The aim of this study is to examine 8th grade students' Van Hiele geometry thinking levels, proof writing and justification skills. The research was carried out with sixteen eighth grade students of a private school in Sivas. Participants were selected based on an easily accessible sample. The data were collected from the students who participated…

We present a case study of proving by three 12-13-year-old students with different levels of mathematical giftedness. After analysing students' proofs, we conclude that: there was a relation on the consistency and the students' levels of mathematically giftedness, being the least consistent the student not mathematically gifted and the most…

In this paper, Harel and Sowder's proof schemes of taxonomy were applied for identifying eighth grade students' learning of proof and proofing. This study aimed to examine what kind of proof schemes are used in geometry and measurement learning areas and student's skills in giving proof and their opinions about proof. Qualitative methods were…

In this study, it is aimed to reveal what kind of relationship exists between prospective teachers' thinking structures and their level of writing proofs. This study was carried out as a case study. The study was carried out with 82 prospective teachers enrolled in the Department of Secondary School Mathematics Teaching of a state university…

This study investigated the effect of situated learning environment in enhancing mathematical reasoning and proof among tenth grade students. To achieve the aim of the study, a pre-posttest of mathematical reasoning and proof was used, and its validity and reliability were verified. The sample of the study consisted of 50 female students who were…

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

Proof is a key indicator for a student in developing mathematical maturity. However, in the process of learning proof, students have the difficulty of being able to explain the proof that has been compiled using good arguments. So we need a strategy that can put students in the process of clarifying proof better. One strategy that can explore…

Proof, though central to mathematical practice, is rarely explored through the lens of embodiment because of the centrality of abstraction and generalization. We use the case of a high school geometry student to investigate two research questions: (1) How do embodied processes facilitate mathematical learning? (2) How can generalized mathematical…

In a Swedish second semester course on Euclidean and non-Euclidean geometry in mathematics education at Karlstad University, a bridging teaching strategy comprising elements from Mathematics, Didactics, History, Literature, and Technology was applied by using the concept of Narrative Didactics and Digital Interactive Mathematical Maps developed by…

Thinking development processes among high-school students is an important and significant issue that has been widely investigated (Leviathan, 2012; Ball, 1996; De Risi, 2015). A few studies discuss the development of mathematical thinking as this field contains additional difficulties to the traditional factors, teachers, students, and parents,…

It is widely accepted by the field of mathematics education that proof and reasoning should be integrated into students' mathematical experiences across all grades and across a breadth of content areas. However, studies have shown that both secondary students and teachers have encountered difficulties with learning and teaching geometry proofs. By…

Despite Common Core State Standards for Mathematics (CCSSI 2010) recommendations, too often students' introduction to proof consists of the study of formal axiomatic systems--for example, triangle congruence proofs--typically in an introductory geometry course with no connection back to previous work in earlier algebra courses. Van Hiele…

This study aimed to document pre-service elementary teachers' (PSTs'), who are going to teach K-5, ability to construct as well as evaluate justifications varied in terms of levels of sophistication. Additionally, this study aimed to investigate how PSTs' knowledge of content in which they were being asked to prove influenced their ability to…