Toward Developing Mathematical Thinkers: Problem Based Learning

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Toward Developing Mathematical Thinkers Problem
Based Learning

• Geoff Krall
• emergentmath.wordpress.com

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• 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?
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Why teach math?

• Conrad Wolfram TED Talk
• Technical Skills
• Everyday math
• Logical thinking and reasoning

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Framework for mathematical tasks
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A diagnosis
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A diagnosis
We are not teaching kids to solve problems. We
are teaching them to follow procedures.
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Traditional Instruction to Project Based Learning
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My Exponential Growth and Decay project
Local!
Relevant!
Authentic!
21st Century Skills!
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My Exponential Growth and Decay project
9.756 sq in/101.6832 sq in 0.0959
Wheres the Math?
About 10 of the final product included
mathematics???
2. 466 sq in
1.37
7.29 sq in 2.466 sq in9.756 sq in
1.8
7.29 sq in
1.62
5.12 in
4.5
101.6832 sq in
19.86 in
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Problem Based Learning
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Problems, three ways
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Problems or Projects?
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Lets 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?
Task Type
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Lets create a decision tree
When might each task type be most appropriate?
Guided Instruction Projects Problems
Lower priority (quadratic formula) When you dont want to teach the Why Consider the audience Remediation/Reinforcement Deeper Understanding Lack of prior knowledge Skill focused Provide Relevence, RW applications Integrated disciplines Instill responsibility and accountability Allow for creativity Community needs 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
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A Framework to think about the net benefit of
mathematical tasks.
Use
Dont Use
Task Type
Using Problems to leave nowhere for the math to
hide.
Some decision points to decide when to use
problems, projects, and guided instruction.
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Resourcesemergentmath.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?

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End of Class Debrief

• Geoff Krall gkrall_at_newtechnetwork.org
• emergentmath.wordpress.com

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