Is "How Do We Help?" the Right Question?

I got to(1) attend a workshop today. It was the Gates Foundation bringing people together to think about Algebra 1. We know that student success in Algebra 1 is strongly correlated with graduation rates, college attendance, and other measures of success in school. So the end goal was to imagine products, programs, and approaches to improve the success rate of Black, Latine(2), EL-designated, and students affected by poverty in Algebra 1. But we didn't start there, and the process we experienced was thought provoking. What follows is my processing of my learning. None of these ideas are mine alone, but since this was a flowing and building discussion I won't be citing anyone in particular either. I spoke about individual vs. collective cultures and learning today, I'm clearly still learning about what it means to attribute ideas in a collective environment.

As we brainstormed all the stakeholders, relationships, and influencers a student experiences I realized how many back up plans a student has. Lately conversation has focused, and rightly so, on how many roles schools serve and how hugely disruptive it has been for schools to be closed. For some students, school is food, shelter, safety, healthcare, and learning. However, a community center can also be food, shelter, safety, and learning. So can a home. Healthcare can happen at a doctors office, or a clinic, or the friendly neighbor with expertise. Learning happens in classrooms, but students have the back up plan of their teacher from last year, their classmates, their peers in a different class, siblings, adult family and friends, tutors from a variety of programs, online programs, the list goes on! Would I love to live in a world where a student leaves math class every day with a full understanding of the day's topic and they never need any outside resources? I'm not actually sure I would. Of course I want students to leave math class feeling successful. But I also love the idea of them leaving with questions, and knowing that there are many options for them to continue investigating those questions on their own or in community. The benefit of students have many options is that if one becomes unavailable the others can substitute. The problem is when the entire system breaks down and not only does the primary method of learning (or food, shelter, healthcare) fail to serve the individual, all of the back up plans fail as well. I have too many stories of that happening in my own child's education, but that's not today's post.

Moving past stakeholders in the workshop, we examined a case study. We thought of barriers as well as supports for this student's math success. We allowed for certain ideas to live in the tension of both/and. Being pulled out of math class for intervention is a barrier to full participation (compared to a student who shares all the experiences with the rest of the class). And, being pulled out of math class for intervention provides a supportive space where learning happens. A student can think math is fun and hard. Can get good grades and think that they're not good at math. 

So when we finally reach the section of the workshop where we imagine products, programs, and approaches to improve the success rate of Black, Latine(2), EL-designated, and students affected by poverty in Algebra 1, there is so much context already on the table/slide it's hard to imagine where to start. Maybe "How do we help?" isn't the right question at all. Students don't need fixing, especially not marginalized students. But systems do need re-imagining. Mostly I want to re-imagine in context of all the connected systems. A grant I'm part of allows me to connect with 2 local school districts, we're working on connecting them to each other. I'm also connecting with after school programs in those same cities. What if all those organizations communicated to share information? They don't need to be the same, I just established that I like the idea of students leaving math class and going to engage in math conversations in different spaces. The after school program shouldn't be teaching from the curriculum the teachers are using, that defeats the point of having different spaces. But what if the teachers knew about the after school program for new immigrants and encouraged students to do both/and? Students could engage in class AND get support outside of school. What if the after school program knew about the cohort model the school is running? Then counselors could encourage students to join the program where Black and Latine students see themselves reflected in their math classes by being placed in classes with peers who both share an aspect of their identity and are also striving to excel in math. These programs and approaches aren't about fixing students, they're about bringing students together in spaces where they're allowed to be themselves. Their brilliant, wonderful, mathematician selves. Maybe "How do we help?" is the right question, but we need to be ready for the answer to be "remove the barriers." The kids don't need fixing, they're ready to thrive in the world together, but we can help them find each other, and make the world ready for them.

(1) I went through a series of reactions to being invited to attend. First I was honored. Then I was unenthusiastic about the idea of a 4 hour online workshop. Then I was appreciative that they asked us for our thoughts about how to make an online workshop not miserable. After that I was busy with a million other meetings and not sure this would make the cut. When I saw the rest of the invite list I was intimidated. But then I saw how mindfully they'd built the slide deck we'd be collaborating on, and the conversation topics, and finally decided for sure to attend.

(2) They said Latino. Mostly I see people use Latinx to eliminate the default male or gender binary. But if you speak Spanish you know that x isn't a common ending, whereas plenty of words end in e and they aren't necessarily masculine or feminine, you have to know. Just like you have to know a person to know their pronouns. I'm not sure if Latine is catching on elsewhere but it flows nicer when I read it, so I'm using it for now, until I know better and then I'll do better if need be!

