These guidelines can provide six or more hours on early mathematics in a three-unit semester preschool curriculum course. It is broken into two segments, but can be broken into shorter segments.

Preparation homework for participants

• Readings: The Mathematics of Geometry and Spatial Relations, DLLs: Assessing Geometry and Spatial Relations, and When is a Triangle a Triangle?  
• Homework: When is a Triangle a Triangle? worksheet (downloadable at the bottom of this page).

Classroom Activities

• Share the video of Dr. Levine talking about spatial relations. 
• Implement the When is a Triangle a Triangle activity.
• Distribute (electronic, paper, or display) copies of the Sawyer’s Shapes text. Show the video pieces interspersed with whole-class discussions of interpretations of Sawyer’s words and actions (e.g., “Do you agree with Rau’s interpretation of Sawyer’s understanding?” “Thinking about the DLLs: Assessing Geometry and Spatial Relations reading and what you know about mathematical development, would you have done something different at this stage with Sawyer?”). At the end, wrap it up by asking how clinical interviews such as these can inform our thinking about children’s understanding.

Preparation homework for participants

• Readings: Objects and Our Place Among Them, Making Shapes activity (downloadable at the bottom of this page), and More than Hearts and Diamonds.
• Homework: More than Hearts and Diamonds worksheet (downloadable at the bottom of this page).

Classroom Activities

• This session will engage participants in Making Shapes, a preschool classroom geometry activity that is used as a tool for preservice teacher learning (downloadable at the bottom of this page). See More than Hearts and Diamonds activity for instructions.