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jedediyah.com
Jed
@jedediyah.com
860 followers 820 following 540 posts
Teacher ◦ Robots and mathy science ◦ He/Him
#ITeachMath #ITeachPhysics #TeamCompSci
#mtbos #PAEMST

https://jedediyah.github.io/
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jedediyah.com
In #MathsToday we rolled a lot of dice and found estimates of probability mass functions for sums of n=2,3 4 dice.

In #MathsNextWeek we start to explore broken stick problems!

Draft of next week's guide:
williams-bhs.github.io/docs/Broken_...
Desmos plot of three histograms that look like triangles.
November 14, 2025 at 6:02 PM
jedediyah.com
In #MathsToday we played with the "Cat Machine" and talked about theoretical probabilities, experimental probability, and confidence in our experimental probabilities.
The Cat Machine has a random probability of generating a cat. Try the machine and then guess P(cat)! A button labeled "Cat Machine" with an arrow pointing to ten pictures, 8 of which are cats.
November 13, 2025 at 8:43 PM
jedediyah.com
Was really curious to see how these problems would go over in #MathsToday. It was great!

We talked about how to map all of the problems onto the last problem and the usefulness of knowing "how to solve it" when we can recognize and abstract problems to known strategies.
A series of combinatorics problems. First problem asks: On a 2x2 grid of squares, in how many ways can we color the squares black or white?
November 4, 2025 at 6:00 PM
jedediyah.com
I once gave a talk called "AI is not what you think it is unless you think it is hot garbage"

I've just enjoyed and highly recommend @chrissimon.au's "AI is a hype-fuelled dumpster fire that will burn down the planet and get you thrown in jail"
www.youtube.com/watch?v=0bF_...
AI is not what you think it is unless you think it is hot garbage. Four images depict robots and trash bins on fire. Jedediyah Williams, PhD Belmont High School ATMIM 2024 Spring Conference: All Students Deserve a Piece of Pi March 14, 2024 AI is a hype-fuelled dumpster fire that will burn down the planet and get you thrown in jail Chris Simon
November 2, 2025 at 11:03 PM
jedediyah.com
In #MathsToday, trying to talk about state machines without talking about state machines.

Also debated with students whether we should fully represent all 12 states or reduce the number of bits to the minimum required (depending on number of states used).
Four faces of a 4-way stop light labeled L1, L2, L3, L4. Greens on L1 and L3, reds on L2 and L4. There are twelve total lights that can be On (1) or Off (0), and we can represent the current state of those lights with a -bit binary word. For example, with green lights both On in one direction while the other direction has red lights, we can write: 001100001100 which means that G1 and G3 are On while and R2 are R4 on. Create a directed graph to represent the behavior of the stop lights as they transition from one state to the next.
October 29, 2025 at 10:30 PM
jedediyah.com
In #MathsToday we continued working on our graph theory exercises.
Fred, along with the five people from the previous problem need to split into two groups of three for a project. However, there is drama! Alejandro refuses to work with Camille or Elias; Dalia "just can't even" with Ben or Camille; Ben and Camille both had a falling out with Fred; "aint no way" Elias will work with Dalia. a. Define and draw a graph W, with six vertices, to represent who CANNOT work with whom. b. Show that it is possible to create two groups of three by partitioning into a bipartite graph with three vertices on each side. c. Find W', the complement of W. What does W' represent?
October 28, 2025 at 11:12 PM
jedediyah.com
In #MathsToday we are working on graphs, and getting some motivation for our next unit on combinatorics.
Given the graph T = {{w,x,t,z},{{w,x},{x,y},{x,z}}} Draw T and all of the possible subgraphs.
October 23, 2025 at 4:15 PM
jedediyah.com
A major obstacle to students' going beyond the basics is that their teachers often have never gone beyond the basics. Many teachers, particularly those who teach at lower grade levels, have never themselves been engaged in a single true mathematical problem-solving activity or been asked to explain or justify their reasoning. They use worksheets to provide lots of practice for their students, thinking that they are engaging their students in problem solving, but not realizing that there is a difference between a problem and an exercise. What makes a problem “a problem” is that the solution is not directly linked to previous activities. The mathematics standards expect students to go beyond the basics – in terms of additional content and a substantial increase in problem solving and reasoning, and in terms of applying the mathematics they learn in school to daily situations. Teachers who have never gone beyond the basics themselves, then, cannot reach all students as recommended in the standards, and will therefore “leave some children behind.”
October 21, 2025 at 3:28 PM
jedediyah.com
🤔
Two BSky posts. 1. "Up to four satellites from Elon Musk's massive Starlink constellation are falling to Earth every day, according to space trackers." 2. Airliner hit by possible space debris.
October 19, 2025 at 10:47 PM
jedediyah.com
Two things from #NCTMatl25 that I'm going to be using *this* week:

