Author: tzager

In January of 2015, when I was deep in the throes of chemotherapy, I received an email out of the blue from Zak Champagne, Dan Meyer, and Mike Flynn, asking if I’d “give a highly provocative ten-minute talk at a special kind of session” at a rogue, after-hours conference at NCTM in April. That was the inaugural year of ShadowCon. Mike, Zak, and Dan selected a diverse group of six speakers, each paired with a live-tweeter. They left the topics open to us, but asked that we each end our talks with a “Call to Action,” something for folks to go and try in their practice after the conference. Furthermore, they asked us to follow up with people online as they tried out the Call to Action.

None of us really knew what to expect. I can tell you that it was a wild ride and something I was honored to do. I suspect it meant extra to me because of the timing–because it came as this much needed reminder that I had ideas. I had something to say.

Even while bald.

So ShadowCon has a very special place in my heart. In the years since, Zak, Mike, and Dan have experimented with different aspects of ShadowCon. It continues to be a venue to build community, to nudge the profession, to extend the conference experience, to press on thinking, to raise new voices, and to listen to people testify about their ideas and passions within math education. People have talked about play, race, humor, hints, empowerment, bias, teacher learning, collaboration,  curiosity, storytelling, inclusion, representation, and so much more.

Check them all out–totally worth your time: 2015,  2016, 2017, 2018.

This year, Mike, Zak, and Dan reached out to Javier Garcia and me to see if we would join the organizing board. Mike wrote:

We want to expand the circle of people who are contributing to the ideas and organization of ShadowCon annually. Zak, Dan, and I have become particularly aware that as three white men we have massive ideological blind spots. Our identities may inhibit folks from presenting who might want to present and those identities may prevent us from seeing great ideas when they’re presented.

Thumbs up. We’ll keep bringing in new voices and perspectives going forward as well.

This year, we’re trying two new things. First off, this is the first year where applications are open. Literally anyone can apply! Here’s the form. The hope is that an open application is one way we can reduce bias in this process.

Second, we’re offering mentorship for the application process. There are three main reasons:

• Each year, we watch aspiring presenters receive rejections and express frustration that they didn’t get the type of feedback that would help them improve their proposals for future conferences. Proposals are a specific and challenging genre, and figuring out how to write them takes practice and feedback. We thought we could help with that.
• We are aware of the informal support networks that exist out there, where people who have learned how to write proposals will offer to read over or workshop new folks’ proposals. That’s great. But the problem is, that well-intentioned mentorship likely contributes to continued inequity in who is selected to speak because people help other people within their networks, and many of these informal networks are extremely white spaces. We wanted to disrupt that pattern.
• Finally, several of us have sat on conference committees and read proposals, and we’ve been struck by the number of people who submit proposals that had good ideas, but really could have benefited from revision. We hope that, through mentorship and explicit focus on proposal-writing, we can help colleagues learn how to write clear, clean proposals that meet professional standards and stand a higher chance of being accepted, both for ShadowCon and for any other future conferences. (As conference-goers ourselves, we selfishly want new and aspiring speakers to get their proposals accepted to state, regional, and national conferences so we can go to their sessions!) Therefore, we wrote a rubric to help proposal writers read and improve their work.

We reached out to the ShadowCon alumni–speakers and live-tweeters from ShadowCons past–to see if they’d be willing to mentor potential speakers. The positive and thoughtful responses started pouring in immediately. I was so moved, and I wasn’t the only one. Javier emailed the board:

Can I just say how amazing it’s been seeing the responses to the call for support the last couple of days… It’s like watching the Avengers assemble.

Heck yeah! So that’s where we are. We have assembled a remarkable group of people to help folks improve their proposals, and they are standing by, waiting to help. Now all we need is for you to start writing! And here’s our biggest challenge, I think. Can I be real a second? (For just a millisecond? Let down my guard and tell the people how I feel a second?)

That year, when Zak, Dan, and Mike wrote and asked me to present, I was floored. If they’d had an open application instead of that personal invitation, there’s no way I would have applied. I didn’t think I was ready for prime time. Hearing that they believed I could do it made a difference to me. Like, maybe if they thought I could do it, I could actually do it. I know other speakers felt the same way.

But this year, we have an open application. So in some ways, we have a bigger ask:

1. We need you to believe in yourself and toss your hat in the ring. Take a chance to speak your truth.
2. We need you to encourage others. Think for a minute about who you want to learn from. Whose voice needs to be raised? Who has something to say? And then go encourage that person to submit! If you believe in them, they might actually do it.

Details:

#ShadowCon19 will be Thursday, April 4th at 5:30PM in San Diego. You have to be able to be there, in person.

Applications are due by December 15th. Now that your regional proposals are in, it’s ShadowCon time!

You’ll be able to revise and resubmit up until December 30th.

That said, if you all wait until the 15th, we may not have enough mentors to go around. So the sooner the better!

Rubric.

Application.

Feel free to reach out to any of us with questions.

We are excited to hear your ideas!

~Tracy

 

This post is a contribution to the amazing, wonderful Virtual Conference of Mathematical Flavors hosted by the amazing, wonderful Sam Shah. I spent much of yesterday reading everyone’s sessions and it was the best PD I’d been to in a while. Highly recommended.

Sam asked us, “What flavor of mathematics are you serving up in your classroom?” First off, I don’t have my own classroom anymore. This coming Tuesday is the first day of school this year, and I always cry on the first day of school because I miss it so much. I miss the energy, the nerves, the long pencils that still have erasers, the excitement about the new year, the relationship-building. I miss it all and feel no small amount of grief. But, gratefully, I get to spend most of my school days in my colleagues’ classrooms or working with teachers as a coach, and I continue to work on my teaching practice in that different setting.