Every Single Meeting

One of the reasons I was most excited to get the job I have now was the research project we're working on. It's focused on building teacher capacity and increasing the number of underrepresented students in upper level mathematics. [Fun fact, it's funded by Biogen. Yea, that Biogen. No one on my team was at that conference so I wasn't exposed to the virus due to that event, and they have been generous in broadening our funding as we scrambled to support teachers in the transition to emergency remote teaching.]

When I started my new job last September I didn't know how to describe my role. Sometimes I'd lead professional development. Other times I'd coach teachers. Still other times I'd work on a grant with an ed tech company. At first it felt like I was a lot of different people doing very different things, but as the year went on, and most especially as I transitioned to working from home and switched hats from hour to hour rather than from day to day, I realized that I'm the same person doing largely the same thing in all those spaces. I'm a coach. And I'm living the dream where the values I hold close are also the ones that I'm supposed to focus the majority of my effort on at work!

Whether I'm working through the research project or not, I'm always focused on equity and building up teachers. Even though this is my personal passion project as well as a stated focus of both the center and the university at large, it's still an anxious moment as I start to broach the subject of equity with new people. Where is this teacher/administrator in their equity journey? Sometimes districts call me because they want to eliminate tracking, other times that's not what they were looking for but I'm going to bring it up anyway. Sometimes I'm in a room full of teachers I would have described as traditional and it turns out they're eager to adopt new practices to better engage all learners. Other times I'm at a school that prides itself on its up to date technology, but they're referring to students as high kids and low kids. But here's the thing, the whole reason why I gave you nearly 1500 words of context in the previous post: I strive to bring up equity in every single meeting.

We cannot solve a problem like racism by retweeting the pretty quote in an image on MLK day and saying "I can't believe it." when another police shooting occurs. Inequity is a systemic and cultural problem that requires large scale efforts to counter. I'm lucky to be in a position where I can do system level thinking (whether that be department, school, or district), but system level change only happens if all the stakeholders buy in. Which means talking about it at every single meeting.

 

Being the lone person bringing up equity is hard, and if you're in a position like a classroom teacher it can get you into the kind of trouble I found in both schools I taught at. When I enter a new school I'm looking for the people who are already doing this work, and then I work with them. It's so much less exhausting when you can tag team or even just catch someone's eye to know we're on the same page and will debrief that moment later. In other cases I've read and discussed Catalyzing Change with people. Thank you NCTM for creating this resource so we can develop shared language and I can point to an external authority. Find your community wherever you can, hopefully someday it will be within your school, but while you wait for more people to step forward know that there's a long list of authors to keep you company, and a lot more people on Twitter ready to collaborate. Because here's the thing, if you can find the energy and support you need to do this enough times, things happen. When people meet with me they know that I'll push back if a proposal isn't going to support students adequately. Eventually that gets internalized and they push back on their own ideas before I get a chance. 

I've evolved from the new teacher who wants to change everything yesterday. And I'm continuing to grow. There are still books to read, conversations to have, and things to do. The more I learn the more I realize my (largely fantastic fancy suburban public school) education was filled with glaring holes. But I know enough to ask questions and invite people to consider alternatives. I know enough to seek out experts because I don't have to have all the answers.

The only way to see systemic change is ongoing effort. It cannot just be people of color putting in this effort, systems are made of many parts and all of them have to be working in sync. It is hard (I do this all the time and it's still nerve wracking). It is a risk (administrations at both my schools didn't appreciate my methods of advocacy). It feels small (I'm literally just bringing up ideas in meetings). It is essential. I know you can do it.

Choose Your Own Adventure

I opened this blog post more than 12 hours ago. I had a thought this morning I wanted to share, but it requires context. Luckily I just remembered that I had a whole document of pre-written context! We were supposed to do a panel at NCTM in Chicago. Hema Khodai, Marian Dingle, Julie Wright and I. It was titled Choose Your Own Adventure: Equity-Minded Teacher Edition. We were going to share some of our stories, the choices we made, what it's like trying to be an equity minded teacher. To prepare for that I sat down and wrote out my whole story. I'm pasting it here, lightly edited. This isn't the format we'd intended to share, but maybe you'll learn something?

