Knowledge Representation of Mathematics Education Program among Students in Euclidean Parallelism

This research aims to reveal students' perception-based knowledge representation from mathematics programs in Euclidean Parallelism. Students were asked to do parallelism exercises presented in a verbal and picture form. The data were analyzed by knowledge representation theory based on meaning and perception. There were students who have amodal-multimodal-transition hypothesis. Students' assumptions about the verbal and picture information of not-perfectly-drawn parallel lines varied: assuming that angles appear to be the same measure are congruent, the two lines would intersect, considering the two lines parallel but redrawing picture to determine the pair of congruent angles and using other perspectives to interpret the picture. This study recommends action research for geometry learning that provides not-perfectly-drawn parallel lines for students who have amodal and amodalmultimodal- transition hypothesis and observe its effect on their non-Euclidean geometry learning. It may also familiarize students with getting to know parallelism in R3.

Download Full-text

PENERAPAN METODE PROBLEM SOLVING DALAM MENINGKATKAN KEMAMPUAN PEMECAHAN MASALAH PADA MATA KULIAH ALJABAR DAN TRIGONOMETRI

MES: Journal of Mathematics Education and Science ◽

10.30743/mes.v3i2.496 ◽

2018 ◽

Vol 3 (2) ◽

pp. 159-166

Author(s):

Imelda Imelda

Keyword(s):

Mathematics Education ◽

Action Research ◽

Problem Solving ◽

Education Program ◽

Education Student ◽

Math Problem ◽

Mathematics Problem Solving ◽

Math Problem Solving ◽

Catholic University ◽

Mathematics Problem

Abstract. This study is a classroom action research. The purpose of this research is (1) to describe the application of problem solving method in improving mathematics problem solving students of mathematics education program of Catholic University of Santo Thomas North Sumatera and (2) to describe the improvement of mathematics problem solving ability of mathematics education student in Algebra and Trigonometry. The result of this research shows that the result of problem solving test of mathematics cycle I is students who do not have problem solving ability as much as 3 people (30%), while students have math problem solving ability as much as 7 people (70%) and percentage of observation sheet lecturer activity amounted to 70.90%. Based on the result of math problem solving test in cycle 2, there were 1 (10%) students who did not have the ability to solve mathematics problem, while the students who have problem solving ability 9 students (90%) and lecturer activity percentage of 85.50% experienced an increase from cycle I of 6.5%. Based on the results of this acquisition then the group (classical) can be said that students have the ability to solve problems in Algebra and Trigonometry courses and increase problem-solving abilities by 20%. Keywords: problem solving method and problem solving ability.

Download Full-text

The Development of Euclid Geometry’s Teaching Materials Based on KKNI to Improve Students Cognition Analysis and Deductive Reasoning Abilities

Journal of Medives Journal of Mathematics Education IKIP Veteran Semarang ◽

10.31331/medivesveteran.v5i1.1439 ◽

2021 ◽

Vol 5 (1) ◽

pp. 74

Author(s):

Dwi Antari Wijayanti ◽

Pinta Deniyanti Sampoerno ◽

Qorry Meidianingsih

Keyword(s):

Mathematics Education ◽

Action Research ◽

Deductive Reasoning ◽

Field Trials ◽

Teaching Material ◽

Teaching Materials ◽

Study Program ◽

Education Study ◽

Classroom Action Research ◽

Geometry Learning

This research aims to develop teaching materials that have been produced by the application of the learning model Means Ends Analysis in the form of Classroom Action Research. The development carried out in this study resulted in Euclid Geometry teaching materials based on KKNI to improve cognitive analytical skills and deductive reasoning of students of the Mathematics Education Study Program, State University of Jakarta. There were five steps carried out in developing this teaching material, including initial research, collecting data and information on needs, planning changes to teaching materials, developing early teaching materials, field trials, and revisions. The teaching material developed is suitable for use in Euclid's Geometry learning because it has passed the expert validation process. Also, this teaching material has been tested on students who have been and are currently taking Euclid's Geometry courses. This concludes that Euclid Geometry teaching materials based on KKNI are feasible and can be used as a handbook for students in taking Euclid Geometry courses in the Mathematics Education Study Program of FMIPA UNJ. Keywords: Euclid's geometry, learning models, means-ends analysis, classroom action research.

