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…

Bayesian Knowledge Tracing (BKT) is a well-established model for formative assessment, with optimization typically using expectation maximization, conjugate gradient descent, or brute force search. However, one of the flaws of existing optimization techniques for BKT models is convergence to undesirable local minima that negatively impact…

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…

With a forward-looking and problem-solving mindset, this article aims to combine theoretical knowledge and empirical evidence from different schools of thought in the field of second language (L2) learning and teaching--namely, instructed second language acquisition, generative linguistics, and an ecological perspective that includes multiple…

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…

Purpose: To determine the factors influencing the perception of undergraduate students toward research--teaching nexus and also to examine its impact on the attitude of the students. Design/methodology/approach: The study used a quantitative design to examine the perceptions of students in higher education institutions in India. Descriptive and…

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…

Background: Both learning and problem solving are major goals of complex problem solving in engineering education. The order of knowledge construction and problem solving in learning through problem solving, however, has not been explained in current literature. Objectives: To understand their relationships, this study compared the effects of…

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'…

Meaningful and impactful learning experiences are rife with failure. And yet, students struggle with framing, tolerating and attributing failure in a positive manner within the post-secondary learning context. This paper explores whether using design thinking as a pedagogical approach might help students learn to tolerate, reframe and attribute…

Purpose: The purpose of this article is to describe the similarities between abductive reasoning and entrepreneurial learning processes in order to contribute to the conceptual understanding of learning as an entrepreneurial process in itself. Design/methodology/approach: The research is theoretically rooted in a conceptual development of the…

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] This manuscript discusses how learning theories have been applied to shape multiple aspects of the design of curricular activities combining interactive computer simulations and University of Washington style tutorials (so-called simulation-tutorials).…

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…