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.

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.

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 High School Geometry Controversy: Is Transformation Geometry the Answer?

1971 ◽  
Vol 64 (1) ◽  
pp. 37-40
Author(s):  
Richard H. Gast
Keyword(s):  
High School ◽  
Secondary School ◽  
High School Geometry ◽  
School Geometry ◽  
Transformation Geometry

Before I attempt to answer the question posed in the title of this article, I shall present the various proposals for and against the inclusion of transformations in secondary school geometry that have influenced my response.

Experimental Programs: High school geometry via ruler-and-protractor axioms— report on a classroom trial

1961 ◽  
Vol 54 (5) ◽  
pp. 353-360
Author(s):  
Max S. Bell
Keyword(s):  
High School ◽  
Secondary School ◽  
Curriculum Reform ◽  
Past Experience ◽  
Secondary School Mathematics ◽  
High School Geometry ◽  
Solid Geometry ◽  
School Geometry ◽  
Twelfth Grade ◽  
The Stability

There is considerable talk these days about curriculum “reform” in secondary- school mathematics. From our past experience, however, we can infer that such reforms will be very difficult to implement; witness, for example, the stability of solid geometry as a semester course in the twelfth grade despite repeated recommendations over a number of years for change to something more fruitful and useful.

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