As this school year gets going, I find myself reflecting on an experience I had last week at Math on a Stick at the Minnesota State Fair, and how it relates to a practice I see in lots of classrooms. I spent a fair bit of time watching a four-year-old-boy play at the eggs station.

I love the eggs table. It’s a phenomenal place to watch young mathematicians while they play. This particular child chose two colors of eggs and put them in rows, alternating colors in each row. When he was done, he studied his crate for a while. He made this tiny, almost imperceptible nod with his chin after a bit. The word that flew right into my mind was satisfied. He was satisfied. He then turned his attention to another crate and made new rows with two new colors, but this time on the diagonal. When he was done, his two crates looked like this:

 

He stepped back again and studied what he made. A long time went by and I wondered what he was thinking. He finally put a hand on each crate and began rotating both crates, first in the same direction, then in opposite directions, then adjusting both until his rows went perfectly straight across both crates, pink-to-orange, and blue-to-yellow. He studied them again. This time, there was a tiny smile in the corners of his mouth as he nodded his chin once, decisively. Now he was really satisfied. He turned the crates back before I could take a picture and moved over to the pattern machines. I didn’t ask why he turned them back so I don’t know, but my instinct at the time was that his solution was his. His discovery was a secret, one he wanted to treasure and keep, just for himself.

In math education circles, I increasingly hear words like agency and ownership. I can’t think of a better example of these words than the boy with his eggs. The ideas were entirely his. The discoveries were entirely his. The decisions to (1) do math publicly, but then (2) keep a bit just for himself (he was so engrossed he never noticed me watching) were entirely his. The locus of control for deciding what was interesting, valuable, worth doing, or “solved” resided within him. It was beautiful, and a lump grew in my throat as I watched him.

Know what I didn’t do? I didn’t walk over and talk about his eggs, or other people’s eggs, and express a value judgment about which crates of eggs were better, more efficient, more abstract, more impressive, or more sophisticated. It wasn’t tempting at Math on a Stick.

In classrooms, I see those value judgments become tempting. I absolutely love the 5 Practices for Orchestrating Mathematical Discussions by Smith and Stein, but I worry about the “selecting and sequencing” steps of the share-out devolving into just this sort of judgment and ranking. The authors talk about crafting a storyline when selecting student work to share, and I think they genuinely mean it. I can think of so many possible storylines to craft when looking at and discussing a range of solutions (Intentional Talk by Kazemi and Hintz blew my mind on this front). But in practice, somehow “stories” are reduced to “ranking” more often than not. And ranking is treacherous.

Don’t get me wrong. I sequence sometimes. For example, when I work with teachers, we often work on the Noah’s (or Nora’s) Ark problem, which I learned about from Fawn Nguyen and love with all my heart (I love her too).

(By all means, if you haven’t worked on it yet, stop right now and play. I mean it!)

When I facilitate this problem, I strip all the text off and ask folks what they notice and wonder for a long time. They talk in groups, we share in the large group, ideas get flowing. Then I finally share the question and everyone’s pumped to work. I give them five full minutes of silence to work on their own, and I’m strict about that. If somebody starts talking, I’ll even use proximity to quiet them down. Everyone needs a chance to get oriented. While they’re working, I walk around looking for some possible first steps. Not solutions; first steps. For example, usually somebody tries putting everything in terms of one animal–usually polar bears. I snap a picture of their first swaps. Somebody else starts using symbolic notation, writing 1E = 2B. I snap a picture there too. Somebody else might start assigning values to animals, such as, “If a polar bear is worth 3, then a zebra is worth 1,” and they go from there. I grab a picture. And somebody usually starts throwing animals overboard, crossing them off if they balance each other on the ship.

Again, I grab a picture before they get too far. After five minutes, I pull everyone together and I ask these folks to share their first steps so that, if people haven’t found a toehold in the problem yet, they might hear an idea that appeals to start. I also talk about how most people find they need to switch strategies partway through this problem, so listening to some of these other approaches might help them get unstuck. When I share these first steps, I do sequence them in one important way, which is that I share the symbolic language last. In my experience, folks who haven’t found a way to start yet would shut down if I started with pages with equations. So I hold that one for a sec. My goal here is to increase access to the problem, not to intimidate. That, to me, is a reason to sequence carefully.

But then I cut everyone loose to work, talking or not talking as they organically feel the need. We’ve already talked about norms a lot, and I hope folks state their needs, (“I’d love to hear your strategy but I’m not ready to listen yet. I’ll be with you in a few minutes, once I’ve got my ideas sorted out.” “If anyone is ready to talk, it would help me to think this through together.” And so on.). And they work. I don’t stop them until everyone is satisfied.

At the end, I try to share some strategies we haven’t seen yet. And the lovely twist to this problem is that people who use a lot of algebraic expressions are often stunned by the beauty of a purely visual strategy. It’s a great surprise, especially for folks who assume that the solutions that look the most like 8th grade math will be deemed the most sophisticated.

My point is that, when I sequence, I am doing so for mathematical and cultural goals. I’m trying to share solutions that will reveal the mathematics, will surprise and delight, will enable students to make connections, will spark new questions and conversations that will keep going after we pause our discussion. I’m trying to build a conversation and understanding, not build toward some culminating, “best” solution.

The first time I played with this sort of conversation was with my colleagues and the cheese problem:

Take a sec and anticipate how students just beginning to study division might solve it.

We saw a range of solutions, as we expected. Lots of circles and stars and skip counting by fours. We saw one student use multiplication to solve it, keeping track of his partial products. If we were ranking, we would have called this the “most sophisticated” strategy. But we weren’t ranking. We were exploring division. We ended up deciding to put his strategy next to a grouping strategy, hoping students would see some connections:

It took a while, but then they saw it. “I see the ten fours! It’s like a ten-frame! And the four fours!”

