Hidden Figures – Info for Teachers

Hidden Figures comes out today. I haven’t seen it, but I fully expect it to become my new favorite movie. I have a ticket for 4:15 this afternoon. It was the soonest I could possibly make it.

The bite sized version is this: You know John Glenn because he’s a famous hero – I certainly don’t want to discount his achievement as being the first American to circle the globe in space, but he was only able to do it because of KATHERINE JOHNSON AND THE BLACK FEMALE COMPUTERS AT NASA. 

You should learn about them. Then you should talk to your students about them so they can also learn about them. You should read this book.


Here are some resources to help you learn more about this if you don’t have time for the book. Also, go see the movie.

NASA Resources h/t Norma Gordon

Popular Mechanic’s The True Story of ‘Hidden Figures’ and the Women Who Crunched the Numbers for NASA

NPR’s The Hidden Figures Who Crunched the Numbers in the Space Race

NY Magazine’s The Hidden Black Women Who Helped Win the Space Race

About Katherine  Johnson

About Dorothy Vaughan

About Mary Jackson

Trailer with interviews

Have more good sources? Add them in the comments and I’ll link them here.

Ms. Perkins is the Grinch: Denying My Students Flexagons

I did a bad thing. I showed kids something awesome, and then I got mad at them when they tried to do the awesome thing. In hindsight, I feel pretty crappy about it.

Knowing students were going to be nuts the week before break, I assigned projects in the hope that they could be nuts, but hopefully get their work done amidst the complaining and excitement and fear about break coming. Students were to calculate the trajectories of Angry Birds. “Fun!”, I said. “Hooray!” I declared. Boring. I thought. Vomit. I felt. But I have to make sure they can compare quadratic functions, and this project summed up what they needed to know pretty nicely.

The day before break, I like to do something fun, so I bust out hexaflexagons. Although students had plenty of time to get their projects done, some weren’t finished, so this seemed a perfect solution: students who needed the time could work on their projects, and students who finished get to do fun stuff. That’ll teach ’em to procrastinate! Like I don’t do that every day. What a moron/jerk I am.

Before I give students work time, I show them Vi Hart videos about flexagons, and jaws drop. I show them fabric flexagons I’ve made, and there is a scramble to get to play with them first. I explain that you can make a flexagon with as many sides as you like, but I haven’t succeeded in engineering a 12 sides one yet. I do have the template. I show them. Students are chomping at the bit to make their own. Then I dropped the hammer. If you’re done with your project, you get to make flexagons. If you aren’t, you have to finish your project. No fun for you!

It didn’t seem like I was being mean at the time. I was annoyed with students who hadn’t used their time in class before now, but I wanted them to have a chance to finish the project. To show what they know. So I let them use this time to get it done. Tried to be the nice guy. They could ask questions of me and their peers, and get the project done, and the rest of the students would be happily working away at flexagons. The perfect solution.

I flutter around the room, helping students see symmetries and guiding them in folding their first flexagon, gleeful over how happy students are figuring this out. Clapping with joy when a student makes an interesting design to suit the transitory nature of flexagons. Marveling at how their brains make sense of the work.

Then a student who was finishing their project called me over for help with a quadratic equation, and in my head I groan. Uuuuuuugh, I’ve shown you this 10 times, I think. But off I go, wanting them to learn. Trying to be helpful. But really, I was just eager to get back to flexagons. Thankfully, a flexigator would need me next and I could go back to being happy. But then someone couldn’t identify a vertex and I would slump my shoulders, hang my head, and drag my feet to go help them do the boring stuff again.

The moods of my students mirrored my own. Those working on “work” were miserable and panicky and hated that they couldn’t figure it out. Or they hated that they could figure it out, but would much rather be making flexagons. Students working on flexagons were happy and engaged and even though they got frustrated, they were so relieved and joyful once they succeeded. Students who finally got their quadratic equation weren’t joyful. They were just grateful it was over.

This was supposed to be a “fun” project. Except that it wasn’t fun. I didn’t care about it except that I was pleased it was a “real life” application of quadratics that seems intuitive to students. A colleague of mine presented it to me, and she genuinely seemed to enjoy it. Was happy about it. I bet her students felt that. I bet they liked it more. I’m ashamed I couldn’t bring that enthusiasm to my students. I’m ashamed I didn’t push to find out why my colleague enjoyed it so much. The premise of the project is fine. It nicely summarized things students learned about quadratics, but my “enthusiasm” for the project was fake and my students can always tell.

