The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out…

Research into mathematics education at university level includes a wide range of theoretical approaches. This poses considerable challenges to researchers in terms of understanding and harmonizing the compatibility and commensurability of those approaches. The research community has already problematised and studied these challenges using…

When children engage in play, they develop essential skills like creativity, flexibility, imagination, and problem-solving. Children who engage in STEAM (Science, Technology, Engineering, Arts, and Math) activities also build similar skills. Both play and STEAM enable children to ask questions, try different solutions, and develop explanations for…

Some readers thrive more than others because they are more actively involved in their learning. All students can become active participants in their learning through quality teacher prompting. In this article, teachers will learn how to promote emergent learners' active participation as they decode and comprehend, while problem-solving unknown…

To expand students' preparation for civic life, many teachers regularly engage students in discussions related to contentious issues. These discussions, however, typically restrict the range of communicative styles allowed and prioritizes disagreements between fixed and competing choices. Keith C. Barton & Li-Ching recommend that educators…

The tradition of studies involving the combinatorial approach to recurring numerical sequences has accumulated a few decades of tradition, and several problems continue to attract the interest of mathematicians in several countries. This work specifically discusses the Fibonacci, Pell, and Jacobsthal sequences, focusing on Mersenne sequences. The…

Like other health care practices, the increasing complexity in dentistry signals the need for a reconceptualisation of dentist professional learning. Professional dental bodies, at large, still privilege formal continuing professional development (CPD) provisions focusing on off-the-job activities despite growing evidence that much invaluable…

Context-aware mobile learning applications provide learning materials to suit the needs of individual learners. Despite several applications developed, there is a lack of architectural support for developing these applications. This has resulted in a number of challenges; lack of standardization, poor quality of developed applications, and…

Building on the original work of Bunker and Thorpe and their Teaching Games for Understanding (TGfU) approach to physical education, there is now a proliferation of Game Based Approaches (GBA) in the research literature (Bunker & Thorpe, 1982, A model for the teaching of games in secondary schools. "Bulletin of Physical Education,"…

Providing quality hands-on exercises in a GIS course is essential in enhancing problem-solving skills and student-led learning activities. However, the strategies and instructional methods of managing hands-on exercises, which have been used in traditional face-to-face classes, will require new interpretations in a virtual learning environment and…

Effective learning is viewed as an evolutionary process, and as such, it involves an expanded version of the Crenshaw-Collins view of "intersectionality." It demands an in-depth view of the complex socio-cultural-ethnic milieu in which students are embedded. Even more, effective learning requires effectance problem-solving, investigation…

Years of failed attempts to engage my mathematics teacher students in exploration and co-creation led me to radically change my teaching approach. Inspired by literature that uses the jazz improv metaphor for teaching, I derived three tenets based on principles from jazz improv. First, I would bring no more than a single problem-solving task to…

In research on mathematical problem posing, a broad spectrum of different situations is used to induce the activity of posing problems. This review aims at characterizing these so-called problem-posing situations by conducting three consecutive analyses: (1) By analyzing the openness of potential problem-posing situations, the concept of…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

Since Bruner's introduction of discovery learning in the 1960s, there has been an ongoing and intensive debate on the value of inductive teaching methods (e.g., problem-solving followed by instruction, such as in problem-based learning and productive failure) compared to deductive teaching methods (instruction followed by problem-solving, such as…