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.

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.

What are Perpendicular Lines?

1967 ◽  
Vol 60 (1) ◽  
pp. 24-30
Author(s):  
C. R. Wylie
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
School Mathematics ◽  
Experimental Program ◽  
Study Group ◽  
Recent Issue ◽  
High School Geometry ◽  
School Geometry ◽  
Coordinate Geometry

In a recent issue of The Mathematics Teacher,1 Harry Sitomer described an experimental program in high school geometry originally recommended to the School Mathematics Study Group by some of its advisers but finally undertaken by the Wesleyan Coordinate Geometry Group.

Subject Matter Knowledge of Geometry Needed in Tasks of Teaching: Relationship to Prior Geometry Teaching Experience

2020 ◽  
Vol 51 (5) ◽  
pp. 600-630
Author(s):  
Inah Ko ◽  
Patricio Herbst
Keyword(s):  
High School ◽  
High School Teachers ◽  
Subject Matter ◽  
Teaching Experience ◽  
Subject Matter Knowledge ◽  
School Teachers ◽  
Knowledge For Teaching ◽  
High School Geometry ◽  
School Geometry

This study proposes task of teaching as an organizer of dimensionality in teachers’ subject matter knowledge for teaching (SMK) and investigates it in the context of measuring SMK for teaching high school geometry (SMK-G). We hypothesize that teachers use different SMK-G in different aspects of their teaching work and that such differences can be scaled and associated with key elements of instruction. Analyses of 602 high school teachers’ responses to two sets of items designed to measure the SMK-G used in two particular tasks of teaching—understanding students’ work (USW) and choosing givens for a problem (CGP)—suggested the two scales of SMK-G to be distinguishable and differently related to experience in teaching high school geometry.

What Mathematics Do High School Teachers Need to Know?

2010 ◽  
Vol 103 (6) ◽  
pp. 418-423
Author(s):  
Michael J. Gilbert ◽  
Jacqueline Coomes
Keyword(s):  
High School ◽  
High School Teachers ◽  
School Mathematics ◽  
High School Mathematics ◽  
School Teachers ◽  
Mathematics Knowledge

The MC3 project defines, describes, and characterizes the mathematics knowledge needed for teaching high school mathematics.

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.

Prove It

1998 ◽  
Vol 91 (8) ◽  
pp. 726-728
Author(s):  
Amy A. Prince
Keyword(s):  
High School ◽  
School Mathematics ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry

Ask anyone who has taken high school geometry, and he or she will have a notion of a proof— generally, a two-column proof of statements and reasons. The two-column proof has fallen out of favor in such reform documents as the NCTM's Curriculum and Evaluation Standards for School Mathematics, which seeks to emphasize “deductive arguments expressed orally or in sentence or paragraph form” (NCTM 1989, 126). The two-column proof is a somewhat rigid form, yet it demonstrates to the students that they may not just give statements or draw conclusions without sound mathematical reasons.

Doing Algebra in Grades K-4

1997 ◽  
Vol 3 (6) ◽  
pp. 346-356
Author(s):  
Zolman Usiskin
Keyword(s):  
High School ◽  
Elementary School ◽  
Elementary School Teachers ◽  
Elementary Grades ◽  
School Teachers ◽  
High School Geometry ◽  
School Geometry

About thirty-five years ago the movement to incorporate geometry into the elementary grades began. To many elementary school teachers, the mention of the word geometry brought back memories of a high school geometry course that dealt with abstraction and proof. The thought of teaching children this geometry was naturally viewed with incredulity.

Connecting Research to Teaching: Mathematics as Reasoning

1995 ◽  
Vol 88 (5) ◽  
pp. 412-417
Author(s):  
Peter Galbraith
Keyword(s):  
High School ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematical Quality

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) defines a role for reasoning in school mathematics that is far different from the norm of recent practice. Until recently, the study of mathematical reasoning was largely confined to high school geometry. Further, as Schoenfeld (1988) pointed out, the approach used in geometry was often so rigid that it conveyed the impression that the style of the response—for example, the two-column-proof format—was more important than its mathematical quality. The Standards document notes that reasoning is to have a role in all of mathematics from the earliest grades on up and that the form of justification need not follow a pre scribed format. Indeed, students are encouraged to explain their reasoning in their own words. Teachers are asked to present opportunities for students to refine their own thoughts and language by sharing ideas with their peers and the teacher.

Using The Geometer's Sketchpad to Visualize Maximum-Volume Problems

2000 ◽  
Vol 93 (3) ◽  
pp. 224-228 ◽  
Author(s):  
David C. Purdy
Keyword(s):  
High School ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Geometer's Sketchpad ◽  
Maximum Volume ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Traditional Courses

An underlying tenet of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and other movements toward reform in school mathematics is breaking down content barriers between traditional mathematical topics, with the goal of teaching mathematics as a logically interconnected body of thought. As teachers move toward integrating the various areas of mathematics into traditional courses, problems that were once reserved for higher courses, for example, precalculus and calculus, now surface earlier as interesting explorations that can be tackled with such tools as the graphing calculator. One such problem is the well-known maximum-volume-box problem. Although this problem and related optimization questions have been common in advanced algebra, precalculus, and calculus textbooks, they have only recently found their way into high school geometry textbooks, including Discovering Geometry: An Inductive Approach (Serra 1997).

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.

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