Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier for their inclusion in mathematics. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

Dan Meyer (00:04):
Hey folks, welcome to math teacher lounge. My name is Dan Meyer

Bethany Lockhart Johnson (00:07):
And I’m Bethany, Lockhart Johnson.

Dan Meyer (00:09):
And this is the teacher learning week. We’re thinking this week about how we grow as teachers. And to start with, I just wanted to ask Bethany, uh, first Bethany, how are you doing? And second <laugh>. Um, what is, what, what has been your like most favorite and least favorite, most effective least effective professional learning experience when you were a classroom teacher?

Bethany Lockhart Johnson (00:30):
I think for me, most effective was definitely when I could use it right away. Right. Whatever we were talking about, whatever we were learning, like I got to go put it into practice. Sure. Uh, I, I remember we did something where we designed a lesson and then we went and taught it like one person taught it and the rest of the people watched. And then we kind of like got to workshop it, which that was like a one off the fact that we got to go out of our classroom and go observe somebody teaching. It was gold. It was gold. Um, so that was probably the most effective, because there was so much opportunity for reflection and least effective was something that felt like just completely unconnected to, you know, kind of either so theoretical that it wasn’t like touching on what we were navigating right there in the classroom. I don’t know. What about you? What can you think of times that, are you gonna say times you led a PD? Those were the most effective?

Dan Meyer (01:26):
Yeah. My favorite ones are my sessions, of course. But if I had to throw those out for a second, um, yeah, I, I like, I want, I want both, I want it all. I want the, um, the big ideas that take a long time to settle in that also have like small bits that can carve off and use relatively quickly to test my understanding of the ID is, yeah. I’ve had some, some PD where I’m like, this is very relevant to tomorrow. And I also don’t care. Like for instance, like how to use the CD, the, the, like the, the software, you know, on the, on my curriculum, for instance, it’s like, okay, yeah, this is just a little, little too practical. You know what I’m saying? I want some bigger ideas to chew on. Um, I would also say like, I love my favorite PD by a long was writing up thoughts about how the day went and putting that on the internet in a public place that we used to call a blog and where people would come along, cuz there was like 10 blogs and like, tell me like that’s no good.

Dan Meyer (02:16):
Like the thing that you like is not a thing you should like, here’s the thing you should like instead, or try instead, or just this weird community that sprung up, you know, when I was, uh, starting to teach relatively new teacher and uh, I feel like I grew a lot

Bethany Lockhart Johnson (02:28):
Go back to this idea blog. If people would call you, they’d call you on the phone. What, what

Dan Meyer (02:32):
Was they would fax me? They, it would be a fact. So

Bethany Lockhart Johnson (02:35):
Fax,

Dan Meyer (02:36):
I got it. Fax a comment. Yeah. Got it. So, uh, that’s, that’s Bethany and I, and we’re super excited to have people who have a bit broader of a perspective, a bit more of the land than what, what the two of us, um, think about with our own professional learning experiences.

Dan Meyer (02:52):
We’ve invited on an expert. We hope will help us understand alternate ways to do professional learning as teachers to grow as teachers besides, you know, all of us getting into the same room once every, every, uh, few months together, Elm Cosmi is a professor of mathematics education at the university of Washington, Elm studies, how strong professional communities develop in schools and how schools can be organized. So teachers learn from and what their students, this work is informed by equity oriented research on thinking, uh, on children’s mathematical thinking and classroom practice. She is co-author with Allison hints of intentional talk, which focuses on leading productive discussions in mathematics. And she edited coral counting and counting collections with Megan Frankie and Angela tau, which focuses on the importance of counting from preschool to fifth grade. Looking forward to a great chat with Elham, welcome Elham to the show.

Elham Kazemi (03:43):
Thanks for having me, my favorite topic ever to talk with you both about,

Bethany Lockhart Johnson (03:47):
I think something that I just deeply, deeply respected admire is that I feel like you are constantly sharing about how you are learning. You’re continue to learn, continue to, to try out new ideas and you do a very good job of like highlighting things that you’ve learned, whether that’s sharing it through a tweet or sharing it amongst colleagues or peers. And I, I just really appreciate that because I feel like being in the mathematics community with you, I feel like I grow by, I just like paying attention to like, Hey, she’s a learner, she’s done all these amazing things and thinks in these amazing ways and has shifted my thinking in such amazing ways. But she’s saying, Hey, I I’m still learning. So yeah. Hi, thank you. Thank you for your, I don’t know. We’re just glad to have you here.

