Web Links on Geometry and  Proof

 

 

Euclid’s Elements:

Hilbert’s Geometry

Hilbert’s Axioms

Spherical Geometry I: Polking's webpage

Spherical Geometry II: pictures from Wood's freshman seminar and some content

Proofs of the exterior angle theorem; flaws in Euclid; Do you believe Hilbert's fix?

Zalman Usiskin on `Teacher’s mathematics’ with a nice analysis of `parallelism

Shapiro-Categories, Structures and the Frege-Hilbert Controversy

Glencoe Geometry

Raimi: Why the ‘New Math’ brought algebra into geometry

 

Solomonovich: review of modern  geometry books

Hanna: Challenges to the importance of proof

Usyskin and Wu on the role of high school geometry

Harel and Souder on the nature of proof

Marker: The definition of truth (excerpt from standard model theory book)

Chval and Khisty: An article with exemplary use of geometric vocabulary in grade school

Baggett and Ehrenfeucht: On the Consistency and Correctness of Grade School Mathematics

 

Web Links on the Teaching of Mathematics

Standards

·  NCTM Standards

·  Illinois State Standards

·  California Mathematics Framework (1999 draft)

·  PDF version of NCTM Standards 2000

·  Colorado Standards

Studies

 

·  International Center for the Advancement of Scientific Literacy

·  Eisenhower National Clearing House

Articles

Vocabulary and Mathematics by Francis

Inside the Black Box, Black and Dylan on formative assessment

(Balanced Assessment)

(Ann Shannon: Keeping Score)

Common Errors in student mathematics

Tarski's High School Algebra Problem

·  Statement of James Hiebert

·  My Dear Aunt Sally has no excuse, Frank Pecchioni

·  Concepts and Computation, Cathy Kessel and John Baldwin

·  On My Mind:Dispelling Myths about Reform in School Mathematics,Fran Curcio

·  Operation Sense, Tool-Based Pedagogy, Curricular Breadth: A Proposalby Henri Picciotto

·  Relationships Between Research and the NCTM Standards, James Hiebert

·  NCTM Journals

Curriculum Projects

 

·  The Algebra Project

·  Show Me Center (review of 5 NSF projects)

·  Interactive Mathematics Project

·  Connected Mathematics Project

·  Everyday Math - UCSMP

·  TERC links

Equals/Family Math

Activities

Ring Theory  (This is a course outline. There is a clear statement of the ring axioms on pages 3 and 4.)

inscribed, central angles and the law of sines   

Fundamental Theorem of Arithmetic

·  Catalan Numbers

·  Fraction Activities

·  NASA Spacelinks

·  Amazing Space Look for Estimation Activity

·  Eratosthenes Noon Middle School Project

·  Aunty Math Open Ended problems for elementary students

·  Math Circle Neat problems from a gifted grade/high school student program

·  Henri Picotto's Math Ed Page

·  Colorado Math Olympiad: Problems for all ages

Further Links

 

·  University Education links

·  UIC Math-SciTeacher Education

·  Math Forum

·  Discovery Method of R.L. Moore This is a series of papers outliningthe famous (among university mathematicians) `discovery teaching' ofR.L. Moore

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