NC NAEP Project

1. NC NAEP Project Activity 4 Assessing Proportional Reasoning

2. Goals • Develop knowledge about proportional thinking and related tasks • Describe how students’ proportional thinking can be assessed • Make observations about proportional thinking and extend that understanding through a limited review of the literature

3. Three types of proportional tasks • missing value • numerical comparison and • qualitative prediction and comparison (see Cramer & Post, 1993; Heller et. al., 1990; & Post, Behr, and Lesh, 1988).

4. Missing Value • In the missing value task type, there are three pieces of numerical information that are known and one value that is unknown. • Missing Value Problem: A car is driven 175 km in 3 hours. How far will it travel in 12 hours at the same speed? (Karplus, Pulos, & Stage, 1983, p 220).

5. Numerical Comparison • In the numerical comparison task type, two rates are given that require the rates to be compared though a numerical answer is not required. • Numerical Comparison Problem. Car A is driven 180 km in 3 hours. Car B is driven 400 km in 7 hours. Which car was driven faster. (Karplus, Pulos, & Stage, 1983, p 220).

6. Qualitative Prediction and Comparison • In the qualitative prediction and comparison task type, reasoning about comparisons is not dependent on specific number values (Cramer & Post, 1993). • Qualitative Prediction Mixture Problem: If Nick mixed less lemonade mix with more water than he did yesterday, his lemonade drink would taste a) Stronger b) Weaker c) Exactly the same or) Not enough information to tell. • Qualitative Comparison Density Problem: Two friends hammered a line of nails into different boards. Bill hammered more nails than Greg. Bill's board was shorter than Greg's. On which board are the nails hammered closer together? a) Bill's board b) Greg's board c) Their nails are spaced the same d) Not enough information to tell. (Cramer & Post, 1993, p. 405).

7. Assessing Proportional Thinking Task • Individually read Bright, Joyner, & Wallis (2003) article Assessing Proportional Thinking using the Reading Guide as a framework. (Approximately 17 minutes) • Pair or Small Group Sharing. Share ideas with your peers about the reading using the questions from the Reading Guide. Be prepared to share your discussions with the larger group.  (Approximately 12 minutes) • Large Group Discussion (Approximately 15 minutes)

8. Discussion Assessing Proportional Thinking • What do we learn about students’ proportional thinking from the results on these five tasks? • What are the instructional implications that follow from the students’ performance on these tasks? Additional Questions for Large Group Discussion • What are the key concepts and processes in these tasks? • How might you use this task with students? Would you modify the tasks? How? Why?

9. Observing and Reflecting • Think back on your involvement with the module. Identify one observation, or conclusion, or idea relative to what you have experienced. • Record that observation, conclusion, or idea. • Now, consider that key piece of information that you recorded. Conduct a brief review of the literature related to your observation, conclusion, or idea. You might identify four or five key articles or pieces that respond to what you have identified. • Write a short reflective piece.

10. Writing Guide for Reflection • State your observation, conclusion, or idea. Describe the content or pedagogical nature of what you have identified. • Briefly describe what the articles you found have to say relative to your topic. • End your reflective piece with a few ideas about how this information informs you as a teacher. What do you know about student learning? How might teachers better support students’ development of proportional thinking? • Be sure to include a reference list of your readings.