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Jed

@jedediyah.com

840 followers 790 following 500 posts

Teacher ◦ Robots and mathy science ◦ He/Him #ITeachMath #ITeachPhysics #TeamCompSci #mtbos #PAEMST https://jedediyah.github.io/

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Jed @jedediyah.com · Nov 21

Math educators, where do you fall within the levels of ethical engagement??

arxiv.org/abs/2212.11713

#iteachmath #iteachcs #mtbos

6 Levels of ethical engagement for mathematicians:

Level -1: Actively obstructing efforts to address ethics in mathematics (a new level not explicitly stated in Chiodo and Bursill-Hall (2018), but suggested here as an extension)

Level 0: Believing there is no ethics in mathematics

Level 1: Realising there are ethical issues inherent in mathematics

Level 2: Doing something: speaking out to other mathematicians

Level 3: Taking a seat at the tables of power

Level 4: Calling out the bad mathematics of others

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Jed @jedediyah.com · 11h

❤️ It's basically a talk about the yearbooks you sent me!

I'm sadly missing ATMNE. It's a stretch to do both conferences (and my proposal wasn't accepted🤣).

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Jed @jedediyah.com · 15h

I'll be sharing slides and a whole bunch of resources here on BSky!

Reposted by Jed

benjamin dickman @benjamindickman.bsky.social · 18h

[digging through my twittxr archives]

do you want non-routine quadratic problems?

here are 20 💌:
www.desmos.com/calculator/d...

cc. #iTeachMath #MathSky #EduSky #AlgebraSky

Particular Parabola Problems

www.desmos.com

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Jed @jedediyah.com · 17h

Th, 10/16
Event Title: 140 - Mathematics for Machine Learning & Artificial Intelligence.
Session Type: Workshop
Time: 1:00 PM - 2:15 PM
Location: Georgia World Congress Center, A406-A407

Jed @jedediyah.com · 17h

Getting pumped to present at @NCTM.org 2025!

Come to an awesome workshop on "Mathematics for Machine Learning and Artificial Intelligence". We'll play with dynamical systems and filters, feature engineer some classifiers, and talk about how not to AI.

#NCTM2025 #NCTMATL25 #mtbos #IteachMath #NCTM

Mathematics for Machine Learning and Artificial Intellgience
Jedediyah Williams, PhD
NCTM Atlanta 2025
Image in center of slide is a graph with the minimum spanning tree highlighted.

What is the math for AI and ML?
Discrete, Stats, and Computing.
Logic, Linear Algebra, Graph Theory, Set Theory, Combinatorics, Difference Equations, Recursion, Iteration

Two images of a cake, before and after filtering RGB pixel values.
Two histograms display the RGB distributions before and after the filter.

Try isolating different objects with the filter.
An RGB filter has sliders for red, green, and blue minima and maxima. An image shows the moon with robotic hardware before and after the filtering.

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Jed @jedediyah.com · 23h

Is there a name for that phenomenon in bad curric design where you write your Qs kind of backwards, i.e., you have a goal for where you want students to get to, but you end up writing the questions in a way that someone has to already know the answer to understand the question? We call it Engage NY.

Jed @jedediyah.com · 1d

Worrying about protecting students does not seem to be a consideration. Presenters are often dismissive of privacy and safety of students if not explicitly promoting unethical or even illegal practices with student data.

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Jed @jedediyah.com · 1d

You tend to get 59 minutes of AI hype with the same 2 sentences buried somewhere: "The data that the AI is trained on *could* be biased, so it might possibly produce biased results. So you have to look out for that".
Any time someone cites "data" as *the* source of bias you know something is wrong.

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Jed @jedediyah.com · 1d

Basically none, right? I believe part of the reason is that people pushing hardest have an understanding of AI derived from sales pitches. They tend to be woefully naive of critical tech research. It is clear when you hear the same check-box acknowledgement of "bias" during terrible AI PD...

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Jed @jedediyah.com · 2d

I've made a point this year of printing out student work and writing feedback by hand, being explicit about how I read and think about everything they submit.

Some of my colleagues have been explicit about using AI to grade and I sense that it is making the game of school much worse...

Jed @jedediyah.com · 2d

In #MathsToday we reached the topic I've been waiting for in Data Science, Dynamical Systems.

Highlighted Robert L. Devaney: www.youtube.com/watch?v=TVfn...

Referenced the outstanding book/course from @stevenstrogatz.com on Nonlinear Dynamics and Chaos.

Connected back to our reading of Poincaré

A block diagram of a feedback loop. The output of F(x) is fed back into the input.

Block diagram of a feedback loop for a movie recommendation algorithm. Movie recommendations feed into user's choices and habits which affect movies watched which loop back into recommendations.

Pretty much everything is a dynamical system with feedback (ok not everything).
Images display a circle of ants, a toy car with a weighted trailer, a network diagram of the internet, global temperature chart, a flock of birds against the sky.

