School Geometry Research Articles

The Effects of Differentiation of Content in Problem-solving in Learning Geometry in Secondary School

Background:The aim of the study was to examine the effects of problem-based learning which was established on differentiation of content at three levels of complexity in the processing of the content of Analytical geometry in the plane.Material and methods:In this context, an experimental research was conducted, on a sample of secondary school students (N = 165) in order to examine whether methodical approach designed on the principles of problem-based learning based on differentiation of content gives better effects in learning compared to the traditional mode.Results:The results of the final measurement shown that the experimental group achieved better overall success than control group.Conclusions:The results suggest that the proposed methodical approach contributes to better student performance in teaching geometry and that the most significant progress is achieved in the group of students who are average in terms of success and with ones below the average.

Lessons Learnt From Employing van Hiele Theory Based Instruction In Senior Secondary School Geometry Classrooms

Background:This paper reports on a part of a study which was conducted to determine the effect of van Hiele theory based instruction in the teaching of geometry to Grade 10 learners.Materials and methods:The sample consisted of 359 participants from five conveniently selected schools from Mthatha District in the Eastern Cape Province. There were 195 learners in the experimental group and 164 learners in the control group. The experimental group was given van Hiele theory based geometry instruction and the control group were exposed to the traditional method of geometry instruction. The researchers administered a multiple choice geometry test to the participants before and after five weeks of instruction (pre- and post-test design).Results:The results indicated a statistically significant difference between the groups. An inspection of the mean revealed that these were higher for the experimental group.Conclusions:The significant improvement in the performance of the experimental group having more learners at level 2 than at level 0 and level 1 suggest that the van Hiele theory based instruction had a positive effect compared to traditional instruction. This suggests that lessons following van Hiele theory based instruction seem to raise learners' level of thinking.

예비수학교사의 MKT에 관한 연구

본 연구에서는 내용 지식 교육의 측면에서 예비수학교사 교육의 방향을 탐색하고자 예비수학교사들의 MKT에 대한 인식 조사와 더불어 실제 과제 수행 과정에서 드러나는 MKT에 대한 분석을 실시하였다. 26명의 예비수학교사가 MKT에 대한 인식 설문 조사와 중학교 수준의 기하 영역에 해당되는 2개의 MKT 과제의 수행에 참여하였다. 본 연구에 참여한 예비교사들은 KCT-2 범주를 제외한 MKT 하위 범주 각각에 대한 지식이 충분하다고 인식하는 것으로 나타났고, 예비교사교육에서 MKT의 각각의 하위 범주에 대한 교육은 중요하게 생각하고 있었다. 그러나 MKT 과제 수행 분석으로부터 본 연구에 참여한 예비수학교사들은 SCK, KCS, KCT를 요구하는 문항에 어려움을 겪고 있는 것을 알 수 있었고, 특히, SCK와 KCT를 요구하는 문항에 적절한 응답을 준 예비교사의 비율이 50% 이하로 나타나 MKT에 대한 예비교사들의 일반적인 인식과 실제적인 지식 발현 과정 사이에는 불일치되는 부분이 있음을 확인할 수 있었다. The purposes of the study were to analyze pre-service mathematics teachers' MKT and to examine the perceptions of MKT to find implications for the improvement of pre-service mathematics teacher education program in the aspect of teachers' content knowledge. Twenty-six pre-service mathematics teachers participated in the survey to examine the perceptions of MKT and they also finished two MKT tasks which focused on a specific area of middle school geometry. According to the survey results, the participants thought that they have enough knowledge in all categories of MKT except KCT-2 and they appreciated the importance of MKT education in pre-service mathematics teacher education program. However, the participants showed difficulties in MKT task items which required SCK, KCS, KCT, especially, the proportions of those who showed appropriate knowledge on the items required SCK and KCT was less than 50%. These results show disagreement between the perceptions of pre-service mathematics teachers' MKT and practice of MKT.

Geometri Sekolah Dasar dan Pengajarannya: Suatu Pola Penyajian Berdasarkan Teori Piaget dan Teori Van Heile

Content and techniques of its presentation are currently the two basic problems in the elementary school geometry. No serious solution to the problems may make the position of geometry in the curriculum weak which in turn leads to the students' poor mastery of geometry. Sufficient content of Geometry should now be included appropriately in the curriculum by considering the intellectual developmental stages of the students and relevant learning theories. In this case, Piaget's theories of cognitive development and Van Heile's geometry learning theories should be considered in solving the problems

THE EFFECT OF COOPERATIVE LEARNING MODEL OF NUMBER HEAD TOGETHER (NHT) TYPE ASSISTED ANIMATION ON STUDENT’S LEARNING OUTCOMES OF X CLASS SMA 2 LINTONGNIHUTA A.Y. 2014/2015

