The Pirie-Kieren Model (PKM) was a paradigm shift in theories of learning by presenting a coherent, consistent theory compatible with complexity theory. PKM recognized that learning is non-linear, recursive, iterative, and emergent. PKM was one of the first theories to depart from the linear models of learning that dominated theories of learning…

This study proposes a model of several dimensions through which products of teachers' context-based mathematics problem posing (PP) can be modified. The dimensions are Correctness, Authenticity, Task Assortment (consisting of Mathematical Diversity, Multiple Data Representations, Question-Answer Format, Precision-Approximation, and…

We live in an increasingly worrying future, where researchers are looking at how we can create education for a sustainable world. In this study we investigate what such education could look like, especially for young students, reinforcing hope and an ability to act and come up with ideas of sustainable solutions with no obvious 'good' solution.…

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…

Geometry and spatial reasoning form the foundations of learning in mathematics. However, geometry is a subject often ignored by curriculum writers and teachers until high school, leading to students lacking in critical skills in geometric reasoning. As the United States moves into a new curriculum epoch, heralding the commencement of the national…

We investigated the advancement of self-regulated learning (SRL) in diverse educational settings, including science, mathematics, and humanities disciplines. We identified practices for assessing students' SRL and encouraging reflection. The research questions were: (1) Can sustained changes in students' perceptions of SRL over time be assessed,…

Researchers have suggested that initial attempts to change mathematics instruction often leave educators "with no framework for the kinds of specific, constructive pedagogical moves" they might make (Chazan & Ball, 1999, p. 2). The intent of this article is to introduce a framework for teaching and learning mathematics that is robust…

In mathematics education research, proofs are often conceptualized as sequences of mathematical assertions. We argue that this ignores proofs that contain instructions to perform mathematical actions, often in the form of imperatives, which are common both in mathematical practice and in undergraduate mathematics textbooks. We consider in detail a…

This research reports the implementation of an evaluation instrument of the slope concept in high school students. The design of this study was based on four dimensions: Skills, Properties, Uses and Representations (SPUR model; Thompson & Kaur, 2011) and on three conceptualizations: constant ratio, behavior indicator and trigonometric…

The review followed the preferred reporting items for systematic review and meta-analysis (PRISMA) standard to search and report relevant articles on the use of SOLO model in mathematics. A systematic search was conducted in Education Source, ERIC, JSTOR, and PsycINFO databases and yielded 198 studies. After screening and appraisal, 62 papers (37…

Most mathematicians state mathematics is a field of beauty, creativity, and innovation, yet what is echoed by students is not how mathematics allows students to explore, but rather the ways in which it constrains and does not necessitate creativity. In comparison, many students associate coding with freedom, and the ability to create and express…

Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

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…

There has been great progress towards Reinforcement Learning (RL) approaches that can achieve expert performance across a wide range of domains. However, researchers have not yet applied these models to learn expert models for educationally relevant tasks, such as those taught within tutoring systems and educational games. In this paper we explore…

While the importance of collaborative problem-solving has been highlighted as an important skill by the OECD (Organisation for Economic Co-operation and Development), no specific model exists for mathematics facilitators to implement when engaging their students in group problem-solving. In this paper, we introduce the CoPs model for Collaborative…