Non-Euclidean Geometry Lesson Promotes Mathematical Reasoning

2021 ◽  
Vol 114 (11) ◽  
pp. 869-877
Author(s):  
Derek A. Williams ◽  
Kelly Fulton ◽  
Travis Silver ◽  
Alec Nehring
Keyword(s):  
High School ◽  
High School Students ◽  
Euclidean Geometry ◽  
Mathematical Reasoning ◽  
School Students ◽  
Non Euclidean Geometry ◽  
Taxicab Geometry

A two-day lesson on taxicab geometry introduces high school students to a unit on proof.

Activities: The Conic Sections in Taxicab Geometry: Some Investigations for High School Students

1998 ◽  
Vol 91 (4) ◽  
pp. 304-341 ◽  
Author(s):  
Fernand J. Prevost
Keyword(s):  
High School ◽  
High School Students ◽  
Euclidean Distance ◽  
Euclidean Geometry ◽  
Pythagorean Theorem ◽  
Conic Sections ◽  
School Students ◽  
Taxicab Geometry

The urban world in which many of us live does not lend itself to the metric of Euclidean geometry. Assuming that the avenues are perpendicular to the streets in a city, the distance from “fifth and fifty-first” to “seventh and thirty-fourth” is not the familiar Euclidean distance found by applying the Pythagorean theorem. The distance must instead be measured in blocks from fifth to seventh avenues and then from fifty-first to thirty-fourth streets. This taxicab metric, one of several me tries used in mathematics (Eisenberg and Khabbaz 1992), is practical for many applications and helps students pursue interesting investigations while deepening their understanding of familiar topics.

scholarly journals HUBUNGAN MINAT BELAJAR TERHADAP KEMAMPUAN PENALARAN MATEMATIK SISWA SMP PADA MATERI LINGKARAN

2018 ◽  
Vol 1 (2) ◽  
pp. 93
Author(s):  
Winda Awaliyah ◽  
Aflich Yusnita Fitrianna
Keyword(s):  
High School ◽  
High School Students ◽  
Student Learning ◽  
Junior High School ◽  
Junior High ◽  
Mathematical Reasoning ◽  
Circle Method ◽  
Junior High School Students ◽  
School Students ◽  
Learning Interest

This research aims to determine the relationship of student learning interest to the mathematical reasoning ability of junior high school students in chapter circle. Method used is quantitative with correlation method. this research was conducted in one of  junior high school in Cimahi with population of all students of  class IX and sample IX-M as many as 30 people. Instrumen used in this research is a questionnaire instrument to measure the level of student learning interest and test instrument to measure the ability mathematical reasoning of students. Analysis results visible there is a significant relationship between student learning interests with the ability of mathematical reasoning and contribution/ influence interest in learning on the ability of mathematical reasoning of junior high school students of class IX is positive is equal to 74,64% while the remaining 25,36% influenced by other factors.

scholarly journals IMPROVING STUDENTS’ MATHEMATICAL UNDERSTANDING AND REASONING ABILITY AND MOTIVATION THROUGH THINK TALK WRITE APPROACH (TTW) JUNIOR HIGH SCHOOL STUDENTS

2018 ◽  
Vol 1 (2) ◽  
pp. 194
Author(s):  
Diky Irawan ◽  
Euis Eti Rohaeti ◽  
Asep Ikin Sugandi
Keyword(s):  
High School ◽  
High School Students ◽  
Junior High School ◽  
Junior High ◽  
Mathematical Reasoning ◽  
Mathematical Understanding ◽  
Junior High School Students ◽  
Learning Motivation ◽  
School Students ◽  
Class Viii

This study aims to examine the achievement and improvement of the ability of understanding and mathematical reasoning and motivation through Think Talk Write (TTW) approach to junior high school students. The population in this study is all junior high school in West Bandung Regency and the sample is class VIII of SMPS Darun Nasya, The instrument used in the research is a question of understanding and mathematical reasoning and questionnaire of learning motivation attitude, then the data obtained is processed through a two-way ANOVA test and correlation and regression test, data processing using IBM Statistics SPSS 21. Results of research involving TTW as independent variables in the experimental class and direct learning in the control class showed: There was a difference in achievement and improvement of mathematical understanding between control and experiment class, There are differences in achievement and improvement of mathematical reasoning between control and experiment class, There is difference of student's learning motivation between control and experiment class.