Now it’s break and I have all this free time. I wake up, make some coffee and assess my options. I could grade those projects, or I could quilt an impossible triangle. I could  enter grades, or I could make an origami icosahedron to hang on my Christmas tree. Needless to say, I have not finished grading projects, but I do have a lot of new mathy art in my house.

So why am I making my students pick the boring thing? Why am I requiring it? Because the standards say:

  • Students are able to write a quadratic equation given two points.
  • Students are able to identify the zeroes of any quadratic equation.
  • Students are able to do boring stuff and I have to teach it to them because I have to.

I genuinely do love teaching. I love seeing students get it. I love watching them help each other get it. I really wish that the standards were different. I honestly think the skills making flexagons are important. Here are the flexagon standards:

  • Students are able to measure accurately.
  • Students are able to identify and create congruent triangles.
  • Students are able to plan ahead.
  • Students are able to identify and create symmetries. 
  • Students are able to notice and describe patterns. 

We want students to be able to do these things! I’m not wasting time when we make flexagons. I get so frustrated that I have to teach things few students care about when I could be teaching good things and both I and my students will be happier for it.

But I’m not in control of the standards. (At least not yet.) So given what I have to work with, and given that I do want to teach and I do want both my students and me to be happy, here’s the plan.

  1. Never again will I introduce amazing math and deny that option to students. I am frankly pretty shocked at myself that I would show students flexagons and then tell a student they weren’t allowed to make one. I did that. I remember the look on the students face. They were so sad. This ranks pretty high on my list of horrible, regretted teaching moments. I will find time after break to make it up to my students. They all should get a chance to make flexagons. Shame on me.
  2. Even though the standards can be boring, find something in them that I care about. Students pick up on that. They know when my enthusiasm is real and when its fake. I love patterns – fall back on that when necessary, because it’s freaking everywhere in math. I should’ve made a bigger deal about the symmetrical patterns in quadratics. I shouldn’t have given up on this project. I could have pushed more for myself to find the things that I love in it. I could have made less of a deal about averaging the roots and more of a deal about logically where the bird would fall if it started here and reached a maximum height here.

We all fail sometimes, but this was a big one for me. I screwed up, and I need to own that. Now I’m going to go make myself feel better by decorating cookies after my favorite proofs.

Seeking Inspiration

It’s December. My students are nuts. No joke, yesterday I had a student tell me he might throw up. I asked if he needed to see the nurse, was he okay? He said he’d probably be fine, but he probably shouldn’t have eaten soap after his friend dared him. You can’t make this stuff up. We’re all in the long, slow slog to winter break and I feel like I have to pull teeth to get them inspired about math.

On my way home from work I was mulling this over and tried to recall when I was most happy at work recently. It hasn’t been too often. What I came up with had a pretty obvious common element. See if you can spot it.

-I was happy when I asked #mtbos about complex numbers and learned a ton of new-to-me information about what the complex plane is. Sharing that with students who peppered me with incredulous questions and mind-blown expressions was awesome. Loved it.

-I was happy when my geometry class got into a fight over whether 2√2=√8 was true or not.

-I was happy when I saw some students put together that three different quadratic equations were related to the same graph.

-I was happy when, during a number talk, a student came up with a totally wrong way to get the right answer and it took us several minutes to figure out what the heck had happened.

-I was happy when, rather than lecturing a student who has missed class and done a terrible job on homework, I just started going through examples with the student and found myself enjoying it.

-I was happy when tracking Jill Stein’s fundraising and attempting to guess what function would fit it best.

-This past year, I was happiest when I saw and did for myself the derivation of an explicit formula for the Fibonacci sequence.

Can you spot it? Subtle, huh? I FLIPPING LOVE MATH, and I am happiest when I am discussing and doing interesting math with my students. I am miserable when I’m fighting behavior and grading boring assignments.

There’s a pretty easy fix for this: Don’t give boring assignments and give students math that is interesting and helps to quell the behavior because they want to do the math. That is clearly easier said than done, but it’s pretty easy to motivate me to work for it because I’m clearly so much happier for it.