Suddenly, students who had no idea where those equations came from could literally see them. The student who had written the equation might have been the most surprised.

What was really important here was these solutions weren’t ranked from least to most sophisticated. These solutions were side-by-side because looking at them together was mathematically productive. The student who had drawn the blue dots helped her peers learn, which is something we value. Her solution enabled the class to see new mathematics, to learn something, to connect ideas. Her solution revealed the mathematics. During and after the share-out, both students felt respected, and both students were satisfied.

Toward the end of my time at Math on a Stick, I hung out by the Stepping Stones a lot.

I saw such beauty. I saw a young child walking carefully, one leg forward only. He’d stand on one and take a step with his left foot. Say “two” out loud. Take another step with his left foot. “Three.” He went up and back and up and back, over and over. Eventually, he started striding normally, alternating left and right feet, saying, “One, two, three…” A little while later, I saw him walking like that with his hands in his pockets, (“Look, Ma! No hands!”), thinking hard but with confidence, no longer vocalizing the numbers. He was satisfied.

A few minutes later, a grandmother cutting through the booth hopped along from 23 down to 1. She turned to me and said, “I just can’t help myself.” We shared a grin.

Later in my shift, I saw two young adults jumping from step to step, counting on their fingers, loudly. The young man was on 12. “1100!” he said, fingers out. She was one step behind him: “1011.” They were laughing, delighted. Each time they stepped, they’d look toward the sky or the ground, concentrating hard. Partway through, she said something about how she was adding one each time as she counted in binary. He said, “I can’t do that yet. I have to derive every single number.”

I was struck by how similar this pair of friends looked to the young child from earlier in the day. Each person was working on a new-to-them number system. Everybody went to the sure ground of using fingers, talking out loud, and taking as much time as needed. They were all working on mathematics that felt novel and interesting and enticing, to them.

Was one more sophisticated? Efficient? Abstract?

Honestly, who cares?!

Answers to those questions would necessarily be subjective, and would be relative to my mathematics, not theirs. Asking those questions would have stopped their play, ended their ownership, taken their agency.

So I didn’t. I was just the lucky person standing by, bearing witness to their joy. And that, to me, is the greatest privilege of teaching. I will forever be addicted to being in math classrooms with children and teachers because some of the time, I’m the lucky one who gets to bear witness to someone else’s joy and discovery. Some of the time, students’ and teachers’ discoveries will lead to new mathematical thinking in me. But all of the time, their discoveries belong to them.

I go into this year more wary than ever before of the moves we make–with the best of intentions–that take over those discoveries, that diminish that satisfaction, that co-opt that joy for our own instructional purposes. I continue to love strategy share-outs. They’re some of the most complex teaching to facilitate, and “orchestrating” productive conversations for mathematical and social goals takes a lot of finesse and skill.

The moment I’m attuned to is when sequencing a storyline turns into a temptation to rank student work. That’s the moment to pause and think about the folks on the stepping stones, giggling as they tried to figure out 19 in binary. Or the young child with his egg crates, who explored his own ideas because they were his, and thinking about them was interesting and joyful.

That little chin nod he made, that moment when he stepped back and looked and was pleased with what he’d done? That’s the thing. That’s the flavor I want to serve up. I want mathematicians of any age to experience that deep satisfaction for themselves.

 

Postscript: I found myself thinking, this morning, about a reference that’s implicit in almost everything I wrote here, which I wanted to make explicit. When I ask teachers what they need from one another in their groups, I often find myself talking about my friend and colleague, Christopher Danielson. He’s my favorite person to do math with, and I talk about why. What’s interesting is that Christopher knows much more advanced mathematics than I do, but I never, ever feel dumb when I work with him. Over the years, I have learned how to articulate what feels different about doing math with Christopher: he takes delight in the discoveries of others. This is the biggest lesson he has taught me, by example.

When I work with teachers on setting norms before we engage in something like the Nora’s Ark problem, for example, I ask what we should do if one person in the group finishes sooner or knows more or goes faster or something like that. Teachers often suggest that person should bite their tongue, sit on their hands, walk away so they won’t be tempted to blurt out a way to deal with those pesky kangaroos. And yes, this is a start. We need to not just tell people how to solve it or “what I got” or “how I did it.” When someone does that with me, I feel like they are unwrapping my birthday presents for me. They are depriving me of the satisfaction I described above–satisfaction that often follows a period of being stuck.

But what’s interesting about Christopher is he is never tempted to tell his solution. He is, instead, interested in my solution, and on the experience I’m having while working toward it, (whether I get there or not). I have observed that my solution paths are often very different than his precisely because I don’t have the advanced mathematics background he does, and he finds the questions I ask or the approaches I try refreshing and surprising. Sometimes we are then able to connect what he knows and what I know and we each learn something new, like the students did with the cheese problem above. Other times, my discovery is fully settled mathematics for Christopher, and he just takes delight in watching me wrestle with something that is not yet settled for me. Bearing witness, as I wrote about above.

I was recently reminded of all of this–of Christopher’s spirit and purpose and genuine curiosity about other people’s thinking and discoveries–at Math on a Stick, which is where Christopher is most at home. He’s made something marvelous, and he shared it with my children and me. We are filled with gratitude.

 

 

I was working on this one down to the wire, so didn’t get my slides on the NCSM site in time. Mea culpa. But here they are!

Teachers First. Everything Else Follows. Zager NCSM 2018

Note! I meant to delete “risk-free” on the non-negotiables slide. I think I’m gonna have to blog about this properly soon…

“What should we have kids doing on the Chromebooks?”

“What do you like on the iPad?”

“What are good apps for fact fluency?”

