June 15, 2019

Following a Pattern

After making a few more math play mats I returned to the other pattern I was working on. (By the way, surface crochet works great! So I set up an info/order page here.) The project requires making lots of squares and then eventually joining them together. Since I was going to be repeating the same pattern so many times (42!) I decided to write it on paper so I didn't have to pull the pattern up on a device every time I took out my yarn, and also so I could make it clearer.

These are the squares I've crocheted so far. Lots more to go!
The pattern is freely available from a well known site. Lots of people have used it. It's completely accurate, but it reads like this:

Rnd 6: Slip st in next dc, ch 4 (counts as dc, ch 1), * (dc, ch 3, dc) all in next ch-3 space, [ch 1, skip next dc, dc in next dc, ch 1, dc in next ch-1 space] twice **, [ch 1, dc in next ch-1 space, ch 1, skip next dc, dc in next dc] twice, ch 1; repeat from * around, end at **; ch 1, dc in next ch-1 space, ch 1, skip next dc, dc in next dc, ch 1, dc in next ch-1 space, ch 1; join in 3rd ch of ch-4.

Even if you don't know how to interpret ch as chain, dc as double crochet, and st as stitch (or what any of those look like as a series of loops on a hook), you can still see that there are parentheses, brackets, and asterisks to navigate what gets grouped and repeated. Do you know what that entire paragraph is saying? All the way around the entire square I'm supposed to alternate a tall stitch (dc) and a single loop (ch) that will create a space between the tall stitches. That's it! So I rewrote it as:

Rnd 6: Slip st in next dc, ch 4 (counts as dc, ch 1),
In each corner: (dc, ch 3, dc)
Around the edges: ch 1, skip next st, dc in next st or space

The original instructions aren't wrong. They tell me exactly what to do every step of the way. I don't mind brackets or asterisks in patterns in general, it's much easier to be told to repeat something than it is to keep track of where I am on a long list of stitches. But my version is even easier to keep track of. Because I understand what I'm doing, I have easy to reference landmarks, and I just don't need that level of detail.

Why is the original so complicated? The previous round was worked in groups of 3. So when you're working groups of 2 into groups of 3 sometimes you land on a stitch in the middle of the group and sometimes you land on a space between the groups. Sometimes that matters, but here it really doesn't, I do the same steps to make my stitch either way and it just makes it easy to lose track of where I am when they specify the difference. Also, you don't start on the corner so you have to say "do this little bit of the side, then a corner, then a whole side, now repeat from the corner, but stop before you finish the last side because you already did a little bit of it at the beginning." My rewrite assumes you're looking at your square as a whole piece and can identify corners as well as deduce where to stop so you end up going around exactly once.

Why am I talking about crochet patterns on a math education blog? I'm sure you've already drawn parallels. It's tempting to give kids precise instructions that help them navigate every little difference they might encounter, that way they're sure to get it exactly right! But at what cost? Providing every little step means we lose track of the big picture. It's so easy to skip a step when we don't understand what it is we're trying to accomplish. And if this problem were a little different (in my case if I wanted to change the design to be a larger square or a rectangle) the hyper detailed instructions are useless and we have to start from scratch. When we're asking kids to follow a pattern, let's be sure to point out the landmarks as we go. Because that's what will help everyone navigate when they're on their own - which is absolutely my goal.

June 2, 2019

Math Play Mats

In March I'd bought some yarn and was looking up crochet patterns. I came across fiddle mats for people with dementia. I wondered whether my friends with toddlers would like such things, and then I wondered if I could make it a mathematical play thing. Turned out I could! A math play mat includes a ten frame, a rekenrek (or is it a pair of rekenreks?) and a pocket full of felt shapes. My beta testers have found lots of great ways to play, and made one request for a change to version 2.

I'm so glad I made these because I got to play math with littles. I learned that I am sorely lacking giggles in my life. I played on the floor of a conference center, at a cafe, and in a living room. So I can attest to the fact that these are great portable toys. Soraya, Jenna, and I played for almost an hour and only stopped because we wanted to go to the park before it rained. She played more, and in different ways the very next day. I love it when the best case scenario you imagine is surpassed by reality!

