The primary goal of the study was to explore first-grade children's reasoning about plane and solid shapes across various kinds of geometric representations. Children were individually interviewed while completing a shape-matching task developed for this study. This task required children to compose and decompose geometric figures to identify…

This study aimed to investigate the informal cognitive structures regarding "point" and "straight line"--two basic and undefined terms of geometry--in children registered in preschool--the previous step before in-class formal education process. The study was conducted with the participation of 50 children enrolled in nursery,…

The ability to rotate visual mental images is a complex cognitive skill. It requires the building of graphical libraries of information through short or long term memory systems and the subsequent retrieval and manipulation of these towards a specified goal. The development of mental rotation skill is of critical importance within engineering…

Technology is an indispensable part of the educational curriculum, and large budgets have been allocated to provide technological infrastructure in secondary education institutions in Turkey. It is important that teachers have the technological pedagogical content knowledge (TPCK) to successfully integrate technology into their courses. The aim of…

The important role that geometry plays in the mathematics curriculum has been extensively documented. However, the reduction of geometry in school mathematics, and the focus on basic computation and procedures, raises the question of the competencies students acquire and the classroom atmosphere in geometry lessons. The goal of this multiple case…

Many aspects of the geometry of linear statistical models and least squares estimation are well known. Discussions of the geometry may be found in many sources. Some aspects of the geometry relating to the partitioning of variation that can be explained using a little-known theorem of Pappus and have not been discussed previously are the topic of…

Symmetric objects are known to be perceived easier than asymmetric objects, because less information has to be processed. Therefore, symmetric objects are often used for spatial tasks. However, in perspective-taking the use of symmetric objects can also cause difficulties, as two side-views of these objects are mirror-images of each other. To…

The aim of the research is to investigate the transformation of the perception process through mathematics education, by an example of scanning the Cartesian coordinate system in order to locate a target point. We compared participants with different competence in mathematics. Historically, motion along axes appeared as a specific…

Purpose: In spring 2020, educators throughout the world abruptly shifted to emergency remote teaching in response to an emerging pandemic. The instructors of a graduate-level synchronous online geometry and measurement course for practicing school teachers redesigned their summative assessments. Their goals were to reduce outside-of-class work and…

Students' difficulties in mathematics and science may stem from interference of irrelevant salient variables. We focus on the comparison of perimeters task, in which area is the irrelevant salient variable. A previous fMRI brain-imaging study related to the comparison of perimeters task suggested that increasing the level of salience of the…

This study investigates the effectiveness of a teaching activity that aimed to convey the meaning of indeterminate forms to a group of undergraduate students who were enrolled in an elementary mathematics education programme. The study reports the implementation sequence of the activity and students' experiences in the classroom. To assess the…

This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts,…

As indicated in numerous research studies, schoolchildren encounter many difficulties and obstacles in learning the multifaceted concept of the angle. In order to explore the possibility of enhancing schoolchildren's understanding of such a concept, the authors present a study that aims at investigating some structural characteristics of…

Students engage in proportional reasoning when they use covariance and multiple comparisons. Without rich connections to proportional reasoning, students may develop inadequate understandings of linear relationships and the equations that model them. Teachers can improve students' understanding of linear relationships by focusing on realistic…

This research explores the question, "Do students who were accelerated in grade eight complete high school mathematics courses at a similar rate to students who were not accelerated?" Data was examined for students who took the New York State (NYS) 2012 Integrated Algebra assessment and students who took the 2015 Common Core Algebra…