Everywhere I go, people ask for apps. Especially fluency apps, but apps. I live in a 1:1 state, and people feel like they need to use the things. I mean, they have the things, so they have to use the things.

These questions put me in a tricky spot because I’m not into tech for the sake of tech. Don’t use it just because you have it. Use it when it adds value.

The question becomes, when does it add value? I hadn’t looked in a while, so decided to do a roundup of what I see out there. This list isn’t exhaustive, but it’s a start. It’s also a living list, for me. By all means, tell me what’s good that I missed and I’ll update periodically.

There are lots of options. Spoiler alert: most are not good. In particular, the fluency apps are generally horrid. Here are the non-negotiable criteria I used to evaluate apps:

1. No time pressure. Some of the recommended apps have the option of timing or the option of disabling the timer. I recommend disabling the timer in all cases. If you can’t disable or mellow out the timer, don’t use the app.
2. Conceptual modeling. There are plenty of apps that have flashcards embedded in sushi restaurants, caves, junkyards, etc. But I’m looking for programs that relate the concepts of the number and operations to the fact. This usually means some form of visual modeling (arrays, dots, etc.).
3. Productive handling of mistakes. They’re opportunities to learn and should be framed as such. Also, competition is to be avoided for most students.

Beyond that, I look for a whole host of other attributes. Too many to name here, but if you’re interested, I wrote about my criteria a while back.

Here’s what I found this winter:

Board Games

Psyche! I know everyone wants to use tech, but for addition and subtraction, you can’t beat the classic dice-based game Shut the Box! It’s the best. Kids compose and decompose constantly. (Protip: I put a second layer of adhesive felt in the box to keep the sound down.) This is a description of standard play, and here are extensions with multiplication.

For multiplication (as well as number sense, structure, prime and composites, factors, etc.), I am a big fan of Prime Climb. It’s great and once kids know how to play (which takes a couple of times), they really enjoy it. Add it to your game cabinet, along with classics like 24.

Supplemental web curriculum that includes fluency, integrated with conceptual math

DreamBox. Only one of its kind. K-8, strong modeling and conceptual underpinning, excellent teacher dashboard and parent communication, facts embedded and conceptual, solid research base.

Suites of very good games that are also available individually

Motion Math has a strong vision. I’m a huge fan of Cupcake, which is a great game on a coordinate grid that also involves graphing, pricing, addition and subtraction, microeconomics, percents, etc. (Pizza is similar, but my kids don’t like it nearly as much as Cupcake, which they play all the time.) The full suite comes with a teacher dashboard, or you can buy individual apps only. They were originally all designed for iPads, and some games involve using the gyroscope and touch so much that I don’t know that they’ll ever have a Chromebooks version, but many of the games are now Chromebook compatible.

Math Snacks is newer to me. I really like Game Over Gopher, another coordinate grid game (why is that topic so gameable?). It’s written with a sense of humor and has rock-solid math.

Virtual Manipulatives

Lots of people sent me a link to the Math Learning Center’s free, virtual manipulatives. Yes. Thumbs up.

Apps for Specific Concepts

Numbers and operations

Dragonbox Numbers is playful and strong for K, in particular. I’m not such a fan of the sequel, Dragonbox Big Numbers, which I think pushes the standard algorithm too early, but the first one is really good, with truly charming animated Cuisenaire Rod-inspired monster-ish creatures and plenty of decomposing and composing.

Hungry Fish. I like it for addition and subtraction, including of integers.

Bunny Times. Not fancy, but sweet, free, and the math is right.

Match. As long as you set it to be the chilled-out time pressure setting, it’s strong for fluency. I like the variety of models a lot.

Number line/place value

Zoom. Zoom is not a game, per se, but students move up and down the number line and then zoom in and out on different intervals to place numbers. There are different animals at the different scales (e.g., dinosaurs, rhinos, dogs, frogs, bees, lice, amoeba). I think it’s a pretty amazing mental model of a dynamic number line, and I’m grateful for it.

Bounce. Bounce is another interesting number line game from Motion Math. Kids rock the iPad to bounce numbers on the line, starting with whole numbers and including fractions, decimals, etc. Clever.

Gate. Slightly creepy, but in a good way, according to one of my kids.

Fractions/decimals/ratios

Wootmath. Wootmath is not so much a game, but an educational app based on the Rational Numbers Project, which is great stuff. It has beautiful virtual manipulatives.

Slice Fractions. Nice visuals for fractions in this game and its sequel.

Refraction. A classic, at this point. Good stuff.

Sumaze2. Lovely. Challenging!

Bounce. (Described above.)

Ratio Rumble. My older daughter is way, way into this game. Ratios in a potions lab.

Ratio Rancher. It’s a solid game but we’ve found it to have a little bit of a temperamental user interface.

Coordinate Grids (Category winner: best in show)

Cupcake. My own children never get sick of Cupcake. They’ve been playing it for a year, and their intuition on the coordinate plane is pretty mind-blowing.

Game Over Gopher. A recent discovery for me. I really like it. Nicely done.

Relational Thinking

Solve Me Mobiles. From EDC. Really nice for equality and algebraic concepts.

Beauty, delight, puzzling, enrichment, problem solving

Nrich. Hands down, one of the best math ed sites out there. Great source of rich problems, for both students and teachers.

Math Munch. “A weekly digest of the mathematical internet.” There’s tons here.

Sumaze. Worthy challenges and puzzles.

Math Doodles: Delightful!

Teacher.desmos.com, student.desmos.com, desmos.com. 

Game about squares. Fair warning. Highly addictive.

Symmetry Artist. So. Much. Fun!

Update. Julie Wright has assembled two great collections of visual math and puzzles.

