The present study aims to examine 8th grade students' proof writing and justification skills. The research was conducted using the document analysis method. The participants of the study consisted of 16 voluntary 8th grade students. The participants were determined according to the convenience sampling method. Data were collected with the…

This study lies within the field of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

Previous research has verified the benefits obtained when learners trace out worked examples with the index finger. Our study conducted two experiments to explore the reasons for this phenomenon and its generalizability. Experiment 1 compared the learning effects among tracing, non-tracing, and cueing methods. The cueing method was included to…

The authors who are mathematics teacher educators, have found that classifying, composing, and transforming shapes (in particular, rotations and reflections) are areas of difficulty for adults as well as for children. However, these are also some of the most important geometric ideas. They are fundamental topics in the K-8 Geometry and Measurement…

Students often view mathematics as a set of unrelated facts and procedures and fail to make the connections between and among related topics. One role of a teacher is to help students understand that mathematics is an interrelated discipline. Another role is to assist students in the scaffolding of their knowledge so that they can make connections…