scholarly journals INCREASING STUDENT’S UNDERSTANDING ABILITY AND MATHEMATICAL REASONING AND LEARNING MOTIVATION OF JUNIOR HIGH SCHOOL STUDENTS USING DISCOVERY LEARNING METHOD

2018 ◽  
Vol 1 (2) ◽  
pp. 143
Author(s):  
Ida Juhanah ◽  
Jozua Sabandar
Keyword(s):  
High School ◽  
High School Students ◽  
Junior High School ◽  
Junior High ◽  
Mathematical Reasoning ◽  
Discovery Learning ◽  
Junior High School Students ◽  
Control Group ◽  
Learning Method ◽  
School Students

This research aims to examine the improvement of understanding ability and mathematical reasoning as well as the motivation of learning of junior high school students by discovery learning method conventional method. In addition, it aims to check the improvement of understanding ability and mathematical reasoning as well as the motivation of learning though junior high school students. This research was quasi experiment which was designed to nonequivalent control group. The study The population on this research was all the junior high school students of Cipeundeuy 2 Junior High School West Bandung Regency. The Sample was two classes of 7th grade students. The data was attained by understanding thinking and mathematical test which using material of algebraic form and questionnaire motivation to learn

Tessellating the Sphere with Regular Polygons

2004 ◽  
Vol 97 (3) ◽  
pp. 165-167
Author(s):  
Hortensia Soto-Johnson ◽  
Dawn Bechthold
Keyword(s):  
High School ◽  
High School Students ◽  
Euclidean Geometry ◽  
Spherical Geometry ◽  
Regular Polygons ◽  
School Students ◽  
Disney World ◽  
Spaceship Earth

Spherical geometry can be used to entice students into a deeper understanding of Euclidean geometry. Determining which regular spherical polygons tessellate the sphere is another motivating topic that is accessible to high school students. The most recognizable tessellations of the sphere are found on balls, such as soccer balls, volleyballs, and golf balls. Even Spaceship Earth at Epcot Center in Disney World involves tessellation.

scholarly journals ADVERSITY QUOTIENT DAN PENALARAN KREATIF MATEMATIS SISWA SMA DALAM PEMBELAJARAN ARGUMENT DRIVEN INQUIRY PADA MATERI TURUNAN FUNGSI

2017 ◽  
Vol 2 (1) ◽  
pp. 15 ◽  
Author(s):  
Wahyu Hidayat
Keyword(s):  
High School ◽  
High School Students ◽  
Mathematical Reasoning ◽  
Senior High School ◽  
Control Group ◽  
Reasoning Ability ◽  
School Students ◽  
Learning Factors ◽  
Senior High School Students ◽  
Creative Mathematical Reasoning

This study is designed in the form of experiment with the design of control group and posttest only aimed at investigating the role of learning that Argument Driven Inquiry (ADI) in improving senior high school students’ creative mathematical reasoning ability. The population of this study was senior high school students’ in Cimahi City and the samples were 69 senior high school students’ set purposively and randomly to be included into the experimental class and control class. Based on the results and discussion, it is concluded that: (1) creative mathematical reasoning ability of the students who received Argument Driven Inquiry (ADI) instruction is better than those who received direct instruction is reviewed based on the whole and the type of Adversity Quotient (Quitter / AQ Low, Champer / AQ Medium, and the Climber / AQ High); Learning factors and type of Adversity Quotient (AQ) affect the achievement of creative mathematical reasoning skills students. In addition, there is no interaction effect between learning and AQ together in developing the creative mathematical reasoning ability of students'; (3) creative mathematical reasoning ability of students’ has not been achieved optimally on the indicators novelty.

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