Research on geometric transformations suggests that early learners possess intuitive understandings grounded in motion metaphors, transitioning to mappings. The processes through which students transition between these two conceptions are not fully understood. We propose that Vygotskian hybridizing (related to Vygotsky's articulation of everyday…

"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to…

The purpose of this study was to investigate the tessellation performance of 8th-grade students and factors affecting their performance. Student performances have been examined in two dimensions: identification and completion of tessellation. In this context, a diagnostic test containing two main questions with the content of determining whether…

The purpose of this study is to analyse geometric transformations of children in the early childhood period. The study utilised a case study to design one of the qualitative research methods. Interviews were conducted with 6-, 7- and 8-year-old children, in total 24 children, who were enrolled in a private pre-school and a primary school of the…

This article provides a range of activities designed to engage students in using an early form of graphing. While the "Australian Curriculum: Mathematics" (2014) highlights understanding, fluency, problem-solving, and reasoning, the National Research Council (2001) describes five strands of mathematical proficiency, with the additional…

The use of concrete objects in a real-life situation is one of the effective ways for teachers to teach and students to explore and learn transformation geometry. The present study, which used a local wisdom or learning context (called Malay woven motif of Kepulauan Riau), focused on developing the reasoning of transformation geometry with…

Flexibility in transforming algebraic expressions is recognized as fundamental for a rich procedural knowledge. Here, flexibility in-depth is proposed as the ability to apply one strategy to a wide range of unfamiliar expressions. In this study, design experiments with four groups of students were conducted to support students' flexibility…

People need the idea of transformation geometry in order to understand the nature and environment they live in. The teachers should provide learning environments towards perceptual understanding in symmetry training and development practice skills of the students. In order to make up such a learning environment, teachers should have information…

The majority of large-scale assessments develop various score scales that are either linear or nonlinear transformations of raw scores for better interpretations and uses of assessment results. The current formula for coefficient alpha (a; the commonly used reliability coefficient) only provides internal consistency reliability estimates of raw…

The overall aim of this study is to search whether teaching geometry with Cabri Geometry Plus II software have effects on 7th grade students' learning transformation geometry in mathematics. In this context, the researcher has used a pre-test and post-test research design with a control group. The research sample consisted of 135 students in total…

This study investigated how female elementary education pre-service teachers in the United States, Turkey and Taiwan learned spatial skills from structured activities involving discrete, as opposed to continuous, transformations in interactive computer programs, and how these activities transferred to non-related standardized tests of spatial…