ABSTRACT Aims of study to determine the effect of cooperative learning model of NHT type to learning outcomes of students in subject matter optical geometry in high school N 2 Lintongnihuta A.Y. 2014/2015.Kind of this research is quasi experimental. The population in this research were all students of class X Semester II SMA N 2 Lintongnihuta which consists of two classes. Sampling was done by purposive research by using two existing classes, namely class X Mia 2 were 26students as experimental class and the class X Mia 1 amounted to 30 students as the control class. The instrument used is a cognitive test in the form of multiple choice question number 20 and observation sheet of student’s activity. Experimental class was given treatment by cooperative learning model of NHT type and grade control with conventional learning. Before being given different treatment performed pretest, which is the average value of the experimental class pretest 48.65 with a standard deviation 11.45 and the average value of the control class pretest 48.67 with a standard deviation 14.07. Second class pretest data testing showed that both classes of data were normally distributed and homogeneous. The test results obtained pretest tcount<ttable (0.0057 <2,14) then H0 is received, it means the ability of students' initial experimental class and control class alike. Then given treatment that is experimental class with cooperative learning model of NHT type and grade control with conventional learning models. During thelearning processinthe experimental classlearning activities of studentsincreased, the meetingI59.79%, 72.07%meetingIIandIIImeeting of75.30%.After the study was completed, given postest with an average 66.53 for experimental class with a standard deviation 11.64 and 48.66 with the control class standard deviation 14.07. On testing normality and homogeneity of data obtained postest that both classes of data were normally distributed and homogeneous. The data processing postest obtained that tcount= 5.1 and ttable = 2.14, so that t count > t table (5.1> 2.14) then Hareceived means there is influence of cooperative learning model of NHT type to students learning outcomes in optic geometry material to X class SMA N 2 Lintongnihuta A.Y. 2014/2015. Keywords: Cooperative learning model of NHT type , animation, learning outcome, activity.

Teacher Mathematical Knowledge for Teaching Geometry in Mongolian Secondary Schools － Focusing on Concept Image and Concept Definition Theory

Teacher Mathematical Knowledge for Teaching Geometry in Mongolian Secondary Schools － Focusing on Concept Image and Concept Definition Theory

BỒI DƯỠNG THỦ PHÁP BỔ SUNG YẾU TỐ PHỤ CHO HỌC SINH TRONG DẠY HỌC HÌNH HỌC Ở TRƯỜNG TRUNG HỌC CƠ SỞ

BỒI DƯỠNG THỦ PHÁP BỔ SUNG YẾU TỐ PHỤ CHO HỌC SINH TRONG DẠY HỌC HÌNH HỌC Ở TRƯỜNG TRUNG HỌC CƠ SỞ

English

This study is an attempt to solve the persistent poor performance of students in geometry in senior secondary schools in Kaduna State, Nigeria. The study was guided by two research questions and two hypotheses. The quasi experimental research design involving a pretest and posttest was used. The population of the study comprised of 4624 senior secondary school year two (SS2) students of the public secondary schools in Zaria Educational Zone. Two coeducation schools were selected by the simple random sampling as the schools sampled for the study. The sample of students for the study comprised of 144 students from two schools from intact classes (Experimental = 72 and Control = 72). The Geometry Performance Test (GPT) was used as instrument for collecting data. The research questions were answered using descriptive statistics while the research hypotheses were analyzed by the t-test statistics at P ≤ 0.05 level of significance with the aid of the Statistical Packages for Social Sciences (SPSS version 21). The study revealed a significant difference in performance in favour of students exposed to the J4CLS. With regard to gender performance, no significance difference was found. The study concludes that the J4CLS is gender friendly and effective in the teaching and learning of geometry. Based on these findings, it was recommended that teachers should employ the J4CLS in the teaching of geometry in senior secondary schools to enhance students’ performance in geometry. Also, workshops and seminars for mathematics and science based teachers should be organized by the Ministry of Education for each Education Zone in Kaduna State on the use of the J4CLS in classrooms.

Virtual Miniature Golf

Current standards place significant emphasis on transformations in school geometry: “Fundamental are the rigid motions: translations, rotations, reflections, and combinations of these,” and “dynamic geometry environments provide students with experimental and modeling tools that allow them to investigate geometric phenomena” (CCSSI, 2010, p. 74). With these aims in mind, we share a favorite classroom activity—virtual miniature golf. Building on the work of Coxford and Usiskin (1991) and Powell et al. (1994), this activity provides geometry students with a real-world context for exploring reflection and reflection composition in technology-rich settings.

