Knowledge Representation of Mathematics Education Program among Students in Euclidean Parallelism (original) (raw)
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Students’ Levels of Recognition of Parallelogram and of Establishment of Connections
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Journal of Mathematics Education, 2021
The objective of this paper is to identify some student's conceptions of the straight line and two parallel lines. This will allow us to evaluate the distance that exists between their conceptions and the theory of these concepts. In doing so, we analyzed the students' answers to a questionnaire: the questionnaire concerned the explication of the straight line and two parallel lines. The results indicate that the students have difficulties to produce an acceptable definition of a straight line and two parallel lines. They have difficulties to find appropriate terms to express their comprehension of these concepts. The definitions they produce are ambiguous and seem to be related to the drawings they have encountered in the classroom. Their answers indicate that their comprehension on the straight line and two parallel lines seem to be in conflict with the theory of these concepts.
ANALYZING STUDENT'S UNDERSTANDING THE RELATIONSHIP BETWEEN QUADRILATERAL AT THE EARLY FORMAL STAGE
Learning of geometry must be allowed to the students' thinking skills will enhance the intellectual engagement of students. One of the thinking skills used in solving geometry problems is the ability to think geometry that helps the student in directing his thoughts so that the solution of the problem being solved tends to be true and correct. Differences in students' ability to think geometry is most likely influenced by their formal operational stage based on development of cognitive. The purpose of this study was to obtain description of student's understanding the relationship between quadrilaterals at the early formal stage. To achieve these objectives, the researchers conducted interviews with task-based by drawing activities, identifying and stringing the relationship between quadrilateral recorded with the recorder. This study includes qualitative and exploratory research. Subject had been taken from class VIII SMP who is at the early formal operational stage. To test the credibility of the data, the researcher used triangulation time. The results of this research showed that the student who is at the early formal operational stage stringing 14 of 15 relationships and the student might tend to use 3 attributes that position, the size, shape of quadrilateral. A. BACKGROUND Geometry occupies a special position in the secondary mathematics curriculum because there are many concepts contained in there. The concept is closely associated to other forms of objects that are often encountered by students in everyday life. Various opinions emerged that addresses geometry both definitions and chances to be taught in schools. Abdussakir [1] states that, basically, geometry has a better chance to be understood by students for ideas of geometry have been already known by students since before they enter school, for example, line, area, and space. However, the expectation is different from the reality in real life where various studies show that mastery of mathematics, especially geometry achievement is still low [2]. The above opinion is supported by the results of Setiawan's research [3] states that the fifth grade of elementary school students did not master the concepts and principles of geometry. While in junior high school [4] found that many students were wrong in solving the problems of parallel lines. Based on this, the geometry is looked as part of math given to students classified as difficult. Students' s learning difficulties can not be separated from the practice of learning that has been in progress [5]. Idris [6] suggested that learning of geometry is not easy and some students fail to develop an understanding of the concept of geometry, geometric reasoning and skill to solve the problems of geometry. Furthermore, Idris stated that a number of factors that lead learning of geometry is difficult which they are language of geometry, visualization and learning abilities are less effective for the low mastery of facts, concepts and principles of geometry. According Soerjono [3] one of among the causative factor is the intellectual ability of students. The results of Burger and Shaughnessy's research [7] demonstrated that the intellectual ability of students plays an important role in the mastery of facts and concepts of geometry. Intellectual abilities are spatial ability and auditory ability which are very close relationship with the cognitive aspects of students in general. Research shows that the understanding of spatial knowledge can affect the performance related to academic tasks especially math, reading and
A Pedagogical Synergy of Visualization Pictures and Scenarios to Teach the Concept of Parallelograms
Many problems in geometry require students to perform a number of steps in a particular order using congruence theorems. According to "the Mathematics Intermediate Level -8th year Book, Puissance Collection" set by the mathematics curriculum in Lebanon, a new spirit conserving the individual construction of notions is advised. However, in practice this new spirit is not smoothly delivered to students. In this study, we observed the effect of the Active Learning Process in the chapter of "Parallelograms" in the 8th grade Math classes on students' academic realization, concept learning and approach changes, according to their results combined with their feedback. It was detected that after comparing the test scores of the active learning model which uses figures and models is more successful than the traditional teaching methods since there was a rise in success in students' results.
