pbl pedagogy & bc calculus curriculum

pbl pedagogy & the bc calculus curriculumcarmel schettino, ph.d.

@SchettinoPBL

carmelschettino.org

tcm, january 25, 2014

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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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

©carmelschettino.org

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