Download Full-text

Elementary Considerations relating to the Absolute

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500034829 ◽

1909 ◽

Vol 28 ◽

pp. 65-72

Author(s):

Duncan M.Y. Sommerville

Keyword(s):

Fixed Point ◽

Special Interest ◽

Euclidean Geometry ◽

Criterion A ◽

Parallel Lines ◽

Non Euclidean Geometry ◽

The Absolute ◽

The Given

Non-Euclidean geometry in the narrowest sense is that system of geometry which is usually associated with the names of Lobachevskij and Bolyai, and which arose from the substitution for Euclid's parallel-postulate of a postulate admitting an infinity of lines through a fixed point not intersecting a given line, the two limits between the intersectors and the non-intersectors being called the parallels to the given line through the fixed point. In a wider sense, any system of geometry which denies one or more of the fundamental assumptions upon which Euclid's system is based is a non-euclidean geometry. Of special interest are, however, those which touch only the question of parallel lines ; and there exists, in addition to Lobachevskij's geometry, another, commonly associated with the name of Riemann, in which the parallels to any line through a fixed point are imaginary. The three geometries, Lobachevskij's, Euclid's, and Riemann's, thus form a trio characterised by the existence of real, coincident, or imaginary pairs of parallels through a given point to a given line. With reference to this criterion, a consistent nomenclature was introduced by Klein, who called these three geometries respectively Hyperbolic, Parabolic, and Elliptic.

Download Full-text

UPAYA MENINGKATKAN PRESTASI BELAJAR MAHASISWA PADA POKOK BAHASAN INTEGRAL MELALUI PEMBELAJARAN KOOPERATIF TIPE TEAM GAMES TOURNAMENT (TGT) PADA PROGRAM STUDI PENDIDIKAN MATEMATIKA FKIP UNIVERSITAS MATARAM

JURNAL PIJAR MIPA ◽

10.29303/jpm.v4i2.187 ◽

2009 ◽

Vol 4 (2) ◽

Author(s):

Mamika Ujianita Romdhini ◽

Laila Hayati

Keyword(s):

Mathematics Education ◽

Action Research ◽

Cooperative Learning ◽

Education Program ◽

Action Observation ◽

Team Games ◽

Cooperative Team ◽

Class Room ◽

Academic Year ◽

Planning Action

Abstrak: Penelitian ini bertujuan untuk meningkatkan prestasi belajar mahasiswa program studi Pendidikan Matematika FKIP Universitas Mataram tahun 2007/2008 pada mata kuliah Matematika Dasar pokok bahasan Integral. Jenis penelitian ini adalah penelitian tindakan kelas yang dilaksanakan dalam 3 siklus, dengan setiap siklus terdiri dari tahap perencanaan, pelaksanaan tindakan, observasi, evaluasi, dan refleksi. Adapun indikator keberhasilan setiap siklus adalah tercapainya ketuntasan belajar klasikal, yaitu minimal 85 % mahasiswa memperoleh nilai minimal 56 (pada skala 100) atau mendapat nilai C. Hasil penelitian pada siklus I menunjukkan ketuntasan belajar 41,2 %, pada siklus II mencapai ketuntasan 83,8 % dan pada siklus III mencapai ketuntasan 86,8 %. Dapat disimpulkan bahwa model pembelajaran kooperatif tipe Team Games Tournament (TGT) dapat meningkatkan prestasi belajar mahasiswa program studi Pendidikan Matematika FKIP Universitas Mataram pada pokok bahasan Integral.Kata-kata kunci: kooperatif, Team Games Tournament (TGT), Integral, ketuntasan belajar Abstract: The research aims are to improving students academic reward in Mathematics education program study FKIP Mataram University in academic year 2007/2008 of the Basic Mathematics Lecture on subject integral. This class room action research was done in 3 cycles and every cycle contain 5 steps that is planning, action, observation, evaluation, and reflection. The research is called success if 85 % of the students has score of evaluation minimum 56 or get C at every cycle. The result of research in cycle I was 41,2 %, in cycle II got 83,8 %, and the cycle III achieve 86,8 %, of the students have score minimum 56 . the conclusion is cooperative learning can be improved achievement of the mathematics on subject integral in academic year 2007/2008.Keywords: cooperative, Team Games Tournament (TGT), integral, achievement of the mathematics.