Al-Jabar : Jurnal Pendidikan Matematika
Students learn mathematics through practical applications without applying it. Consequently, the concept images and definitions that students offer do not match. This study examines the gap in mathematical ability between the concept images of professionals in mathematics education and students' concept images of content, including quadrilaterals. This study employed a qualitative approach with a hermeneutic phenomenology method. Sixty-two seventh-grade students were involved in conducting this study. Some instruments, such as quadrilateral-related tests and semi-structured interview questions, were used to collect the data. The results of quadrilateral-related tests and interviews revealed that most students with high mathematical ability, some with medium mathematical ability, and a small number with low mathematical ability have a concept image that matches the definition but cannot produce proof of the properties of a quadrilateral. In addition, a small number of students wi...
Journal of Mathematics and Science Teacher
This study was set up to investigate the newly admitted senior high school graduates’ geometric representation of corresponding and alternate angles in contexts where parallel and non-parallel lines are cut by a transversal. The study also examined their reasoning about parallelism. 25 volunteers, through a pilot study, responded to a series of geometric tasks meant to assess geometry reasoning and understanding. This study reports on the data dealing with the afore-mentioned concepts. The findings indicate that: the participants were more able to identify geometric representation of alternate angles (64%) than they were with corresponding angles (44%); participants’ written narratives demonstrated evidence of imprecision in their reasoning about parallelism; and most participants showed limited knowledge and use of necessary keywords to justify parallelism. The findings suggest participants showed diverse conceptual understanding of alternate and corresponding angles and demonstrat...
2013
In the Republic of Srpska elementary school system there no any official evaluation of mathematics education outcome exists. This work is a part of our broader research on students' geometrics knowledge in the primary schools. The goal is to investigate geometric competencies of children from six to ten years old at the elementary school level in the Republic of Srpska, Bosnia & Herzegovina. Towards this end, the authors offered geometric tasks about parallelograms to a small number (15) of elementary school students via interviews. In this paper, some selected results are presented with the focus on students' conceptualization of geometric shapes. The emphasis of this study is on classification, identifying differences, and defining geometric objects.
This study attempts to reveal pre-service teachers' conceptions, definitions, and understanding of quadrilaterals and their internal relationships in terms of personal and formal figural concepts via case of the parallelograms. To collect data, an open-ended question was addressed to 27 pre-service mathematics teachers, and clinical interviews were conducted with them. The factors influential on pre-service teachers' definitions of parallelograms and conceptions regarding internal relationships between quadrilaterals were analyzed. The strongest result involved definitions based on prototype figures and partially seeing internal relationships between quadrilaterals via these definitions. As a different result from what is reported in the literature, it was found that the fact that rectangle remains as a special case of parallelogram in pre-service teachers' figural concepts leads them not to adopt the hierarchical relationship. The findings suggested that learners were likely to recognize quadrilaterals by a special case of them and prototypical figures, even though they knew the formal definition in general. This led learners to have difficulty in understanding the inclusion relations of quadrilaterals.
The lessons allowed to the students' thinking skills will enhance the intellectual engagement of students in learning geometry. One of the thinking skills used in solving geometry problems is the ability to think geometry that helps the student in directing his thoughts so that the solution of the problem being solved tends to be true and correct. Differences in students' ability to think geometry is most likely influenced by their learning style. The purpose of this study was to obtain a profile of geometric thinking students in understanding the relationship between quadrilaterals based on the student's learning style. To achieve these objectives, the researchers conducted interviews with task-based by drawing activities, identifying and stringing the relationship between quadrilateral recorded with the recorder. This study includes qualitative and exploratory research. Subject had been taken from class VIII SMP which has auditory-sequential learning styles. To test the credibility of the data, the researcher used triangulation time. The results of this research showed that the student who has auditory-sequential learning style stringing 7 of 15 relationships and the student might tend to use 4 attributes that position, the size, shape and rotational symmetry.
Investigation of Prospective Primary Mathematics Teachers' Perceptions and Images for Quadrilaterals
Kuram Ve Uygulamada Egitim Bilimleri, 2013
Teaching geometry is as many researchers stated (Baykul, 1999; Duatepe, 2000; Fujita & Jones, 2007) not only means of comprehending information and relations about point, line, figures, space but also important in the sense of improving spatial thinking and visual skills. In the education of many subject in mathematics, people form an image in their mind about the concepts. This concept image changes and takes shape in time. Tall and Vinner (1981) defined concept image as the cognitive structure which includes mental image, features and processes about the concept. There are 3 different cases in geometrical concepts. These are the a Elif TÜRNÜKLÜ, Ph.D., is currently an associate professor at the Department of Primary Mathematics Education. Her research interests include teaching and learning geometry and mathematics teacher education.