1. NC NAEP Project Middle Grades Module 2 – Activity 4 Research Reflections

2. Goals Develop knowledge about geometric thinking and related tasks Describe levels of students’ geometric thinking Make observations about geometry and extend that understanding through a limited review of the literature

3. Perimeter and Area Task Assume that the edges of the small squares in this figure are one unit in length. Add tiles so that you have a perimeter of 16. Squares that are added must meet so that they are touching on at least one side of the figure. Malloy, C. E. (1999). Perimeter and area through the van Hiele model. Mathematics Teaching in the Middle School, 5(2), pp. 87-90.

4. Perimeter and Area Task and Article Discussion – Pairs or Small Groups What was your solution? What strategies did you use? How did you learn about perimeter and area? How was your experience similar or different to the activity described in the article? What does students’ performance look like at the concrete, analysis, and informal deduction levels? What geometric content area(s) are described in this article? How can you use the van Hiele levels to help students learn mathematics?

5. NAEP Item Sort – Small Group Sort the assessment items into the van Hiele levels Identify the geometric content area for each item

6. NAEP Item Sort Discussion – Large Group In which level did you place this item? Why? Did anyone place the item in another level? Why? How might you modify the item to fit into another van Hiele level?

7. Tables at a Birthday Party - Individual Work the Tables at a Birthday Party task After you have worked the task, take some time to reflect on geometric thinking module. ◦ What observations can you make about geometric thinking? ◦ What conclusions can you draw? ◦ What ideas do you have about the Tables at a Birthday Party task? ◦ How is geometric thinking related to algebraic reasoning?