The things they've played:
  • Match my shape. 
  • Sort all the shapes.
  • Name my shape. (Some are standard shapes but others are flowers or snowflakes. Which leads to - what's the difference between a flower and a snowflake?)
  • Can you find a ____? (Green shape? Square? Green square?)
  • Put things in the pocket and take them out.
  • Move the beads so the top row matches the bottom.
  • Count the beads.
  • Count the shapes.
  • How many ____? (Count, cover, how many are hidden? How many more to fill the squares?)
  • Comparisons (are there more purple or green?)
  • Decorate mom with the shapes.
  • Put the shapes in the ten frame.
  • Make a pattern in the ten frame.
At one point Soraya made a joke that turned into a pattern. She announced she was going to make groups of four. So she put one shape down in the ten frame saying “one.” Then she put another shape down and said “four!” And giggled. This small human who's still working out how the numbers go after 10 knew full well that saying four after one was unexpected and would make us laugh. So of course Jenna and I laughed! And Soraya continued saying one then four until she was laughing so hard she couldn’t talk. It was adorable, I'm grinning just remembering it. And it gets better! When we recovered from laughing, Jenna and I got instructions to make new number patterns. I was supposed to say one, then say fifteen, as I put shapes in the squares. Jenna and I started strategically picking shapes to go with the numbers we were supposed to say (like green for one and yellow for fifteen). Soraya picked up on what we were doing and made lots of rules.

The one complaint: 
Jenn's kiddo, Z, kept asking her to cut off the beads so she could make more patterns. While I won't remove them entirely, because I'm confident eventually Z will find cool things to do with them, I do want to make them less floppy so they won't get in the way. Added bonus: they're currently made by threading beads onto braided yarn which is omg so tedious. My upgrade is to use pipe cleaners which will make my life so much easier! Plus it's easy for adults to take the pipe cleaners off the mat if anyone else demands it and then put them back later.

Can you see the concentration? These people are doing math. (Z, Soraya, and Shelby's kiddo)

I would love to see what happens with these toys at different ages. The difference between an almost 3 year old and an almost 3.5 year old was noticeable (yes, I know, tiny sample size). While I'm no expert in the trajectory of learning to count, I have done enough reading about it to know that the answers to all of these questions are different:
  • Can they count the shapes in a pile? 
  • Can they count the shapes organized in a ten frame? 
  • Can they count the beads by pointing to each one? 
  • Can they count the beads by sliding each one?

Seeing where kids are and how they grow is so fun. Another place for growth was one kiddo could find me a square, and could find me a green shape, but finding a green square was too much. I hadn't thought about how much harder searching for two characteristics simultaneously was until I was gifted a green shape that wasn't a square!

Fave tweet:

So what's next? I'm definitely going to try the pipe cleaner method for the rekenreks, and I'm playing with different methods to get the ten frame on there because sewing isn't my favorite and I'd like that part to look cleaner. If I can come up with a quick way to outline the ten frame and attach the rekenreks then I'd love to make a whole bunch of these and bring them to something like toddler play time at the library. I could also send them to you, dear reader, if you have a kiddo in your life, a classroom full of them, or you're a kid at heart. Because lets be honest sensory play with felt shapes is fun for everyone! I do recommend playing together though, as the potential for giggles is much higher. And we could all use more giggles in our life.

May 18, 2019


Last February I left teaching and started working for Illustrative Mathematics. It's been an amazing opportunity to think deeply, collaborate with fantastic people, learn new things, and build a product I'm immensely proud of. More units have been released since our initial preview, go check them out! https://curriculum.illustrativemathematics.org/HS/teachers/index.html

One thing I got to learn at IM was how to code images using tikz. Who knew all those "graphing a picture" projects in Desmos would turn out to be so useful? Not only can I generate a stick figure, my code is so fancy it's easy to move the arms around to recreate the entire semaphore alphabet. So cool right?? (This is where you nod and say, "Sure Tina..." while waiting for the point of this post.)

