Empowering Mathematics

Zach Cresswell
Twitter: @z_cress

Email: z_cress@pm.me

zachcresswell.wordpress.com

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About Zach

Empowering Mathematics

Zach Cresswell
Twitter: @z_cress

Email: z_cress@pm.me

zachcresswell.wordpress.com

Presentation

bit.ly/3sfSIwl

bit.ly/empoweringmath2022

Joining via Zoom? 

Find all referenced docs here:

My Story

Teaching Math "These Days"

The Truth Between us

How I Teach Critical Thinking 

Optic Blind Spot

My Story

Am I developing better thinkers?

Ask Questions Here

bit.ly/empoweringmathquestions

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.

Complexity

Emergence, chaos, adaptation

Missing Concepts

Psychology

Understanding how our minds get in our way.

Missing Concepts

My Story

Ask Questions Here

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My Story

What happened in 2016? 

My Story

  • 2016 election
  • Academia
  • How do we make sense? 

My Story

My Story

Teaching Math "These Days"

Ask Questions Here

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My Thesis

  • Educators must consider their role in each moment in history, preparing students for the world as it is
  • Increasingly, one narrative is driving how educators should approach that role
  • It is, sometimes explicitly, politically motivated
  • There is not robust conversation about the second-order consequences of this direction
  • Every educator needs to think about this direction and form opinions
  • Ideas are stronger through diverse, honest conversation

Teaching Math in Context

  • Four types of educators
    • "Old School" - things aren't so bad
    • Progressive in the traditional sense - we've got problems and should be open to change - drastic change, if needed
    • Progressive in the political sense - fixing problems requires politically left ideas - Equity, Inclusion, Antiracism 
    • Radically progressive - the purpose of education is revolution - every act of teaching is political

Social Justice (math) 

  • The latter two camps provide an answer to the context question - and they're growing in popularity 
  • This means we all need to consider what these ideas mean for education

Social Justice (math) 

  • The latter two camps provide an answer to the context question - and they're growing in popularity 

Social Justice (math) 

  • The latter two camps provide an answer to the context question - and they're growing in popularity 

Social Justice (math) 

  • The latter two camps provide an answer to the context question - and they're growing in popularity 

My Story

Teaching Math "These Days"

My Story

Teaching Math "These Days"

The Truth Between us

Ask Questions Here

bit.ly/empoweringmathquestions

The Truth Between Us

  • What do we all want? 
  • Defining "Empowerment"
  • What is required? 

What do we all 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
  • Our students to be empowered

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 game theory is empowering. 
  • Understanding the mathematics of networks and systems is empowering. 

Empowerment

  • Understanding logic and computational reasoning is empowering.
  • Understanding our bias to confirm & weigh what we see more than what we can’t see 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.

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
  • 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 psychology of probabilistic reasoning
  • The faultiness of our memory
  • The Dunning Krueger Effect

Unit 1 - Thinking Clearly

Probabilistic Reasoning Activity

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

Reasoning with Probability and Statistics​

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

Game Theory

Unit 3 - Identifying Structure

  • Graph Theory 
    • Basic definitions
    • Cycles (Oberwolfach problem)
    • Vertex coloring
    • Spanning Trees
  • Dynamical systems (Complex Systems and Chaos)

Unit 3 - Identifying Structure

Dynamical systems

(Complex Systems and Chaos)

All the answers?

  • Awareness of powerful math concepts - maybe they pick up the torch
  • Students don't leave knowing all the answers, but...
    • They can ask better questions 
    • They have frameworks for moving towards answers

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

  • 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 and References

Other Resources and References

Heterodox Academy

heterodoxacademy.org/

Empowering Mathematics

Zach Cresswell

Email: z_cress@pm.me

Twitter: @z_cress

Website: zachcresswell.wordpress.com

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