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…

This study explored mathematical values espoused by senior high school (SHS) mathematics teachers in mathematics teaching and learning in a municipality in Ghana. To achieve this aim, we employed an explanatory sequential mixed methods design. In the quantitative study, a census was employed to include all 53 SHS mathematics teachers in a…

Research in mathematics education constantly oscillates between theoretical or 'Is' questions and practical or 'Ought' questions: Researchers are not only pursuing theoretical questions by investigating what those involved in the teaching and learning of mathematics do, but they are also working on practical recommendations for what they ought to…

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…

The purpose of this article is to describe and illustrate learning trajectories (LTs) and introduce a new, comprehensive set of resources that support teaching meaningfully and joyfully. An LT for a topic has three parts: (1) a mathematical goal; (2) a developmental progression of levels of thinking; and (3) teaching practices (environments,…

Human intelligence is related to cognitive skills such as the acquisition of new knowledge, problem-solving and abstract thinking in learning processes. These processes are of great importance in mathematical education. Artificial intelligence (AI) can help students develop these cognitive skills by providing customized teaching methods according…

Although reformers have embraced learning trajectories (LT, also called learning progressions) as an important tool for improving mathematics education, the efficacy and assumptions of LT-based instruction are largely unproven. The aim of a recently completed research project was to fill this void. Fulfilling this aim was more challenging than…

This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students' mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students' mathematical potential, quality…

The notions of meaning and sense, which are closely related to understanding, play an essential role in educational processes in general and, therefore, in the teaching and learning of mathematics. However, the terms 'meaning' and 'sense' are unevenly used in the theory of language, semiotics, philosophy and psychology. After describing the main…

Learning progressions have become increasingly prevalent in mathematics education as they offer a fine-grain map of possible learning pathways a child may take within a particular domain. However, there is an opportunity to build upon this research in ways that consider learning from multiple perspectives. Many current forms of learning…

Learning channels refer to the way students receive instruction and respond to it. We examined the relationship between See-Say and See-Write learning channel sets during the mathematical practice of four male autistic students, aged 8 to 14 years. Participants received practice in the ×7 and ×8 tables across both channel sets. Lessons included…

In the last two decades, studying the possible relations between the history of mathematics and mathematics education has revealed the importance of certain foundational issues concerning the nature, relevance and validity of historical knowledge vis-à-vis problems of teaching and learning, which call for deeper exploration. Reviewing aspects of…

United States math achievement has long lagged behind that of other nations and has been relatively stagnant for 8th-graders on national assessments over the past 2 decades. The need to understand how teachers can better support mathematics learning is particularly acute in the wake of pandemic-era learning disruptions, which impacted already low…

In the United States, stagnating mathematics achievement and persistent racial and socioeconomic disparities in math performance point to a need to understand how math teachers can more effectively support the learning of each and every student. Given a growing body of research that emphasizes the impact of the classroom environment on student…

The literature has identified a significant dropout of students at the transition from high school to higher education, especially in areas related to mathematics. Therefore, new didactic tools have been identified to help teachers in the process of knowledge transfer, as simulators are an increasingly popular tool in their integration into…