This study aimed to develop and validate the Creative Problem-Solving Skills Test (CPSS-T), grounded in Torrance's creativity theory, to assess these skills in university students. The CPSS-T consists of five open-ended question types, each designed to measure different aspects of creative problem-solving: Alternative Use, Hypothetical Scenario,…

In XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus' "Arithmetica", Pierre de Fermat stated that Diophantine equations of the Pythagorean form, x[superscript n] + y[superscript n] = z[superscript n], have no integer solutions for n > 2, and (x, y, z) > 0. Of this statement, however, Fermat…

Background: One area that has been dramatically changed by artificial intelligence (AI) is educational environments. Chatbots, Recommender Systems, Adaptive Learning Systems and Large Language Models have been emerging as practical tools for facilitating learning. However, using such tools appropriately is challenging. In this regard, the…

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely…

There is a clear need for highly competent health sciences experts. No instrument currently exists for assessing the generic competences of health sciences students. The aim of this study is to develop and psychometrically test the Health sciences Generic Competence (HealthGenericCom) instrument. The instrument development four step process has…

In this cross-national study, we explore the different ways of reasoning-and-proving (RP) presented in three 8th grade textbooks, one from each country: Turkey, Norway, and Slovakia. While the analysis revealed that all three textbooks contain similar numbers of problems involving some form of RP, differences exist in terms of the dominating ways…

Background/purpose: The application of learning models is expected to significantly promote the enhancement of students' problem-solving abilities through the development of interactive learning models. This study aims to (1) determine whether the Development of the Component Display Theory (CDT) Model is categorized as valid, practical, and…

The literature on proof by contradiction (PBC) is nearly unanimous in claiming that this proof technique is "more difficult" for students than direct proof, and offers multiple hypotheses as to why this might be the case. To examine this claim and to evaluate some of the hypotheses, we analyzed student work on proof construction problems…

This study aimed to develop a valid and reliable scale for determining teachers' needs to increase their efficiency in professional practice. The stages of creating an item pool, consulting expert opinions, pilot testing, and conducting validity and reliability analyses were followed. Initially, a 46-item pool was created based on a literature…

Education currently only prioritizes mastery of scientific aspects and students' intelligence. Math problems are still related to fictitious general knowledge. For this reason, local wisdom-based learning is needed whose learning is packaged using objects, events, and various things that are close to students' lives to raise the local potential of…

In recent years, numerous research studies have highlighted how teachers' perceptions of educational robotics (ER) and their sense of self-efficacy can influence the learning process. Although different instruments exist to investigate teachers' perspectives on ER, the Robotics Interest Questionnaire (RIQ) scale, developed within the Portuguese…

Educational leaders' effectiveness in solving problems is vital to school and system-level efforts to address macrosystem problems of educational inequity and social injustice. Leaders' problem-solving conversation attempts are typically influenced by three types of beliefs--beliefs about the nature of the problem, about what causes it, and about…

We present a validation study of fifteen new math anxiety scale items designed to augment the widely-used Revised Mathematics Anxiety Scale (RMARS). While the RMARS and other standard instruments measure students' anxiety in response to computation, test situations, and math course activities such as buying a textbook or watching a lecture, the…

Failure to deduce false suppositions in proof by contradiction is still considered "more difficult" than proving the conditional ?? to ?? in proof by contraposition. This study aims to identify the types of proof construction failures based on the action steps of proof by contradiction, then offer a framework of construction failure…

Bayesian Knowledge Tracing (BKT) is a well-established model for formative assessment, with optimization typically using expectation maximization, conjugate gradient descent, or brute force search. However, one of the flaws of existing optimization techniques for BKT models is convergence to undesirable local minima that negatively impact…