1. pbl pedagogy & the bc calculus curriculum carmel schettino, ph.d. @SchettinoPBL carmelschettino.org tcm, january 25, 2014

2. new focus on pbl

3. what is problem-based learning? Goals are for students to become better problem solvers Four C’s – creativity, communication, collaboration, critical thinking Encourages inquiry and questioning in problem solving Two men are walking in the woods when a ferocious Grizzly bear charges at them and they start to run. ©carmelschettino.org

4. what is the right problem-solving question? Man 1 asks: Can we outrun the bear? Man 2 asks: Can I outrun you?

5. directly related to ccss practice standards make sense of problems and persevere in solving them reason abstractly and quantitatively use appropriate tools strategically look for and express regularity in repeated reasoning construct viable arguments and critique the reasoning of others look for and make use of structure ©carmelschettino.org

6. what is problem-based learning? an approach to curriculum and pedagogy where student learning and content material are co-constructed by students and teachers through problems that are: both contextually-based and abstract discussed and presented by students in a non- hierarchical environment deliberately scaffolded based on students’ prior knowledge ©carmelschettino.org

7. project v. problem- based http://www.edutopia.org/blog/pbl-vs-pbl-vs-xbl-john-larmer ©carmelschettino.org

8. my view of project v. problem- based Deliberately scaffolded whole-problem curricula Preauthentication of problems for mathematical experience Student Agency stems from student presentations of problem solutions from prior knowledge and collaboration problem-based Larger picture projects with direct instruction units Emergent authenticity in mathematical experience Student Agency stems from directing project with knowledge from instruction and collaboration project-based Where does the learning happen? ©carmelschettino.org

9. the pbl classroom student presentation of partial solutions Student discussion of mathematical ideas for student authority with teacher facilitation ©carmelschettino.org

11. aspects of problem-based learning facilitation of discussion student listening metacognitive journaling assessment of problem solving pedagogy discourse moves conjecturing skills assessment student questioning curriculum Safe Environment for Risk- Taking technology ©carmelschettino.org

12. classroom setups ©carmelschettino.org

13. new purpose of homework Try an Idea Find the flaw Fix it Burger and Starbird, The Five Elements of Effective Thinking, 2012 ©carmelschettino.org

14. challenges with ap bc syllabus completion test prep student motivation authentic assessment ©carmelschettino.org

15. ap bc philosophy Calculus AB and Calculus BC are primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The courses emphasize a multirepresentational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important. Broad concepts and widely applicable methods are emphasized. The focus of the courses is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types. Thus, although facility with manipulation and computational competence are important outcomes, they are not the core of these courses http://apcentral.collegeboard.com/apc/public/repository/ap-calculus-course-description.pdf

16. focus on connected curriculum scaffolded problems decompartmentalized topics the connected nature of mathematics ©carmelschettino.org

17. topics for perusal – look for prior knowledge triggers and scaffolding developing understanding of parametric equations exploring more advanced polar graphs developing understanding of polar area and arc length motivating MacLaurin polynomials developing chase problems with differential equations geometrically ©carmelschettino.org

18. consider the scaffolding ©carmelschettino.org

19. could you have anticipated this? why? ©carmelschettino.org

20. connecting geometry with differential equations ©carmelschettino.org

21. dog chase problem ©carmelschettino.org

22. zoom into a corner infinitely small

23. references Burger & Starbird (2012). The 5 Elements of Effective Thinking, Princeton University Press. Larmer, John (2014) Project –Based Learning vs. Problem Based Learning vs. X-BL, January 2, 2014, http://www.edutopia.org/blog/pbl-vs-pbl-vs-xbl-john-larmer http://www.edutopia.org/blog/pbl-vs-pbl-vs-xbl-john-larmer www.carmelschettino.org ©carmelschettino.org

24. if you would like to learn more about pbl Lots of references at my website – links to sites with great problems Follow me on twitter @SchettinoPBL or like me on Facebook Carmel Schettino, Ph.D Take my courses at the Anja S. Greer Math, Science Technology Conference at Phillips Exeter Academy Moving Forward with Problem-Based Learning Advanced PBL Instruction – Pedagogy & Development ©carmelschettino.org