Pivotal teaching moments in technology-intensive secondary geometry classrooms

This study investigates three teachers’ uses of a dynamic geometry program (The Geometer’s Sketchpad) in their high school geometry classes over a 2-year period. The researchers examine teachers’ actions and questions during pivotal teaching moments to characterize mathematics instruction that utilizes technology. Findings support an association between teacher–tool relationships, predominant teacher actions, and questioning.

ATIVIDADES DE GEOMETRIA PARA O ENSINO MÉDIO

http://dx.doi.org/10.5902/2179460X14227This work suggests activities to introduce and develop content for Solid Geometry, particularly prisms and pyramids with High School students, prioritizing the visualization of solids in space, identifying the differences in the shape and characteristics of its elements, without requiring memorization formulas. Also emphasizes the importance of recapitulation of concepts of Plane Geometry. With the passing of years, students have encountered difficulties in mathematics in Middle school and this has a direct consequence on learning of these students in contents related to the High School. To check the veracity of this statement, a survey was conducted through a questionnaire with teachers working with Solid Geometry in seven High Schools in southern State of Rio Grande do Sul. Suggested activities that introduce and complement the contents found in traditional textbooks. Teachers, even with limited resources may use these activities with their students to improve the learning of Solid Geometry in High School.

Incorporating GeoGebra into Geometry Learning-A lesson from India

Students often find geometrical concepts abstract and difficult to understand. This results in poor performance, which contributes in the declining interest in geometry. The aim of this study was to examine the impact of using the free educational software program, ‗GeoGebra‘ on 9th grade student‘s mathematics achievement in learning geometry. A total of 50 students were selected from a government school located in the eastern part of India. The experimental group (25) was taught theorem on circles using GeoGebra while the control group (25) was taught utilizing traditional teaching methods. At the end of the treatment, students‘ mathematics achievements were measured using a post - test. The result indicated that GeoGebra is an effective tool for teaching and learning geometry in middle school

Geometry in the early years: a commentary

The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical ideas; the teaching and learning of geometry; and assessment of children’s learning in geometry. The author outlines his views based on the literature and the papers in this issue and concludes with an outlook on the future teaching and learning of geometry in schools.

New opportunities in geometry education at the primary school

This paper outlines the new opportunities that that will be changing the landscape of geometry education at the primary school level. These include: the research on spatial reasoning and its connection to school mathematics in general and school geometry in particular; the function of drawing in the construction of geometric meaning; the role of digital technologies; the importance of transformational geometry in the curriculum (including symmetry as well as the isometries); and, the possibility of extending primary school geometry from its typical emphasis on vocabulary (naming and sorting shapes by properties) to working on the composing/decomposing, classifying, comparing and mentally manipulating both two- and three-dimensional figures. We discuss these opportunities in the context of historical developments in the nature and relevance of school geometry. The aim is to motivate and connect the set of papers in this special issue.

Increasing Student Engagement, Self-Efficacy, and Meta-Cognitive Self-Regulation in the High School Geometry Classroom: Do iPads Help?

Teachers are increasingly integrating mobile digital technology into the classroom. The purpose of this study was to assess the effect of incorporating iPads in a secondary-level geometry course on academic achievement, student engagement, self-efficacy, and meta-cognitive self-regulation. Students in the iPad-using classroom experienced lower levels of geometry proficiency scores, higher levels of off-task behaviors, and similar levels of self-efficacy and meta-cognitive self-regulation compared to the non-iPad group. However, the results may have been affected by several latent variables that can be controlled for in future research.

Secondary and Higher School Succession Examplified by the School Geometry Teaching

The paper analyzes the content of school geometry education; a number of reasons behind the degrading level of geometry training of sec ondary school leavers being discussed. The author argues that, in spite of the decline of the geometry research in modern mathematics, its educational and practical significance is growing along with the development of knowledge and technology. The author welcomes the introduction of elective courses in profile schools (e.g. solving geometrical problems based on the vector method, representation of geometrical figures in a parallel projection, etc), and regards it as the important means of content succession and continuity of mathematical education in secondary and higher schools; the problems of content and teaching method selection for given courses being discussed providing the effective link between the profile and professional education. The research findings can be of interest to the experts in mathematical teaching methods, elective course developers and school teachers of mathematics.

