Henri Picciotto

Rate of Change: No One Way! Many good teachers end up leaving the profession for a variety of reasons, often after only a few years in the classroom. Part of it, surely, is how teachers are treated in the US, as shown in Punc…

Ten approaches to slope! There is no one way.

blog.mathed.page/2026/01/23/r...

My response to an insightful post by Dan Meyer.

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book cover

Info about my book about math pedagogy (There Is No One Way to Teach Math — with Robin Pemantle), including a 20% discount until March 31:
www.mathed.page/teaching/no-...
The book addresses just about every aspect of the job, avoids oversimplifying, and suggests discussion questions for departments.

Unexpected ratio Triangle ABC is equilateral. MA/ME is the golden ratio! (George Hart showed me this result some time ago.)Vynce Montgomery pointed out that therefore, this could be a way to construct a pentagram. …

Unexpected ratio:

blog.mathed.page/2013/10/30/u...

@johngolden.bsky.social

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See some of you soon?

Nicely done! Good puzzle with lots of possibilities, as your samples show.

In my Pentomino applet, you flip by clicking on the black dot, and drag the usual way.

www.mathed.page/puzzles/pent...

You went the other way. I prefer my interface, but I'd learn something by studying how you did it

Also, if you'll continue working on this, make it possible to hide the control points, so as to get a better-looking final result.

I don't mind the kite. At least for the eight-piece square I found it's more interesting than the obtuse + equilateral option.

Eight-piece solution?

I made an eight-piece square, I think.

It would be nice to be able to flip the pieces.

@johngolden.bsky.social
Possibly useful:
www.mathed.page/puzzles/tear...
and
www.mathed.page/puzzles/tang...

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Making Algebra Click Using Manipulatives Manipulatives Make Algebra Learning Concrete for Upper Levels  Every middle school math classroom presents a unique set of opportunities and challenges. Students arrive with solid arithmetic skills bu...

The publisher of the Lab Gear materials posted an excerpt from my book on their blog:
www.didax.com/blog/making-...

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Some pundits (and some colleagues) claim we teach too much math. How do we respond? I'll share some thoughts at the CMC-North conference in Asilomar.

Algebra and Geometry for All Students!
December 6, 9:20am

I hope to see some of you there!

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oops — I'm not here very often

Always of interest! As much time as I've spent on your mathed.page there's always new-to-me stuff! I think I should be able to turn the geometric info into algebraic, just have never figured it out. Feel free to add my applet to your links if it's of interest.

And here is something from @hpicciotto.bsky.social
www.mathed.page/kinesthetics...

Sorry for the delayed response — I've mostly been out of social media.

What's worked for my dept is NOT merging algebra and geometry into the same units, but inserting algebra units in "Math 2", and geometry units in "Math 3". Likewise, distributing trig units in Math 2, Math 3, and Precalc.

Looking forward to trying out this series of lessons with my math club.

www.mathed.page/puzzles/maps/

Thank you, @hpicciotto.bsky.social , for your amazing lessons!

#MTBoS #MathsToday #ITeachMath

paging @hpicciotto.bsky.social www.mathed.page/manipulative...

Letter from a Homeschooling Mom Today, another guest post, this time from a homeschooling mom. — Henri Algebra and Geometry Greetings!   I hope this email finds you well. I know you don’t know us, but I wanted to personally…

Letter from a Homeschooling Mom who finds that my approach to curriculum works best with her son — going from specifics to generalizations, and from the informal to the symbolic, with problem solving and visual representations throughout.
blog.mathed.page/2025/10/15/l...

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Recognizing functions: from graphs, from tables, from geometry, from experiments, from function diagrams.
Free curriculum materials:
www.mathed.page/recognizing....

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Mentoring and Coaching Today, I share a guest post by Margot Schou, who I had the good fortune of mentoring at the start of her career. With her permission, I inserted footnotes with links to some relevant further readin…

Mentoring and Coaching: a guest post by Margot Schou about how we transmit teacher know-how to the next generation.

blog.mathed.page/2025/10/01/m...

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Same! I used to step out with my daughter to look at the night sky. Now that she is in her fifties, she still texts me about interesting moon and planet sightings.

A naked-eye astronomy unit for grades 4-12 I developed back in the 1970's.
www.mathed.page/look/
It was written on an antediluvian computer and hand-illustrated, but it's free!

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New issue of my newsletter:
www.mathed.page/newsletter/2...
Interdisciplinary learning, habits of mind, story tables, plus lots of links.

Subscribe! www.mathed.page/e-list.html

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Guest post by Frank Cassano and Anya Sturm: how to seamlessly integrate argumentation in curriculum and assessment.

blog.mathed.page/2025/08/06/i...

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My hand drawn mage based on an Alhambra. repeat pattern . Within this ten inch square there are lines colored with red, chartreuse, turquoise, purple and a bit of gold and black. The systems of interlocking and woven paths are kind of mind boggling and seems to have worked their way into my soul .

A close up of my drawing of the Alhambra tiling. Even in this small area there are dozens of under and oven weaving of lines. There are many shapes that are locked together.

A photo of The tiling at the Alhambra, taken by Henri Picciotto

Recently took a class that deciphered the line work in an Alhambra tiling. I decided to color and weave it, too. Then went looking for a photo of the actual wall. Hard to find! Was so pleased to find a collection taken by @hpicciotto.bsky.social posted on www.mathed.page/symmetry/spa....

Well, yes, but with the added constraint that two or three faces are Pythagorean triples. I didn't see that in that article, but maybe I didn't look closely enough.

A guided inquiry introduction to taxicab geometry for students is in Geometry Labs 9.1 and 9.6.
www.mathed.page/geometry-labs
An extended version for teachers and everyone is here:
www.mathed.page/geometry-lab...

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→ But now I wonder: is there a box with _two or three_ "pythagorean faces", _and_ a whole-number long diagonal? I haven't been able to find one. But to be honest, I probably didn't put enough time and energy into it. If you find such a box, let me know!

During a bout of insomnia, I asked myself: what should the height of a box with base 3 by 4 be, so that its long (internal) diagonal is a whole number? I found an answer, and in the morning was able to generalize it into a way to get a pythagorean quadruple from any triple. →

Oops. I posted the wrong link. Trying again.

blog.mathed.page/2025/05/27/i...

Integrating Problem Solving Seamlessly: A guest post by by Frank Cassano and Anya Sturm.

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Integrating Problem Solving Seamlessly: A guest post by by Frank Cassano and Anya Sturm.

www.mathed.page/teaching/ful...

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