So if you have mathematically fun and inspiring things, please send them to me. Here are a couple to get you started thinking:

-A complete Venn diagram (all intersections accounted for) can only be rotationally symmetric if the number of sets is prime. WHAT!?!? That’s insane. Here’s an 11 set venn diagram and the shape of one of its sets. (Took the pictures at Macalester College, not sure of the artist-mathematician)

-Apparently ln(1) is complex. Don’t totally get this one yet, but goodness gracious am I totally into figuring it out. (If you get it, don’t ruin it for me.)

The Election, Trump, & My Students

The difference between Tuesday at school and Wednesday at school was incredible and heartbreaking.

On Tuesday, I had kids in my classroom. They were worried about their crushes, the quiz on Friday, what their clothes look like.

On Wednesday, no one joked. No one smiled. No one laughed. Some cried. Many expressed their fears. Some expressed frustration that “people were stupid enough to think this wouldn’t happen. Of course it was going to happen.” Continue reading “The Election, Trump, & My Students”

Quick, Impactful, Awesome: Post Math Norms

I recently posted Jo Boaler’s 7 Math Norms in the front of my room, and I’m in love with it.jo-boaler-posters

I regularly tell students that “mistakes are helpful, we need them”, and while the message eventually gets through, it is SO MUCH MORE POWERFUL  when I say it while pointing directly at the norm “Mistakes are valuable”. Students know I’m not just covering for their mistake in front of their friends. I took the time to print and post these things – I really mean them. Continue reading “Quick, Impactful, Awesome: Post Math Norms”

So I guess I teach HS now…

I got an email reminder, per the suggestion of Sam Shah, about my goals this year, and one of them is written reflection for myself. So here goes.

I’m now 3 weeks into teaching HS and it’s… mostly really good. I feel good going to work, I feel good when students are in my room, I generally look forward to each day. Still, there’s a lot of adjusting to do.  Continue reading “So I guess I teach HS now…”

Math On A Stick, Part II: Stepping Stones, Parent Talk, Teacher Lessons Learned & Mathematical Depth

Part I here.

After the phenomenal time I spent last weekend at Math on a Stick, I signed up for 2 more slots this week – making a total of 4 for this year. Here are some more stories about why it’s so great and then some teacher musings.

The Stepping Stones

math on a stick stepping stones.jpg

Math on a Stick is blessed to have Max Ray-Riek and Annie Fetter as volunteers, and while I have sadly missed working with Annie this year, I have gotten to spend a fair amount of time there with Max. He is extraordinarily awesome.


‘Twas Wednesday evening when Max came over to tell me he’d just had a great experience at the stepping stones with a mom and daughter. I hope he’ll write up his version of events, because I came in only halfway through. Anyhow, he told me this girl was so excited about them that he’d exhausted the problems he usually uses (count by 2s; 23 minus 24, etc.). They even counted PRIME NUMBERS on the stepping stones. They also did it in an awesome way. They figured out which stones they would not step on if they were skip counting, and stepped on those! (Mom did a lot of carrying her daughter between stepping stones that were too far apart.) Awesome!

Continue reading “Math On A Stick, Part II: Stepping Stones, Parent Talk, Teacher Lessons Learned & Mathematical Depth”

A Question on Language and the Mathematicians project

I often feel very odd speaking about this project in the negative:

The project is about not white male mathematicians.

Part of me enjoys the bluntness of calling out the issue as starkly as that, and part of me likes honoring that “not white dudes” is how the student who sparked the whole thing put it.

That said, I can also acknowledge that if I want this project to be open and inviting to as many people as possible that perhaps putting it in a positive sense…

The project consists of mathematicians with an oppressed identity.

…might put less people off. 

(Note: I’m stealing that language from Jonathan Osters. He put together a beautiful write up for his students which you can see here.)

I would appreciate any thoughts you have on this. My goal has never been to prevent my students from learning about white-male mathematicians. It’s just that they will learn about white-male mathematicians if they happen to learn about any mathematicians at all. They will likely not learn about any others unless we make the conscious decision to include them.

Please add any thoughts you have in the comments. Thanks!