toward developing mathematical thinkers: problem based learning

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?]

END OF CLASS DEBRIEF

Geoff Krall | gkrall@newtechnetwork.org

emergentmath.wordpress.com