Using Balacheff's (2013) model of conceptions, we inferred potential conceptions in three examples presented in the spanning sets section of an interactive linear algebra textbook. An analysis of student responses to two similar reading questions revealed additional strategies that students used to decide whether a vector was in the spanning set…

The introduction of games as a teaching and learning strategy in the classroom is a pedagogical resource that presents excellent results, as it creates situations that allow the students to develop problem solving methods, stimulate their creativity and at the same time generate motivation. The theories of learning are used to describe the motives…

Intelligent tutoring system (ITS) provides learners with step-by-step problem-solving support through scaffolding. Most ITSs have been developed in the USA and incorporate American instructional strategies. How do non-American students perceive and use ITS with different native problem-solving strategies? The present study compares Stoich Tutor,…

In this paper we present a novel adaptation of a tri-phase assessment tool, originally devised to investigate students' linear equations-related strategy flexibility, to evaluate Danish grade-six students' multidigit arithmetic-related strategy adaptivity and flexibility. Participants, 731 students, median age 12 years and drawn from 20…

The process of creative problem-solving (CPS) commonly demands that individuals consciously or unconsciously integrate creative ideas from a vast array of diverse information. Using a masked priming paradigm and the Chinese remote associates test (RAT), this study provides innovative behavioral evidence for the integration of multiple unconscious…

The flipped classroom (FC) and case-based learning (CBL) are recognized as effective instructional models that emphasize the development of problem-solving ability. However, the implementation of FC combined with CBL has not been well explored. This study aims to investigate the effect of FC combined with CBL on students' problem solving by…

In this paper, the multidigit arithmetic-related strategy adaptivity, strategy flexibility and solution accuracy of Danish compulsory school students is examined. Participants, 749 grade three, 731 grade six and 818 grade eight, were drawn from twenty demographically different schools. Drawing on a tri-phase assessment tool, each student completed…

Despite the growing emphasis on integrating collaborative problem-solving (CPS) into science, technology, engineering, and mathematics (STEM) education, a comprehensive understanding of the critical factors that affect the effectiveness of this educational approach remains a challenge. This study aims to identify effective strategic and behavioral…

In the realm of mathematics education, geometry problems assume a pivotal role by fostering abstract thinking, establishing a connection between theory and practice, and offering a tangible portrayal of reality. This study focuses on comprehending problem-solving methodologies by observing the eye movements of 45 primary and multi-year grammar…

This study examines the solutions of 34 kindergarten children as they create equal groups from n bottle caps, where n was equal to 8, 9, 22, and 23. For each n, children were asked to find as many different solutions as possible. The number of solutions they found, i.e., children's fluency, as well as the strategies used to create equal groups,…

Idea evaluation has been identified as a critical step in the creative problem-solving process. Yet, it is unclear how exactly individuals evaluate and compensate for weaknesses in their creative ideas. In the present study, both qualitative and quantitative methods were used to identify the compensatory strategies that undergraduate participants…

Problem-solving strategies are crucial in learning programming. Owing to their hidden nature, traditional methods such as interviews and questionnaires cannot reflect the details and differences of problem-solving strategies in programming. This study uses the Hidden Markov Model to detect and compare the problem-solving strategies of different…

Problem-solving strategies, such as visual imagining and self-questioning, may assist children with autism spectrum disorder (ASD) in recalling past events. In the current study, at the start of each session, a 7-year-old boy with ASD engaged in a novel activity with a behavior therapist who took pictures of the activity. Ninety minutes later, a…

Public education in the United States is breaking down on two dimensions: its bureaucratic organization and its conceptualization of the learning process. These breakdowns result from attempts to deliver public education using business models and have failed to support the needs of both students and teachers. This breakdown has been further…

Self-explanation prompts in example-based learning are usually directed backwards: Learners are required to self-explain problem-solving steps just presented ("retrospective" prompts). However, it might also help to self-explain upcoming steps ("anticipatory" prompts). The effects of the prompt type may differ for learners with…