In agreement with the main tenets of the anthropological theory of the didactic (ATD), this study uncovers dependencies between what students can learn, the established curriculum and the current state of mathematicians' mathematics ('scholarly mathematics'). One main result is that the mathematics taught, too often taken for granted by curriculum…

The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

This article revisits and expands upon a previous phenomenographic study characterising the qualitatively different ways in which South African undergraduate physics students may experience the use of +/- signs in one-dimensional kinematics (1DK). We find the original categorisation as applicable for interpreting Swedish university-level students'…

In this study, we aim to investigate the role of language in small group peer collaboration. Based on the notion of symmetrical scaffolding, we draw on theories of dialogic space and functional linguistics to analyse a transcript of three six-year-old students as they explore a shared understanding of 'two more than'. Using Martin and White's…

Transformative learning theory has provided a sound theoretical base for adult education's Western and Eastern academic field. This article aims to introduce the mandala model of transformative learning by transferring Mezirow's theory of perspective transformation onto a mandala map. In the mandala model, the learning agent exercises two…

In this paper I analyze a problem solving event in a secondary mathematics classroom. As the event unfolds, the teachers, including me, understand the event as involving interactions that were not related to learning. By adopting an expansive view of learning, I advance a different interpretation, that the interactions tell a story of student…

We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The…

Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.Motivated by the work of…

This paper presents a model for mastery learning. The framework for this model overlays the cognitive and knowledge dimensions from Krathwohl's revision of Bloom's Taxonomy, the Revised Taxonomy, with Polanyi's theory of personal knowledge. A simplified framework integrates Polanyi's concepts of subsidiary and focal awareness with the Revised…

This paper examines current views and definitions of learning transfer as well as their dominant characteristics. An alterior way to view learning transfer as preparation for future learning (PFL) is presented along with its defining features. This paper is divided into five sections: (a) what comprises learning transfer, (b) the conventional…

Research shows that teachers and educators struggle to act when conflict appears in the classroom. This article argues that (political) conflict should not be avoided or eradicated. Teachers should enable conflict and attend to their pupils in the process, in order to enable further understanding of each other and their differences, as part of…

Coordination class theory has proven to be a useful theoretical framework for describing processes of conceptual change in certain physical and mathematical concepts. Its development throughout different studies has allowed us to understand numerous mechanisms of conceptual learning by individual subjects. There have been attempts to implement…

In this study, we explored the ways in which listening tools within technology-mediated environments can facilitate children's self-regulation of instrumental music learning between lessons. This interpretive multiple case study utilized a software application assigned for 22 weeks to a piano teacher and four students (ages 8-10). Data sources…

Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on…