Reflecting on Practice: Using Inquiry to Build Thinking Classrooms Unit 1, Session 4 2017 Reflecting on Practice Park City Mathematics Institute

Reading Reflection Share what you took away from the reading with respect to techniques you can use to make a task worthwhile.

Worthwhile Tasks in a Thinking Classroom [Across the 3 Rooms] Engage each student through an appropriate level of cognitive demand Promote discussion to make student thinking visible Relate to an important mathematical goal Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Asking a question Original task: Solve 2x2+5x=3 Modified task: Explain how you can tell whether the equation 2x2+5x=3 has a solution. Reflecting on Practice Park City Mathematics Institute

Choose a problem to modify Write your mathematical goal and modified task. 1. A flowerpot is cylindrical. The radius of the base is 14 cm. The height is 25 cm. What is the volume of the flowerpot? 2. c is a zero of the polynomial. Find the rest of the real zeros and factor the polynomial x3 +2x2 −3x−6, c=−2 3. Solve the formula C= (5/9)(F-32) for F Reflecting on Practice Park City Mathematics Institute

Worthwhile Tasks in a Thinking Classroom [Across the 3 Rooms] Engage each student through an appropriate level of cognitive demand Promote discussion to make student thinking visible Relate to an important mathematical goal Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Gallery Walk Move to the next station to your right when you are facing the workspace. Write comments related to the characteristics of worthwhile tasks. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Gallery Walk Return to your own station and read the comments. Consider any revisions you want to make to your task given the comments. Full Group: Did you notice any task modifications that were really cool? Anything surprising? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Bringing it together Let’s watch a clip of a 7th grade class figuring out the formula for the surface area of a cylinder. As you watch, see if you can identify two or three characteristics you think contribute to or hinder a thinking classroom. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Share with a partner Take a few minutes and talk with a partner about the characteristics you each saw that contribute to a thinking classroom and those that did not. Reflecting on Practice Park City Mathematics Institute

A Thinking Classroom is conducive to thinking and occasions thinking, a space that is inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion …a space where the teacher not only fosters thinking, but also expects it, both implicitly and explicitly. Reflecting on Practice Park City Mathematics Institute Liljedahl, in review

Optional Reading In your folders is a research brief from the National Academy of Science on the benefits of this “active learning” you are welcome to peruse.

Park City Mathematics Institute Final Reflection Reflection: What's one thing you're really excited about, or have found useful, that you've encountered this week? Exit Questions [Note card, no name] What are you wondering about? What comments do you have? What do you want us to know? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute References Harper S., & Edwards, M. (2011). A New Recipe: No More Cookbook Lessons. The Mathematics Teacher, 105(3), pp. 180-188. Reston VA: National Council of Teachers of Mathematics http://www.jstor.org/stable/10.5951/mathteacher.105.3.0180 . Herbel-Eisenmann, B. & Crillio, M. (2013). Two versions of same task adapted from Association of Mathematics Teacher Educators presentation, Mathematics discourse in secondary classrooms: A case- based professional development curriculum. Orlando FL Liljedahl, P. (under review). On the edges of flow: Student problem solving behavior. In S. Carreira, N. Amado, & K. Jones (eds.), Broadening the scope of research on mathematical problem solving: A focus on technology, creativity and affect. New York, NY: Springer. Modeling Change. (2004) PCMI Teacher Program Lesson Study. Sanchez, W. (2013). Open ended questions and the process standards. The Mathematics Teacher, 107(3), 206-211. Solving Equations, (2005). Break Through Mathematics. Lesson Lab. Pearson Education Company. Reflecting on Practice Park City Mathematics Institute