Geometric representations of irrational algebraic numbers in Hungarian high school mathematics education

2021 ◽  
pp. 323-340
Author(s):  
Anna Stirling ◽  
Csaba Szabó ◽  
Júlia Szenderák ◽  
Scilla Bereczky-Zámbó ◽  
Sára Szörényi
Keyword(s):  
High School ◽  
Mathematics Education ◽  
Everyday Life ◽  
Rational Numbers ◽  
Elementary Geometry ◽  
High School Mathematics ◽  
Algebraic Numbers ◽  
Irrational Numbers ◽  
Problems And Solutions ◽  
Geometric Representations

Irrational numbers are present in our everyday life but their exact values cannot be given in a form that students easily understand. Therefore in this paper we show geometrical constructions and calculations in which non-rational numbers naturally arise and gain meaning. We look at numbers which are expressible with at maximum two roots and are present in the Hungarian curriculum. For each number we present how they appear in Hungarian textbooks, and show multiple problems and solutions in which they arise. These solutions differ in their level of mathematical complexity, from elementary geometry to higher algebra. Introducing these solutions to students, shows them, that the different areas of mathematics are interrelated. This approach may inspire students to use their mathematical knowledge not only from the area in which the problem was presented.

The Atlanta meeting of the National Council of Teachers of Mathematics

1964 ◽  
Vol 11 (6) ◽  
pp. 449-450
Keyword(s):  
High School ◽  
Elementary School ◽  
Mathematics Education ◽  
Rational Numbers ◽  
National Council ◽  
Peach Tree ◽  
College Level ◽  
Probability And Statistics ◽  
The City

In the height of autumn, the City of Peachtree Street in the Peach Tree State will be the locale of the Atlanta Meeting of the National Council of Teachers of Mathematics. This event, a first of its kind for Atlanta and for Georgia, is designed to attract persons interested in mathematics, kindergarten to the college level. From geometry in the kindergarten to probability and statistics in high school; from the rational numbers in the elementary school to applications of mathematics in the senior high school, from the role of reading to the role of the administrator in improving mathematics education; in short, whatever aspects of mathematics on the school and college levels fascinate one will be presented during the Atlanta Meeting, November 19-21, 1964.

The College Board Scholastic Aptitude Test: An Overview of the Mathematical Portion

1978 ◽  
Vol 71 (3) ◽  
pp. 168-180
Author(s):  
James S. Braswell
Keyword(s):  
High School ◽  
Mathematics Education ◽  
Mathematics Teachers ◽  
Scholastic Aptitude Test ◽  
School Mathematics ◽  
High School Mathematics ◽  
Aptitude Test ◽  
College Board ◽  
Current Information ◽  
Scholastic Aptitude

From time to time I have been asked to speak to groups of high school mathematics teachers about the mathematical portion of the Scholastic Aptitude Test (SAT). This article affords an opportunity to provide current information about this test to a greater audience of mathematics teachers and others interested in mathematics education.

NCTM's Catalyzing Change in High School Mathematics: Our Role in the Middle

2019 ◽  
Vol 24 (5) ◽  
pp. 290-294
Author(s):  
Sarah B. Bush
Keyword(s):  
High School ◽  
Mathematics Education ◽  
Middle Schools ◽  
Shared Responsibility ◽  
School Mathematics ◽  
High School Mathematics

The success of Catalyzing Change is contingent on the preparation and experiences that students bring with them to high school—which is the role of middle schools. We have the shared responsibility of providing an equitable mathematics education for each and every student.

Civic Mathematics: A Real-Life General Mathematics Course

1994 ◽  
Vol 87 (6) ◽  
pp. 396-401
Author(s):  
Terry Vatter
Keyword(s):  
High School ◽  
Mathematics Education ◽  
School District ◽  
Mathematics Teacher ◽  
Mathematics Curriculum ◽  
Real Life ◽  
Democratic Society ◽  
Future Generations ◽  
High School Mathematics ◽  
The World

Our hopes for education coincide with those for our children: we want to help them grow into adults who will make the world an even better place for future generations. This goal may be a lofty one for a high school mathematics teacher, but it is important to keep our ideals clearly in mind as we develop ways to equip our students to live full lives and to make positive contributions to society. As educators we need to be responsible for teaching the skills that will enable students to (1) enter into a career or pursue their mathematics education and (2) become informed participants in a democratic society. The civic mathematics curriculum described in this article was driven by those objectives. It was developed over a summer and partially funded by a stipend from my school district

From the 2000s: Facing Facts: Achieving Balance in High School Mathematics

2006 ◽  
Vol 100 (5) ◽  
pp. 86-95
Author(s):  
Lynn Arthur Steen
Keyword(s):  
High School ◽  
Mathematics Education ◽  
Comprehensive Analysis ◽  
The State ◽  
School Mathematics ◽  
High School Mathematics ◽  
New Strategy ◽  
Unique Power ◽  
Current Curriculum ◽  
Mathematical Applications

This article from 2005 presents comprehensive analysis of the state of mathematics education since launching of soviet Sputnik till now concluding that despite extraordinary efforts today's typical 17-year-old knows no more mathematics than his or her grandparents at the same age. After the analysis of the problem author proposes two recommendations balancing interests of different stakeholders. He concludes that due to the extraordinary recent expansion of mathematical applications a new strategy may be used. He believes that the unique power of mathematics that the current curriculum provides for a minority of calculus-bound students, such as reasoning, abstraction, generalization, can extended to a substantial majority of students through a more diverse curriculum designed to offer breadth, balance, utility, and coherence.

The Junior High School Mathematics Program— Past, Present, and Future

1970 ◽  
Vol 63 (5) ◽  
pp. 383-390
Author(s):  
W. Eugene Ferguson
Keyword(s):  
High School ◽  
Mathematics Education ◽  
Junior High School ◽  
Junior High ◽  
School Mathematics ◽  
High School Mathematics ◽  
Mathematical Ideas ◽  
Mathematics Program ◽  
Education Today ◽  
High Level

Many teachers believe that the junior high school is “where the action is” in mathematics education today. Students at the junior high level usually are intellectually curious, full of life, and willing to spend some time exploring in depth mathematical ideas and concepts.

Experimental Programs: Research in the Teaching of High School Mathematics

1966 ◽  
Vol 59 (1) ◽  
pp. 53-57
Author(s):  
Kenneth E. Brown ◽  
Theodore L. Abell
Keyword(s):  
High School ◽  
Mathematics Education ◽  
School Mathematics ◽  
National Council ◽  
High School Mathematics ◽  
Present Survey ◽  
The U.S ◽  
Research In Mathematics Education

Since 1952 the U.S. Office of Education, in cooperation with the National Council of Teachers of Mathematics, has prepared a biannual summary of research in mathematics education. The present survey is based on the 645 replies from a thousand colleges that were sent the questionnaire. Many of the colleges responded even though they had no research to contribute to the study. In their answers they requested a report of the findings. About 125 of the reported studies for the calendar years 1961-62 were on mathematics education in grades 9-12.

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