pbl pedagogy & the bc calculus curriculum carmel schettino, ph.d. @schettinopbl...
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pbl pedagogy & the bc calculus curriculumcarmel schettino, ph.d.
@SchettinoPBL
carmelschettino.org
tcm, january 25, 2014
new focus on pbl
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.
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what is the right problem-solving question?
•Man 1 asks: Can we outrun the bear?
•Man 2 asks: Can I outrun you?
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
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
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project v. problem-based
http://www.edutopia.org/blog/pbl-vs-pbl-vs-xbl-john-larmer©carmelschettino.org
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?
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the pbl classroom
student presentation of partial solutions
Student discussion of mathematical ideas for student authority with teacher facilitation
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aspects of problem-based learning
facilitation of
discussion
student listening
metacognitive journaling
assessment of problem
solvingpedagogy
discourse moves
conjecturing
skills assessment
student questioning
curriculum
Safe Environment
for Risk-Taking
technology
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classroom setups
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new purpose of homework
Try an Idea
Find the flaw
Fix it
Burger and Starbird, The Five Elements of Effective Thinking, 2012 ©carmelschettino.org
challenges with ap bc syllabus
•completion
• test prep
•student motivation
•authentic assessment
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ap bc philosophyCalculus 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
focus on connected curriculum
• scaffolded problems
• decompartmentalized topics
• the connected nature of mathematics
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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
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consider the scaffolding
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could you have anticipated this? why?
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connecting geometry with differential equations
225dy x
dx x
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dog chase problem
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zoom into a corner infinitely small
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
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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
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