Comprehending and formulating strategies for geometry problems that require higher-order thinking skills (HOTS) is crucial in enhancing mathematics education. This study implements a qualitative case study approach to comprehend how prospective mathematics teachers with varying Adversity Quotients (AQ) solve geometry Higher-Order Thinking Skill…

This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

The authors present mathematics problems related to the packaging of sporting goods which they used to motivate and engage their students in the USA. This article reports on a series of questions/problems that were explored in groups by the students in a college class designed for sophomores, as part of a program to prepare them to be teachers at…

Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…

The ability to solve geometric construction problems is justly regarded as an essential component of mathematical culture. The dynamic, general nature of objects provided by dynamic geometry systems allows the development of intuitive methods for solving construction problems. The core mathematical concept underlying this approach is the loci…

Problem solving is one of the high-level thinking skills and essential in teaching mathematical concepts and procedures. The eye-tracking method allows educators to see and interpret different problem-solving behaviours of students. The purpose of this study was to investigate the problem-solving behaviours of university students based on eye…

This paper seeks to answer the question: How does the handling of the contradictions that emerge in activities of initial mathematics teacher education contribute to the learning of geometric knowledge when pre-service teachers and the teacher educator solve geometric construction problems with GeoGebra? A dialectical-materialist approach is used…

The purpose of this study was to investigate university students' conceptions of the definite integral in the process of finding the volume of a solid of revolution. The participants were four students enrolled in a university calculus course in Turkey. Data were obtained by task-based interviews, in which the participants had to work on a problem…

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

This study aims to test the effectiveness of GeoGebra Augmented Reality in improving students' mathematical problem-solving skills. The method used is a quasi-experiment with a posttest-only control group design. The research population is students of the Mathematics Education Study Program at a private university in Indonesia, with a sample of 32…

The current research trend of metacognitive regulation has shifted from an individual to a social context. One such social context is collaborative problem-solving. Interaction between group members is an essential factor in completing collaborative problems. Metacognitive regulation is divided into four forms based on the interaction in…

This study aims to determine the proof schemes used by primary education teacher candidates when solving a given problem and in their instructional explanations. Having a qualitative nature, the study utilized data collected from 277 third-year teacher candidates studying at the primary education department of the education faculty of a state…

This paper details an exploratory study of ten elementary preservice teachers (PSTs) involvement in the problem-solving process in a mathematics methods course. The dynamic, messy and nonlinear nature of this process was demonstrated by discussing PSTs' solution process of an open box construction problem. Effective approaches to solve this…

Habermas' construct of rationality is a tool adapted from social sciences into mathematics education to identify the difficulties in the proving process and to plan the teaching of proof for reducing these difficulties. According to Habermas, people engaged in an activity/action are considered to "act rationally" if they choose and use…

The aim of this study is to examine the effect of the learning environment designed based on different approaches on the change in pre-service teachers' approach preferences and geometry achievement in geometry problems. Twenty pre-service mathematics teachers were involved in geometry lessons for 10 weeks in a learning environment designed based…