Job 1: I was one of 4 math teachers in my wing. Each wing of the 3,000 student school functioned as a separate school. It was an immigrant community, 90% of the students were latinx. I was a first year teacher, but I was also the only one in my department with a high school teaching certification. It was a very confusing place of high status (I’d taken a full licensure program, I’d student taught, I was involved in a group of teachers across campus who met with Al Cuoco of the EDC- I knew him as the Focus on Math guy, the rest of the math education world knows him as a Big Deal) and low status (young, female, brand new teacher). Sometimes admin wanted my opinion and other times they didn’t but I didn’t know (or care?) the difference. A friend and colleague once asked me if it was possible for me to sit quietly during a faculty meeting, not speak up about what I disagreed with, and then do whatever I wanted in my own classroom. I really appreciated her phrasing because it gave me space to reflect, but also to answer “no.” I was fresh out of an empowering women’s college experience, I was not going to sit quietly! It felt impossible to sit in a room where people were making decisions that didn’t make sense and could harm students without saying so. At the end of my third year my contract wasn’t renewed. They didn’t want to be stuck with an outspoken young female as part of the tenured faculty. 

I was also a privileged white person teaching kids from vastly different backgrounds than my own. While I was advocating for all gender bathrooms in 2009, I was also learning, clumsily, about cultural differences, the impacts of racism, trauma, and a host of other things I’d been largely sheltered from for my entire life.

Job 2: I lasted longer here! 8.5 years of growth as an individual and an educator. I still spoke up, but I was in a larger school and a larger department, so my voice didn’t stick out so much. A chorus of people questioning and pushing, taking turns, and speaking in unison is much different than a lone voice. I also learned to differentiate when my opinion was wanted, when I felt like it was needed, and when it would serve everyone best to bide my time and speak out in a different venue later. Despite these improvements, as years passed we could all see the school culture declining. In my first years here it would take just a few weeks to convince my students that my classroom was a place they could take risks, where I would support them, where mistakes were okay. In my final year my Algebra 2 classroom was just beginning to believe me that I really did want to help them reach my high expectations in January. (And then I left them.)

The decline was due to testing pressure, administration jumping on the next bandwagon every quarter without giving us time to settle into the previous initiative, and public doubt in the school due to a low state level assignment that led to further white flight. I had thoughts and ideas on how to counter these trends, but no power to implement them. The benefit of a larger school is I could blend in. The problem of a larger school is my voice didn’t carry enough weight to have an impact. I made suggestions, signed up for committees, offered to organize things, but it didn’t seem to matter. As my evaluation scores started reflecting my frustration with the system, I decided it was time to get out. I left midyear (at the end of the semester) which felt awful because I was abandoning my students, but also freeing because I was escaping a miserable school culture.

At first I was focused solely on math content with a sprinkling of pedagogy. I got my masters, attended summer programs like PROMYS, TMC and PCMI, joined the math teacher circle at school. But as time went on I expanded my equity work beyond the GSA to learning about all the parts of history and current events that my suburban white upbringing skipped right over. I acknowledged my white savior tendencies and opened my eyes to systemic racism. Now I get my professional development from #ClearTheAir and equity workshops. Twitter has continued to be a main source of community and growth, but who/what I’ve focused on has shifted.

Job 3: I left teaching to write curriculum. It was amazing! Of course I missed the interaction with students and the immediate field testing of all my ideas. But I had time and space and mental capacity to think deeply about all the aspects of teaching that could come from curriculum. I was working with people who also wanted to think deeply about all these same things. I received positive feedback on a regular basis! This was mind boggling. Feedback of any form is rare in teaching, but genuine appreciation of my work? So cool! We collaborated to learn about math, equity, typical schools, atypical students. Everyone was considered and the culture welcomed critical feedback. My voice didn’t stick out because everyone was critiquing, but my voice mattered. I was invited to organize discussion groups, develop features, and share all my ideas.

Unemployment: Sadly grant funded curriculum projects don’t last forever. I’d already quit the board of TMC a few months earlier so I spent the summer feeling extremely untethered. What was left of my identity? I even applied for jobs with the Elizabeth Warren campaign - far outside of my comfort zone as someone who has only ever worked in math education. I considered going back to school as a student (PhD) as well as going back to school as a teacher. I knew I couldn’t work in a school that wouldn’t listen to my concerns around equity, it was too frustrating and exhausting to be constantly fighting a brick wall. As I considered where I wanted to spend my time going forward I wondered how to choose among the best aspects of each job:

• Small company/school where I can be heard

• Working in community

• Both math and equity are centered

• My contributions would be valued

• I’d have a large impact

Currently: I am a math coach, professional development provider, and researcher at a university. I work at the Center for Math Achievement, which is made of me, the director, and the program manager - my voice is definitely heard! During the regular school year I got to visit one school on a weekly basis for coaching, which allowed me to build community there. My work is all about math equity, one of the grants we’re working on is researching how to get more underrepresented students into upper level STEM courses. The combination of small projects (a school with under 500 students) and large ones (2000 student schools, research) is meeting all of my requirements!

