Soundoff: High School Geometry Should Be a Laboratory Course

1990 ◽  
Vol 83 (1) ◽  
pp. 4-5
Author(s):  
Ernest Woodward
Keyword(s):  
High School ◽  
Mathematics Assessment ◽  
Pythagorean Theorem ◽  
Educational Progress ◽  
National Assessment ◽  
Laboratory Course ◽  
High School Geometry ◽  
School Geometry

Present day instruction in geometry is ineffective. Results of the fourth mathematics assessment of the National Assessment of Educational Progress (NAEP) (Brown et al. 1988) indicate that fewer than half the eleventh-grade students who had taken geometry could apply the Pythagorean theorem in a routine problem and that fewer than a third of these students could find the perimeter of a rhombus drawn on grid paper. Eleventh-grade students who had taken geometry performed only slightly better on spatialvisualization tasks than eleventh-grade students who had not taken geometry.

A Geometry lesson from National Assessment

1981 ◽  
Vol 74 (1) ◽  
pp. 27-32
Author(s):  
Donald R. Kerr
Keyword(s):  
High School ◽  
Mathematics Assessment ◽  
Educational Progress ◽  
National Assessment ◽  
Formal Geometry

The geometry exercises administered during the 1977-78 mathematics assessment of the National Assessment of Educational Progress (N AEP) focused primarily on concepts of informal geometry rather than the more formal deductive geometry typically taught in a high school course. Results did show that students who studied formal geometry performed better.

Results and Implications of the NAEP Mathematics Assessment: Secondary School

1975 ◽  
Vol 68 (6) ◽  
pp. 453-470
Author(s):  
Thomas P. Carpenter ◽  
Terrence G. Coburn ◽  
Robert E. Reys ◽  
James W. Wilson
Keyword(s):  
High School ◽  
Secondary School ◽  
High School Dropouts ◽  
Mathematics Assessment ◽  
Educational Progress ◽  
School Dropouts ◽  
National Assessment ◽  
Mathematical Concepts ◽  
Academic Year

During the 1972-73 academic year. the National Assessment of Educational Progress (NAEP) conducted its first assessment in mathematics. Representative national samples of 9-year-olds, 13-year-olds, 17-year-olds (including high school dropouts and early graduates), and adults between the ages of 26 and 35 were assessed to determine their levels of attainment in mathematical concepts and skills.

Historically Speaking,— Pappus's extension of the Pythagorean Theorem

1958 ◽  
Vol 51 (7) ◽  
pp. 544-546
Author(s):  
Howard Eves
Keyword(s):  
High School ◽  
Pythagorean Theorem ◽  
High School Geometry ◽  
School Geometry

Every student of high school geometry sooner or later becomes familiar with the famous Pythagorean Theorem, which states that in a right triangle the area of the square described on the hypotenuse is equal to the sum of the areas of the squares described on the two legs. This theorem appears as Proposition 47 in Book I of Euclid's Elements, written about 300 B.C.

Using Puzzles to Teach the Pythagorean Theorem

1989 ◽  
Vol 82 (5) ◽  
pp. 336-339 ◽  
Author(s):  
James E. Beamer
Keyword(s):  
High School ◽  
High School Students ◽  
Careful Analysis ◽  
Pythagorean Theorem ◽  
Alternative Proof ◽  
School Students ◽  
High School Geometry ◽  
School Geometry ◽  
Starting Point ◽  
Senior High School Students

One of the aims of a mathematics prog- gram is to familiarize the students with the Pythagorean theorem. The result, stated algebraically, is c2 = a2 + b2. Stated geometrically, the Pythagorean theorem refers to squares drawn on the three sides of a right triangle. The theorem states that the square drawn on the longest side has exactly the same area as that of the other two squares combined. Is it possible systematically to dissect the two smaller squares into pieces that will cover the larger square? The answer to this question is the focus of this article, which offers sugges-tions about how the Pythagorean theorem can be introduced to students in the middle school years. Enrichment challenges in the form of proofs suitable for high school geometry students are also included. Finally, three proofs of the Pythagorean theorem based on careful analysis of the puzzles are discussed. Senior high school students can be asked to prove that the pieces actually fit and to use this tessellation as a starting point to provide an alternative proof of the theorem.

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