While in traditional mathematics teaching methods, it is possible to prove concepts while teaching geometry and to reach generalizations that require more complex definitions by using concept findings, while in today's geometry teaching, learning that activates the student's discovery process gains importance. In this context, the aim of this…

A one-degree angle would certainly be difficult to draw accurately, especially without the aid of other tools like a protractor. However, mentally making a one-degree angle in visualized imagination is not only possible, but it is important for students' emergent understandings of angular measure. When students begin learning about length,…

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

In this paper, a learning progression for geometric transformations is developed based on research that demonstrates the importance of viewing transformations as functions of the plane. The 5 levels of the progression reflect a student's evolving understanding of transformations as functions and their evolving understanding of the domain of these…

The purpose of this study was to examine the primary and secondary color preferences of students with special needs as well as their color preference for an object regarding their disability types, school levels, and gender. The study employed a survey research design with quantitative methodology. It was conducted with the participation of 549…

In this study, we devised research design that provides pre-service teachers to effectively experience embodied geometric thinking with the goal that it will impact teachers' instruction to students in their classrooms. Using a motion-capture video game and design tool, we offered opportunities for pre-service teachers to experience of performing…

This study aims to explore an educational learning environment that supports students to learn conceptual modelling with the unified modelling language (UML). In this study, we call the describing models "UML programming." In this paper, we show an educational UML programming environment for science, technology, engineering, art, and…

In this article, we develop a theoretical model for restructuring mathematical tasks, usually considered advanced, with a network of spatial visual representations designed to support geometric reasoning for learners of disparate ages, stages, strengths, and preparation. Through our geometric reworking of the well-known "open box…

Incorporating Vygotsky's concept formation theory and Berger's appropriation theory, an assessment which highlights authentic operations with the concept of area was designed and administered to 44 sixth grade students to determine what types of understanding they maintained. The results indicated the more novel the situation, the more diverse…

Adoption of the Common Core State Standards present challenges to school districts, school administrators, and teachers. To assist in this endeavor, we present our work on unpacking the CCSS-M for the length, area, and volume Learning Trajectory (LT). The overarching theme of "genetic epistemology" and a five-characteristic framework…

This dissertation reports the results of a qualitative research project on area measurement. The study utilized structured, task-based interviews with students to (a) investigate the ways students enumerate and structure two-dimensional space with a variety of area units; (b) identify conceptual, procedural, and intuitive aspects of area…

This study was designed to determine if a relationship exists between student characteristics and the practice of grade retention. Specifically, student characteristics include gender, ethnicity, socioeconomic status, early birth date, and students who are English Language Learners (ELL). The student sample included 1,187 participants from a large…

Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)

Discusses solving rotation problems and shows that there is an alternative to using mental rotations or their encoding into verbal terms, namely using geometrical properties. Presents an analysis of the functionality and effectiveness of the different kinds of strategies as a function of the task's characteristics. Describes research to improve…

Details of pupil exploration as to the largest number of sides that a polygon could have on a geoboard are presented. The problem is not seen as open-ended, but many different avenues of pursuit stem from it. (MP)