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PBL Pedagogy & BC Calculus Curriculum
This document discusses problem-based learning (PBL) pedagogy and its application to a Calculus curriculum. PBL aims to develop students' problem solving skills through inquiry-driven problems. It encourages creativity, communication, collaboration and critical thinking. PBL is directly related to Common Core standards involving problem solving, reasoning, argumentation and using appropriate tools. The document outlines aspects of PBL including discourse, assessment, pedagogy and creating a safe environment for risk-taking. Challenges of applying PBL to the AP Calculus syllabus are also discussed.
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Similar to PBL Pedagogy & BC Calculus Curriculum
PBL Pedagogy & BC Calculus Curriculum
- 1. pbl pedagogy & thebc calculus curriculum carmel schettino, ph.d. @SchettinoPBL carmelschettino.org tcm, january 25, 2014
- 2. what is problem-basedlearning? • 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. What’s the right problem-solving question? ©carmelschettino.org
- 3. directly related toccss practice standards make sense of problems and persevere in solving them reason abstractly and quantitatively construct viable arguments and critique the reasoning of others use appropriate tools strategically look for and express regularity in repeated reasoning look for and make use of structure ©carmelschettino.org
- 4. what is problem-basedlearning? • 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 knowledge ©carmelschettino.org scaffolded based on students’ prior
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- 6. my view ofproject v. problembased problem-based • Deliberately scaffolded whole-problem curricula project-based • Preauthentication of problems for mathematical experience • Student Agency stems from student presentations of problem solutions from prior knowledge and collaboration ©carmelschettino.org • Larger picture projects with direct instruction units • Emergent authenticity in mathematical experience • Student Agency stems from directing project with knowledge from instruction and collaboration
- 7. the pbl classroom studentpresentation of partial solutions Student discussion of mathematical ideas for student authority with teacher facilitation ©carmelschettino.org
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- 9. aspects of problem-basedlearning discourse moves assessment of problem solving skills assessment pedagogy ©carmelschettino.org student questioning metacognitive journaling facilitation of discussion technology curriculum student listening conjecturing Safe Environment for RiskTaking
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- 11. new purpose ofhomework Try an Idea Fix it Burger and Starbird, The Five Elements of Effective Thinking, 2012 Find the flaw ©carmelschettino.org
- 12. challenges with apbc syllabus • completion • test prep • student motivation • authentic assessment ©carmelschettino.org
- 13. ap bc philosophy CalculusAB 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
- 14. focus on connectedcurriculum • scaffolded problems • decompartmentalized topics • the connected nature of mathematics ©carmelschettino.org
- 15. 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
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- 17. could you haveanticipated this? why? ©carmelschettino.org
- 18. connecting geometry withdifferential equations dy dx ©carmelschettino.org 25 x x 2
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- 20. zoom into acorner infinitely small
- 21. 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 • www.carmelschettino.org ©carmelschettino.org
- 22. if you wouldlike 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