Learning Transformation Geometry (TG) needs a more informal approach to concern situational problems. This study aims to develop actionable knowledge of TG in the form of design related to context and yet general enough to use digital manipulative activities in new situations. We propose such knowledge in the form of conjectured Local…

Although geometric transformations are functions, few studies have examined students' reasoning about these two important concepts. The purpose of this study was to examine the various ways students reasoned about functions in the context of pre-constructed, dynamic sketches of geometric transformations. We found that, regardless of prior…

The purpose of this study is to investigate how students' in senior grade of the high school participate in and interpret the transformational geometry activities integrated with cultural context. 5 students in senior grade participated in this study, all of whom live in Aydin district of Turkey. The main design of the study is qualitative.…

The relationship between spatial conceptions and students' spatial abilities is still rarely studied specifically, even though this is the basis for students to think in learning geometry. This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students'…

The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…

In a typical high school course, the complex physics of collisions is broken up into the dichotomy of perfectly elastic versus completely inelastic collisions. Real-life collisions, however, generally fall between these two extremes. An accurate treatment is still possible, as demonstrated in an investigation of coin collisions. Simple…

When examining transformations of the plane in geometry, teachers typically have students experiment with transformations of polygons. Students are usually quick to notice patterns with ordered pairs. The Common Core State Standard, Geometry, Congruence 2 (G-CO.2), requires students to describe transformations as functions that take points in the…

In this paper, we present the results of an experimental sequence of classroom activities on geometric transformations, proposed to high-school students. The activity is based on the use of a dynamic geometry system. Planned by a group of four people, two university professors and two research teachers, the activity has been elaborated together…

The main goal of the Learning and Teaching Geometry project is to build professional development materials that provide opportunities for teachers to learn about mathematical similarity through the use of videocases, in which specific and increasingly complex mathematical ideas are presented within the dynamics of classroom practice. The central…

This article reports on a qualitative, interpretivist study that focused on the use of visualisation and analytic strategies by Grade 12 learners when working with problems based on transformation geometry. The research was conducted with 40 learners from a Grade 12 class at one high school in the north Durban area of Kwazulu-Natal. Participants…

Many American students begin their high school mathematics study with the algebra 1-geometry-algebra 2 sequence. After algebra 2, then, students with average or below-average mathematical ability face a dilemma in choosing their next mathematics course. For students to succeed in higher mathematics, understanding the concept of functions is…

This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and…

Analysis of students' work on tasks relating to reflections, translations and rotations is discussed. Findings from research with regard to students' understanding of a subject would help teachers prepare for the class.

This research explored students' views of geometric objects through the implementation of a curriculum module that allowed them to explore the relationships between transformational geometry and linear algebra. The majority of the students were middle and secondary mathematics education majors enrolled in a one-semester geometry course that is…