Lightnews — Scholar-powered news

Jed

@jedediyah.com

830 followers 790 following 480 posts

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

jedediyah.github.io

Posts Media Videos Starter Packs

Pinned

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

1 9

Jed @jedediyah.com · 14h

👀

Jed @jedediyah.com · 14h

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 · 15h

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 · 15h

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.

1 2

Jed @jedediyah.com · 1d

Venn diagram worksheet colored with pencils.

Jed @jedediyah.com · 1d

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: ...

2 1 6

Jed @jedediyah.com · 2d

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.

1 3

Jed @jedediyah.com · 2d

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 · 3d

As an example of pernicious feedback loops and manipulating data.

Jed @jedediyah.com · 3d

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.

1 2

Jed @jedediyah.com · 3d

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

Jed @jedediyah.com · 3d

Vibes

1 2

Jed @jedediyah.com · 3d

💯

1 2

Jed @jedediyah.com · 3d

Yeeeeeees

1 1

Jed @jedediyah.com · 3d

Thinking about cultural as well, i.e., A Mathematician's Lament

1 2

Jed @jedediyah.com · 3d

Nice. Very reasonable. Several of these eras are connected with some significant publications, e.g., some of the standards documents or some of the responses.

Any particularly influential publications in your view?

3 2

Jed @jedediyah.com · 3d

Suggesting the machines will display "evidenced-based effective pedagogy" is speculative at best, and completely unreasonable to assume. Oh as I keep reading, I see it is all speculation about the best case outcome hoped for, and not a description of reality.

Jed @jedediyah.com · 3d

So professors (real ones) will meet with the same number of students, but just all day long instead of all at once, so that they can build personal relationships with them.

Based on large language models?! Uh oh.

"Learning styles"...

1 1

Jed @jedediyah.com · 3d

"AI professors" aren't professors. Classic "AI [thing a person is]"

It sounds psychologically dubious that we should make them as realistic as possible. Why anthropomorphize machines SO intensely? Just call them something accurate instead of pretending they are people.

Jed @jedediyah.com · 3d

You are explaining history of math education to a new teacher. What significant events, publications, background do you include?

E.g.:
1920 - NCTM Founded
1957 - Sputnik
1958 - New Math
1973 - Why Johnny can't add
1981 - MAA report on recs
2010 - CC standards

#ITeachMath #mtbos #mathed #math

11 3 9

Jed @jedediyah.com · 5d

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.

1 5

Jed @jedediyah.com · 6d

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.

Reposted by Jed

robertfathauer.bsky.social @robertfathauer.bsky.social · 6d

I just finished a new website on fractal self-replicating tiles ("reptiles") based on polyominoes, polyhexes, and polyiamonds: www.mathartfun.com/fractaldiver...

2 12

Jed @jedediyah.com · 7d

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.

2 7 26

Jed @jedediyah.com · 7d

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.