Differential equations (DEs) are a powerful tool for modeling real-world contexts. Most research in this area has examined students' understanding and reasoning with pre-packaged DEs, with little attention being given to setting up sophisticated DEs to model complicated real-world situations. This study contributes through a collective case study…

The invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on…

The objective of this work was the theoretical modeling of a construct based on teaching practice about the perception that pupils have of difficulties in problem solving (PS) in experimental sciences, specifically physics, to predict pupil performance in PS. The research was carried out with an incidental sample of second year of secondary…

Successful computer-based assessments for learning greatly rely on an effective learner modeling approach to analyze learner data and evaluate learner behaviors. In addition to explicit learning performance (i.e., product data), the process data logged by computer-based assessments provide a treasure trove of information about how learners solve…

The aims of this study were to synthesize and evaluate the learning model in gamification environment together with cartoon animation media to promote students' creative problem-solving skills. This study was divided into three phases, (i) synthesized and evaluated the appropriateness of learning model (ii) developed cartoon animation and (iii)…

One of the popular creativity methods to solve technical problems is the Theory of Inventive Problem Solving, (TRIZ), however, requires a considerable investment of time. A teaching methodology for a simplified version of TRIZ (TRIZ10) has been developed for reducing learning time and improving the creative process in solving technical problems.…

In this paper, we draw on recent research on so-called Fermi problems and situate the fundamental principles underlying this type of tasks and their use from a task design perspective. We use the models and modelling perspective on teaching and learning to elaborate on aspects related to the design of single-use, as well as sequences of, Fermi…

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…

Mathematical modelling is an interlinking process between mathematics and real-world problems that can be applied as a means to increase motivation, develop cognitive competencies, and enhance the ability to transfer mathematical knowledge to other areas of science, such as engineering disciplines. This study was designed to investigate the effect…

This study proposes a model of several dimensions through which products of teachers' context-based mathematics problem posing (PP) can be modified. The dimensions are Correctness, Authenticity, Task Assortment (consisting of Mathematical Diversity, Multiple Data Representations, Question-Answer Format, Precision-Approximation, and…

Critical thinking is a key transversal competency of the 21st century, but some students have difficulty, especially during the transition to online learning due to the COVID-19 pandemic. This study aims to identify epistemological obstacles in critical thinking related to proof, generalization, alternative answers, and problem-solving. This…

This study investigates the affective and performative effects of ludicization, i.e., the process of transforming the original contexts into immersive ludic experiences based on metaphorized desired behaviors and reflexive space, on language learning. The effects of ludicization are based on an integrated model involving multidimensional…

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…

Nature-inspired designs/organic designs exhibit a very close resemblance with nature especially in terms of form and structure. Form giving for organic design is a special class of design problem that involves the use of inspiration and analogies from nature for creative problem-solving. There is insufficient research in understanding this…

Problem posing is a promising teaching method for enhancing motivation and performance in mathematics and more specifically in mathematical modelling. Hence, the goals of our study were twofold: (1) to examine the effects of problem posing on modelling performance, self-efficacy, and task values in solving modelling problems, and (2) to analyze…