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…

A new approach, termed the "scale factor method," is presented for solving a variety of stoichiometry problems. Students taught to solve mass-mass stoichiometry problems using this method found it more intuitive and had a higher rate of success than students using the traditional dimension analysis approach. The scale factor approach…

One hundred years ago, Paul Weiss and Ludwig von Bertalanffy independently proposed that living organisms interact with their environment through systems. In the century that has followed, systems thinking and modeling have grown in tandem with discovery of the vast complexity of the universe at microscopic through astronomic levels. As our…

In this article, the author will demonstrate how gestures--often used in combination with offloading information on scratch paper--can be used to help students with difficulties in mathematics succeed with secondary level algebra. The authors will provide key examples from three studies of the algebra learning of students with mathematics…

In the context of a rapid digital transformation, digital competence is now regarded as a fourth cultural skill complementing reading, writing, and arithmetic. We argue that a well-structured and sound competence model is needed as a shared foundation for learning, teaching, pedagogical diagnostics and evaluative schemes in the school system.…

Cognitive load theory's incorporation of evolutionary perspectives has generated several instructional designs based on movement, including the tracing effect, occurring when learners benefit from explicit instructions to trace out specific elements of lesson materials with the index finger. Historical descriptions of children's tracing behaviours…

The nature of the development of arithmetic performance has long been intensively studied, and available scientific evidence can be evaluated and synthesized in light of Nelson and Narens' model of metacognition. According to the Nelson-Narens model, human cognition can be split into two or more interrelated levels. Obviously, in the case of more…

The author presents a child-centered approach to teaching, developed through longtime connections with colleagues, which concentrates on the children and provides them time to make their own connections, to learn, to think, and to develop at their own pace with the support of their classmates. Two examples of how mathematics interlaced into…

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…

Research suggests that most college and beginning graduate students lack the cognitive complexity required to engage in effective practical and ethical reasoning. Studies on cognitive development support the view that how people approach complex problems varies significantly depending on the underlying epistemic assumptions they use to guide their…

It is often necessary to enrich the teaching environment in order for students to learn optics in depth and to interpret the real optical situations with the information they have learned. In this study, a virtual teaching environment was developed using by Algodoo, a 2D simulation software. An eye model was created in order to explain the…

Visual literacy is essential for engineers. Technological professions have important visual characterization, both in the transmission of information and problem-solving. This means that future engineers must be proficient at communicating, thinking, and learning visually. However, engineering curricula takes partially the need to have visually…

Amidst a steady clamor about "learning loss" during the pandemic, a minority of educators have cautioned we must, in the words of Donna Haraway, "stay with the trouble," giving children space to grieve, explore, and make sense of a new reality. In this paper I interrogate what it means to stay with trouble and specifically call…

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…

Retrieval practice has been widely studied as an effective strategy for enhancing memory. In this review article, we discuss how its effects on learning complex problem-solving procedures are less straightforward, however, with repeated studying of worked examples sometimes more effective than problem-solving practice. This worked example benefit…