Download Full-text

PENERAPAN MODEL TSTS UNTUK MENINGKATKAN KEPERCAYAAN DIRI MAHASISWA PRODI PENDIDIKAN MATEMATIKA UNIVERSITAS MUHAMMADIYAH PONOROGO PADA MATA KULIAH TEORI BILANGAN

Jurnal Silogisme Kajian Ilmu Matematika dan Pembelajarannya ◽

10.24269/js.v2i2.802 ◽

2017 ◽

Vol 2 (2) ◽

pp. 56

Author(s):

Uki Suhendar

Keyword(s):

Data Analysis ◽

Mathematics Education ◽

Action Research ◽

Education Program ◽

Learning Model ◽

High Confidence ◽

Self Confidence ◽

Final Data ◽

The Subject ◽

Improvement Effort

Self confidence in learning must be owned by students. However, the fact that happened to the students of semester 1 year 2016/2017 in Fondasi Matematika course still not maximal. Teori Bilangan is a course given to students of the second semester of mathematics education program at Muhammadiyah University of Ponorogo. The purpose of this research is to increase students' self confidence in the subject of Teori Bilangan using Two Stay Two Stray learning model. Thus it is expected that students will be more confident in learning in other subjects in Mathematics Education program. This classroom action research is conducted in two cycles. Results of data analysis before the implementation of the study is 18.52% of the overall students who have high confidence. After analyzing the final data of cycle 2, it is found that the percentage of students who do not have high confidence is 22.22%. The TSTS steps used to improve students' self-confidence is with the improvement effort in the form of lecturers providing assistance to groups that have difficulty in solving the LKM problem..

Download Full-text

Euclidean and Non-Euclidean Geometry

10.1017/cbo9780511806209 ◽

1986 ◽

Cited By ~ 17

Author(s):

Patrick J. Ryan

Keyword(s):

Euclidean Geometry ◽

Non Euclidean Geometry

Download Full-text

IMPROVEMENT OF LEARNING OUTCOMES IN RESULT USING REALISTIC MATHEMATIC EDUCATION APPROACH IN BASIC SCHOOL

Unes Journal of Education Scienties ◽

10.31933/ujes.2.2.157-165.2018 ◽

2018 ◽

Vol 2 (2) ◽

pp. 157

Author(s):

Mimik Fernandes ◽

Farida F ◽

Yanti Fitria ◽

Ahmad Fauzan ◽

Nelvyarni Nelvyarni

Keyword(s):

Mathematics Education ◽

Action Research ◽

Student Learning ◽

Learning Outcomes ◽

Student Learning Outcomes ◽

Class Action ◽

Realistic Mathematics Education ◽

Realistic Mathematics ◽

Multiplication Of Fractions ◽

Mathematic Education

Based on experience and reflection multiplication of fractions learning at fifth class SDN 33 VII Koto Padang Pariaman district. Student learning outcomes is still low and the learning undertaken by teachers arenot using realistic problem to beginning of learning. So the author through this research trying to improve student learning outcomes in subjects multiplication of fractions. The purpose of this study was to describe the planning, implementation and learning outcomes. This research is action research (class action research), this study used a qualitative and quantitative approach. Learning is used by using the realistic mathematics education approach. After doing research hence an increase in student learning outcomes in multiplication of fractions lesson using realistic mathematics education approach. It can be seen, both from the ability of teachers in designing learning from 83% up to 94%, implementation of learning increased 94% from 77%, and learning outcomes increased to 86,87 from 74,04.

Download Full-text

“I have Learned Non-Euclidean Geometry Just from this Book” - Some facets of the correspondence between Friedrich Engel and David Hilbert

Results in Mathematics ◽

10.1007/s00025-021-01431-4 ◽

2021 ◽

Vol 76 (3) ◽

Author(s):

Peter Ullrich

Keyword(s):

Present Article ◽

19Th Century ◽

Euclidean Geometry ◽

Academic Life ◽

David Hilbert ◽

Non Euclidean Geometry ◽

The 19Th Century

AbstractFriedrich Engel and David Hilbert learned to know each other at Leipzig in 1885 and exchanged letters in particular during the next 15 years which contain interesting information on the academic life of mathematicians at the end of the 19th century. In the present article we will mainly discuss a statement by Hilbert himself on Moritz Pasch’s influence on his views of geometry, and on personnel politics concerning Hermann Minkowski and Eduard Study but also Engel himself.

Download Full-text