The goal of this article is to propose a framework for understanding the nature of "how people construct problems" by interacting with situations and subsequently to offer implications for instructional design and future research. We propose that people must interactively frame the components of a situation in order to establish the…

Process data from educational assessments enhance the understanding of how students answer cognitive items. However, effectively making use of these data is challenging. We propose an approach to identify solution patterns from operation sequences and response times by generating networks from process data and defining network features that…

Open mathematical modelling problems that can be solved with multiple methods and have multiple possible results are an important part of school curricula in mathematics and science. Solving open modelling problems in school should prepare students to apply their mathematical knowledge in their current and future lives. One characteristic of these…

Serious games are a growing field in academic research and they are considered an effective tool for education. Game-based learning invokes motivation and engagement in students resulting in effective instructional outcomes. An essential aspect of a serious game is the method of support for presenting the teaching material and providing feedback.…

This paper presents results of a study aimed at describing and discussing evidence/features of advanced algebraic thinking processes. To achieve these objectives, we analysed the written production of students enrolled in engineering courses working on mathematical modelling tasks related to differential equations. Our guiding question was as…

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in…

Complementary to existing "normative" models, in this paper we suggest a descriptive phase model of problem solving. Real, not ideal, problem-solving processes contain errors, detours, and cycles, and they do not follow a predetermined sequence, as is presumed in normative models. To represent and emphasize the non-linearity of empirical…

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…

In this integrative literature review, we synthesize the scant literature from the last 40 years of educational research on how school principals make difficult decisions. Reviewing 15 peer-reviewed articles, articles were coded for the methods used and their substantive findings. We review sampling techniques, the types of problems and methods…

Project-based learning (PBL) plays a critical role in fostering interdisciplinary integration within science, technology, engineering, and mathematics (STEM) education. However, its complexity often hinders students' ability to apply knowledge and solve problems, particularly in environments that lack psychological and cognitive support. This…

Creativity and problem-solving are 21st-century skills that students must have to respond to the complex world dominated by technology. Teaching activities integrating Design Thinking (DT) have the potential to cultivate individual skills. As future in-service teachers, pre-service teachers need to understand DT so as to be able to use it in their…

This paper develops a method for the construction and evaluation of cognitive models to support students in their problem-solving skills during robotics in school, aiming to build a basis for an implementation of a tutoring system in the future. Two Wizard-of-Oz studies were conducted, one in the classroom and one in the lab. Based on the…

Even after many decades of productive research, problem solving instruction is still considered ineffective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the…

Research often examines cognitive load as it relates to direct instruction, worked examples and problem-solving combined as an integrated whole. The present study examines these strategies in isolation to see their effect on cognitive load. Using learning materials covering the basics of critical thinking to undergraduate law students (n = 160) at…

Combinatorial proof is an important topic both for combinatorics education and proof education researchers, but relatively little has been studied about the teaching and learning of combinatorial proof. In this paper, we focus on one specific phenomenon that emerged during interviews with mathematicians and students who were experienced provers as…