Elham Kazemi (04:41):
Thanks. I do feel like the perpetual student, like I’ve never left school and I wonder like one day maybe I will, when I grow older, when I grow up, will I ever leave school? Maybe not.

Bethany Lockhart Johnson (04:52):
<laugh>

Dan Meyer (04:53):
Great. Let’s dig in. Yeah. So please tell us you partnered with a school for some professional learning that wasn’t the sort where you would go in and offer brilliant ideas and then leave. But rather it, it seemed like it was more of a job embedded sort, the sort of thing that might have a life of its own after, you know, after the, the grant ends or the program ends. Can you describe what it was you did and what the effect was?

Elham Kazemi (05:15):
I think I wanna first say that everything that I have done and experimented with as really the result of working with fabulous people, teachers, coaches, principals, other, um, colleagues and peers in the field who are constantly trying to work on what good teaching looks like and how you learn to do it. And mostly because we care about kids and we care about what students experience in the classroom. And we want kids to love school, to have school, be a place where they’re known, they’re loved, um, that they look forward to being in every day. And I think there’s that, um, the why that, that, um, per that makes you want to learn is really about the students and being, doing things in service of them. Because when, uh, as one of my colleagues said, when children thrive, teachers thrive. So what does it mean for us to thrive?

Elham Kazemi (06:06):
If we are focused on our kids’ experiences in schools, what we did at this, this particular school and a group of schools is kind of tap into a, all that curiosity and drive that teachers have to do a good job and to use their imaginations well, and to engage the actual ideas that children have in their classroom together, not separately, not like get a great idea and be inspired by it and then go figure it out by yourself, but be inspired by ideas and then try to figure them out together. Because, um, as you both know, very talented teachers, uh, who also have been inspired to change your classroom teaching. Once you figure something out or as you’re figuring it out, there’s all kinds of intricacies. Like I remember when I first learned about three act tasks, I thought what a brilliant idea, but it’s not so simple to try to enact the brilliance of it because you can simplify it too much or you can get stuck and not really know how do you move from one act to the next, or what’s the point of the third act?

Elham Kazemi (07:12):
Do you just like reveal the answer and that’s it. And then you move on. Um, how do you even do design the tasks to begin with all of those things, raise questions and working on them together, uh, and carving up that space and time to work on them together is sorely missing in schools. And so that’s what we were able to do with the schools that I parted and it is find the time and then design the structures so that teachers could, um, <affirmative> think about their teaching together and then also be in the classroom together with kids. So the kids see that we are also learning to be responsive to them. That’s the point. So we have to work stuff out when kids are present, which is the part that usually trips a lot of people up.

Bethany Lockhart Johnson (07:55):
Well, that to me is I think the part that shifted my teaching and continues to is this, it is a culture shift to tell your students, to invite your students into your learning, to tell them I’m, I’m learning too. It was an invitation to, to be vulnerable in a way that I think sometimes teachers are very afraid to be vulnerable. Uh, if they don’t know what the student response is gonna be, or they don’t know, they don’t wanna seem like they don’t know the answers or they don’t know how to figure out a problem. I think that’s a real shift in the, in the culture for, for compared to maybe what we, we experienced growing up.

Dan Meyer (08:33):
I hated not knowing the answer to a math problem. I admitting I, I was uncertain with the mathematics, but to admit that I am like a, a work in aggress as a teacher, feels like an extra admission, an extra layer of humility, which is, I don’t know, it’s a really special thing that you were up to with that school. I’d love to hear like about specific structures that you worked with to help make that transition feel, you know, more natural, more welcoming, more productive.

