## Monday, June 6, 2011

### How might this change things?

Here is another statistics workshop used in a class for preservice K-8 math teachers. The goals of this workshop are: (1) develop familiarity with the lists on the TI-84; (2) practice applying Polya's problem-solving phases; and (3) develop conceptual understanding of the measures of center (mean, median, and mode) and variability (mean absolute deviation). It has been updated to reflect my current understandings about teaching and learning and the Common Core State Standards (CCSS).

Grade 7 CCSS in Statistics and Probability [7.SP]
Draw informal comparative inferences about two populations
(3) Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities...
Standards of Mathematical Practice
(1) Make sense of problems and persevere in solving them.

Schema Activation: Teacher Recount
"Last class, we were introduced to the Penny for Peace contest going on between the middle school math classes at a local school. We used this data to develop a procedure for finding the mean absolute deviation (MAD). This involved: (1) finding the mean of the data; (2) finding the distance (absolute value) between the mean and each data point; and (3) averaging these distances to determine the MAD."

Focus: Problem Solving
"Today, we are going to use Polya's problem-solving phases to explore, 'What happens if...' Recall that our modified phases are: Understand the problem; create a plan; carry out your plan; and look back and look forward. Also, remember that the phases are not intended to be linear. Effective problem-solvers jump between the different phases as they work toward a solution. Please be sure to record all of your work and your thinking so we have an artifact that we can refer to during our reflection. Are there any questions?"

Activity: Transforming Data
Understanding the problem

It turns out that the principal, Ms. Sanchez, decided to add \$10 to all the class totals.  How do you think this will affect the three central tendencies (mode, median, and mean) and the mean absolute deviation?  Start by making a prediction.

 Classes 6.1 6.2 6.3 7.1 7.2 7.3 8.1 8.2 8.3 PfP \$76 \$76 \$76 \$74 \$73 \$71 \$69 \$68 \$65 PfP+10 \$86 \$86 \$86 \$84 \$83 \$81 \$79 \$78 \$75

Create a plan
With your group, work on a plan to use your calculator's list feature to explore this problem.

Carry out your plan
Keep a record of your efforts and your thinking.

Looking back & looking forward
• What happened to the central tendencies and the MAD when you transformed the data?
• How did you go about obtaining your results?
• Why do you think this happened?
• What do you think would happen if the original amounts were doubled?

Reflection: Problem Solver's Chair
The teacher selects a learner to recount his/her group's problem-solving exhibition. This learner can be a volunteer, selected at random, or chosen based on something interesting observed by the teacher during the activity portion of the workshop. After the recount, other learners offer observations or ideas based on their own experiences