I keep expressing surprise that people in schools listen to me. Not many people understand why that’s surprising to me. They see me with my large twitter following and status as an author, but they don’t see how I was ignored as a classroom teacher in my own districts. Not just ignored, but pushed out. It’s frustrating that the only way for me to get a school to listen to me was by leaving the classroom. But a large part of my role is now revoicing all the things teachers say. And giving them the power to decide how to spend their PLC time. It shouldn’t be novel that teachers have important ideas, but for as long as it is, I’ll be using whatever status I have to amplify them. And the same goes for students, but that's another post.

Modeling my Commute

When I was deciding if I wanted to work at the Center for Mathematics Achievement the only drawback was the commute. It's a mere 15 miles as the crow flies from home to the office so it shouldn't be that bad, right? Nope. To get there at 10:30 am on a weekday google tells me it could take anywhere from 45 minutes to an hour and a half to drive! An arrival time between 8 and 9:30 could easily take 2 hours. Those numbers are awful, and I'm committed to not being the traffic (https://twitter.com/Dale_Bracewell/status/1176980860525895680) so I started researching public transportation options. This is where the fun started, because I'm really lucky to have lots of options.

• I could walk to the bus
• I could drive to the commuter rail
• I could drive (farther) to the subway

Each of these has advantages and disadvantages - total time, cost, schedule flexibility. So I started with the cheapest option (no parking and bus/subway) and worked my way down to the option I thought I'd dislike the most (I really don't like driving).

The research was somewhat challenging in terms of identifying all my options, but once I thought of an option it was easy to look up schedules and costs. Then I had to dig deeper, at which point I learned some compounding factors - like the train station closest to my house has really limited parking. But at this point I still had 3 viable options, the 3 bullets I started with. The cheapest option takes the longest. The next cheapest option requires lots of driving. The most expensive option requires little driving, an easy transfer - the trains are all in the same building, and I get to sit on the train where I'd be stuck standing on the rush hour subway. 

At this point I was really wishing I could do some calculating - but I didn't have a way to calculate this. What multiplier do I give for driving (yuck) vs. subway (meh) vs. train (yay)? No one wrote this problem for me so I don't know if Tina dislikes driving twice as much or three times as much or ten times as much as the train. One of the things I really like about the high school curriculum from IM is that we wrote modeling prompts exactly like this. There are scaffolded versions where we provide the data or guiding questions, but there are also wide open versions like Tina needs to get from Salem to Cambridge, what should she do? It's realistically challenging.

So what did I do? The first day I drove to the Lynn train station. First I learned that while driving south seems logical because I'm trying to go south, so is everyone else so I was sitting in traffic and trying to make a tricky left turn across traffic. Then I learned that it's an amazing $2 a day to park there. And finally I learned the trains don't run exactly at the times they say so my train to train transfer was really tight. On the way home I tried subway to train and the subway was just as crowded as I'd worried it would be. The next day I drove north to the Salem train station. There was no traffic because I could leave after both schools on my route started and I was going in the opposite direction of the rest of the traffic. It costs more both to park and to ride the train from Salem, but there's an express train which gets me there with a cushion to make my train transfer. So for the month of October I'm committing to this plan because it's the one that ranks highest for personal happiness during the commute. At the end of the month I will see if my bank account happiness and my personal happiness balance out. This program Lesley University offers should help with my bank account happiness:

My personal happiness at work has definitely been high enough to outweigh the pain of a long commute. I'll be sure to tell you all about what I'm doing at work soon, but for now you should read this newsletter because I wrote it and it tells you some of what we're up to!

Dreaming and Deliberating

In May I announced I was starting a job search. Since then I've had lots of time to think more deeply about what I want to do. The big things are still true:

• My values are community and making a difference.
• I'm only looking at jobs I can do remotely or commute to from Salem, MA.
• I'm trying to cast a wide net as I consider options and opportunities.

The other things I've refined:

I believe in the power of a public education. Public schools are essential to the kind of society I want to live in. Our current public school system is broken. I spent over a decade working within the system, and I just can't imagine going back to that right now. I miss having students, I have so many ideas I want to test out, and I really want to see what the curriculum I spent the last year and half writing feels like from the teacher perspective. However, I don't want to be part of a testing culture that prioritizes compliance or graduation rates over students as human beings. And I just don't have any faith left that a local public school is doing that. Alternative public or semi-public schools (thinking ones for students with disabilities) fit within my realm of acceptable options, charter and private schools are off my list. I need to learn a bit more about how necessary a PhD is for the variety of college teaching options that exist.

