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…

Background/purpose: This research is motivated by the difficulties often experienced by students in adapting to their first year of college, especially related to learning calculus. To address these difficulties, a solution needs to be found so that these problems can be resolved. One solution that is expected to yield optimal results in…

Thirty-seven third graders and thirty-two first graders engaged in solving a tangram puzzle in the shape of a fox. They had five minutes to solve the puzzle, and after this time, they received guidance on the particular piece they had difficulties with. Through the lenses of navigating flexible abstraction, reinterpretation, combinations, and…

Do children consider how others learned when seeking help? Across three experiments, German children (N = 536 3-to-8 year olds, 49% female, majority White, tested 2017-2019) preferred to learn from successful active learners selectively by context: They sought help solving a problem from a learner who had independently discovered the solution to a…

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…

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…

Word problems are frequently taught in shallow contexts, where students primarily use procedural knowledge to solve problems and struggle to transfer their learning to real-life situations. This study examines how extra-mathematical knowledge and motivation may enhance the learning process. The study involved 345 fifth-grade students (51.2% male)…

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…

The creative programming language Processing can be used as a generative architectural design tool, which allows the designer to write design instructions (algorithms) and compute them, obtaining graphical outputs of great interest. This contribution addresses the inclusion of this language in the architecture curriculum, within the context of…

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…

Gestures--hand movements that accompany speech and express ideas--can help children learn how to solve problems, flexibly generalize learning to novel problem-solving contexts, and retain what they have learned. But does it matter who is doing the gesturing? We know that producing gesture leads to better comprehension of a message than watching…

Productive peer talk moves have a fundamental role in structuring group discussions and promoting peer interactions. However, there is a lack of comprehensive technical support for developing young learners' skills in using productive peer talk moves. To address this, we designed iTalk-iSee, a participatory visual learning analytical tool that…