Jed

@jedediyah.com

905 Followers 913 Following

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

Spreadhseet with columns Unit, Class #, Topic(s). Under Topic(s), the first three classes are "The Course", "Ethics", "Hardware"
Teaching Statistics and Probability National Council of Teachers of Mathematics 1981 Yearbook
The Missing Strand Reviving NCTM's Vision for computing in Mathematics Education
Artemis II capsule against the sky.
Plot of FEV for Smokers and Non-Smokers. Smokers appear to have a higher FEV which can be (erroneously) inferred as having "healthier" lungs.
Pyplot figure of atmospheric CO2 data oscillating while increasing from 1958 to present. A model is well-fit to the data.
Ten plots corresponding to column sums of images of the digits 0 through 9. The top left plot corresponds to zero, and has two distinct peaks corresponding to the left and right sides of the zero, suggesting people write zeros taller than wider. The next plot corresponds to one, and has a concentrated narrow peak.
Image of a hand-written 0, composed of pixel values, next to an image of a 1 also composed of pixel values.
Linear regression on CO2 data displays slope of 1.66
Bar plot of NCTM articles per year containing code. There is a surge in the 60s and huge surge in the 80s.
HELLO MARY, I AM A COMPUTER. I CAN DO MANY THINGS. I CAN TYPE AND I CAN READ SOME MESSAGES THAT YOU GIVE ME BY TYPING. I C AN ALSO DO PROBLEMS CORRECTLY AN D I C AN HELP YOU BECOME VERY GOOD AT ARITHMETIC. I Will ASK YOU TO DO SOME EXAMPLES. IF YOU ARE CORRECT I WILL GIVE YOU ANOTHER QUESTION. IF YOU ARE WRONG, I WILL TELL YOU TH E ANSWER AND THEN REPEAT THE QUESTION. IF YOU ANSWER A QUESTION FIVE TIM ES WITHOUT A MISTAKE, I WILL RETIRE THAT QUESTION. IF YOU MISS A QUESTION THREE TIM ES I Will NOT ASK IT AGAIN TODAY. MY OPERATOR WILL HELP YOU WITH THE KEYBOARD. NOW, LET US BEGIN .
Scatter plot of trending YouTube videos, Number of Views vs. Character Count of Title. There are some distinct peaks around 35, 50, and 65.
The Rubik’s WCA World Championship 2025 took place at the Seattle Convention Center on July 6, 2025. The sixteen finalists are listed in the DataFrame below, along with their country and their times from five rounds of solving. A code block displays the creation of a Pandas DataFrame.
Book cover of "Weapons of Math Destruction" by Cathy O'Neil.
Many AI technologies are simply broken. That doesn't seem to be stopping anyone from deploying them. Large language models, for example, are fundamentally the wrong choice for many applications. A critical question becomes: In what contexts does it matter that these technologies often do not work?
A white board with experimental data from a pendulum lab. Columns include: 1-swing, 10-swings, 10-careful swings. Above the white board are several student made posters, an origami piece, and a street sign that reads Williams Ln.
because the Skinnerians do not.) There are two fundamental and intractable troubles with CAI and PI. Every conception of pedagogy is based on a concept of knowledge, and CAI and PI are based on a falsified concept: that knowledge is the ability to respond in the expected way. For reasons I dis- cussed earlier, the use of this idea produces cognitive knowledge-at least for the moment-at the price of psychic intelligence. When advocates of CAI or PI are exuberant, they claim that their methods supersede other teaching styles. When challenged, they sometimes retreat to the position that their methods replace various kinds of drill that do not deserve the attention of a human teacher; but these retreats are instances of the Law of
Then your friend Chelsea, also from twenty-eight thousand years ago, notices another connection: sometimes she can combine two arrangements from Pattern 2 to get a bigger arrangement also in Pattern 2, but it doesn’t always work. She finds this one: 9 with 16 makes 25
"Find the following sums" followed by four sigma notation expressions.
Scatter plot of beak depth vs beak length for three species of penguin.
LinkedIn post from CSTA referring to Microsoft as "our partners".
Screen capture of several problems about sets, binary words, permutations, and graphs.
>>> import numpy as np >>> r = np.random.rand(3,4) >>> r array([[0.18487845, 0.57661705, 0.04339225, 0.34596879], [0.71953505, 0.9111707 , 0.62555752, 0.91202757], [0.91937155, 0.69415961, 0.17472662, 0.47850455]]) >>> r[0] = r[0] / r[0][0] >>> r array([[1. , 3.11889819, 0.23470691, 1.87133115], [0.71953505, 0.9111707 , 0.62555752, 0.91202757], [0.91937155, 0.69415961, 0.17472662, 0.47850455]]) >>> r[1] = r[1] - r[1][0]*r[0] >>> r array([[ 1. , 3.11889819, 0.23470691, 1.87133115], [ 0. , -1.33298588, 0.45667767, -0.43446079], [ 0.91937155, 0.69415961, 0.17472662, 0.47850455]]) >>> r[2] = r[2] - r[2][0]*r[0] >>> r array([[ 1. , 3.11889819, 0.23470691, 1.87133115], [ 0. , -1.33298588, 0.45667767, -0.43446079], [ 0. , -2.17326664, -0.04105624, -1.24194406]]) >>>
