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…

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…

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…

This study aims to clarify the role of generating questions in mathematical modeling and construct principles for teaching and learning mathematical modeling with an emphasis on generating questions. To achieve this purpose, the role of generating questions was determined by solving a sprinkler problem and considering the investigation process.…

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…

Background and Context: Productive failure (PF) is a learning paradigm that flips the order of instruction: students work on a problem, then receive a lesson. PF increases learning, but less is known about student emotions and collaboration during PF, particularly in a computer science context. Objective: To provide insight on students' emotions…

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…

This research aims to explore both the individual and combined relationships between the use of GeoGebra and productive disposition with students' strategic competence. The use of GeoGebra involves teacher-led activities designed to assist students in managing and engaging with learning, serving as a tool to enhance mathematics learning outcomes.…

Pair programming (PP), as a mode of collaborative problem solving (CPS) in computer programming education, asks two students work in a pair to co-construct knowledge and solve problems. Considering the complex multimodality of pair programming caused by students' discourses, behaviors, and socio-emotions, it is of critical importance to examine…

In this essay, I review Sarah M. Stitzlein's "Teaching Honesty in a Populist Era: Emphasizing Truth in the Education of Citizens," which addresses the decline of honesty in education and politics in the context of rising populism. Stitzlein advocates for a pragmatist inquiry approach to teaching, arguing that students should engage in…

Fostering creative thinking and promoting metacognitive processes are two major goals of 21st -century education. Recent research has pinpointed the essential role of meta-creativity in the process of creative thinking. Nevertheless, the concept of meta-creativity has not been widely adopted. The purpose of the present study is, therefore,…

This paper illustrates the design-based learning (DBL) approach to promoting the deep learning of students and improving the quality of teaching in engineering design education. We performed three aspects of research with students in a typical educational activity. The first study investigated students' deep learning before and after the DBL…