof…

This study explores the inclusion of the visual arts in mathematics instruction as a means of piquing students' interest in a topic that is frequently regarded as difficult. We evaluate numerous research that have been undertaken in this situation by completing an extensive literature study. Our findings show that the inclusion of visual arts in…