 

(This post might read like inside baseball for those who aren’t interested in our math education professional associations in the US. If that’s not your jam, feel free to skip this one.)

The news has broken that NCTM is planning to dissolve its partnership with the Math Forum, effectively dissolving the Math Forum, which has been an incredible leader in math education since 1992. As was entirely predictable, the math internet is freaking out at this news, for all the right reasons. I’m afraid this blowback is probably catching NCTM by surprise: it will be a much bigger deal to us than they probably anticipated. I wanted to take a stab at articulating why.

My first annual NCTM was in New Orleans, in 2014. One of my more searing memories was a dinner with a bunch of #MTBoS folks (MathTwitterBlogoSphere–a collection of math educators who share their work and support others online). At that dinner, there was serious angst and even some rage about NCTM. The general sentiment was, Why do I need NCTM when I get everything I need from you all?

Being a member of NCTM is expensive. There are significant annual dues: $124 if you want the journal. And then attending the conference costs thousands of dollars. This coming year, in DC, the conference block rooms start at $289 and go well into the mid $300s, without fees. Registration is $445. And then there’s airfare, meals, etc. Teachers are usually not funded to go to conferences, and some I know have to pay for their sub coverage to miss school (this is insane) and pay out-of-pocket for the conference.

At dinner, teachers wondered aloud about what they get for all that money. An annual conference and a journal was consensus. They didn’t feel much support the rest of the year, via affiliates. They didn’t see evidence of advocacy on the national stage (not saying it wasn’t happening; just that people didn’t see it). And, most of all, they saw zero interest or involvement from NCTM in the thriving online math community, the MTBoS, which was the best source of PD they knew.

There were interesting discussions. I learned the average age of an NCTM member was 55. The average age of people around that table was lower, probably early- to mid-40s. They were also passionate and exciting and innovative team players. They made amazing resources for each other and shared them freely. I remember thinking clearly If NCTM is irrelevant to these people, NCTM is going to die. 

I wasn’t the only one with that thought. There was a lot of talk about what would happen. What obligations do current teachers have to support their national professional association? NCTM had been a leader in Math education for decades, and there’s gratitude for that work, and a desire to pay it forward. One option was to get very involved in NCTM and try to help it grow toward something more relevant for teachers, so membership would begin to rise again.

But did NCTM want that involvement? Or would they roll their eyes at the “kids” and their twitter and do everything they way it had always been done? In New Orleans, that felt like an open question to me. I’m sure I missed loads of nuance, but that was my impression. It was tense.

In 2015, two very big things happened that made that tension dissipate and dissappear. The first was the announcement at Twitter Math Camp that NCTM and the Math Forum were merging. The optics of this announcement mattered. It was at Twitter Math Camp–the conference the MTBoS created to meet their needs.

HUGE announcement from @mlarson_math and @maxmathforum that @NCTM and @themathforum have merged. A #tmc15 highlight pic.twitter.com/YY5kQPRoyj

— Andrew Stadel (@mr_stadel) July 24, 2015

I can’t speak for everyone in that room or following along online, but for me, this announcement was enormous. At that point, I knew four of the Math Forum people–Max, Annie, Suzanne, and Steve–and admired them so much in every possible way. NCTM’s decision to merge with the Math Forum showed that NCTM was moving toward the future, bringing on people with expertise and relationships in the online world, and recognizing and picking up talent. It was huge. It brought them credibility.

The second thing that happened in 2015 was Nashville. NCTM intentionally invited MTBoS participation on a conference committee, and wow did that make a difference. Robert Kaplinsky shared about his experience online. The keynote was an invitation to join the MTBoS. There was a tweet-up afterward, and Diane Briar came. I remember some of the very same people who were upset in New Orleans saying, “I feel none of that tension now.” We were all excited to see these worlds coming together. To see NCTM becoming more inclusive and inviting and forward-leaning. To see no choice necessary. It felt like our professional association had recognized what we needed, and adapted and evolved. The future looked bright.

Since then, there’s been Math Forum and MTBoS representation on every committee. NCTM offered to host game night, supported ShadowCon, and tweets much more actively. It took a year for the legal teams to allow the Math Forum to work at NCTM, but as soon as they could, they made great and visible changes to NCTM. As just one example, The Math Forum made NCTM Central a thriving part of conferences, drawing many of us into the exhibit hall throughout the conference. We’ve made so much progress.

But now, NCTM is ending it’s partnership with the Math Forum and dissolving its resources and contributions. Institutions like Problem of the Week (POW) and Ask Dr. Math will be lost, which impact tens of thousands of students annually. NCTM owns the brand The Math Forum, and it’s making it go away.

Like many others, I am crushed and angry and worried. First, the people at the Math Forum are some of the most gracious, smart, professional people I know. I mean, I love these people. I am so grateful for all their work, from bringing us together and raising new voices at ignites to the positive, productive attitude they’ve brought to every conference and committee. I can’t believe NCTM is disbanding them. My first concern is for Max, Annie, Suzanne, Steve, Richard, and Tracey.

My second concern is for the future of NCTM. This move threatens all the hard work and relationship-building they’ve been doing. Over the past few years, they’ve built a lot of loyalty among the MTBoS. I have been excited for the future, knowing the Math Forum people are there and working behind the scenes. Now, I honestly don’t know what the future holds.

This move is so damaging. Damaging to trust, relationships, credibility.

It’s not too late to repair, though. I hope beyond hope that the NCTM board will reconsider this decision and repair these relationships. This is a moment to determine the future.

I think Graham summed it up perfectly:

 

There’s a lot of angst in education about the role of research. What’s good enough? What’s not good enough? How do we know “what works?” How are some studies considered convincingly quantitative by some but held up as poor use of meta-data by others? Likewise, how are some studies considered robust and qualitative by some, but dismissed as anecdotal and subjective by others?