Gail Burrill's algebra problem, and @gwaddell.bsky.social and Ed Keppelmann's 4 pile Nim.
Slide shows: "Solve (x^2 -5x +5)^(x^2 -9x +20) = 1 NIM: 4 pile game - Draw 4 piles of dots, one has 8, one has 4, one has 2, and the last has 1 dot. - You can take as many as you want each turn, but only from 1 pile. - The winner takes the last dot. Do you see a winning strategy?
October 18, 2025 at 11:18 PM
jedediyah.com
Idk where I adapted / stole this from, but it is this week's problem of.
#mtbos #ITeachMath
A size n equilateral triangle is broken into smaller triangles as shown here for n = 1, 2, 3: A triangle is considered “chill” if every row, beginning with the top row 1, has a number of small triangles filled in equal to the row. For example, the following are three different chill triangles for n = 3: How many different chill triangles are there for a size n triangle?
October 14, 2025 at 1:01 PM
jedediyah.com
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
October 12, 2025 at 6:32 PM
jedediyah.com
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.
October 12, 2025 at 6:32 PM
jedediyah.com
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
October 10, 2025 at 7:41 PM
jedediyah.com
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?
October 9, 2025 at 10:50 PM
jedediyah.com
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.
October 9, 2025 at 10:31 PM
jedediyah.com
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.”
October 8, 2025 at 9:54 PM
jedediyah.com
Venn diagram worksheet colored with pencils. Venn diagram worksheet colored with pencils.
October 7, 2025 at 10:04 PM
jedediyah.com
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: ...
October 7, 2025 at 8:22 PM
jedediyah.com
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.
October 6, 2025 at 9:22 PM
jedediyah.com
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
October 5, 2025 at 6:33 PM
jedediyah.com
Last week's problem of the week is still tormenting students.

#mtbos #ITeachMath
How many rectangles are there below such that the sum of the numbers within the rectangle are a multiple of seven? A 7x7 grid shows numbers 1 yo 49 from left tro right, bottom to top.
October 3, 2025 at 1:15 PM
jedediyah.com
This question came back around in #MathsToday

Some were struggling with the sum of triangular numbers and in real-time a student realized that you get a "pyramid" because it's like stacking the triangles!!

"But a 3 sided pyramid"
A sequence of triangular numbers represented as groups of "stones". A sketch of layered triangles forming a 3 sided pyramid.
October 2, 2025 at 8:07 PM
jedediyah.com
Prompt engineering is less an AI skill than it is you putting your expert knowledge to work on a system that is not likely to provide useful results without an expert there to prompt, parse, and iterate until some threshold of confirmation bias is reached.
October 2, 2025 at 12:10 AM
jedediyah.com
In #MathsToday we practiced some exploratory mathematics and approached proving some things.

There were super insightful questions from students who have already taken calculus, and have several convergence formulas memorized, but didn't know what to make of this at first!

#mtbos #ITeachMath
The Fibonacci sequence is defined as: F1 = 1 F2 = 1 Fn = F_n-1 + F_n-2 Write the first ten Fibonacci numbers. Write the first ten reciprocals of Fibonacci numbers, i.e., 1/F1, 1/F2, 1/F3 Find (or approximate) the sum from 1 to infinity of 1/Fi Spreadsheet with four columns: n, F(n), 1/F(n), Sum to F(n). The F(n) column displays the Fibonacci sequence to row 29.
October 1, 2025 at 8:49 PM