Elham Kazemi (08:58):
So, I mean, you probably have experienced common planning time, right? This is a thing that often happens for us teachers. I think that common planning time looks a lot sometimes like, uh, what are we gonna do on Monday, Tuesday, Wednesday? Okay. What do we need? What are the materials we need? Who is gonna do that? Will you write this? And that’s what kind of common planning time, and then it’s over. And then you might see each other at lunch and say, well, how did that go? And you’ll talk a little bit about it, but common planning time and learning labs, which is sort of what the, what we call the, the PD that we designed means. Okay. So let’s take three act task. We, we write a little bit about it. We’ve seen a couple, but okay. What would it really mean to plan this particular one?

Elham Kazemi (09:42):
So common planning time is thinking like, how are we gonna launch that first act? What are we actually gonna say? What do we think the kids are gonna say? Why would we say it that way? What if they say something else? Um, and then, okay, so what does it actually sounds like to transition from act one, to act two? What might we say, what would happen with this particular task and actually getting into the details of how you imagine, like, what, what you would do when you were actually planning the specifics of a particular lesson, but leaving it loose enough that you’re not trying to make it perfect. And I think that’s the trick. So, so that you are not so invested, that goes in that particular way or that you fail. If it doesn’t go that way. Um, but that you have something you wanna learn together and trying out this three act task with a particular group of kids so that when you go into the classroom, first of all, you’ve all thought through the full R of the lesson.

Elham Kazemi (10:40):
And you’re curious enough about what’s gonna happen at particular points that you’ve left room for uncertainty and the taking of some risks. So then when you go together into a classroom and kids start to say things that you didn’t anticipate you or, or they start to do something that you’re so jazzed about, that you didn’t anticipate that you’re like, this is the thing we should pursue more. You give each other permission to do that. You’re like, whoa, wait, did you hear what so? And so said, I think we should follow that road and see where it takes us, or, huh. Okay, hold on. And that’s what we call teacher timeouts, where you actually confer briefly and you tell the kids, this is a super special day. We’ve tried to design something. We’re very curious how you are gonna react to it. So we’re gonna try it out. And along the way, we might pause to get your ideas or for us to make some decisions and steer the ship in a, in a new directions and see what happens. So we’re gonna be sitting closely to you among you. Um, and you get to be our teachers today while we teach. That’s how it’s framed.

Bethany Lockhart Johnson (11:46):
Like, what were you seeing in professional development or in that wasn’t happening amongst teachers? Like where, where are the gaps? Because it feels like so much of your work. You’ve just looked in such nuanced ways at how teachers can continue to grow and be more reflective of their own teaching. And I’m just kind of curious where that came from or where you’re seeing the landscape.

Elham Kazemi (12:10):
Yeah, that’s a good question. Well, I, oh, everything I know about, children’s thinking to Megan Frankie and the beautiful body of work called CGI, but, um, one of the things that we noticed, there’s so many great CGI workshops, and even like all the seminars and conference presentations and amazing things that you can design to have engaging work time for teach in, in professional development, outside of their classroom, people get super jazzed, you know, they get, um, uh, they have meaningful experiences, but to contextualize that back into their classrooms with their own students is like where, where often I would see like, wait, the same group of teachers I just saw in my classroom or in either in math methods or in this PD seminar, or even myself, like noticing, like I have seen and thought about stuff a lot. But when I went to go do it with a particular group of kids, holy moly was that so hard. And I saw all kinds of new complexities that I didn’t anticipate. And if I were just left to my own devices, I might very easily say, whew, this seems a little too hard.

Bethany Lockhart Johnson (13:21):
Right,

Elham Kazemi (13:22):
Right. And that’s the thing that I always hated. I was like, oh, if only we had, or you, or if you watched somebody do a demo lesson and you saw something that was like, kind of cool that you wish you had done afterwards. I often this happened in reflections. I wish we had, because we weren’t allowed to interrupt each other during teaching. Cuz somehow that would be rude or that would undermine the teacher’s authority. But that’s only the way we frame it. If we say actually we’re all capable people. So a question we ask ourselves during instruction doesn’t mean you don’t know what you’re doing. It means actually we’re thinking together then the interruptions aren’t about undermining authority. They’re about thinking together.