Another thing I learned about while working at a non-profit was the grant process. And this post is a riff off of the RFP, Request for Proposals. Since the HS curriculum will be finalized in June I'm looking for a new job. I have some ideas, but I know that the collective mind of this community will help me dream up things I can't even imagine. The more I learn the more I realize that this world is filled not just with jobs, but entire careers, that I never even thought of. So I'm asking for your help.

As I've mentioned before, during my reading of Dare to Lead I identified my values as community and making a difference. So I'm holding those two ideals close as I consider possible paths. Community means a variety of things, but it includes my family, so I'm restricting myself to jobs I can do remotely or locally. Other than that I'm trying to cast a wide net as I consider options and opportunities.

Current thoughts:
- Follow our curriculum to its next stage by working with one of IM's partners to get our materials professionalized according to their style and added to a new platform.
- Coach or teach at a local high school.
- Open a math and science museum downtown.
- Do a variety of consulting work and write a third edition of Nix the Tricks to help market that.
- Find something short term and apply for a PhD program (I even came up with a topic last night - studying math instruction for students with disabilities, specifically how they so often get stuck doing rote work with tricks or a list of steps).

I'd also love to work for Elizabeth Warren's campaign, but based on the fact that I get daily emails from her asking for money, I'm feeling doubtful that she's looking to pay people with no campaigning experience. However, activism work both within and outside of math education is appealing. That's definitely an area where I don't even know what jobs exist, let alone how to find them.

So, let me know what job openings you hear about, what avenues you think I should research, and your favorite parts of the new IM HS curriculum!

April 10, 2019

How to Lead Conversations on Equity

I started my last post talking about #ClearTheAir and I'm going to do the same thing again. That community has had a huge impact on me. Thank you Val! In the fall we read White Fragility and it was eye opening. Everything in that book seemed so obvious, yet I'd never really paid attention before. Once I had that experience I wanted everyone to join me in my new enlightened state!

My current work is all remote so it wasn't quite as simple as hanging out in the staff room and raving about the book until I found people who would discuss it with me. But, we'd had a book discussion at work before (Radical Candor) so when my colleague spoke up about our lack of action steps toward a new organization goal (Attract, retain, and support a diverse community.) this seemed like a good opportunity to find a partner in this effort. We decided that our co-workers were in a variety of different places and maybe starting right in with White Fragility would be too much. We needed an entry text.

Point #1: Know your audience. The goal is to move forward in the work, but if you jump straight to the finish line you'll be the only one there.

So we read The Loudest Duck with anyone who wanted to join us (15 people out of under 50 full time employees). The very first thing we asked people to do was to state why they were joining. It was great to read different reasons and see a few perspectives, but also to hear a reverberating commitment to learn about diversity and equity. For the book discussion we alternated between asking people to post things on slack and having video conference calls in small groups. I liked being able to read everyone's thoughts when they posted, but we got feedback that people were more comfortable discussing where they could see each other, hear tone and get immediate feedback.

Point #2: Push people a little outside their comfort zone. You have to push, otherwise you'll never get any closer to that finish line. But not too far, or you'll be alone again.

After we finished the book we wanted to continue the conversation, but with a less work intensive method than a book discussion. We moved to discussing articles, podcasts, tweets, and other questions that arose. To honor the request for discussing in person rather than via text, we set up this awesome slack app called Donut. The app randomly pairs people who signed up every 2 weeks so they can go out for donuts! (Or in our case as a remote organization, conference calls. But once I ate a bagel while I was on the call...) It's been great because we're building connections across the organization, which is a great way to increase the all important sense of belonging, while continuing to have conversations about equity, so we can find other ways support everyone in the organization.

Point #3: Keep going! You don't finish equity work in a day, week, month, or semester. Find ways to follow up and sustain conversations. That finish line we're aiming for? It's really far away.

