Connecting Research to Teaching: Count on Number Theory to Inspire Proof

2009 ◽  
Vol 103 (4) ◽  
pp. 298-304
Author(s):  
Anne Larson Quinn
Keyword(s):  
High School ◽  
Number Theory ◽  
Secondary School ◽  
Secondary School Students ◽  
School Mathematics ◽  
School Students ◽  
High School Geometry ◽  
Mathematical Proofs ◽  
School Geometry ◽  
Principles And Standards

Many students find proofs frustrating, and teachers struggle with how to help students write proofs. In fact, it is well documented that most students who have studied proofs in high school geometry courses do not master them and do not understand their function (Battista 2007; Harel and Sowder 2007). And yet, according to NCTM's Principles and Standards for School Mathematics(2000), “By the end of secondary school, students should be able to understand and produce mathematical proofs … and should appreciate the value of such arguments” (p. 56).

The Second U.S.A. Mathematical Olympiad

1974 ◽  
Vol 67 (2) ◽  
pp. 115-119
Author(s):  
Samuel L. Greitzer
Keyword(s):  
High School ◽  
Secondary School ◽  
Secondary School Students ◽  
School Mathematics ◽  
New Venture ◽  
High School Mathematics ◽  
School Students ◽  
Mathematical Talent ◽  
Honor Roll ◽  
Mathematics Examination

Because the U.S.A. Mathematical Olympiad is a new venture, a brief explanation is pertinent. The purpose of the Olympiad is to attempt to discover secondary school students with superior mathematical talent—students who possess creativity and inventiveness as well as computational skills. Participation is limited to about one-hundred students selected mainly from the Honor Roll of the Annual High School Mathematics Examination plus a few recommended students from the states that sponsor their own high school mathematics competitions. The Olympiad consists of five problems of the essay type requiring mathematical power on the part of the participants.

What Do Mathematics Teachers Think about the High School Geometry Controversy?

1975 ◽  
Vol 68 (6) ◽  
pp. 486-493
Author(s):  
George Gearhart
Keyword(s):  
High School ◽  
Secondary School ◽  
Mathematics Teachers ◽  
School Mathematics ◽  
Secondary School Mathematics ◽  
High School Geometry ◽  
School Geometry

A survey of the attitudes of secondary school mathematics teachers toward geometry.

The First U.S.A. Mathematical Olympiad

1973 ◽  
Vol 66 (3) ◽  
pp. 223-227
Author(s):  
Samuel L. Greitzer
Keyword(s):  
High School ◽  
Secondary School ◽  
Secondary School Students ◽  
School Mathematics ◽  
Computational Techniques ◽  
High School Mathematics ◽  
School Students ◽  
Mathematical Talent ◽  
Honor Roll ◽  
Mathematics Examination

At ITS meeting on 1 September 1971, the Mathematical Association of America agreed to sponsor a U.S.A. Mathematical Olympiad in addition to the Annual High School Mathematics Examination. The purpose of tlie Olympiad was to attempt to discover secondary school students with superior mathematical talent, students who possessed mathematical creativity and inventiveness as well as competence in computational techniques. Participation was to be limited to about 100 students selected from the Honor Roll on the High School Mathematics Examination, plus a few students of superior ability selected from those states that did not participate in the High School Mathematics Examination. The Olympiad itself was to consist of five essay-type problems requiring mathematical power on the part of the participants.

scholarly journals EFFECTIVENESS OF SCHOOL COUNSELING PROGRAMS ON ACADEMIC ACHIEVEMENT OF SECONDARY SCHOOL STUDENTS IN KIAMBU COUNTY, KENYA

2020 ◽  
Vol 5 (35) ◽  
pp. 58-64
Author(s):  
Lucy Gachenia ◽  
Margaret Mwenje
Keyword(s):  
High School ◽  
Academic Achievement ◽  
Academic Performance ◽  
Secondary School ◽  
School Counseling ◽  
Secondary School Students ◽  
Counseling Services ◽  
Counseling Program ◽  
School Students ◽  
Counseling Programs

The school counseling program is meant to assist students to deal with psycho-social and behavioral challenges, which normally affect their academic performance. In order to achieve this goal, the Kenyan government has previously committed resources towards establishing counseling programs in schools. The aim of this study was to establish how effective these counseling programs are in assisting secondary school learners in Kiambu County to achieve academically. Primary data was derived from 80 high school adolescents, 8 counselors, and 8 academic Dean of Students who were purposively sampled from 8 schools that were randomly selected. The study was qualitatively done, and self-determination theory was used to guide the study. Data were analyzed for the identification of counseling program characteristics and student improvement indices. These were presented in tables, charts, frequencies, and percentages based on the responses from the respondents. Further, a correlation between the two variables of the study was examined. Findings depicted that 65.7% of the students sampled said that counseling services offered at school satisfied their needs, 74.3% reported an improvement in their academic performance as a result of those counseling services and 87% felt more positive about school life after receiving counseling services. The study concluded that comprehensive counseling programs improved academic performance among high school students. The study intended to inform education planners, principals, and administrators on the role counseling would play in enhancing academic achievement among secondary school students.