Dan Meyer (14:04):
There’s a performative aspect to a lot of teaching. Like the like teaching feels like a performance and you don’t, the movie’s playing or there’s a play that’s going on. It feels like inappropriate to interrupt that in any way. Cause the performance is going and I, I love what this that’s. I love what this idea does to kind of, to redefine teaching is not a performance, but this, this co-constructed thing. Or if it’s a performance, it’s a performance, the stars, all of us, like we’re all a part of the cast and always a it’s always the dress rehearsal.

Elham Kazemi (14:30):
<laugh> it is like the dress rehearsal. Although some of my brilliant colleagues with backgrounds in drama and theater, Sarah Kavanaugh and Holly GU and Elizabeth dure, they actually were at a meeting together. And they talked about how this like breaks the fourth wall, you know, mm-hmm, <affirmative> like, which is out of theater, um, where the performer speaks to the audience, you know, I know you’re there and I have something to say to you. Yep. And I was like, well, we should, why can’t we do that in teaching? So we actually wrote a little paper, um, that’s called breaking the fourth wall as a way. That’s so cool as a metaphor for understanding and reframing what these interruptions could meet. Cuz we often get people when we about this for academic audience who say like, aren’t you using the children and what are the children gonna do while you just pause? Are they supposed to freeze? And uh, you know, while you talk about them, but it’s not really that it’s like, Hey students, we’re here because of you. So shouldn’t, we try to involve you and are decision making. To some extent, it’s not like we don’t know what we’re doing, but we’re doing things because we wanna advance your learning.

Bethany Lockhart Johnson (15:40):
I mean, I still remember the first time I did a teacher time out and it, it was, I, it was breaking the four, it was this like, okay, you’re gonna see what happens, kids like, look at my, my tap dances stopped. And you’re you mean like, you know, whoa, wait a second. And I think it is about how you frame it. Right? It’s a celebration of their thinking and you, you use the term ambitious teaching and it, to me that is such a joyful way to think about it.

Elham Kazemi (16:06):
It is risky. And you would never say anything to shame any student, no. Or to shame your colleagues. Clearly it’s not a about that kind of discussion. Right. And they’re so brief. They’re like, it, it seconds. It’s not like you’re wasting time. You’re actually trying to understand what’s happening here. And I’ve just had so many instances where something goes on. Um, like we were doing a growing patterns task in a classroom and the student built the fourth term and they built stuff that did not follow the pattern. And I was so confused. I, I just didn’t understand like what was going on. And one of the kids said, well, if you, if you did follow the pattern, that’s not her words. But you know, she’s like, well, if we built it this way, that would be too obvious. Because if you just, if you saw that and you’re like, oh, that lesson failed.

Elham Kazemi (16:59):
Now we, our kids don’t understand what patterns are. We did it. Like, we gotta pause here and we gotta say, and we’re like, well, what do you mean? Can you say more about that? And basically what they said is that, um, well, first of all, they’re, they’re right. A pattern could change at any time, but it’s like, it would be more interesting if they, they knew how many cubes it would take for the fourth term that it would be nine, but they’re like, Hey, let’s rearrange that nine in some cool new ways. <laugh> cause that’s more interesting. It was like more interesting to them if, if they didn’t keep the pattern. So like, you kind of had to wrestle with that in the moment <affirmative> with them. And that’s how they can actually be partners with you in the teacher, timeout.

Bethany Lockhart Johnson (17:40):
Right. That’s making it about them and their learning. It’s not about that. It’s not about your performance and like looking all shiny and, and I’ve got it all together and I know exactly how this lesson’s gonna go. It that’s so interesting.

Elham Kazemi (17:53):
And sometimes you pause and like some cuz somebody else who’s watching is noticing something about what the kids are doing. And while you’re, if you’re happen to be the person who’s upfront at the time leading, you’ve got so many things going on in your head that some times the person who’s just been sitting on the rug with the kids mm-hmm <affirmative> has noticed something. And they’re like, can I ask something right now? And that’s a great teacher timeout too. Mm. Because they’re interrupting you cuz they’re like, I think I, I wanna see what kids will say. If we ask this question next and those moments have been like amazing because someone has noticed something that another person hasn’t in the room and it’s been very helpful to illuminate how kids are processing something or what two ideas they could connect. That would be really powerful based on what we were hoping to learn that day or do with the kids that day.

