jedediyah.github.io/nctm2023
About Jed
Teaching
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Outline
I . Beauty
II . Utility
III . Consequence
IV . Our Teaching
These themes are not mutually exclusive.
I . Beauty
II . Utility
III . Consequence
I . Beauty
II . Utility
III . Consequence
I . Beauty
II . Utility
III . Consequence
There is tremendous beauty in mathematics, and the sources of beauty are diverse in nature and mode.
Beauty often involves acts of creativity that satisfy constraints.
I . Beauty
II . Utility
III . Consequence
I . Beauty
II . Utility
III . Consequence
I . Beauty
II . Utility
III . Consequence
The justification for teaching mathematics is often tied to utility in the solving of real problems.
I . Beauty
II . Utility
III . Consequence
The justification for teaching mathematics is often tied to utility in the solving of real problems.
I recently asked my students what real-world problems they had worked on in their math classes.
I . Beauty
II . Utility
III . Consequence
Much of the history of and motivation for mathematics has deep cultural connections.
Tallying, astronomy, calendar, navigation, trade, bookkeeping, surveying, measuring (the Earth), enumeration, physics, statistics, engineering, communication, computability, encryption, analysis, analytics,
There is often a distinction between pure mathematics and applied mathematics.
There is a huge body of literature going back many decades, if not millenia, which discusses what mathematics is, and you can read endlessly on critisisms of views that treat math as neutral and value-free.
In any case, I think it is fair to say that we are not teaching pure mathematics in grade school.
"
Davis and Hersh. "The Mathematical Experience" p. 129
I . Beauty
II . Utility
III . Consequence
I . Beauty
II . Utility
III . Consequence
IBM's support of Nazi Germany with compute power for census, statistics, and logistics calculations.
You could build an entire course on the mathematics of World War II
Encryption
Cryptanalysis
Computation
Statistical Research Group
Ballistics
Fluid dynamics
Warcraft engineering
Manhattan project
Operation Paperclip
Recommended reading: "Crypto" by Steven Levy
I . Beauty
II . Utility
III . Consequence
"Essentially, all models are wrong, but some are useful." - George Box
I . Beauty
II . Utility
III . Consequence
What are some consequences of data technologies?
↓
Some of the more well known harms
I attended a virtual ASA meeting recently on ChatGPT.
Respectfully, I disagreed with basically all of it.
One teacher shared that their district is spending an hour of PD per month on practicing using ChatGPT for lesson planning and *grading*.
Adversarial attack
Algorithms are brittle - Melanie Mitchell
Lack of oversight or auditing
We are being experimented on.
"Our success, happiness, and wellbeing are never fully of our own making. Others' decisions can profoundly affect the course of our lives... Arbitrary, inconsistent, or faulty decision-making thus raises serious concerns..."
- Fairness and Machine Learning , Barocas, Hardt, and Narayanan
Math-based technologies are ubiquitous, often do not work, and are capable of broad and arbitrary harm.
Are we training the next generation of phrenologists?
Are we training the next generation of eugenecists?
To what extent should ethics be incorporated into mathematics classrooms?
"Yes, train these young people to get these skills, but integrate into that not only the technical capacity but the critical capacity to question what they're doing and what's happening.
To me, it is not true empowerment unless people can have the power to question how these skills are going to be used."
Our students are future engineerings.
Data Modeling Process
Data
→
Preprocess
→
Explore
→
Model
→
Communicate
Data Modeling Process
Environment
→
Data
→
Preprocess
→
Explore
→
Model
→
Communicate
→
A framework for critical analysis
Data
• Harmful data collection, lack of consent, insecure / lack of privacy, historical, representational, or measurement bias, ...
Preprocess
• Labor exploitation, labeling by non-experts, incorrect labeling, trauma experienced by labelers, ...
Explore
• Feature selection bias, bias in interpretation of data visualization, data manipulation, feature hacking, ...
Model
• Bias in model choice, model-amplified bias, environmental impact, learning bias, evaluation bias, peripheral modeling, ...
Communicate
• Biased model interpretation, ignoring variance, rejecting model, deploying harmful products, deployment bias, ...
Meta
• "Pernicious feedback loops", runaway homogeneity, susceptability to adversarial attack, lack of oversight or auditing, ...
Critical Questions:
What are the motivations for the project?
What is the intended use?
What is the unintended use or misuse?
Where does the data come from?
Who collects the data?
Who owns the data?
How is the data collected?
How is the data stored?
How old is the data?
When will the data expire?
How will the data be secured?
What happens with the data when the company is sold?
Who does the labeling?
What labels will they decide to use?
Are the labelers experts?
Are the labels accurate?
What biases are represented in the data?
How is data included or excluded?
How are outliers addressed?
What subpopulations are represented?
What subpopulations are over- or underrepresented?
What portions of the data are inspected?
What features are selected for modeling?
What model is chosen?
What features do we think are being modeled?
What latent features are actually being modeled?
What is the domain of the model?
What are the consequences of error?
What decisions will be made with the model?
What biases are perpetuated?
Where will the model be deployed?
What could go wrong?
Who is responsible when things go wrong?
How can issues be reported?
Will new data be fed back in to update the model?
Students should witness math fail. They should experience models performing poorly.
Data and all of its questions
Privacy, security, power, surveillance, consent, access, stereotyping, fairness,...
Encryption
Military
The pitfalls of our predecesors
Misuse
Notation is convention
See models break
Bias and variance
Environment
Complexity, incompleteness, decidability, the unfinished state of mathematics
Accountability
Justice
...
When handing over the tools of mathematics, we are responsible as educators for teaching their responsible use.
It is a sin of omission when we fail to acknowledge the consequences of the content we teach; Consequences which include ethical and technical pitfalls.
To what extent are the three themes of
I . Beauty
II . Utility
III . Consequence
experienced in our classrooms?