@KarenCampe@mathstodon.xyz
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KarenCampe

@KarenCampe@mathstodon.xyz

Math teacher using technology for understanding • Connecticut USA
Reflections & Tangents blog: https://karendcampe.wordpress.com
#MTBoS #iTeachMath #T3Learns

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DavidKButler, to random
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Taught my daughter C how to factorise quadratics today by focusing on the sum coming out to the coefficient of x before the product coming out to the constant term. It worked extremely well.

KarenCampe,
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@DavidKButler @hpicciotto
David, so if I understand correctly, to factor x^2 + 8x + 12, you focused on addend pairs that make 8 first (& checked which pair multiplies to 12) instead of listing factor pairs of 12 first (& checking for sum = 8)?

KarenCampe,
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@DavidKButler @benleis @hpicciotto
I'm very intrigued.
My initial reaction is that the factor pairs seem like a smaller set vs the addend pairs.
But... I need to dig in more WRT negative b and c values.
So back to my example x^2 + 8x + 12.
12 has 3 factor pairs 1•12, 2•6, 3•4 but then there are various combos with negatives.
8 has 3 addend pairs of both positive 1+7, 2+6, 3+5 but many more if we include negatives (depends on c)
So... I feel like factor pairs are limited but addend pairs not. If a student doesn't know divisibility &/or if the c value has many factors then looking at b addend pairs is useful. (But we always look at b to get clues for which factor pairs might be useful)
Hmmmm...

KarenCampe,
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@ColinTheMathmo @DavidKButler @benleis @hpicciotto
Colin, I've been saying "Try and revise" instead of "Guess and Check"

fractalkitty, to random
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Is anyone up for a zoom or chat that has submitted to JMM art exhibition before? I'd like to submit this year and am unsure of what it's like. JMM2024 will be my first one.

KarenCampe,
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@fractalkitty have you checked with @PaulaKrieg ? I don't think she's here, but message her on tw...

divbyzero, to random
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I couldn't get my Apollonian gaskets post to go through yesterday. Today I woke up to find that it did... twice.

KarenCampe,
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@phonner @divbyzero @christianp
Yes !
I was trying to search for an old post from July, that had been inspiration for my newest blog post (Area Arrangements, published today, please read! It's an entry for SoME3) and had to be very patient until the server was ready to cooperate 😉

johncarlosbaez, (edited ) to random
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"Stock and flow diagrams" are a nice graphical tool for modeling systems. People have had success teaching them to students starting at a young age. It's a way to teach them math, economics, ecology, and other subjects in a unified way.

When you include functions describing the flows - shown as faucets here - you can turn these diagrams into differential equations. But you don't need to do that for young kids: there's a lot you can learn from these models in a purely qualitative way. Basic concepts like feedback, etc.

And once you introduce the flow functions, you can let software solve the resulting differential equations and graph their solutions even before the kids know anything like the definition of derivative! This is a good way to gently get them interested in calculus.

For example, below you can see a model of reindeer population on an island created by middle school students. The population soared and then crashed:

"Students built System Dynamics models to study human population dynamics, non-renewable and renewable resource utilization, economic influences, etc. In these lessons students were asked to build the model, anticipate model behavior, explain discrepancies between anticipated model behavior and actual model output, analyze feedback, then test policies on the model to determine leverage points."

For details try this:

• Diana M. Fisher, Systems thinking activities used in K-12 for up to two decades, https://www.frontiersin.org/articles/10.3389/feduc.2023.1059733/full

(1/2)

KarenCampe,
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@johncarlosbaez my school district's gifted program is centered around systems thinking from 3rd - 8th grade. It is "pull-out" for 3-5, then replaces social studies class from 6-8. Wonderful approach with lots of deep learning and frameworks for making connections. Not at all connected to math but very impactful program.

