This paper presents a novel figure for teaching multiple geometric proofs of the Pythagorean theorem. Because it consists only of congruent given right triangles, the figure can be constructed using a template of the given right triangle or, if available, a computer program. Within the figure, called a Pythagorean multi-proof square, there are…

This study aims to describe how subjects construct explicit warrant derived from implicit warrant when completing mathematical proof. This research was conducted on seventeen students of mathematics education study programs by providing tests on vector material in elementary linear algebra courses. The test results show that there are four…

This study aims to explore all the types of students' mental models of number patterns. The study used a qualitative approach with an explorative type. The subjects used to characterize the student's mental models in this study were 46 eighth grade students in Indonesia. To reveal the subjects' mental model, they were asked to solve the number…

As proof and proving are the key elements of mathematics, several frameworks evaluating this process have been presented. Proof image, being one of them, was introduced by Kidron and Dreyfus (2014) through analyses of two mathematicians' activities. Authors clarified it in the context of components, and emphasized its relation with formal proof.…

This study aims to describe the ability of students' mathematical connections in solving problems in the circle equation material through transposition studies. The method in this research is a descriptive qualitative approach, the techniques used in the study are tests, interviews, and documentation to explore data in research. Test and interview…

Acknowledging the importance of mathematical reasoning in mathematics teaching, the present study analyzes middle school mathematics teachers' understanding of reasoning. In line with the purpose, the study was performed using a phenomenological design, which is one of the qualitative research methods. The study was carried out with a total of 16…

The study aimed at describing university students' ability in constructing mathematical proofs using logical arguments and constructing an effective teaching-learning map. The study adopted a correlational research design. An open-ended mathematics assessment involving questions on mathematical logic and construction of mathematical proofs was…

This is a descriptive research on the difficulties of Filipino high school students in translating algebraic word problems into mathematical equations. This research is composed of three parts: (1) development of an 11-page "Filipinized" questionnaire; (2) analysis of the mathematical thinking processes of the respondents based on the answers to…

Geometry is one of the most important branches of mathematics education, because the aim of the geometry teaching is to provide students with the ability of critical thinking, problem solving and a better understanding of the other subjects in mathematics by making the students have a high level of geometric thinking skills (Sahin, O., 2008).…

Examining the actions taken during a teaching experiment can provide insight into practices applicable to the use of mathematics technology to assist adult learners. A case study in the form of a teaching experiment was conducted with a small number of subjects to allow for detailed examination of the influence of technology on student thinking.…

This study investigates the relationship between eighth grade primary school students' success levels in solving equations and proportional reasoning skills. 344 eighth grade students, who were registered at various primary schools in the central districts of Konya in the 2007-2008 educational year, participated in the research. The study had a…

We introduce some concepts for analyzing proofs, including various structures, and for analyzing undergraduate and beginning graduate mathematics students' proving abilities. We then discuss how the coordination of these two analyses might be used to improve students' ability to construct proofs. For this purpose, we need a richer framework for…

The universities and faculties which educate teachers of mathematics for teaching pupils/students of any age group from pre-school age to higher education carefully monitor and compare valuable results of this research, detect the areas in which the mathematical achievements of pupils should be improved at the national level and propose the ways…

Infinity has contradictions arising from its nature. Since mind is actually adapted to finite realities attained by behaviors in space and time, when one starts to deal with real infinity, contradictions will arise. In particular, Cantorian Set Theory for it involves the notion of "equivalence of a set to one of its proper subsets,"…

In this paper, we will discuss the way various features of consciousness interact with each other and with cognition, specifically, the cognition of mathematical reasoning and problem solving. Thus we are interested in how consciousness and cognition "work," in a somewhat mechanistic way, rather than in larger philosophical questions about…