More than half the employees participate in the donut chats every 2 weeks. There have been 62 pair or trio discussions so far in just a few months of running this. Two new employees are leading a discussion on the book Culturally Responsive Teaching and the Brain. A few of us also read Dare to Lead. We're still working on figuring out what our next steps are, but in reading the book we realized we'd like to move from grassroots (anyone who wants to can opt in) to structural change (moving this conversation to formal meeting times).

Next fall at the Boston NCTM regional conference my original partner in this work and I will be presenting on equity in the IM curriculum. There was certainly attention paid to equity before we started these conversations, but the sustained conversation has kept equity at the forefront and improved the whole company's understanding of how our design principles align with equity and access.

Now it's your turn to try. I'm happy to share more about our process or prompts but I think the 3 step guidelines I made up in the last half hour summarize it well.

  1. Know your audience.
  2. Push people a little outside their comfort zone.
  3. Keep going!

April 9, 2019

NCTM Annual, San Diego

I recently read Dare to Lead with #ClearTheAir and one part of the process was to identify your values. Mine are community and making a difference. I've found it really helpful to remind myself of my values regularly as I navigate choices, and that was definitely true at NCTM last week.

I wore many different hats throughout the week. I moved fluidly between Tina the IM employee, @crstn85, Tina the Publishing Committee Chair, friend, parent, and author of Nix the Tricks. During my time in San Diego I alternated between catching up with people and attending sessions, because I was alternating between community (building and maintaining relationships) and making a difference (sharing my expertise or learning things that would help build my expertise for when I implement later). I chose what sessions I attended strategically and often attended with others. There's something to be said for the divide and conquer model, but my values don't include conquering, so sometimes I got to build community and learn simultaneously! No matter what part of the conference I was navigating, I was conscious of how to maximize my precious time to live my values to the best of my ability. Maximizing my time doesn't mean doing as many things as possible, sometimes it means sitting on the floor playing shape sort with a toddler. Because I want that toddler to be part of my community (her parents are spectacular people).

The hat that was hardest to wear is the one that's replaced the hat that is no longer mine to wear, my new identity as former TMC organizer. It's been a difficult transition. In January I was fully involved, knew exactly what was going on, and felt confident that I was both building community and making a difference. Even if it felt like a lot of effort, it was effort that clearly aligned to my values. Now I'm disconnected and have no idea if anything is even going on. The silence is deafening. Did anything that I was building toward survive? It was entirely unclear. But then I went to NCTM and heard some whispers. People who read what happened and said they were moving from talk to action in their organization. I'd love people to move from whispers to shouts. The Southeast Math Summit is finding their voice, who else will join in?

Since I no longer have TMC organizing to do, I am shifting my focus toward NCTM as a community where I could make a difference. Let's be like Dr. Robert Berry and ask NCTM how it's doing. NCTM is truly wonderful and getting better, of course!

Truly wonderful:
  • the conference is a physical space where all of my math ed friends gather, since it's so large friends from several circles (and countries!) end up in the same space
  • a large organization can invite high profile speakers, we had 3 fantastic keynote speakers this year
  • there were many important ideas being shared in the space, I mostly stuck to the equity sessions but even when I ventured outside of that strand people were incorporating equity into their other sessions
Getting better:
  • the conference feels like a 3 day event where I see people from other circles, as opposed to a community in and of itself
  • there was nothing at this conference to encourage me to be an active member of the organization outside of "come to Chicago" which is an entire year away
  • I happen to be an active member, this is my 3rd year on a committee, but I'm still trying to figure out how the inner workings of the organization function
  • I spent a lot of time explaining what I do know of those inner workings, without a clear way to help others learn more or get involved
As always, people who have rejuvenated their connections are engaging in conversation on twitter. I invite you to join us as we brainstorm how the NCTM of the future could be even more truly wonderful. If you have any examples from your other communities about how to address issues, especially issues of equity, please share!