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?
- 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
- 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 mini-series 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
