Ill-structured problem solving is widely believed to promote learning in higher education but its multiplicity (i.e. multiple solutions and evaluation criteria) is often seen as a challenge to manage. This study shows that the multiplicity can be managed as well as leveraged to enhance learning effectiveness through online co-creation. Three…

An escape room can be a great way for students to apply and practice mathematics they have learned. This article describes the development and implementation of a mathematical escape room with important principles to incorporate in escape rooms to help students persevere in problem solving.

We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the…

In case library learning, an instructional method that promotes case-based problem solving, learners often struggle with indexing cases. Poor case indexing may hamper retention and retrieval of cases, hindering the construction of mental libraries in learners. To address this issue, the authors developed two indexing prompt types,…

Igniting excitement for physics in our students is a goal of every instructor. In this paper, we discuss a unique example of the concept of density, a subject that is rarely viewed as intriguing by students. By combining a problem involving dinosaurs and an effective density, our students' interest is often captured through calculating an…

This descriptive, cross-sectional study aims to examine the mediator role of problem-solving skills in the relationship between communication skills and classroom management. The participants were 431 randomly-sampled pre-service teachers who were studying at a university in the central Anatolia region of Turkey. The study data were collected via…

The purpose of this research is to classify the mathematical modelling problems produced by pre-service mathematics teachers in terms of the number of variables and to determine the mathematical modelling skills and mathematical skills used in solving the problems in each class. The current study is a qualitative research and the data was analyzed…

Case-based reasoning posits that learners can use their prior experience to solve new problems. This theory is cited to explain the benefits of problem-based learning (PBL), especially as it relates to knowledge structure development. However, critics argue that learners lack the relevant knowledge structures to simultaneously learn new content…

Intrapreneurship competence, as one of the main twenty-first century skills, has moved into focus, as it enables benefits for both organizations and individuals. To foster associated competencies and enable tailor-made instruction, teachers need knowledge not only about what their students can do but also about which errors are typically made…

Measurement concepts such as volume and surface area provide rich contexts for real-world applications of number processes. Despite their importance, many students and prospective teachers show superficial understanding of measurement concepts. A lack of spatial reasoning and integration of geometric knowledge in problem solving situations may be…

Two problem solving cycles are problem-based learning with two learning cycles that can improve students' higher order thinking skills. The knowledge of reproductive health is needed by the student, due to the student as future generation must be ready to facing the reproductive health problem in the future. This study aimed to determine the…

Collisions are real-world situations from everyday life (such as car crashes, playing billiards, etc.) that can be described and understood by the principle of conservation of momentum. One might expect that learning from simple collisions might help students understand more complicated physical phenomena. However, from our teaching experiences we…

In learning from examples, students are often first provided with basic instructional explanations of new principles and concepts and second with examples thereof. In this sequence, it is important that learners self-explain by generating links between the basic instructional explanations' content and the examples. Therefore, it is well…

Psychophysiological responses have been studied as objective indicators for measuring a learner's cognitive load. Previous studies have correlated pupil dilation or fixation length with increased cognitive load. Our aims were to confirm whether these findings could be applied in a general learning context and to verify the additivity hypothesis of…

The article uses dynamic visualizations in Excel to examine a variety of ways in which students can attain a much greater depth of understanding of optimization problems in introductory calculus. The topics discussed include a variety of common optimization problems that appear in virtually every calculus textbook that can all be enhanced…