Geometry in the American school curriculum

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Geometry in the American school curriculum
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Brief timeline

• 1804, Flint published a book on surveying that
  included 12 pages devoted to geometry
• 1834, Davies publishes a revision of Brewsters
  translation of Legendres Elements becomes most
  widely used geometry text in America until 1870
• 1850s-gt
• Geometry made part of college entrance
  requirements (Yale 1865), hence entering
  secondary curriculum as formal, demonstrative
  subject. Informal geometry advocated for lower
  grades but makes minimal appearance.
• 1858, Greenleafs geometry text introduces
  originals
• 1894, NEAs Committee of Ten convened (wanted
  geometry to replace so much arithmetic in lower
  grades)
• 1895, Committee of Fifteen convened (wanted
  algebra to replace arithmetic)

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• 1899, Committee on College Entrance
  Requirements-encourages geometry to be included
  in grades 7,8
• 1910-gt
• Junior high movement, informal geometry gains a
  foothold in the curriculum of grades 7-9
• 1911,National Comm. Of 15 on Geometry syllabus
  algebra in the 9th, plane geometry in the
  10th,. , leave out some material
• 1912-1917, International Commission formed to
  survey the status of teaching mathematics- first
  attempt at national assessment
• 1921, First published Mathematics Teacher
• The 1923 Report by the MAA- include informal
  geometry in the lower grades

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• 1932, NCTMs Committee of Geometry reports that
  informal geometry seen as jr high subject
• 1924, Glass confirms in his detailed study that
  geometry is definitely being taught in grades 7-9
• 1940-gt World War II reveals the shortcomings of
  the mathematical prep of our soldiers
• 1950s-gt School Mathematics Study group and U of
  I Committee on school mathematics formed
• 1963, Cambridge report- integrate geometry
  throughout curriculum starting in grade K
• 1970s-gtGeometry throughout the entire
  curriculum, arguments have shifted to the method
  of its presentation in high school

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Approaches to teaching geometry

• Conventional- most prevalant
• Coordinates
• Transfomational
• Affine
• Vector

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The conventional approach-3 major sources for a
teaching philosopy
Descartes Analytic (coordinate system imposed)

• Euclid
• Synthetic
• (No coord. system)

Hilbert Reconciliation of Euclid with Descartes
Legendre Numbers associated with line segments,
rigor decreased, change in theorem sequence
Current text
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The current conventional (U.S.) text-its two
concerns

• 1. Content
• A list of axioms must be chosen, usually a
  subset of Euclids Elements that have been
  patterned after Moise texts produced by the SMSG
• 2. Organization of content
• A single deductive system
• Most results derived from several lists of
  undefined terms and postulates