Dan Meyer (18:47):
It’s like you have a bonus brain attached to you there in the room. Sounds really powerful. I wonder a couple about the student experience of this. I’m imagine if I was a student in the room and I heard the two teachers like kind of pause, take this time out and like talk about how interesting my thinking was like behind my back a little bit, like trying to strategize about something interesting. I had said, I just imagine I would, I would feel very good about like, that would be a very positive experience for me. Um, but I’m just curious, can you speak to how students reacted when they’re,

Bethany Lockhart Johnson (19:16):
You mean, if you had been a student in the class and you saw two teachers conferring about your work?

Dan Meyer (19:21):
Yeah. Yeah. Like I, my classmates had of thing that was like, it, it kind of like was so novel that it stymied the teachers and then they like had to pause and like talk about what are we doing? Oh, I don’t know. I can imagine that’d be like know a fun feeling. Maybe I just tell more about me than about the kids, but

Elham Kazemi (19:35):
<laugh> it points to like, how would you go about starting to do this work? Right. Because one is you do, you do have to tell kids, Hey, I’m here with so and so and so, and so, and so, and so it might be just two of you. It might be five of you. It might be more and you know how we’ve been working on X thing in class? Well, today we wanted to try this new thing and, but we’re not sure how it’s gonna go and we need, we need your feedback. Right. So here’s something that might happen. We might pause you, you, I mean, you really do directly tell the kids to do that. And then we’re gonna ask you how it felt and we’re gonna share those feelings with one another. So you do that, you do a little exit card or you,

Bethany Lockhart Johnson (20:19):
How, what felt the pause or how,

Elham Kazemi (20:22):
How, yeah. How did it feel that, how did this lesson go or how did a lesson, how did it feel when you heard, you know, ALM and Dan talk to each other, doing this lesson and they might say, Hey, it’s cool. It’s fun. Kids have definitely chimed in, in like, if we ask a question like, should we do this next or this, somebody will pipe in and say, do that, you know, do this thing. Instead. If, if you kind of pipe in to say, can I ask a question? They just turn to you and look at you and answer your question. Right. So, and we always thank them and we just like pump it up. Right? Like this is so cool because this is all about you. And usually when you say today, you’re gonna be our teachers, especially the little kids. They like get all giggly. Totally.

Bethany Lockhart Johnson (21:02):
Right.

Elham Kazemi (21:04):
Love it.

Bethany Lockhart Johnson (21:05):
You know, you, you were sharing about this really unique situation, which I wish it wasn’t as unique where you had the whole school involved, but how did that happen? And what if you don’t have the whole school involved? What if it’s just me in my grade level, who’s like, I kind of wanna try this, but what

Elham Kazemi (21:22):
<laugh>, I think you could start with your, a peer in your school or a colleague in your school. Yeah. I mean, it’s a little seed, right. And it’s a little seed and then you could make it grow. I also believe in starting small and growing, cuz you do have to invite people into a different way of thinking about what it means to learn together. So you need to experience it, um, in order to believe it.

Dan Meyer (21:49):
Yeah. It feels like we would not want to write off any student as like, oh, they just don’t wanna learn. I think a lot of, a lot of us just like don’t buy that, that there’s other reasons why people need that. A teacher shouldn’t like shouldn’t, that’s not true of students that they have been told they can’t learn or there’s various circumstances the same. I, I suppose the same as like should be true is true of teachers. Like no teacher doesn’t want to learn more about teaching is at least a helpful Axiom to use, to approach the work of teacher growth. And so maybe they, yeah, maybe I feel like I’m the only person in my school who wants to do this, but perhaps that’s not actually true. Perhaps it’s just a matter of creating an imagination or the right kind of enticement or I don’t know what, um, but to start small and grow from there makes a lot of sense.

Elham Kazemi (22:32):
I feel now, like it would be weird and a lot harder for me to invite someone to just come in and watch me teach and sit quietly in the back when I don’t know anything about what they’re thinking and wait until afterwards to get their opinion.