I would really love to just play math with kids and adults all the time (see my last 3 posts and a growing folder of ideas and resources). I have made some progress in figuring out how to take this from a hobby to a job (see that same folder) but it feels like a giant leap and I'd rather approach it as an incremental transition from individual beta testers, to a library play group, to a thing I try to find funding for. But it sure is distracting to see this wide open public space next to an empty retail shop downtown. I would rather spend time playing than job searching any day.

So to pay the bills I'm applying to all sorts of curriculum jobs. I'm good at that. I enjoy doing it. But again I'm very picky about where I'll work. I'm not going to help someone make their computer program intended for rows of kids staring at screens mathematically correct, but I will gladly help someone make their math content more pedagogically sound.

If I don't find a full time job soon I'll probably write a third edition of Nix the Tricks (anyone want to pay me to do that?) this summer. I do really like writing...

Math Play Mat - Elementary Edition

Yesterday I went to a barbecue at my friend's house. A friend who has kids ages 7 and 9. So I brought along some math play mats and pattern blocks. The 9 year old had a friend over and they spent most of the day inside - he asked what the pattern blocks were when he came out to eat but I decided to prioritize food over math play at that moment, and then he disappeared before I could invite him to play after dinner. The 7 year old and I had a great time playing though.

As soon as I dumped out the pattern blocks she started building things. At one point she told me to make a big shape out of small shapes. So I made a square composed of 4 squares. Then she said I needed to use more than 8 shapes, so of course I made something using exactly 8. She counted the pieces in my design and said, "No, MORE than 8!" In addition to testing her definition of "more than 8" I also tested her definition of "shape." I wondered if she'd restrict me to mathematical shapes she knew the name for, but a house was fine for her definition of shape. It did, however, need to have a triangular roof. We live in a place that gets lots of snow, so this is definitely the smart choice.

We also played guess my pattern. The first pattern I made was yellow/red and her first guess was about color. Great minds! So then I made hexagons composed of different shapes that alternated with squares. She guessed rectangle/square at first (pointing at the hexagons as she said rectangle) but I told her my rule was big/little. Kudos to her mom for not jumping in to say, "That's not a rectangle." during that conversation. Later when she described one of her patterns as rhombus/square, I told her I was impressed she knew the word rhombus and then said, "this pattern could be rhombus/rhombus" which got me a funny look. But then she was accepting of my explanation that a square is also a rhombus since both of them have four equal sides. She even grabbed the tan rhombus to include it in the pattern. She was all about precision - once I guessed a pattern was big/small and she said no, big/little. Here's another example of precision - take a guess what the pattern is before scrolling past the photo.

My first guess was flat/upright, she said it wasn't upright but sideways. I wasn't entirely sure what that meant and it took a few tries to get there.

When she told me that my first guess was wrong her argument was about it not looking sideways from where she was sitting. Fascinating. The second photo was an acceptable match to her pattern (though it wasn't my second guess, I forget what my intermediate steps were). To note: we didn't talk about "red/yellow" patterns but described the pattern as red, yellow, red, yellow, red... while pointing to each shape. I wonder if identifying the unit of red/yellow would have resulted in more patterns with a consistent repeat. She made patterns that didn’t always repeat the same way (big, little, big, little, little). She also made a set of shapes that were increasing in size. Without any prompting she proved to me the square was bigger than the triangle by placing the triangle over the square and pointing to the parts of the square that aren't covered up. While I was appreciating that proof she moved on to the next thing so I didn't get to ask about the square vs. the rhombus.

We played a wide variety of games during the afternoon (including a washer toss where she helped us keep score!) but she came back to the shapes several times, including eagerly nodding when I asked if I should take them out again after we'd cleared the table for dinner. It was fun to play with an older kid and compare to the toddlers. While we certainly didn't need a mat to make up patterns, it was nice to have - putting shapes on the mat was a signal that we were making a pattern so the other person was ready to pay attention.

FYI: The pattern blocks are a foam version from Hand2Mind (yay for conference giveaways!) I had a set of multicolor squares in addition to the standard pattern blocks which made it easier to test color vs. shape patterns. The felt shapes I usually use with the math play mats solve this problem too, but they don't invite building composite shapes in the same way that pattern blocks do.

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.

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)

Trajectories:

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:

“Mama mama! I neeed you to tell me where you put the present from your friend Miss Tina! I NEEED to make the patterns!”

Warms my heart. Thanks again @crstn85 pic.twitter.com/H3QdqsQjIy

— Jennifer White (@JennSWhite) May 12, 2019

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.

Update: my new version worked out so there's now a website for these things: tinacardone.com/math-play-mat

An RFP

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!