Geometric Thinking and Geometric Conceots

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Geometric Thinking and Geometric Concepts

This mind map is geared toward elementary math teachers, regarding geometric thinking and concepts. My goal for this map is to help teachers teach these difficult concepts to their elementary students.
These ideas come from chapter 20 of my elementary ed math methods class text book. [Van de Walle, (2013). Elementary and Middle School Mathmatics: Teaching Developmentally. 8th Ed. Pearson Education Inc. Upper Saddle River, NJ.]
During my research for this mind map, I was able to discover all sorts of games/activities, videos, and lessons for different grade levels. Take a look!

Learning about Transformations

Transformations for Level-2 Thinkers

Symmetries and Transformations

Transformations for Level-1 Thinkers

Tessellations

Similar Figures and Proportional Reasoning

Composition of Transformations

Transformations for Level-0 Thinkers

Line and Rotational Symmetry

Slides, Flips, and Turns

Learning about Location

Location for Level-2 Thinkers

Slope

Applying the Pythagorean Relationship

Coordinate Transformations Revisited

Location for Level-1 Thinkers

Examine Transformations on Coordinate Plane

Learning About Visualization

Visualization for Level-2 Thinkers

The Platonic Solids

Connection Earlier Activities

Visualization for Level-1 Thinkers

Properties of 2-D and 3-D Shapes

Visualization for Level-0 Thinkers

Different Orientations of Shapes

Learning about Shapes and Properties

Shapes and Properties for Level-2 Thinkers

Finding vs. Explaining Relationships

The Pythagorean Relationship

Definitions and Proofs

Shapes and Properties for Level-1 Thinkers

Dynamic Geometry Activities

Dynamic Geometry Software

Circles

Construction Activities

Sorting and Classifying Activities

Special Catagories of 3-D shapes

Special Catagories of 2-D Shapes

Shapes and Properties for Level-0 Thinkers

Composing and Decomposing Shapes

Developing Geometric Thinking

Implications for Instruction

Each activity can be adapted to an adjacent level by changing the way it is presented to students.

Use physical materials, drawings, and computer models at every level.

Adapt activities to the level of individual students to challenge them to operate at the next higher level.

Van Hiele Levels of Geometric Thought

Level 4: Rigor

Sorting and Classifying

Level 3: Deduction

Level 2: Informal Deduction

Level 1: Analysis

Level 0: Vizualization

Geometry Goals for Students

Geometric Content

Visualization

Location

Transformations

Shapes and Properties

Spatial Sense and Geometric Reasoning

Developed through meaningful experiences with shapes and spatial relationships.

The ability to mentally visualize objects and spatial relationships; turning things around in your mind.