Toward Developing
Mathematical Thinkers:
Problem Based Learning
Geoff Krall
emergentmath.wordpress.com
Entry Event:
Our school board is thinking about eliminating mathematics
entirely from the high school scope and sequence.
We have 30 seconds to convince them otherwise.
Come up with 2-3 things about math instruction that are a net
benefit for your students..
What good is it? What is Math instruction uniquely positioned to do for
your students?
Why teach math?
Conrad Wolfram TED Talk
Technical Skills
Everyday math
Logical thinking and reasoning
Framework for mathematical
tasks
A diagnosis
A diagnosis
We are not teaching kids to solve problems. We are
teaching them to follow procedures.
Traditional Instruction to Project
Based Learning
My Exponential Growth and Decay
project
Local!
Relevant!
Authentic!
st
21
Century
Skills!
9.756
sq in/101.6832
My Exponential
Growth and
Decay
sqproject
in = 0.0959
5.12 in
About 10% of
the
2.466 sq in
1.37”
final
product
7.29 sq in + 2.466 sq
1.8”
7.29
sq
in
1.62”
included
in=9.756 sq in
4.5”
mathematics???
101.6832 sq in
19.86 in
Problem Based Learning
Problems, three ways
M
L
Problems or Projects?
Let’s make a decision tree: Problems, Projects, and/or
Guided Instruction
Three tasks types have been placed
around the room, with examples.
In your groups, discuss the following:
When would this type of classroom
activity be appropriate Math
classroom?
Let’s create a decision tree
When might each task type be most appropriate?
Guided Instruction
Lower priority
(quadratic formula)
When you don’t want to
teach the “Why”
Consider the audience
Remediation/Reinforce
ment
Deeper Understanding
Lack of prior knowledge
Skill focused
Projects
Provide Relevence, RW
applications
Integrated disciplines
Instill responsibility and
accountability
Allow for creativity
Community needs
Problems
To begin discourse
To engage people
Inspire and Spark
Encourage divergent
thinking – spur
creativity, multiple
solutions
Formative summative
Enhance, extend
general understanding
Introduction of a
concept
Intro to purposeful
vocabulary
A Framework to think about the net benefit of mathematical tasks.
Using Problems to leave nowhere for the math to hide.
Some decision points to decide when to use
problems, projects, and guided instruction.
Resources
emergentmath.wordpress.com
• Problem Planning Form
[How do we plan for Problems?]
• Scaffolding Activities
[How do we get students to talk and
reason mathematically?]
• Formative Assessment Lessons and
Tasks [Shell Centre]
[Where can I find good examples of PrBL
Lessons?]
Geoff Krall | gkrall@newtechnetwork.org
emergentmath.wordpress.com
END OF CLASS DEBRIEF