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

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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

Teaching Math "these days"

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

Teaching Math in Context

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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

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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.

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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.

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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.

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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.

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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

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

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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

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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

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Unit 3 - Identifying Structure

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

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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

All Minus One website and Resources

My Story

Teaching Math "These Days"

The Truth Between us

How I Teach Critical Thinking