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 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…

In this article, I present selected extracts and formulations from John Dewey's seminal book "Democracy and Education" (1916) that speak to the question of the educational purpose of PBL. Dewey's work, and in particular this book, is in many ways foundational in regard to arguing for PBL as an educational approach. However, in…

This article uses the concurrent mixed methods design to explore the errors made by 171 Grade Seven learners in algebraic problem-solving within the Assin Central Municipality in Ghana. The participants were categorized into low-achieving and high-achieving groups based on their performance in a pretest, to help provide a detailed examination of…

The educational benefits of challenge- or problem-based approaches to learning are now well established. Action Research (AR) and Action Learning (AL) together provide educators with an ethic, a research methodology and a pedagogical strategy for harnessing and developing the motive power of purposeful activity for reflective enquiry in teaching…

In this paper, this theme of the open question is offered as a hermeneutical approach to problem-based learning. Most of the scientific literature on problem-based learning is in the realm of the behavioral-sciences. To the extent that the latter becomes the exclusive focus of research on problem-based learning, there is a risk of…

Example-based learning is a well-known instructional method for effective cognitive skill acquisition in complex domains. "(Contrasting) erroneous examples" are a promising extension that embed errors in instructional material, potentially fostering not only positive but negative knowledge. However, the mechanisms and conditions for…

Research carried out through the last 20 years gave us undeniable evidence that to learn anything we need to be active participants, not passive observers. One of the important aspects of learning physics is constructing explanations of physical phenomena. To support and guide students toward constructing their explanations, teachers need to be…

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…

The study examines language dimensions of mathematical word problems and the classification of mathematical word problems according to these dimensions with unsupervised machine learning (ML) techniques. Previous research suggests that the language dimensions are important for mathematical word problems because it has an influence on the…

The exploration of children's drawings as mathematical representations is a current focus in early years mathematics education research. This paper presents a qualitative analysis of 72 kindergarten to Grade 3 (5 to 8 years old) children's drawings produced during problem-solving tasks centred on multiplicative strategies. Existing frameworks for…

A hallmark of effective teaching is that it grants learners not just a collection of facts about the world, but also a toolkit of abstractions that can be applied to solve new problems. How do humans teach abstractions from examples? Here, we applied Bayesian models of pedagogy to a necklace-building task where teachers create necklaces to teach a…

"Kurikulum Merdeka" is a learning experience framework that offers flexibility and focuses on essential content, character development, and students' competencies. Teachers had the discretion to develop their modules to choose, design, and organize the learning contents for students, based on their needs. By using that module, there is…

Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural…