The purpose of this study was to examine the effects of a number line intervention with supported self-explanation on student understanding of fraction magnitude and quality of explanation. Participants were three U.S. middle school students with significant behavior problems. Participants were given eight lessons containing explicit instruction…

The learning of mathematics generally undergoes a less effective and less appealing learning process, resulting in students' perceived lack of mastery of the material. Consequently, students' insufficient understanding of the concepts leads to a lack of folding back. In the process of understanding, it influences individual characteristics, where…

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…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

When teaching the multiplicative domain in New Zealand primary schools, teachers tend to spend a greater proportion of time on the meaning and processes of multiplication, to the detriment of a specific focus on understanding the concept of division. When division is taught, it tends to be by reversing the context and turning the division…

Recognising the importance of developing creativity in education, the Programme for International Student Assessment (PISA) included an assessment of creative thinking for the first time in its 2022 cycle -- with the results summarised in the PISA 2022 Results (Volume III) report. While that report focused on comparing countries' performance on…

Background/purpose: Although mathematical representation ability is a significant ability and an interesting topic to study, quite a few researchers have studied this ability, and even fewer have examined it through the implementation of epistemic learning patterns based on problem-solving. In fact, this learning pattern is epistemic and makes…

This study explores the ontological perspective in analyzing students' problem-solving related to mechanical energy conservation. The research involves 18 high school students whose explanations were qualitatively analyzed using an extended ontological framework. Initially, students predominantly employed matter-based predicates and…

Spatial thinking is ubiquitous in design. Design education across all age groups encompasses a range of spatially challenging activities, such as forming and modifying mental representations of ideas, and visualizing the scenarios of design prototypes being used. While extensive research has examined the cognitive processes of spatial thinking and…

Students with autism spectrum disorder frequently face challenges when learning mathematical concepts. For example, they may have difficulties solving mathematical word problems, in particular Cartesian product problems. This research is a case study with a multiple probe design in which the participants were three Spanish students diagnosed with…

Embodied forms of representation like gesture have been shown to play an important role in how learners conceptualize phenomena in physics; however, we know little about how students use gesture to capture the idea of "instantaneity." Drawing on multimodal microanalysis of interaction, we examine how undergraduate physics students use…

Cognitive presence is essential for deep and meaningful learning, yet developing it poses challenges. Theoretically, peer-led teaching presence can enhance cognitive presence, but research on this facilitation is limited. This study used behavioural sequence analysis to investigate how peer-led teaching presence promotes cognitive presence…

When teaching STEM courses, it is important to introduce state-of-the-art techniques. Students need to learn how to conduct experiments, analyse data and choose the most effective approaches to address meaningful situations. Here we present the assessment of the implementation of a structured inquiry-based activity aimed at teaching students about…

Creative thinking stems from the cognitive process that fosters the creation of new ideas and problem-solving solutions. Artificial intelligence systems and neural network models can reduce the intricacy of understanding creative cognition. For instance, the generation of ideas could be symbolized as patterns of binary code in which clusters of…

This paper presents the findings of a study involving 16 undergraduate students enrolled in a basic financial mathematics course. The study aimed to examine the nature of the students' problem-posing and problem-solving products and processes, as well as the interactions between the two. The findings revealed that the majority of the posed…