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…

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…

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…

This work provides inspiration to foster Problem-Based Learning (PBL) in teaching practices related to waste management. Problem-Based Learning is about providing a learning environment where students can work practically and theoretically with problems of relevance for society. In this learning process, students themselves will define societally…

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…

Introductory programming courses (CS1) are difficult for novices. Inspired by "Problem solving followed by instruction" and "Productive Failure" approaches, we define an original "necessity-driven" learning design. Students are put in an apparently well-known situation, but this time they miss an essential ingredient…

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…

Functional communication training (FCT) is an evidence-based intervention that has been widely used and implemented to reduce problem behavior and teach replacement behavior in a variety of settings. Specific procedures have been researched and documented to ensure correct implementation. Functional communication training can be broken into three…

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…

Arguably, constructive alignment has been the major challenge for assessment in the context of problem-based learning (PBL). PBL focuses on promoting abilities such as clinical reasoning, team skills and metacognition. PBL also aims to foster self-directed learning and deep learning as opposed to rote learning. This has incentivized researchers in…

Because of the lack of tools available to assess problem-solving skills, teachers often revert to more traditional instructional approaches (e.g. lecture-based, memorization) that fail to prepare learners for the complexity of dynamic work environments. To overcome this challenge, technology solutions are needed that accurately and efficiently…

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…