Empowering Mathematics

Zach Cresswell
Twitter: @z_cress

Email: z_cress@pm.me

zachcresswell.wordpress.com

Presentation

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bit.ly/empoweringmath2022

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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

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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.

Complexity

Emergence, chaos, adaptation

Missing Concepts

Psychology

Understanding how our minds get in our way.

Missing Concepts

My Story

Ask Questions Here

bit.ly/empoweringmathquestions

My Story

What happened in 2016?

My Story

2016 election
Academia
How do we make sense?

My Story

Teaching Math "These Days"

Ask Questions Here

bit.ly/empoweringmathquestions

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

California

Oregon

Social Justice (math)

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

Seattle Math Ethnic Studies Framework

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

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

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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.

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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.

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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
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

Go to galgreen.com/TaxiCabProblem on your device
Work through the Taxi Cabs and 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

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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

Reasoning with Probability and Statistics

Go to projects.fivethirtyeight.com/p-hacking/
Complete the P-hacking activity

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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

Game Theory

Go to ncase.me/trust/
Complete the Evolution of Trust activity

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Unit 3 - Identifying Structure

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

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Unit 3 - Identifying Structure

Dynamical systems

(Complex Systems and Chaos)

Look through the Chaos activity
- The activity relies heavily on this complexity explorable: bit.ly/3o424Jo

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

All Minus One website and Resources

My Story

Teaching Math "These Days"

The Truth Between us

How I Teach Critical Thinking