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…

In this study, we analyzed and compared reasoning and proving opportunities in geometry lessons from American standard-based textbooks and Korean textbooks to understand how these textbooks provide student opportunities to engage in reasoning and proving activities. Overall, around 40% of exercise problems in Core Plus Mathematics Project (CPMP)…

Learning and teaching algebra concepts are frequent problems for both students and teachers alike. Students struggle to learn algebra, and teachers struggle to identify the best way to teach algebra. It is recurrent that teachers use instructional methods that promote memorization, and, consequently, the learning process may prove unsatisfactory.…

This study examined the identity resources used and the subject positions taken by secondary students in autobiographical narratives of their experiences with mathematics (mathographies). Data consisted of mathographies from 54 students in two differently tracked math courses at a large, diverse public high school in Brooklyn, NY. The study asked…

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics…

Educators have realized the importance of engaging students in learning. Teachers often see participatory behaviors like "hand raising" as evidence of students being engaged in an activity. These indications of engagement do not capture motivational factors behind true engagement. A research team developed a five item scale to easily…