This paper aims to characterise an indicator of the development of the number sequence scheme among students at the level of Compulsory Secondary Education (14-16 years old students). To do so, we use a scheme development proposed by the APOS theory to characterise students' use of relations between mathematical elements when solving a…

The aim of this article is to assess the effects on learners' emotions and emotion regulation of an intervention promoting the development of cognitive strategies for mathematical problem-solving and positive perceptions of problem-solving competence (SEP), embedded in an overall self-regulated approach, with upper elementary students (N = 334,…

The National Association for Gifted Children and The National Council of Teachers of Mathematics both call for problem posing. This article illustrates the strategies used during a series of three Three-Act Tasks to foster second grade students' abilities to problem pose. The students' problem posing improved across the three Three-Act Tasks and…

We analyzed the written answers and explanations by 26 Brazilian high-school students who attempted to solve double and multiple proportionality problems using the cross-product algorithm. We focused on students' awareness of the scalar and functional relations among the quantities described in verbal problems, an aspect that has been part of…

This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We…

The impact of solving novel video-inspired homework problems on learning attitudes toward chemical engineering was examined at beginning and end of an undergraduate material and energy balances course using a modified Colorado Learning Attitudes about Science Survey instrument. Mean overall attitude of participants improved by a normalized gain…

According to the Workforce Innovation and Opportunities Act of 2014, literacy refers to "an individual's ability to read, write, and speak in English, compute, and solve problems [emphasis added], at levels of proficiency necessary to function on the job, in the family of the individual, and in society" (Title 2, §203). Yet, according to…

The purpose of this note is to introduce two challenging problems in geometry that were inspired by some well-known problems in high school geometry. These problems can be explored in the dynamic geometry environments of computer construction programmes.

This commentary provides an overview of abduction, also known as Inference to the Best Explanation, and argues that the term and relevant problem-solving methods should be adopted by chemistry educators. Abductive reasoning, especially within the context of science and medicine, continues to be an active area of exploration for philosophers and…

Systematic errors are unfortunately common in analyses performed by students in teaching laboratories. Quality control (QC) tools are required to detect and solve bias in laboratory analyses. However, although QC has become routine in real-world laboratories, it is still rarely applied in teaching laboratories. For this reason, systematic errors…

Eye movement modelling examples (EMME) are computer-based videos displaying the visualized eye gaze behaviour of a domain expert person (model) while carefully executing the learning or problem-solving task. The role of EMME in promoting cognitive performance (i.e., final scores of learning outcome or problem solving) has been questioned due to…

The incubation effect (IE) is a problem-solving phenomenon composed of three phases: pre-incubation where one fails to solve a problem; incubation, a momentary break where time is spent away from the unsolved problem; and post-incubation where the unsolved problem is revisited and solved. Literature on IE was limited to experiments involving…

This study concerns a professional development course designed and implemented for prospective teachers, centred on a teaching method regarding problem-solving activity, namely, the Thinking Classroom. The study is framed in the theory of cultural transposition, a perspective about the encounter with teaching practices from different…

Over its short disciplinary history, computing has seen a stunning number of descriptions of the field's characteristic ways of thinking and practicing, under a large number of different labels. One of the more recent variants, notably in the context of K-12 education, is "computational thinking", which became popular in the early 2000s,…

Scholars have examined Revans' problem-solving praxeology in many contexts but have not fully explored the concept in the case of physical co-location. Hence, we focussed on investigating Revans' conceptualisation in a co-located context by paying particular attention to the 'different forms of learning' that emerged from it. The research setting…