Honestly, I don’t have answers to these questions. I’m not a methodologist. I don’t have a Ph.D. and I haven’t completed a recent, rigorous course in research methods.

What I do have to offer, maybe, is a geologist’s perspective. I’ll try to explain. Bear with me through this bizarro opening.

I recently agreed to an event in Santa Fe,  which triggered a memory of one of my favorite professors from way back in my undergrad days. Kip Hodges was a hotshot geologist and geochronologist at MIT in the 1990s, but told me once that if geology ever interfered with his relationship with his wife or his daughter, he’d find another way to make a living. He thought he’d be just as happy running a restaurant in Santa Fe. That wisdom stuck, especially coming from a young guy who had just gotten tenure at such a competitive institution.

Fast forward to when I was pregnant with Maya in 2006-7. A former classmate and I randomly ended up in the same prenatal yoga class, and she told me Kip had left MIT and moved to the southwest. When I learned I was going to Santa Fe, I gave a quick google in case he was cooking up green chile shrimp tacos, hoping to catch up with him. He’s in Arizona, alas, but up popped this video in which he talked about the fascinating work he now does with astronauts. I smiled as soon as I heard his familiar North Carolina lilt, punctuated by the way he has always slapped one hand into the other when he wants to make a point. I put my feet up on my desk and settled in for some good nostalgia.

Starting at about 3:05, my ears really perked up.

If you talk to physicists, most of the time, they’ll tell you there is a way that you do science. If you talk to chemists, there is a way that you do science, and it’s usually experimentally based and it takes place in a laboratory. But there’s another way of doing science, which is a more observational way of doing science, a more discovery-based way of doing science, and a more exploratory way of doing science, and lots of times that gets short shrift. Lots of times people say, “Well, it doesn’t happen in a laboratory, it’s not experimentally based, it does not use the scientific method, and so therefore it’s not really science somehow.”

Huh. That sounds familiar.

A few minutes later, Kip gave a quick primer about thinking like a geologist. I actually took a year-long class with him called something like “Field Geology” back in college, so this was familiar and happy territory for me. These three points were central to his description:

Field geology on earth–a lot of it is about multi-scale observing. I look at things closely and I look at things far away. I get different perspectives on things to try and understand them.

 

The sampling that you do when you get materials is a very tactical thing. It actually supports the work that you do. It’s not the fundamental thing. I don’t go into the field in the Himalaya or some place like that and pick up stones. I don’t wander and pick up stones and bring them back. I go and I make observations in the field and I collect samples that are gonna tell me something in the lab, but I collect them very very carefully when I go.

 

The other thing about this kind of science is it’s based almost entirely on inductive reasoning. It’s not like making an experiment. It’s like making observations and trying to cull processes out of those basic observations.

Here’s where I’m going to geek out about geology on you. It’s my favorite science, mostly because of the challenge it provides. The earth does this beautiful thing of trapping its own history in the rock record. But then, thanks to dynamic plate tectonics, the earth is constantly writing over, reshuffling, rearranging, and transforming that rock record. Think about the name “metamorphic rocks.” Every time rocks get subjected to enough heat or pressure–both of which happen when a piece of crust gets dragged down in a subduction zone or crumpled up when continents smash into each other–the rock and fossil records are blurred, smudged, confused, moved hundreds or thousands of kilometers away from the related rock record, sometimes completely erased and rebooted. The vast majority of the rock record has been subjected to tremendous forces, repeatedly—forces that are strong enough to rewrite history at a molecular level–and then hidden below the surface of the earth or buried under vegetation, cities, and water.

Hence the geologist’s challenge! She can’t recreate geologic conditions in a “gold-standard, double-blind, randomized, controlled, replicable experiment.” There are not tens of thousands of fruit flies, mice, or test tubes of centrifuged samples. She can’t make mountains in a lab in a building at a university. In other words, the methods and tools of controlled experiment design are usually off the table. Instead, geologists travel the world and observe, make meticulous records, look for patterns in those observations, create and test plausible hypotheses, and try to disprove theories. It’s a gas, and, as Kip described in his story of Darwin’s training in geology aboard the HMS Beagle, it’s a powerful enough intellectual model to yield the theory of evolution.

Let me be clear. I’m not dissing gold-standard randomized studies. I counted on them every time I went in for chemotherapy during breast cancer (although I also counted on the clinical expertise of my oncologist and her interpretation of that lab-bench research). I yearn for controlled studies when making evidence-based decisions, if results are available. I recently spent an hour rapt, listening to this discussion of a matched-pairs study of youth mentoring programs that blew everybody’s mind, including mine, because the robust data disproved all our hypotheses and wishes. I was glad for the well-designed, well-controlled study.

But here’s the thing. Big, robust, randomized studies are expensive and hard to get, even when you have trained lab staff, grant money, and genetically identical mice from Jackson Labs. When it comes to schools and education and kids and teachers and communities, they strike me as damn near impossible. Reality is just too messy and varied and complex to isolate single variables across classrooms and schools and time and control for them. I’m skeptical of any study that claims tight control in education.

I don’t feel angst about this, though. I never have. It wasn’t until the moment watching Kip’s video that I realized why. I suddenly saw how my time in geology prepared me to write Becoming the Math Teacher You Wish You’d Had.

What did Kip say field geologists use? Multiscale observation. Tactical sampling. Inductive reasoning.

