Anna Blinstein

A 17-year-old teen refutes a mathematical conjecture proposed 40 years ago Hannah Cairo has solved the so-called Mizohata-Takeuchi conjecture, a problem in harmonic analysis closely linked to other central results in the field. This fall, she will begin her doctoral studies ...

cool
english.elpais.com/science-tech...

the arXiv paper:
arxiv.org/abs/2502.06137

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So many variables to consider! I would weigh the benefit of the inquiry to students (math identity, engagement, problem solving skills, curiosity) vs the cost (usually just time). And sometimes students benefit from explicit teaching after inquiry or vice versa so it's not one or the other!

I compiled all of my weekly material and parent notes for this past 10-week quarter of #mathCircle for 1st and 2nd graders at Stanford Math Circle - what a #mathisfun list of topics! It all added up to 577 pages! #mtbos #iteachmath

I also provide Khan Academy links as resources for extra practice, but that's for students to use independently, not during class. I think the skill of using digital resources independently is a good one to pick up in middle/high school.

If you don't tell the students who is correct, just that they have different answers and should talk to each other and figure out why, you end up stimulating really productive and interesting conversations between kids. This would be much harder to orchestrate without the dashboard.

As others have said, Desmos is one of the better online platforms for structuring digital investigations. I have students working in pairs and find the teacher dashboard helpful - common use case is to identify a pair with an incorrect answer and have them chat with a pair who has the right answer.

Love this! I may tweak this into a jigsaw type thing so that each member of the original group presents to a small group of peers who haven't done that topic. Trickier to assess with a rubric, but maybe more engaging??

Oooh wish I'd been that smart. Maybe next year.

I do include a few review problems on almost every homework assignment, so I've got that going for me, which is nice.

Nothing like desperately making review worksheets at 10 pm on a school night to bring out people's helpful sides!

Follow up question - ideas for fun or creative ways to review? #iteachmath

I'd love to see your materials! This is a weird Alg2 class I'll be teaching again next year for a few very advanced 8th graders. It only meets 3 times per week and has to fit IB specifications so I'm always looking for projects and other ways to hit multiple content objectives while still being fun.

Dope! Thank you!!

Both were super helpful - thank you!!

Cool format! Love the emphasis on justification, not answers.

Does anyone have an Algebra 2 end of year review they wouldn't mind sharing? It's my first time teaching Algebra 2 in over a decade and I would love to have a starting point - thanks in advance! 🙏 #iteachmath

Besides the IM curriculum for A1/G/A2, what are other good problem-based math curriculum for HS? Ones that follow the experience first, formalize later model. I also know of Math/Stats/Calc Medic.

What else is out there?

I believe it was @lenadarnay.bsky.social and Ryan Murray, my colleagues from @keepinlearning.bsky.social who suggested we do the show. We talk about this topic often at our house and it’s particularly controversial for me, which you’ll understand if you listen!

Can you use a goal-setting structure where one of the goals come from them and one from you? Sounds like they may also need coaching to make their goals more quantifiable and actionable (or at least connected to actions under their control).

I limit critique by connecting feedback to the areas that they've identified they want to improve or grow in. Do you find that PSTs that are really confident in their practice are still able to identify areas for growth?

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I would show it just to see their reactions... These are 7th and 8th graders so probably can't pump them full of caffeine, unfortunately.

a woman sitting on a couch with her hand up and the words nailed it written below her ALT: a woman sitting on a couch with her hand up and the words nailed it written below her

Thank you for the help - you rock!

Oh, I wasn't as smart as you. I just wrote out the expression for C(n,2) and generated the first few terms of v_4 and saw they were the same. Your way is better :)

Totally makes sense now! And now I see how you get from f = e - v + 1 to the final formula n C 0 + n C 1 + n C 2. This is very cool - thank you so much!

That's cool!! I still feel like I'm struggling with how to use Euler's formula to generate the rule in terms of n, just for the original problem. So in the explanation below, what do v_3 and v_4 represent and why is 2e = 3v_3 + 4v_4?

What do you think is the source of their discouragement? I think it can be really hard to prioritize suggestions or things to work on when it feels like there are too many things to fix. Do you feel like they know their strengths and how to build from these?

I'm not that surprised!! Great job! 🥳🥳

Number of intersections is just the triangular numbers, which is chill. The connection to Pascal's triangle is more unexpected, but could be cool. Unfortunately, I don't think I understand the connection to Euclid's characteristic well enough myself to go down that path.

That's a long video! I think I know how I want to introduce the problem (max number of pieces when cutting a pie), but I'm still deciding what follow-up questions to ask. I might have them look at number of intersections or connections to Pascal's triangle, 3D for a few who want a challenge.