Although research highlights the importance of analyzing the geometric work of teachers, there are few validated instruments in this line. This study presents the processes of design and validation of a forced-choice questionnaire that allows the characterization, from a theoretical basis, of how geometry teachers organize their teaching practice.…

In the mathematical literature on analytical geometry, various notions of the conics' eccentricity correspond to different approaches to these curves. After making a comparative analysis of well-known textbooks to determine coincidences and differences between the various concepts of eccentricity, as well as how the authors explain the…

This study aimed at investigating two main issues related to counterexample construction: the appropriateness of counterexamples and the types of arguments that are often used when refuting a false conjecture. Twelve pre-service elementary teachers who demonstrated a wide range of reasoning skills participated in this study. The data revealed…

To deepen our understanding of those aspects of problems that cause the most difficulty for solvers, this study integrated eye-tracking with handwriting devices to investigate problem solvers' online processes while solving geometry problems. We are interested in whether the difference between successful and unsuccessful solvers can be identified…

In the present study, we try to understand how students at the end of primary school conceive of angle: Is an angle a magnitude for them or a geometric figure, and how do they manage to coordinate the two aspects in their understanding of the concepts of angle and of angle measurement? With the aim of better grasping the way "angle" is…

"The use of e-learning and modern technologies is an integral part of teaching descriptive geometry" (Rankowski and Minaruth, 1979). Teachers often create Flash animations, websites and other interactive materials for their students using special tools and software; e.g. Cabri, GeoGebra or Construct 3D (García et al, 2007). There is an…

The use of dynamic geometry software (DGS) is becoming increasingly familiar among teachers, but letting students conduct inquiries using computers is still not a welcome idea. In addition to logistics and discipline concerns, many teachers believe that mathematics at the lower secondary level can be learned efficiently through practice alone.…

By considering the example of proving the triangle postulate, this study aimed to explore Hong Kong preservice and novice teachers' knowledge competencies and their beliefs about preformal and formal proofs. The findings revealed that such teachers are not proficient in using preformal proofs and do not realize that preformal proofs are a useful…

Structured abstract: Introduction: Difficulties in science and mathematics may stem from intuitive interference of irrelevant salient variables in a task. It has been suggested that such intuitive interference is based on immediate perceptual differences that are often visual. Studies performed with sighted participants have indicated that in the…

The purpose of this study is to analyze whether prospective teachers believe solving a mathematics problem involves in using different solution methods. 60 mathematics prospective teachers who take the pedagogic training program in a state university were participated in this study. Five open-ended questions were asked. The study was carried out…

Covariational reasoning has been the focus of many studies but only a few looked into this reasoning in the polar coordinate system. In fact, research on student's familiarity with polar coordinates and graphing in the polar coordinate system is scarce. This paper examines the challenges that students face when plotting polar curves using the…

This study investigated middle school teachers' knowledge of students' misconceptions and the sources of these misconceptions related to the volume of prisms. This case study investigated four middle school teachers who taught 8th grade students in Ankara (Turkey). Based on the analysis of the data, two misconceptions related to the volume of…

However, geometry is the area with the most concrete possibility of mathematical topics which contains more abstract concepts, students experience difficulties while understanding. Therefore, the connection of issues with daily life to concrete the subjects and the ability of connecting geometric concepts with daily life of the teachers and…

The article considers the peculiarities of training foreign students subject "Descriptive geometry and Engineering Graphics" in a modern engineering university of Russia. The relevance of the problem conditioned by the fact that virtually there are no special studies of teaching Descriptive Geometry and Engineering Graphics in Russian…

The purposes of this research were to know the validity, practicality, and effectivity of geometrical learning material based on the constructivism to Increase students' mathematic reasoning ability and increasing students' mathematic reasoning ability by using learning material at the grade VIII of SMP Negeri 3 Padangsidimpuan. Type of the…