Geoff Krall, PhD
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geoffkrall.bsky.social
Geoff Krall, PhD
@geoffkrall.bsky.social
450 followers 220 following 510 posts
Math and the like. Asst Professor at Colorado State University. Author of 'Necessary Conditions'.
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geoffkrall.bsky.social
Oh man these are both good suggestions @k8nowak.bsky.social and @triangleman.bsky.social.

I've had students want to fist fight me on these concepts just this semester.
November 8, 2025 at 5:02 PM
geoffkrall.bsky.social
Gonna engage some first year grad students in a conversation about content knowledge (CK) and pedagogical content knowledge (PCK).

Which Venn diagram do you think best represents our current understanding of the interaction between the two? Or what would your venn look like?

#edusky #mathsky
Three venn diagrams 1) two circles overlapping 2) circle (pck) within a larger circle (ck) 3) same circle 4) question mark
October 6, 2025 at 12:20 AM
geoffkrall.bsky.social
Reading Lockhart is a trip. I'll go from agreeing, to vehemently disagreeing and getting red and mad, and then agreeing again all within like a single paragraph.
Excerpt from Paul Lockhart's "A Mathematicians Lament" Teaching is not about information. It’s about having an honest intellectual relationship with your students. It requires no method, no tools, and no training. Just the ability to be real. And if you can’t be real, then you have no right to inflict yourself upon innocent children. In particular, you can’t teach teaching. Schools of education are a complete crock. Oh, you can take classes in early childhood development and whatnot, and you can be trained to use a blackboard “effectively” and to prepare an organized “lesson plan” (which, by the way, insures that your lesson will be planned, and therefore false), but you will never be a real teacher if you are unwilling to be a real person. Teaching means openness and honesty, an ability to share excitement, and a love of learning. Without these, all the education degrees in the world won’t help you, and with them they are completely unnecessary. It’s perfectly simple. Students are not aliens. They respond to beauty and pattern, and are naturally curious like anyone else. Just talk to them! And more importantly, listen to them!
September 22, 2025 at 1:53 AM
geoffkrall.bsky.social
I've been spending the summer adding alt text to various online graphical problems, but I could definitely use assistance if any of y'all have experience. As an example, here's a graph and you can see my alt text the picture. How would you describe it in a manner that is helpful for screen readers?
"A graph of a smooth blue curve with two local minima and one local maximum. Six vertical dashed lines labeled x1 through x6 are shown beneath the curve along the x-axis. The curve starts high to the left and decreases to a minimum just after x1. The function then increases higher through x2 and achieves a local maximum at x3. The function is decreasing when it passes through the y-axis and decreasing more steeply at x4. The function achives a deeper minimum at x5 before rising steeply through x6.
July 21, 2025 at 4:22 PM
geoffkrall.bsky.social
A bit late, but watching in honor of Gene Hackman
Screenshot of the royal tenenbaums starting gene Hackman
March 6, 2025 at 2:48 AM
geoffkrall.bsky.social
might need to outsource this one: I'm teaching the Chain Rule of derivation tomorrow and i want to make a Ms. Casey innie-outie Severance joke. Can someone help me out here?
Screenshot of Ms. Casey from the TV Show Severance.
March 4, 2025 at 7:38 PM
geoffkrall.bsky.social
this popped in my head during class today

I'll try it out and let you know how it goes
The Uruk-Hai from Lord of the Rings. Instead of saying "find the halflings!" he is saying "find the half life!"
February 27, 2025 at 2:05 PM
geoffkrall.bsky.social
Eating like freaking sultans tonight
A picture of eggs and other food items.
February 27, 2025 at 1:20 AM
geoffkrall.bsky.social
MANY ARE SAYING
Local newspaper headline: With high egg prices, is it worth raising backyard chickens? What to know in Colorado
February 26, 2025 at 4:58 PM
geoffkrall.bsky.social
ChatGPT doesn't understand f(x)>0.

Even when prompted, it can't figure it out.

It does suggest (once it's fully out of ideas) to go check out Desmos lol
"Here's a graph that satisfies the given constraints. The function is positive for − 3 ≤ 𝑥 < − 1 −3≤x<−1 and negative for − 1 < 𝑥 ≤ 3 −1<x≤3. It also increases for − 3 ≤ 𝑥 < 0 −3≤x<0 and decreases for 0 < 𝑥 ≤ 3 0<x≤3, with a local maximum at 𝑥 = 0 x=0. Let me know if you'd like any modifications! ​​ " "wait, is that function positive from -3 to -1?" "Here's the corrected graph! Now, 𝑓 ( 𝑥 ) > 0 f(x)>0 for − 3 ≤ 𝑥 < − 1 −3≤x<−1 and 𝑓 ( 𝑥 ) < 0 f(x)<0 for − 1 < 𝑥 ≤ 3 −1<x≤3. It also has a local maximum at 𝑥 = 0 x=0 with the correct increasing/decreasing behavior for 𝑓 ′ ( 𝑥 ) f ′ (x). Let me know if you need any further refinements! ​​ " "It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can plot the function yourself using a tool like Desmos or Python! "
February 21, 2025 at 9:00 PM
geoffkrall.bsky.social
-138 years old 🙏
An AI generated image of an old dude with a birthday cake that says 1887. The caption says "Happy birthday to Grandpa 1887-2025=-138 years old
February 12, 2025 at 7:43 PM
geoffkrall.bsky.social
Thinking of switching careers to full time egg mongol.
A graph showing egg prices going up up and up to 7 dollars per dozen. A picture of my chickens. There are four chickens wandering around a green grassed backyard.
February 6, 2025 at 6:37 PM
geoffkrall.bsky.social
Soccer Mommy releasing a song about and a video about Stardew Valley is a little too "this was made specifically for Geoff Krall"
Screenshot of Soccer Mommy "Abigail". The video is in the style of Stardew Valley
January 13, 2025 at 2:11 PM
geoffkrall.bsky.social
I didn't intend for it, but I ended up writing
* three (3) posts on pre-program consideration,
* three (3) posts for when you're in your program and
* three (3) posts on concluding your program.