KarenCampe,
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@johncarlosbaez "pull-out" class means that the gifted students get pulled out of regular classes (usually during something other than reading or math) to go to the challenge class. So it is an add-on to the rest of their classes, not a replacement.

christianp, to random
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I'm trying out the new @desmos geometry tool beta: https://www.desmos.com/geometry-beta
I know they put a lot of effort into accessibility, so I tried to use it with just my keyboard. It's good!
I also like the interface for applying transformations: you select a transformation, then its action is shown while you select objects. You can repeat previous transformations from the same menu.
The biggest improvement over geogebra's interface is not giving names to every object, and collecting them in nice groups! So much easier to work with.

KarenCampe,
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@christianp @desmos yes the new tool has some good power!!
Btw, you can turn off the labeling of all new objects in GGB.

KarenCampe,
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@christianp aaah I don't think you can stop the platform from "naming" all the new objects. I usually hide that algebra panel when I'm doing geometry work, unless I need to find some particular item's name to use in a calculation or transformation or conditional.

bengrantmath, to random

I’ve heard that Mathstodon supports LaTeX… is this true, and if so, is it supported on mobile?

KarenCampe,
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@ngons @bengrantmath yes! I just added the Mathstodon.xyz page to my phone Home Screen

Sheril, to science
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Happy birthday Rosalind Franklin!

Rosalind Franklin’s research was crucial to discovering DNA’s double helix structure. But she never received proper acknowledgement for her contribution.

James Watson & Francis Crick were awarded the credit & Nobel Prize, but their work was only possible bc they saw her unpublished data & X-ray diffraction images. https://www.nytimes.com/2023/04/25/science/rosalind-franklin-dna.html?smid=nytcore-ios-share&referringSource=articleShare

KarenCampe,
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@Sheril I recently read "The Exceptions: Sixteen Brilliant Women at MIT and the Fight for Equality in Science" which includes Rosalind Franklin's story.

samjshah, to random

@kdykema welcome to mathstodon!!! I’m only just getting used to it but let me know of you need any help! Lots of math teachers are on here ready to help (and… of course… geek out about math)

KarenCampe,
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@kdykema @samjshah
Kevin, I've been using the ice cubes app, and it warms my heart to see "34 new posts" or similar each morning.
Did you know you can "follow" a hashtag here? Search for or or whatever, then click on the search result, then click on the "follow" icon. That way you'll see all posts with that hashtag in your feed.

KarenCampe, to random
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I've added one more thing to my newest blog post "Shout Out for Squares!"

It's the "dividing a square into rectangles" discussion that happened here a few months back, with @johncarlosbaez and @Mathforlove highlighted. THANKS!!

https://karendcampe.wordpress.com/2023/07/13/shout-out-for-squares/

KarenCampe,
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@johncarlosbaez @Mathforlove
Always!! I'm team inclusive.
To be fair, they are more useful once students have had some experiences with the different categories. I consider the inclusive def to be an "upgraded" definition that shows more connections.

ablinstein, to random

Working on Exeter Math 2 problems - is there a more elegant solution to problems 53 and 54 that I'm missing?

@druinok @benleis @jclevelandtran

Here's a link to my work: https://docs.google.com/document/d/1BfPa5wIIgPIx7BF_VNYZ8AohLVwD8H6Pdp8psW9CfV0/edit

Original problem:

KarenCampe,
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@ablinstein @benleis @druinok @jclevelandtran
Ben, YES! The AM-GM inequality is so cool. There's also neat instances of harmonic mean that show up in Algebra 2.

KarenCampe,
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@ablinstein @benleis @druinok @jclevelandtran
Here are some cool diagrams/constructions of the means.
1st diagram from wikipedia, read the ALT text, very interesting.
2nd diagram I think from Jim Wilson, again read the ALT text.
I have an article will link in next post.

