+ Open-Ended Questioning: How to REALLY Get Your Students Thinking! Presenters: Octavia Cutsail and Lindsay Madden

+ Welcome! Solve the following problem in pairs: “A set of nine pieces of data, all of which are different, has a mean of 30 and a median of 10. What could the data values be?*” Think about the following: What concepts are being addressed? How could you increase or decrease the difficulty of this problem? What is a more typical problem that covers the same concepts? *Good Questions, pg. 175

+ Objective: Teachers will learn how to develop open- ended questions in order to foster student perseverance in problem solving. (Standard #1: Make sense of problems and persevere in solving them.) This session will focus on the strategies found in the Good Questions series by Marian Small to help teachers transform recall questions into questions that require students to apply, analyze, and extend.

+ Why ask open-ended questions? Naturally Differentiates Improves reasoning skills Richer discussions Highlights misconceptions Allows students to see problems from multiple perspectives

+ Tips for Creating More Open-Ended Questions: Turning around a question Have students create a problem Replacing a number with a blank

+ Turning Around a Question Traditional Question: Find the product of the following integers: Open-Ended Question: Show -12 as the product of other integers. What is the largest value you can use for the other integers? What is the smallest value?

+ Have Students Create a Problem Traditional Question: Given a set of data, determine if the correlation is negative, positive, or no correlation. Open-Ended Question: Sketch an example of a real life situation that would result in a negative correlation.

+ Replacing a Number with a Blank Traditional Question: Find 80% of 90. Open-Ended Question: Fill in values for the blanks to make this statement true: 72 is ____% of ____.

+ Now you try… Choose an objective that you cover in your class. On one side of your index card, give an example of a traditional question for this objective. On the other side, apply the strategies we discussed to create a more open-ended question.

+ Discussion Questions What could a student response look like? How else could you ask this question to increase/decrease difficulty?

+ Something to think about… “Open questions need just the right amount of ambiguity. They may seem vague, and that may initially bother students, but the vagueness is critical to ensuring that the question is broad enough to meet the needs of all students.*” More Good Questions, pg. 9

+ References: Smalls, Marian. Good Questions: Great Ways to Differentiate Mathematics Instruction. New York: Teachers College Press, Print. Smalls, Marian, and Amy Lin. More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction. New York: Teachers College Press, Print.