Let's use row operations to solve the system: -x-y-3z =-9 3x+0y+z=-1 1x-5y+z=23 A Python script demonstrates row operations on a numpy array.
Screenshot of the Chess.com AI chatbot. A user prompt reads: A HUGE number of my opponents disconnect without resigning. I NEED chess.com to be more active about consequences for abandoning games. The bot then responds to an unrelated concern.
Rock configurations of numbers; rectangular representations of 1, 2, and 3.
Here is a a dataset of water depths: Depths a. Copy and paste the data into Desmos to create a scatter plot. This should create a table. b. We are going to adjust, by hand, the parameters of a sinusoidal model (do not do an automated regression): y = beta_0 + beta_1 sin(beta_2 t + beta_3) Add this model to Desmos as shown (you can type "beta" to create a ). c. Add the sliders and adjust them until your model appears to fit the data. Record your best hand-fit parameter values. d. Interpret each of the parameters in the context of the model. For example, represents a particular property of the tide which you can describe. e. Our model has four parameters. Could you still model the tide well enough with only three?
Title Slide: Sensitive dependence on initial conditions How AI predictably fails unpredictably Jedediyah Williams AAPT Summer Conference 2024 AI in K-12 Classrooms jedediyah.github.io/aapt2024
Model Validation A flow chart depicts splitting data into Training and Testing sets. Modeling uses the training set, and the testing set is reserved until the very end where it will be used for validating the model.
Hand written data tables and plots in a student's notebook.
How high does a bouncy ball bounce? Y = B_1 X A graph of bounce height vs drop height shows a line closely fitting a red scatter plot with a moderate positive slope.
How high does a bouncy ball bounce? A table shows columns h_drop and h_bounce. An image depicts four students next to a whiteboard. One holds a meter stick and another has dropped a bouncy ball. One looks on as another takes a video.
A game tree corresponding to several games of Hexapawn. A Hexapawn board is displayed in the top left; it is a three by three board with three white pawns and three opposing black pawns.
A labeled version of the previous graph containing the quartic function definitions.
A zoomed-in portion of the previous graph. A normalized histogram approximating a probability density function. An orange area corresponds to successful tetrahedra constructions.
A normalized histogram approximating a probability density function. There is a small area on the left that corresponds to successful tetrahedra constructions.
A cross plot of six by six variables. The main diagonal has probability distributions while other cells contain blue and orange points corresponding to failed or successful tetrahedra constructions for the lengths of ordered pairs a through f.
Six examples of tetrahedra formed from a virtual broken stick. Each piece is colored based on its length.
A stack of copies of "Weapons of Math Destruction" by Cathy O'Neil
Let the weight of a binary string be the sum of its bits (or the number of 1s). So the string 101001 has weight 3. a. How many binary words of length 3 have weight 1? b. How many binary words of length 5 have weight 3? c. How many binary words of length n have weight k?
Desmos plot of three histograms that look like triangles.
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.
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?
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
Four faces of a 4-way stop light labeled L1, L2, L3, L4. Greens on L1 and L3, reds on L2 and L4.
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?
Given the graph T = {{w,x,t,z},{{w,x},{x,y},{x,z}}} Draw T and all of the possible subgraphs.
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.”
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.
Slide shows: "Solve (x^2 -5x +5)^(x^2 -9x +20) = 1
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?
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
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.
A block diagram of a feedback loop. The output of F(x) is fed back into the input.
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?
Retro green book cover with old school computer depicted. Computers in Mathematics Education NCTM 1984 Yearbook
“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.”
Venn diagram worksheet colored with pencils.
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: ...