# Geometry Outcomes Outline

## Introduction

In a geometry content course for K–8 teachers, what broad conceptual ideas/topics are essential? We identified five broad topics, and noted that each of them align with one or more of three major themes (goals for the goals).

Note that this is not intended as a curriculum list. Most of these topics would be hard to imagine as separate units in a course. Instead, they are an outline of the types of topics one might address in each part of the curriculum. Also, much of this list would be appropriate in other math content courses for teachers and is not necessarily specific to geometry.

## Themes

• Cover core geometry content
• Explicitly demonstrate and teach elements of mathematical practice (i.e., teach students what mathematics is)
• Where possible, connect with students' interest in teaching

### Proof/justification

• Different levels of "rigor" corresponding to child development levels.
• Importance of definitions in clear communication and proofs.
• Proofs of key geometry results, e.g., congruence of opposite angles, angle sum in polygons, and Pythagorean theorem.

### Fluency in geometric thinking

• Know facts and terms, e.g., names and properties of 2D and 3D shapes.
• Students (future teachers) should communicate correctly and precisely about geometry.
• Motivated by "something to talk about", rather than rote memorization.

### Multiple explanations/proofs of basic results

• gives more robust understanding
• can address different developmental levels of children
• serves to remediate low-level students
• provides good connection to teaching

### Properties of shapes (2D and 3D)

• Explore various 2D and 3D shapes.
• State their properties (and know their names).
• Figure out relationships between various shapes.

### Synthesize geometric and algebraic ideas

• Be able to think visually and algebraically
• Translate from geometric to algebraic ways of presenting concepts and explanations

### Geometry of motion and change

• Transformations
• Symmetries