Mathematical thinking is a complex, multi-faceted process that has been described as messy and difficult but can also show growth and insights into conceptual understanding and knowing. This paper explores the application of Edward de Bono's practical thinking, in particular, the occurrence of porridge words to examine the mathematical thinking of…

Cognitive demand is a crucial dimension of instructional quality. Its heterogenous operationalizations call for refined investigations, with respect to discursive richness (generic conceptualizations) and conceptual richness (subject-related conceptualizations). Considering not only teachers' intended cognitive activation (operationalized, e.g.,…

The present study, carried out in the context of a Teacher Professional Development (TPD) Program on mathematical modelling and digital technologies, focuses on how Italian mathematics teachers refer to digital technologies in designing their lessons and investigates to what extent the TPD program impacted the way by which teachers design their…

This study assessed the effectiveness of modified schema-based instruction (MSBI) in teaching students with autism spectrum disorder (ASD) how to solve additive compare word problems. The study was conducted in Spain, and it involved three students with ASD who were 6, 7, and 9 years of age. A single-case, multiple-baseline across-students design…

Online may not be the ideal format for a mathematics enrichment event, but in some circumstances, it may be the only option available. This article considers a mathematics enrichment programme consisting of a series of masterclasses which were held live online for secondary students in the UK during the COVID-19 pandemic. The series of…

Goal orientation beliefs, self-efficacy, and beliefs about the role of the teacher in mathematics learning have been known as important factors in promoting students' success in mathematics. Beliefs can be shaped through four principles: mastery experience, vicarious experience, social persuasion, and physiological state. This study examined the…

This study aimed to characterise preservice teachers' (PSTs') noticing in a mathematics classroom and its influence on their lesson modification. Written narratives on video-taped lesson observation were analysed qualitatively in two components, attending and reasoning. The findings indicate that PSTs' initial noticing focused on general…

Assessment literacy is the knowledge and skills one needs to develop and practice in order to investigate what students know and can do, interpret the results of assessment, and use such results to decide how to improve learning effectively. This study explored pre-service teachers' assessment literacy and the implications thereof for the teaching…

With the changes in Common Core State Standards, it was essential to explore how elementary pre-service teachers' sense of fractions is developing and their thoughts about how to teach fractions. A gap in practice exists because it is unknown how pre-service elementary teachers, after student-teaching, perceive their level of in-practice knowledge…

Mathematical justifications offer an approach to which students deepen and extend their mathematical thinking. This process has the potential to enhance students' conceptual understanding. Mathematical practices and process standards ask students to use critical thinking skills to justify their reasoning, but this is usually seen as proofs in high…

Purpose: The purpose of this paper is to explore whether and how principles from variation theory can contribute to the planning of teaching and learning beyond learning study. Design/methodology/approach: We study whether and how principles from variation theory contributed to a group of teachers' planning of teaching and learning about decimal…

This article presents a reflection on a teaching experience involving the use of the Brügner tangram, an interesting but little-known manipulative material. It details an activity conducted as part of an undergraduate mathematics education course for prospective primary school teachers. The main objective of this paper is to present the…

In this study, the Mathematical Knowledge for Teaching-Elementary Patterns Functions and Algebra-Content Knowledge (MKT-PFA) test, originally developed in English as part of the "Learning Mathematics for Teaching Project" at Michigan University, was adapted into Turkish. The test comprises two equivalent forms, A and B, each translated…

Reviewing bodies have shown that a high percentage of SHS students tend to underperform in mathematics examinations. In that respect, we examined the influence of two teaching approaches on Ghanaian public Senior High School students' mathematical mindsets. A quantitative research design was used, that is, an ex post facto research design was used…

This qualitative study aims to investigate novice undergraduate mathematics students' first encounter with the First Isomorphism Theorem, which is, more often than not, the pinnacle of a typical introductory course in Group Theory. Several studies have reported on the challenges that this mathematical result poses to inexperienced mathematicians,…