Empowering Mathematics
Zach Cresswell
Twitter: @z_cress
cresswellzach@gmail.com
zachcresswell.wordpress.com
Presentation
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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?
 Projectbased 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
 Daytoday statistics

Statistical reasoning in research
 Univariate and multivariate data analysis
 Sampling, sample size, randomness
 Base rates
 pvalue and phacking
 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 nonzero sum games
 Principalagent 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
 Firstprinciples 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
 How to Fight Fair lesson
 All Minus One lesson outline
 Logical Fallacies slides
Other Resources
Unit 3
Other Resources
Unit 3
Other Resources
Unit 3
Other Resources and References
 Ilana Redstone on The Politics of Critical Thinking
 Beyond Bigots and Snowflakes Youtube miniseries put together by Ilana Redstone
 Critical theory or common humanity? The case for a liberal approach to social studies education
 Antiracism in your School: 9 ways to keep the conversation rational and unifying
 Cynical Theories: How activist scholarship made everything about race, gender, and identity and why this harms everybody (book)
 Teaching Empowerment: Theory of Enchantment (Chloé Valdary), Moral Courage (Irshad Manji), Empowerment Framework (Erec Smith)
Other Resources and References
Heterodox Academy
Empowering Mathematics
Zach Cresswell
Twitter: @z_cress
Email: cresswellzach@gmail.com
Website: zachcresswell.wordpress.com
Please complete the survey!
Presentation
bit.ly/empoweringmath
Empowering Mathematics
By Zach Cresswell
Empowering Mathematics
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