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Jed

@jedediyah.com

830 followers 790 following 490 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 · 15h

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 · 18h

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 · 1d

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 · 1d

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 · 2d

Ain't no way this is real

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Jed @jedediyah.com · 2d

👀

Jed @jedediyah.com · 2d

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 · 2d

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 · 2d

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 · 3d

Venn diagram worksheet colored with pencils.

Jed @jedediyah.com · 3d

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 · 4d

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 · 4d

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 · 5d

As an example of pernicious feedback loops and manipulating data.

Jed @jedediyah.com · 5d

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 · 5d

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 · 5d

Vibes

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Jed @jedediyah.com · 6d

💯

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Jed @jedediyah.com · 6d

Yeeeeeees

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Jed @jedediyah.com · 6d

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

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Jed @jedediyah.com · 6d

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?

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Jed @jedediyah.com · 6d

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 · 6d

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"...

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Jed @jedediyah.com · 6d

"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 · 6d

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

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