Empowering Mathematics

Zach Cresswell
Twitter: @z_cress

cresswellzach@gmail.com
zachcresswell.wordpress.com

Presentation

Survey 

(complete before session)

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About Zach

Empowering Mathematics

Zach Cresswell
Twitter: @z_cress

cresswellzach@gmail.com
zachcresswell.wordpress.com

Presentation

Survey 

(complete before session)

bit.ly/empoweringmath

My Story

Teaching Math "These Days"

The Truth Between us

How I Teach Critical Thinking 

My Story

  • Applying Mathematics
  • Minimizing Concepts
  • Missing Concepts

Applying Concepts

Minimizing Concepts

Game Theory

No, not that kind of game.

Graph Theory

No, not that kind of graph. 

Missing Concepts

Formal Logic

Applied, including logical fallacies.

Applied Statistics

Upgrade your navigation system.

Missing Concepts

Psychology

Understanding how our minds get in our way.

Missing Concepts

My Story

  • 2016 election
  • Academia
  • Thinking models

Teaching Math "these days"

  • We don't teach in a bubble
  • Social Justice (math)
  • Diversity, Equity, and Inclusion

Teaching Math in Context

Social Justice (math) 

  • One answer to the context question
  • Mathematics education is political?
  • Project-based problems? 

Diversity, Equity, and Inclusion

  • Digging deeper on these ideas
  • What does this mean for teacher training? 
  • Common Humanity versus Common Enemy

My Story

Teaching Math "These Days"

My Story

Teaching Math "These Days"

The Truth Between us

The Truth Between Us

  • What does each of us want? 
  • Defining "Empowerment"
  • What is required? 

What does each of us want? 

  • Our students to identify problems in society
  • Our students to have the tools to understand them and do something about them
  • Our students to learn content that is relative to their lives

Empowerment

  • Having a toolkit for understanding the world is empowering.
  • Knowing and applying probabilistic reasoning is empowering.
  • Understanding when statistics and charts are misleading is empowering.

Empowerment

  • Understanding when someone in power is making a fallacious argument is empowering. 
  • Knowing what outcomes are predictable because of the game theory is empowering. 
  • Understanding the mathematics of networks is empowering. 

Empowerment

  • Understanding logic and computational reasoning is empowering.
  • Having a diverse set of lenses and tools for thinking is empowering.
  • Understanding metacognition and how to listen is empowering.

Empowerment

  • Understanding why freedom of speech is vital for thinking is empowering.
  • Understanding the kind of information emotion gives you is empowering.
  • Understanding our bias to confirm & weigh what we see more than what we can’t see is empowering.

What do our overlapping goals require? 

  • Truth

What do our overlapping goals require? 

  • Truth
  • Ethics

What do our overlapping goals require? 

  • Truth
  • Ethics
  • Courage

What do our overlapping goals require? 

Truth

Ethics

Courage

Wisdom

Wisdom

Wisdom

Wisdom

Wisdom

Wisdom

My Story

Teaching Math "These Days"

The Truth Between us

My Story

Teaching Math "These Days"

The Truth Between us

How I Teach Critical Thinking 

How I teach Critical Thinking

  • Unit 1 - Thinking Clearly
  • Unit 2 - Reasoning
  • Unit 3 - Identifying Structure

Unit 1 - Thinking Clearly

  • Metacognition and Listening
  • System one and two thinking - Kahneman
  • Cognitive Ease, What You See is All There is and how this leads to our bias to confirm
  • Other biases - The Spotlight Effect, hindsight bias, the affect heuristic
  • Base Rates and probabilistic reasoning and the psycology of probabilistic reasoning
  • The faultiness of our memory
  • The Dunning Krueger Effect

Unit 2 - Reasoning

  • Formal, symbolic logic
  • How to fight fair - How to argue in such a way that you, at minimum, learn something from each other
  • The importance of Freedom of Speech - an excerpt from On Liberty by John Stuart Mill created by Heterodox Academy
  • Logical Fallacies
  • Identifying Biased Statements and arguments
  • Creativity in reasoning - thought experiments and reasoning by analogy

Unit 3 - Identifying Structure

  • Reasoning with Probability and Statistics
    • ​Basic probability (including "sneaky" probability)
    • Visualizing probability
    • Day-to-day statistics
    • Statistical reasoning in research
      • Univariate and multivariate data analysis
      • Sampling, sample size, randomness
      • Base rates
      • p-value and p-hacking
      • Replication Crisis

Unit 3 - Identifying Structure

  • Game Theory 
    • Trust and reciprocity
    • The prisoner's dilemma
    • Evolutionary stable strategy
    • Race to the bottom, free rider problem, tragedy of the commons
    • Zero sum versus non-zero sum games
    • Principal-agent problems
    • The law of diminishing returns 

Unit 3 - Identifying Structure

  • Graph Theory 
    • Basic definitions
    • Cycles (Oberwolfach problem)
    • Vertex coloring
    • Spanning Trees

Critical Thinking Features

  • Mental Model Mondays

The map is not the territory but you can't fold up the territory and put it in the glove compartmentment. 

  • The Map is not the Territory
  • Antifragility
  • Compounding
  • First-principles thinking
  • Hanlon's razor
  • The Pareto Principle 
  • Telling the Truth

Critical Thinking

  • Mental Model Mondays
  • Thinking Tools Thursdays

Critical Thinking

  • Thinking Tools Thursdays
    • Making mistakes
    • Occam's razor and broom
    • Sturgeon's law
    • Deepity
    • Folk psychology ​

Critical Thinking

  • All Minus One
    • John's Stuart Mill's writings on free speech from his book On Liberty
    • Created by Heterodox Academy

My Story

Teaching Math "These Days"

The Truth Between us

How I Teach Critical Thinking 

Empowering Mathematics

Resources

Unit Plans

Weekly Features

Other Resources

Unit 1

Other Resources

Unit 2

Other Resources

Unit 3

Other Resources

Unit 3

Other Resources

Unit 3

Other Resources and References

Other Resources and References

Heterodox Academy

heterodoxacademy.org/

Empowering Mathematics

Zach Cresswell

Twitter: @z_cress

Email: cresswellzach@gmail.com
Website:
zachcresswell.wordpress.com

Please complete the survey!

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Presentation

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Empowering Mathematics

By Zach Cresswell

Empowering Mathematics

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