• I looked up close at specific interactions between one student and one teacher. I stepped back and looked at how whole classrooms and schools worked. I stepped back further and looked at larger historic trends, and then re-examined classroom observations in light of those larger social contexts. I sought to understand by studying math education at different scales.
• Like Kip doesn’t walk around and pick up stones (lol), I didn’t pick random classrooms. I used my trained eye to select my samples carefully, looking for a range of classrooms that would teach us all something. I planned my traverses with care.
• And then I looked for patterns. I went through my meticulous records of all those observations–audio files, transcripts, student work, video, notes–and culled out larger patterns. What kinds of questions did these different teachers ask? How did they handle student mistakes? What sorts of tasks did they select?

The whole time I was researching the book, I referred to this work as “my fieldwork.” It’s the term that came naturally, that fit best, but it wasn’t until Kip reminded me about the difference between field geology and lab science that it became clear why that was my approach of choice. Why, when dealing with the complex world of teachers’ beliefs, students’ inner lives, different social and cultural contexts, and deeply flawed outcomes-based data, I went right for a field-science approach. Why I was never a tiny bit tempted to gather pre- and post- standardized test scores on the kids I observed. Why I focused on observation, selective sampling, and patterns.

Observational science is science.

Anthropological studies of classrooms are research.

Quantitative data are not necessarily better than qualitative results, and they’re sometimes significantly worse.

If we only believe the results of double-blind, randomized studies, then we’ll only have evidence for things that can be measured, regardless of how valuable the data. This approach often works fine in labs, but not in geology, and not in social science. As sociologist William Bruce Cameron said in 1963:

It would be nice if all of the data which sociologists require could be enumerated because then we could run them through IBM machines and draw charts as the economists do. However, not everything that can be counted counts, and not everything that counts can be counted.

Sociology is valuable without those charts. Field geology is valuable without those charts. And educational fieldwork is valuable without those charts.

At least to me. But then again, I’m comfortable with this idea of field science. I’ve adopted the habits of mind of a field scientist.

It’s how I see the world.

School’s starting soon, so our kids have started anticipating, wondering, and talking about what might come in fifth and third grade. The other night at dinner, soon-to-be-third-grade Daphne burst into tears with worry about high-stakes testing, timed tests for multiplication facts, and math textbooks. My paraphrase of what she said, approved by Daphne:

That’s not even math to me. I mean, getting answers fast without thinking isn’t even math. I like it when there’s a problem I have to work on and work on and work on, where I get parts wrong and I have to go back to it and figure out what I did, where it might take me hours, weeks, or even months to figure it out. That’s the kind of math I like!

 

The kids are always like, “Why did that test take you so long? I thought you were good in math?” Sometimes I’m the last one done and they all talk about it. But as soon as I know the test is timed, I can’t think very well, so it takes me longer. And I also take a long time because I like thinking about the problems, not just rushing to get the answers.

 

And I wonder, you know how they have DEAR–Drop Everything and Read? It’s a time where you don’t have to do worksheets or sticky notes or read something assigned. You can just read what you enjoy. Why don’t they have it for math? I wish we could Drop Everything and Math. Instead of worksheets or tests or problems, the kids could just look around and see what interests them. We could find a question of our own and ask it and work on figuring it out until we’re satisfied. That’s the kind of math I like, like what I did in Ghirardelli Square.

While she talked, I had a flood of conflicting feelings and questions. Of course, I was overjoyed to hear that Daphne still knows what mathematics is, regardless of her experience in school math thus far. She’s still intact, for now.

I was simultaneously crushed, listening to her expectations for math this year. Oof.

But then there was her love of working on a hard problem over time, of persevering and enjoying the grappling. Sam and I told her it’s a much more important life skill than giving quick answers to fact-recall questions. I mean, this is a kid who likes to face down a worthy challenge. Check her out after a hard part of this week’s ropes course in the Adirondacks.

I was also struck by this idea of Drop Everything and Math. Because, while it’s beautiful, we all know that if a teacher at any grade in a U.S. school told students it was time to Drop Everything and Math, that teacher would face a room full of blank stares. A classful of students waiting to be told what to do. Maybe even a group of students angry about the unclear expectations and absence of directions.

Based on their experience, students have concluded that teachers and textbooks ask the questions and students answer them. We tell students what to do at every juncture, right down to whether we want them to box or circle their answer, or fill in a bubble (completely! With no stray marks!).

If our students would be paralyzed by the suggestion to find a mathematical question of their own to explore, then that’s a call to action. We need to do something different. Students need to learn how to pose their own mathematical problems and questions, not just answer somebody else’s. And I’m talking about genuine mathematical questions, not just word-problem writing.

If you want some suggestions to get you started, I’ve gathered a whole bunch of resources around question-asking and problem-posing on the CH 7 page. A few hits, briefly:

• 101questions is a super resource. It’s a huge bank of curiosity-provoking images. Ask your kids “What questions come to mind?” They don’t need to answer the questions–just practice asking. If you can only spare five minutes now and then, you can still introduce question-asking via 101qs. (For a recent blogpost about one way to use 101questions and a bulletin board, take a peek at Mrs. Beauchemin’s “Are Our Students Really Thinking?“)
• Notice and Wonder. As Annie Fetter, Max Ray-Riek, and the rest of the gang at the Math Forum at NCTM have been teaching us, removing the question and asking students What do you notice? What do you wonder? opens tons of possibilities.
• Take a mathematical walk and see what math your students can spot around your school.
• Suggest students bring something mathy from home and have a gallery walk to discuss where they see math.
• If your school is equipped with the technology, you can host your own MathPhoto challenge. Ask students to look for lines, symmetry, curves, intervals, etc. Check the linked archives for more ideas.
• Invest in mathy playthings that spark conversation and delight. Christopher Danielson has you covered on materials, and Kassia Wedekind‘s ShadowCon talk will inspire you to make your math class more playful this year.

Daphne liked the acronym DREAM for Drop Everything and Math. Is hers a pipe dream? Or one that might see the light of day?

