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.

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

2. 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.
What’s the right problem-solving question?
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3. directly related to ccss 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
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4. 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
knowledge
©carmelschettino.org
scaffolded
based
on
students’
prior

5. project v. problembased
http://www.edutopia.org/blog/pbl-vs-pbl-vs-xbl-john-larmer
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6. my view of project 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
student presentation of
partial solutions
Student discussion of
mathematical ideas for
student authority with teacher
facilitation
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8. ©carmelschettino.org

9. aspects of problem-based learning
discourse
moves
assessment
of problem
solving
skills
assessment
pedagogy
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student
questioning
metacognitive
journaling
facilitation
of
discussion
technology
curriculum
student
listening
conjecturing
Safe
Environment
for RiskTaking

10. classroom setups
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11. new purpose of homework
Try an
Idea
Fix it
Burger and Starbird, The Five Elements of Effective Thinking, 2012
Find
the
flaw
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12. challenges with ap bc syllabus
• completion
• test prep
• student motivation
• authentic assessment
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13. 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

14. focus on connected curriculum
• scaffolded problems
• decompartmentalized topics
• the connected nature of mathematics
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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
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16. consider the scaffolding
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17. could you have anticipated this? why?
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18. connecting geometry with differential
equations
dy
dx
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25 x
x
2

19. dog chase problem
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20. zoom into a corner 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 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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