Toward Developing Mathematical
Thinkers: Problem Based Learning
Geoff Krallemergentmath.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 SkillsEveryday mathLogical 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!
21st Century Skills!
My Exponential Growth and Decay project
4.5”1.62”
1.8”1.37”
7.29 sq in
2. 466 sq in7.29 sq in + 2.466 sq in=9.756 sq in
19.86 in101.6832 sq
in
9.756 sq in/101.6832 sq in = 0.0959
About 10% of the final product
included mathematics???
Problem Based Learning
Problems, three ways
Problems or Projects?
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 make a decision tree: Problems, Projects, and/or Guided Instruction
Let’s create a decision tree
Guided Instruction Projects ProblemsLower priority (quadratic formula)When you don’t want to teach the “Why”Consider the audienceRemediation/ReinforcementDeeper UnderstandingLack of prior knowledgeSkill focused
Provide Relevence, RW applicationsIntegrated disciplinesInstill responsibility and accountabilityAllow for creativityCommunity needs
To begin discourseTo engage peopleInspire and SparkEncourage divergent thinking – spur creativity, multiple solutionsFormative summativeEnhance, extend general understandingIntroduction of a conceptIntro to purposeful vocabulary
When might each task type be most appropriate?
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.
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?]