Geometric Thinking and Geometric Concepts

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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!

Geometry Goals for Students

Spatial Sense and Geometric Reasoning

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

Developed through meaningful experiences with shapes and spatial relationships.

Geometric Content

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Shapes and Properties

Transformations

Location

Visualization

Developing Geometric Thinking

Van Hiele Levels of Geometric Thought

Level 0: Vizualization

Level 1: Analysis

Level 2: Informal Deduction

Level 3: Deduction

Level 4: Rigor

Sorting and Classifying

Implications for Instruction

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

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

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

Learning about Shapes and Properties

Shapes and Properties for Level-0 Thinkers

Composing and Decomposing Shapes

Shapes and Properties for Level-1 Thinkers

Special Catagories of 2-D Shapes

Special Catagories of 3-D shapes

Sorting and Classifying Activities

Construction Activities

Circles

Dynamic Geometry Software

Dynamic Geometry Activities

Shapes and Properties for Level-2 Thinkers

Definitions and Proofs

The Pythagorean Relationship

Finding vs. Explaining Relationships

Learning About Visualization

Visualization for Level-0 Thinkers

Different Orientations of Shapes

Visualization for Level-1 Thinkers

Properties of 2-D and 3-D Shapes

Visualization for Level-2 Thinkers

Connection Earlier Activities

The Platonic Solids

Learning about Location

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Location for Level-1 Thinkers

Examine Transformations on Coordinate Plane

Location for Level-2 Thinkers

Coordinate Transformations Revisited

Applying the Pythagorean Relationship

Slope

Learning about Transformations

Transformations for Level-0 Thinkers

Slides, Flips, and Turns

Line and Rotational Symmetry

Transformations for Level-1 Thinkers

Composition of Transformations

Similar Figures and Proportional Reasoning

Tessellations

Transformations for Level-2 Thinkers

Symmetries and Transformations