Given: An isosceles trapezoid with parallel sides of length a and b. Let a < b Construct parallel segments to the bases as follows: GREEN: A parallel segment through the intersection point of the two diagonals (HM=harmonic mean) DARK BLUE: A parallel segment that divides the original trapezoid into two similar trapezoids. (GM=geometric mean) RED: A parallel segment through the midpoints of the slant sides. (AM=arithmetic mean) LIGHT BLUE: A parallel segment that / N divides the original trapezoid into two equalareas. (RMS=root mean square)

KarenCampe,
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@ablinstein @benleis @druinok @jclevelandtran

Here is an article by Jim Wilson about using the means in problem solving:

I myself noticed the Harmonic mean showing up in "Work" problems (if I paint a room in 4 hours and you do it in 6 hours, how long for us to do it together?)
https://www.dropbox.com/scl/fi/e149t8navcblsmpbm70qk/Using-the-AM-GM-Inequality-in-Problem-Solving.pdf?rlkey=nlpop350a3wepipfmcltj2ngp&dl=0

KarenCampe,
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@ablinstein @benleis @druinok @jclevelandtran

And here's links to the fabulous Cut-the-Knot website with articles on the geometric meaning of the geometric mean and the harmonic mean.

https://www.cut-the-knot.org/pythagoras/GeometricMea
n.shtml

https://www.cut-the-knot.org/triangle/HarmonicMean.shtml

And I'm sorry for blowing up your notifications, but I get very excited about the geometric and other means!!! (I might need to write a blog post about it!)

KarenCampe,
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@druinok @ablinstein @benleis @jclevelandtran

Who knows when I'll get to a blog post, so in the meantime:

Calling @Chartodon

ColinTheMathmo, (edited ) to random
@ColinTheMathmo@mathstodon.xyz avatar

So "splooting"(*) is face down ... what is it when one lies spread-eagled face up?

(*) https://en.wikipedia.org/wiki/Splooting

KarenCampe,
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@ColinTheMathmo @benleis
😂🤣

samjshah, to random

I think I’m going to start reading math teacher blogs again. But so many of the ones I used to follow have become fallow —so I’ve deleted them and now I have almost none left. Maybe I’m one of the few left (and I know I’ve posted very little since the pandemic started).

Do you still read math teaching blogs?
Do you still write a math teacher blog?

I’m throwing together a very simple spreadsheet looking for blogs/people to follow! I’d love if you add yourself or anyone you read!

https://docs.google.com/spreadsheets/d/10Wfulfw1wq17y8oNBDBLGv3EPh2L7OORFLMQLacWPZU/edit

KarenCampe,
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@samjshah

Here are some math ed folks I subscribe to that are outside of US:

Amie Albrecht @nomad_penguin
Wonder in Mathematics https://amiealbrecht.com/

David K Butler @DavidKButler https://blogs.adelaide.edu.au/maths-learning/

Jo Morgan mathsjem on TW
https://www.resourceaholic.com/

John Rowe How I Teach Maths
https://mrrowe.com/

Craig Barton mrbartonmaths on TW http://www.mrbartonmaths.com/blog/

Colin Foster https://blog.foster77.co.uk/

Miss Konstantine @giftedHKO https://mathshko.com/

KarenCampe,
@KarenCampe@mathstodon.xyz avatar

@samjshah AND one of my favorites is Paula Krieg's https://bookzoompa.wordpress.com/
Paula is a paper artist who is always looking for the math-y angle on things, so much of her blog is concerned with the intersection of paper arts with teaching math concepts.

She is currently doing a series on tangrams.

KarenCampe,
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@samjshah How did @benleis get overlooked?
He writes Math Off the Grid at https://blog.mathoffthegrid.com/

KarenCampe,
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@samjshah Also Nat Banting and Christopher Danielson and Ben Orlin. They don't blog incredibly frequently, but I want to hear what they have to say when they say it.

KarenCampe,
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@samjshah
Another great source which isn't a blog but is a weekly newsletter sent out by Chris Smith in Scotland. He is aap03102 on TW and you can sign up by emailing that handle at gmail.
Problem of the week and other math-y things in your inbox on Fridays.

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