The Semiotic Structure of Geometry Diagrams: How Textbook Diagrams Convey Meaning

Geometry diagrams use the visual features of specific drawn objects to convey meaning about generic mathematical entities. We examine the semiotic structure of these visual features in two parts. One, we conduct a semiotic inquiry to conceptualize geometry diagrams as mathematical texts that comprise choices from different semiotic systems. Two, we use the semiotic catalog that results from this inquiry to analyze 2,300 diagrams from 22 high school geometry textbooks in which the dates of publication span the 20th century. In the first part of the article, we identify axes along which the features of geometry diagrams can vary, and in the second part of the article, we show the viability of using the semiotic framework to conduct empirical studies of diagrams in geometry textbooks.

The Role and Place of Fusionism in School Geometry Education

The paper deals with the issue of succession in school geometry education. By the analysis and synthesis of the integrative experience of the plane and spatial geometry teaching, it has being substantiated that the application of fusionism elements can provide the effective instrument for implementing the vertical content and process succession in geometry teaching. By means of the activity approach it is being proved that the fusion teaching of planimetry and stereometry in elementary school facilitates the development of children’s learning and cognitive skills. Using fusionism at the final years of Secondary School promotes the school leavers’ readiness for studying general spatial geometry in the system of higher education. The study is addressed to developers of the school mathematical educational standards, authors of school geometry manuals and geometry teachers.

The Effect of Dynamic Geometry Software and Physical Manipulatives on Candidate Teachers’ Transformational Geometry Success

Mathematics, having an important place in human life and playing a great role in developing many human cognitive capabilities, is divided into various subject areas. One of these subject areas is geometry (Kurak, 2009). Geometry consists of geometric objects, shapes, and their features and relationships to each other (Topta§, 2008) Geometry helps students become closely acquainted with the world they live in. For example, the shapes of rooms, their construction and trim work forms are geometrical (Baykul, 2002). According to Struchens, Harris, and Martin (2003), students start to understand the world around of them, can analyze problems, and in order to understand intangible symbols better, define them by shapes (as cited in Gulten & Gulten, 2004). On the other hand, the National Council of Teachers of Mathematics (NCTM, 2000) dwells on the importance of geometry for the principles and standards of school mathematics, and it focuses on the fact that geometry develops the reasoning and proof-finding abilities of students. Jones (2002), on the other hand, states that geometry includes interesting problems and surprising theorems, and this supports students in developing their abilities of visualization, critical thought, instinctive reasoning, perspective, estimation, logical inference, deductive reasoning, and proof-finding. For this reason, geometry is an important subject area which should be addressed from pre-school throughout higher education (Goos & Spencer, 2003). With the implementation of the mathematics program in 2005, some subject areas started to become more prominent. One of these subjects is transformational geometry (displacement, reflection, and rotational transformation) (Guven & Kaleli-Yilmaz, 2012).Transformational geometry, which improves students' geometric experimentation, imagination, reasoning, and three-dimensional perception skills, consists of reflection, displacement, and rotation (Fletcher, 1973; Gurbuz, 2008; Milli Egitim Bakanhgi [MEB], 2005; NCTM, 2000; Soon, 1989). According to Knuchel (2004), people need knowledge of transformational geometry in order to develop qualitative senses about the external world as well as to organize objects and events. Students can establish a connection between art and mathematics thanks to the information they receive on transformational geometry; they can realize the importance of mathematics in daily life. Additionally, seeing geometric figures rotated, translated, and repeated (as in carpet patterns) helps the student who has knowledge about this topic to view things differently (Duatepe & Ersoy, 2001). For this reason the topic of transformational geometry should be taught to students from childhood, and it should be emphasized that reflection, displacement, and rotation can be seen in many natural structures and events.It is very important for primary school students to learn basic knowledge about transformational geometry and continue their education successfully in the years that follow. As Carroll (1998) stated, students who gain effective experience with geometry in primary school are able to apply reasoning to situations which contain geometry in secondary school. For example, reflection transformation relative to a line is used to teach analytical geometry, the following years' topic, and rotational transformation is used to teach solid-body volume. Moreover, transformational geometry basically forms a basis for the concepts of functions, a concrete foundation for vectors, and the formulation of the similarity theorem, making the world mathematical (Schuester, 1973). Transformational geometry should be taught to students beginning at childhood in order to transform their knowledge into conceptual and concrete understandings; teachers should help students understand the topics of reflection, symmetry, and rotational transformation correctly.The topic of transformational geometry is not only in mathematics but is also included in other disciplines. …

The van Hiele Levels at Czech Secondary Schools

This paper focuses on the results of a pilot study based on the van Hiele theory of geometric thinking at Czech secondary schools. The van Hiele theory describes how young people learn geometry. It postulates five levels of geometric thinking. Usiskin later tested the ability of the van Hiele theory to describe and predict the performance of students in secondary school geometry. Our pilot study aimed to verify the test structure of the Usiskińs test in the Czech secondary schools, and to compare the outcomes with American results.