CwiC Session: Framework for PBL

A Framework for
Problem-Based Learning
Classroom :
Optimizing an approach to
mathematics education
Carmel Schettino, Ph.D.
Deerfield Academy
ASG Conference 2013

Mathematical Needs of Modern Industry
©Carmel Schettino.org

How do we teach higher-order skills?
Trilling & Fadel, (2012) 21st Century Skills: Learning for Life in Our Times, Jossey-Bass.

Where are these in the traditional
Mathematics Classroom?
Single
Mathematical
Authority
Passive
Learners
Dependent
Thinkers
Owner of
Knowledge
Director of
learning
Source of
Questions &
Answers
Uninvested
Learning
Teacher

Common Core Standards for
mathematical practice (U.S.)
2
3
4
5
Make sense of problems and persevere in solving them1
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
6 Look for and make use of structure

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
What is Problem-Based Learning?
Schettino, 2010

What is the difference between
mathematical engagements?
Emergent
Authenticity
Preauthentication
Jonassen, D(2011) Supporting Problem Solving in PBL. IJPBL, 5(2), 95-119
Authentic
practice within
mathematics by
engaging in
activity germane
to field
Pre-analysis of
activities
attempting to
simulate authentic
problem in learning
environment

Problem-Based vs. Project-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

Aspects of Problem-Based Teaching
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

Necessary Facets of a PBL Classroom
PBL
Framework
Connected
Curriculum
Justification
not
prescription
Shared
Authority
Ownership
of
Knowledge
Schettino 2013

Problem Purposes
Review material
from past courses
Trigger prior
knowledge for an
upcoming
problem
Inspire
construction of
new knowledge
Introduce new
terminology
Practice new skill
Challenge more
able students
See same new
idea from
different
representation
Introduce new
technology skill
Concretize an
abstract concept

Connected Curriculum
Scaffolded Problems
Decompartmentalized Topics
The Connected Nature of
Mathematics

Ownership of Knowledge
Encouragement of individual
and group ownership
Metacognitive Journals
Student Presentation
Revoicing and Teacher
Discourse Moves

Shared Authority
Dissolution of Authoritarian
Hierarchy
Discourse moves to improve
equity
Send message of valuing risk-
taking and all ideas

Justification – Not Prescription
The point is “why”
Foster inquiry with multiple
perspectives
Value curiosity and Assess
creativity

Resist
temptation to
tell
Stop giving
students the
final product
of our
thinking
Problems
first, teaching
second
Cognitive
Apprenticeship
Stop teaching
decontextualized
content
Teaching for Higher Order Learning
Reevaluate
Evaluation
McCain, T. (2005) Teaching for Tomorrow, Corwin Press.

Coaching Modeling Scaffolding Fading
Cognitive Apprenticeship
Encouraging,
Adding insight,
Asking probing
questions, Holding
back, Supporting
with information
Risk-taking,
Questioning,
Making
mistakes,
Finding
resources,
Conjecturing
Revoicing,
Mapping ideas,
Probing for
explanation,
Requiring
conjecturing,
opportunities for
more student
interaction
Relinquishing/sharing
authority, valuing
multiple perspectives,
allowing students to
be expert
Redefining the role of the Teacher – Teacher
“Repositioning”

A continuum of PBL
Occasional “Problem of the Day”
Math Competitions
Traditional Text book “buffet”
Traditional Textbook supplemented
with “Motivational Problems”
PBL Units with Direct Instruction Classes
Whole Problem-Based Curriculum
decompartmentalization

Where can you get good problems?
Emergent
Math
http://tinyurl.com/aerasigpbl
AERA SIG
for PBL
http://www2.edc.org/mathproblems/sea
rchTopic.asp
Problems
with a
Point
Inside
Mathematics
http://insidemathematics.org/index.p
hp/tools-for-teachers/problems-of-
the-month
http://emergentmath.com/my-problem-
based-curriculum-maps/

It’s not as easy as it looks…
P
R
O
B
L
E
M
S
I
N
V
E
S
T
E
D
L
E
A
R
N
E
R
S
B
U
Y
-
I
N
T
I
M
E
Pedagogy

Pros and Cons

Are you inspired?
P B L
• Check out the PBL Resources List on my
website www.carmelschettino.org
• Follow me on twitter @SchettinoPBL
• Visit schools where PBL is practiced
• Email at carmel@carmelschettino.org

Do you have
any
questions?
??

Reference List
• Lampert, M (2001). Teaching Problems and the
Problems of Teaching. Yale University Press, New
Haven
• Jonassen, D(2011) Supporting Problem Solving in PBL.
Interdisciplinary Journal of Problem-Based Learning,
5(2), 95-119.
• McCain, T. (2005) Teaching for Tomorrow: Teaching
Content and Problem-Solving Skills. Corwin Press,
Thousand Oaks, CA (44).
• Tomlinson. C & Cunningham, C. (2003). Differentiation
in Practice: A resource guide for differentiating
curriculum, Grades K-5. ASCD, Alexandria, VA.
• My website at www.carmelschettino.org
• My delicious account at
http://delicious.com/SchettinoPBL

CwiC Session: Framework for PBL

CwiC Session: Framework for PBL

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