Here's the intro post going back to the start of this project.

emergentmath.com/2024/12/18/e...
A timeline showing the 9 blog posts in this series. The timeline is in the form of an arrow going from left to right and has a gradient from blue to orange.
January 13, 2025 at 2:34 AM
geoffkrall.bsky.social
IT HAPPENED TO ME: After years of thinking it wasn't actually a thing , I found my first rock in my beans.
I am holding a black rock over a pot of soaking pinto beans.
December 28, 2024 at 12:55 AM
geoffkrall.bsky.social
They are ready
Two pots of tamales with a side of sliced green olives
December 26, 2024 at 12:24 AM
geoffkrall.bsky.social
Real ones know
A picture of shredded pork, soaking corn husk and lard, ready to be prepped for tamales
December 25, 2024 at 9:55 PM
geoffkrall.bsky.social
It is also fried drumsticks night
December 23, 2024 at 12:14 AM
geoffkrall.bsky.social
Negroni Saturday
A negroni - a gin drink with vermouth and campairi - in front of a slices orange and a bottle of Jensen's gin
December 23, 2024 at 12:03 AM
geoffkrall.bsky.social
Had some nice PD time with my friends in Laramie. Always love using these Necessary Conditions cards
Geoff, wearing a hoodie over a plaid black and white shirt, is holding a card set based on his book, Necessary Conditions . He is in a workroom
December 18, 2024 at 12:32 AM
geoffkrall.bsky.social
I dunno Duolingo, seems like it was more
The owl from Duolingo telling me I made 597 mistakes this year
December 7, 2024 at 5:49 AM
geoffkrall.bsky.social
Seen on my bike ride home today
Holiday decorations in front of a house depicting classic scenes from Calvin and Hobbes, specifically the scenes with the funny snow sculptures.
December 4, 2024 at 10:12 PM
geoffkrall.bsky.social
lol NY Regents: for what values is this function increasing
December 4, 2024 at 7:57 PM
geoffkrall.bsky.social
Brilliant idea from @dandersod.recursiveprocess.com to have ChatGPT create the LaTeX code which I could then mess with to get function behavior I wanted. (see 🧵)
Simpsons gif of a scientest talking to Chief Wiggum
December 4, 2024 at 7:50 PM
geoffkrall.bsky.social
Cleaning it up a bit I was able to get this beaut in just a few minutes. Thanks @dandersod.recursiveprocess.com & @mythagon.bsky.social !
Piecewise function created in latex using this code: \documentclass[tikz,border=5mm]{standalone} \usepackage{pgfplots} \pgfplotsset{compat=1.17} \begin{document} \begin{tikzpicture} \begin{axis}[ axis lines=middle, grid=both, xmin=-5, xmax=5, ymin=-3, ymax=5, xlabel=$x$, ylabel=$g(x)$, xtick={-5,-4,-3,-2,-1,0,1,2,3,4,5}, ytick={-3,-2,-1,0,1,2,3,4,5}, tick label style={font=\small}, axis equal, ] % First piece: Nonlinear curve \addplot[domain=-5:-2.1, thick, samples=100] {0.1*(x+3)^3 - 1}; \node[draw, circle, inner sep=1.5pt, fill=white] at (axis cs:-2,-0.9) {}; \node[draw, circle, inner sep=1.5pt, fill=black] at (axis cs:-2,0) {}; % Second piece: Continuous quadratic curve \addplot[domain=-2:2, thick, samples=100] {-(x)^2 + 4}; % Open circle (hole) at (0, 4) \node[draw, circle, inner sep=1.5pt, fill=white] at (axis cs:0,4) {}; % Filled circle at (0, 0) for the second piece \node[draw, circle, inner sep=1.5pt, fill=black] at (axis cs:0,0) {}; % Third piece: Goes to infinity (quadratic growth) \addplot[domain=2.1:5, thick, samples=100] {(x-2)^2 - 2}; \node[draw, circle, inner sep=1.5pt, fill=white] at (axis cs:2,0) {}; \node[draw, circle, inner sep=1.5pt, fill=black] at (axis cs:2,-2) {}; \end{axis} \end{tikzpicture} \end{document}
December 4, 2024 at 7:47 PM