scholarly journals Deliberating science in Italian high school. The case of the Scienza Attiva project

2017 ◽  
Vol 16 (01) ◽  
pp. A02
Author(s):  
Federica Cornali ◽  
Gianfranco Pomatto ◽  
Selena Agnella
Keyword(s):  
High School ◽  
Secondary School ◽  
Focus Groups ◽  
Deliberative Democracy ◽  
Mixed Method ◽  
Secondary School Students ◽  
Evaluation Study ◽  
School Students ◽  
National Project

This paper provides an analysis of the implementation and the outcomes of Scienza Attiva, an Italian national project for secondary school students, that makes use of deliberative democracy tools to address socio-scientific issues of great impact. The analysis has required a mixed method including surveys of students' pre- and post-project opinions, focus groups and interviews with students and teachers. The results from this evaluation study provide evidence that the project improves students' understanding of socio-scientific issues, strengthens their awareness of the importance of discussion and positively influences interactions in the classroom.

Vertex-Edge Graphs: An Essential Topic in High School Geometry

2008 ◽  
Vol 102 (3) ◽  
pp. 178-185
Author(s):  
Eric W. Hart
Keyword(s):  
High School ◽  
Secondary School ◽  
Essential Characteristic ◽  
High School Geometry ◽  
School Geometry ◽  
Geometric Objects

Secondary school geometry is perhaps most succinctly described as the study of shape. Many aspects of shape are studied, such as properties of and relationships among shapes, location of shapes, transformations of shapes, and reasoning about shape. Consider an important counterpoint to this shape story or perhaps chapter zero in the story—the study of vertex-edge graphs, which are geometric objects for which shape is not an essential characteristic.

Let’s Use Trigonometry

1975 ◽  
Vol 68 (2) ◽  
pp. 157-160
Author(s):  
John J. Rodgers
Keyword(s):  
High School ◽  
Subject Matter ◽  
School Mathematics ◽  
High School Mathematics ◽  
Mathematics Courses ◽  
High School Geometry ◽  
School Geometry ◽  
The Subject ◽  
Order Of Presentation

All too often in the teaching of high school mathematics courses, we overlook the inherent flexibility and interdependence of the subject matter. It is easy to fall into the trap of presenting algebra, trigonometry, geometry, and so on, as separate areas of study. It is because they were taught this way traditionally. With relatively minor changes in the order of presentation, we can demonstrate to the student the vital interconnectiveness of mathematics. For example, many courses in high school geometry include a unit on trigonometry. The student learns three trigonometric ratios, namely, the sine, the cosine, and the tangent. He also learns to use the trigonometric tables to solve for an unknown side of a right triangle. Generally this material comes quite late in the year.

The Forum: What Should Become of the High School Geometry Course?: The Present Year-Long Course in Euclidean Geometry Must Go

1972 ◽  
Vol 65 (2) ◽  
pp. 102-154
Author(s):  
Howard F. Fehr
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
School Mathematics ◽  
Study Group ◽  
High School Geometry ◽  
School Year ◽  
School Geometry ◽  
Long Course ◽  
Coordinate Geometry

It is assumed that the geometey course refers to one that is commonly taught in the tenth school year. It is traditional Euclidean synthetic geometry, 2- and 3-space, modified by an introduction of ruler and protractor axioms into the usual synthetic axioms. A unit of coordinate geometry of the plane is usually appended. It is a course that is reflected in textbooks prepared by the School Mathematics Study Group and in most commercial textbooks.

Experimental Programs: Coordinate Geometry with an Affine Approach

1964 ◽  
Vol 57 (6) ◽  
pp. 404-405
Author(s):  
Harry Sitomer
Keyword(s):  
High School ◽  
High School Teachers ◽  
School Mathematics ◽  
Study Group ◽  
School Teachers ◽  
High School Geometry ◽  
School Geometry ◽  
Coordinate Geometry

In the spring of 1961, the School Mathematics Study Group convened a group of college mathematicians and high school teachers of mathematics to consider plans for writing an alternate high school geometry course, in which coordinates would be introduced and used as early as feasible.

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