Chaos
A system is chaotic if it exhibits sensitive dependence on initial conditions. A graph shows two orbits that diverge after 12 steps. One for initial condition 8 and the other for initial condition 8.00001

Jed @jedediyah.com · 3d

We reviewed this question in #MathsToday. Many of my students who have already completed AP Calc BC came up with really interesting wrong approaches to d!

Given the sequence:
2/2, 4/3, 6/5, 8/7, 10/11, 12,13, 14/17,...
a. Write the next three terms.
b. Write a definition of the sequence.
c. Find the limit of the sequence.
d. Is the sum of this infinite sequence infinite?

Jed @jedediyah.com · 3d

Just added to my @NCTM.org yearbook collection.

General "computing" had a lot of interesting overlap with current rhetoric around "AI". First glance: historically interesting, still relevant, with some pretty spicy takes mid-book!

Retro green book cover with old school computer depicted.
Computers in Mathematics Education
NCTM 1984 Yearbook

Preface.
As we read and studied the many submitted articles, certain generalized assumptions began to appear. A few of these can be summarized as follows: (1) The computer is definitely here to stay in education, both in the classroom and in the home; (2) to date there is still a shortage of good software; (3) we are desperately in need of more research (4) the integration of the computer into the curriculum is at best in its infancy;

A replacement for the teacher. Despite the cries of those who fear that education will be dehumanized and machines will replace teachers, the computer will, in fact, only enhance the role of the teacher.

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Jed @jedediyah.com · 3d

Ain't no way this is real

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Jed @jedediyah.com · 4d

👀

Jed @jedediyah.com · 4d

Or, hear me out, we choose not to volunteer our students as experimental subjects without their consent for the benefit of tech companies and surveillance capitalism.

“What schools need to do is help teachers and students use [AI tools] in the right and best ways,” said Joseph South, the chief innovation officer for ISTE + ASCD, a nonprofit organization that provides resources for educators about educational technology and curriculum. “If we do that, I believe, over time, we’ll be able to increase the value and decrease the risk.”

Jed @jedediyah.com · 4d

Oh for sure. Related, visit some airports and check out the hardware / software being maintained in the towers! Want to reinstall the software for that navigation box? Here are the floppy disks!

Jed @jedediyah.com · 4d

Astronomers! When I was doing some work in astronomy I was thrilled to discover astronomy lineages traceable through Fortran code handed down from adviser to grad students through multiple generations.

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Jed @jedediyah.com · 5d

Venn diagram worksheet colored with pencils.

Jed @jedediyah.com · 5d

In #MathsToday we worked on set theory.

Some resources came from: @draustinmaths.com
www.draustinmaths.com/set-notation...

And some of the exercises were pulled from @oscarlevin.com's Discrete Math (3rd edition)
discrete.openmathbooks.org/dmoi3/sec_in...

Screenshot of a problem set.

1. Find the power set of A={x,y,z}. The power set is the set of all possible subsets.

2. Given the diagram below: ...

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Jed @jedediyah.com · 6d

First @NCTM.org yearbook (1926) here: catalog.hathitrust.org/Record/00006...

An interesting take on quadratics!

"Nor should we expect to have all the pupils able to factor ax^2+bx+c (a useless accomplishment for most people)"

"If the subject is to be valuable, the learning should be a pleasure"

As a result of this view of the reason for teaching algebra, we have come to see that we should not expect everyone to solve two simultaneous quadratic equations, although out of an entire class there will be found a few who can do so. Nor should we expect to have all the pupils able to factor ax^2+bx+c (a useless accomplishment for most people),

a considerable number will take pleasure in performing such a task and will thereby acquire some special skill which they may find useful in later work. The purpose of teaching algebra is found in none of these details: it consists in giving to everyone a general idea of the meaning of algebra, together with a few definite and useful applications which everyone is likely to meet. If the subject is to be valuable, the learning should be a pleasure, and it may properly be expected that this pleasure will carry the pupil into such manipulations of algebraic expressions as will fix the habit of using algebra in the cases to which it can be applied.

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Jed @jedediyah.com · 6d

Yes, local minimum, as it fits a definition for it. This has practical implications in general, as you should consider end points when looking for exrrema, locally or globally. But if someone wants to reject it as a local min, that's fine too. We should just be clear about corner cases in context.

Jed @jedediyah.com · 7d

As an example of pernicious feedback loops and manipulating data.

Jed @jedediyah.com · 7d

It's more applied than commentary on math, but I've assigned in the past, and am using in Data Science this year, Cathy O'Neil's Weapons of Math Destruction, chapter 3 "Arms Race". It's great with my Junior/Seniors as it talks about how wildy out of control college rankings are.

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Jed @jedediyah.com · 7d

Related: if I am thinking about how I wish more math teachers were familiar with a particular text I found important, then I'm picking the 1991 NCTM yearbook.

Book cover. Discrete Mathematics Across the Curriculum, K-12