On this page you will find resources relating to the teaching and learning of geometries, including Euclidean geometry, coordinate geometry, and transformation geometry.


1. Development of Geometric Thought: Van Hiele Levels (Visualization, Analysis, Informal Deduction, Deduction, Rigor)

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For detailed explanations: Download (PDF)

2. Classifying quadrilaterals: Go Fly a Kite!

We classify quadrilaterals by reasoning with their diagonals: Download (PDF)
Geogebra files: one-bisect-congruent one-bisect-not-congruent two-bisect-congruent two-bisect-not-congruent
CCSS controversy: Inclusive versus exclusive definition of a trapezoid
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3. Pythagoras: Reasoning about the relationship of areas of squares on sides of triangles.

Tile Activity: Download (DOCX)
Tile Squares for Tile Activity: Download (DOCX)
Geogebra File: Pythagorean Relationships of triangles 1
Geogebra File: Pythagorean Relationships of triangles 2
Geogebra File: Pythagorean Relationships of Triangles 3
Liquid "Proof" (YouTube): LINK
Visual Proof (NCTM Illuminations): LINK
Animated proof (YouTube): LINK
Historical approach: Download (PDF)
Inquiry Lesson Video focused on AREAS: https://www.teachingchannel.org/videos/pythagorean-theorem-lesson
Inquiry Lesson Video focused on SIDES: https://www.teachingchannel.org/videos/teaching-pythagorean-theorem

4. Tangrams are not Toys!
Reasoning with Tangrams by finding the underlying structure through a folding activity: Download (PDF)

5. Proving

a. The November 2009 issue of the NCTM journal The Mathematics Teacher is entirely devoted to proving: LINK
b. An article I wrote regarding informal deductive reasoning in sixth graders: Download (PDF)
c. The Travel Metaphor: Download (PDF)
d. Three columns instead of two, a strategy to help students with proving: Download (PDF)

e. Proving and reasoning logically is not exclusive to Geometry. One example, Logic in the coordinate plane: Download (PDF)

6. Proving Congruence and Similarity in the CCSSbad-poster.JPG
Geogebra files:
Congruence Solution
Congruence 2 Solution
Similarity Solution

7. Common Core development of Geometry grades 6-12: Download (DOCX)

PARCC sample Geometry Questions: LINK

8. Transformation Geometry

Rotation Lesson Study PLAN: DOWNLOAD
Rotation Lesson Study WORKSHEET: DOWNLOAD

Composition of reflections: PARALLEL INTERSECTING

9. Longsword dancing and stable geometrical shapes (Video):

http://simonsfoundation.s3.amazonaws.com/jwplayer/longsword/Longsword-dancing-2b_compressed2.mp4