That’s up to you, I think.

I was honored that Middleweb asked me to write a blogpost specifically for new math teachers. Reposting here:

When I was in graduate school preparing to become an elementary-school teacher, my math methods professor, Elham Kazemi, told me it takes five years to become a skillful math teacher. I remember thinking, “Oh no! What about all the kids I’ll have between now and then? Am I going to ruin them?”

Well, the good news is they survived. I think I even did them some good. Sure, teaching mathematics is incredibly complex and I’m a lot better at it now than I was then. I plan to spend my whole career working to become a better math teacher, and I know I’ll never get bored because there is so much new learning to do. Even so, newer teachers have a ton to offer students. I feel proud of and excited by everyone who chooses to become a teacher, and your upcoming students are lucky to have you.

It’s reasonable to set some goals for your development as a math teacher. Be patient and forgiving with yourself while working to get better. Over the years, you’ll build relationships with your students, you’ll figure out how to build a strong classroom community, you’ll grow your content knowledge, you’ll learn how to facilitate conversations about mathematics, you’ll get more discerning about choosing tasks and curriculum for good pedagogical reasons, you’ll become more efficient and focused about gathering and using formative assessment, you’ll anticipate what students might say and do with more accuracy, and you’ll find your teaching style. It will come. But where to start?

In my coaching and my work with preservice teachers, I’ve learned that my square one is always the same: I want teachers to become addicted to listening to students’ mathematical ideas. It might sound like simple advice, but it’s not. Everything else follows. Once we become fascinated by our students’ creativity and ingenuity, we become more motivated to teach math. We enjoy it more, and so do our students. Soon enough, we dive more deeply into the mathematical content so we can understand why our students’ invented methods work. Before long, we recognize patterns in the way students’ ideas progress, and we crave professional learning about the development of mathematical ideas. We start reading, signing up for workshops, going to conferences, joining Twitter, blogging, seeking out colleagues who are as excited as we are to hear the amazing thing a student said or asked in mathematics today. Our curiosity drives us to read the research and find a professional learning community. We aspire to understand, to talk less and listen more, to ask better questions, to make more thoughtful instructional decisions, to support our young mathematicians. We reflect, and learn, and grow.

On the first day of math methods, Elham told us that she was the lucky one who would introduce us to the fascinating world of young children and mathematics. She taught our cohort to listen to children’s mathematical thinking, and be amazed. Pretty much every positive development I’ve made in my math teaching since has followed from close listening. When I feel unsure of what to do, I think, “Don’t just do something; stand there. Listen.”

The rest will come, in due time.

Have a wonderful school year, and let me extend my most heartfelt welcome to this noble profession.

 

(Reblogged from the Stenhouse summer blogstitute. If you haven’t checked it out yet, take a peek–lots of authors wrote posts!)

I periodically hear discussion about whether it’s better to start the new school year by establishing norms for math class, or to dive right into a rich mathematical task. I’m opinionated, and I’m not shy about my opinions, but in this case, I’m not joining one team or another. They’re both right.

The first few weeks of math class are crucial. You have a chance to unearth and influence students’ entrenched beliefs—beliefs about mathematics, learning, and themselves. You get to set the tone for the year, and show what you’ll value. Speed? Curiosity? Mastery? Risk-taking? Sense-making? Growth? Ranking? Collaboration? You get to teach students how mathematics will feel, look, and sound this year. How will we talk with one another? Listen to our peers? Revise our thinking? React when we don’t know?

In Becoming the Math Teacher You Wish You’d Had, I wrote about a mini-unit Deborah Nichols and I created together. We called it, “What Do Mathematicians Do?”, and we launched her primary class with it in the fall. We read select picture-book biographies of mathematicians, watched videos of mathematicians at work, and talked about what mathematics is, as an academic discipline. We kept an evolving anchor chart, and you can see how students’ later answers (red) showed considerably more nuance and understanding than students’ early answers (dark green).

 

Throughout, we focused on the verbs that came up. What are the actions that mathematicians take? How do they think? What do they actually do?

In the book, I argued that this mini-unit is a great way to start the year if and only if students’ experiences doing mathematics involve the same verbs. It makes no sense to develop a rich definition of mathematics if students aren’t going to experience that richness for themselves. If professional mathematicians notice, imagine, ask, connect, argue, prove, and play, then our young mathematicians should also notice, imagine, ask, connect, argue, prove, and play—all year long.

In June, I saw this fantastic tweet in my timeline.

Asked Ss: what’s a mathematician? Blue responses: before 3 act task. Red: after #mathmindset @gfletchy pic.twitter.com/lltkcclb4h

— Sarah Burzynski (@SarahBurzynski) June 8, 2017

It caught my eye because Sarah’s anchor charts reminded me of Debbie’s anchor chart, but Sarah had pulled these actions out of a task, rather than a study of the discipline. I love this approach and am eager to try it in concert with the mini-unit. The order doesn’t matter to me.

We could (1) start with a study of the discipline, (2) gather verbs, (3) dig into a great task, and (4) examine our list of mathematicians’ verbs to see what we did. Or, we could (1) start the year with a super task, (2) record what we did, (3) study the discipline of mathematics, and (4) compare the two, adding new verbs to our list as needed. In either case, I’d be eager for the discussion to follow, the discussion in which we could ask students, “When we did our first math investigation, how were we being mathematicians?”

Whether we choose to start the year by jumping into a rich task on the first day, or by engaging in a reflective study about what it means to do mathematics, or by undertaking group challenges and conversations to develop norms for discourse and debate, we must be thoughtful about our students’ annual re-introduction to the discipline of mathematics.

How do you want this year to be? How can you invite your students into a safe, challenging, authentic mathematical year? How will you start?