Bethany Lockhart Johnson (22:46):
Oh yes.

Elham Kazemi (22:47):
I would be much more willing to co-plan with someone so that we were both on the same page about what we were trying to do and then when you’re in the classroom with me. So that’s the other thing that’s important cuz I don’t think you can just be in the classroom together and I, you know, interrupt each other’s teachers, if you haven’t planned together, cuz you do have to have some common understanding of what are we trying to do here? Oh the

Dan Meyer (23:10):
Intent here.

Elham Kazemi (23:11):
Yeah. So I would definitely say don’t just show up in each other’s classroom and start interrupting each other. <laugh> if you don’t know what the heck is going on. Yeah.

Dan Meyer (23:21):
Yeah. I, I know that’s directed at one person on this call in particular. I hear that.

Elham Kazemi (23:25):
I know who we’re talking about, but you know, I would be way more intimidating for me if I was trying to do a three act task and Dan just came to watch me do it <laugh> and he hadn’t planned with me. He didn’t know why I selected that task. I had no opportunity to talk to him. Then it would be, Hey Dan, would you just like do this with me? Let’s think through this. Why would you do this then? What, what have you normally done? Oh, okay. Why have you done that? Right. And then to like, okay, let’s try it together. Um, and then, and then along the way, if I have questions, you’re there with me. So sometimes there is someone more experience like if right. And sometimes you’re both just like, I just don’t have that much experience with this. I’m learning this for the first time.

Elham Kazemi (24:04):
Right. And the beauty of the math ed community, whether it’s on Twitter or is that we’re kind of pretty accessible to each other. Right. So if I read something and I have a question about it, you bet I’m gonna reach out to the author <laugh> and say, I’ve been thinking about your work and this is what’s been coming up for us. Can you? So like, it definitely happened with hands down conversations. We tried it in the learning lab and we just couldn’t figure out like that. How do you intercede, like into the hands down conversation cuz the kids are supposed to have a conversation. So we had to like give Kaia and her co-author a few specific examples so they could help our thinking so that we could try it again. Right. And make it better. And I think that is, is what it means to be learning in community is that you use the resources more broadly.

Bethany Lockhart Johnson (24:52):
That’s a beautiful reminder too. And it also helps me feel a little better about all the messages I’ve sent you. Like what does this mean? Can you help me with this?

Elham Kazemi (24:59):
<laugh> I mean, that just makes you feel alive. <laugh> I think

Bethany Lockhart Johnson (25:06):
So. I think P part of the beauty of you talking about starting small is that it does give those of us who maybe aren’t seeing that those opportunities for collaboration reflected in our school culture, it gives us kind of some hope for like, wait, don’t just like, think you can’t start. I, how do you, how do you see, how do you see it growing? Or, or do you think like if you could magically <laugh> like wave your wand and, and create some shifts around, around, uh, the culture where folks are feeling isolated or maybe don’t feel like they have the needs to do this work. What could that look like?

Elham Kazemi (25:51):
Yeah. What could that look like? So time, like we need some imagination around the use of time in schools and I have seen some really amazing opportunities where teachers get to co-teach, which means that they really have to co-plan when, um, there’s a break in a regular school session and there’s like an intercession or like a, like an elective that, um, that doesn’t, I haven’t seen it happen a lot in public schools, but I have seen it happen a lot in independent schools where they’ll have like, stop, stop the presses. It’s like a drop everything and read, but it’s like a drop everything and do an R arts week. And then all the kids in the school get shuffled. So they into multiage groupings and the teachers get to plan something special for like the week. But you could start with like a day, which would at least get you to plan something together and try to teach together and be just in each other’s spaces. And I think that might be kind of an interesting way to start where you have to like mess with the schedule somehow. Cuz the schedule is the beast in schools

Bethany Lockhart Johnson (26:59):
Is kind of the first step. Like we are going to create a shared activity, a shared instructional goal, a shared like where do I start?

Elham Kazemi (27:09):
What, where do you start? I mean, there’s so many good books. We all read, start with something that grabs your imagination. That you’re like, if I got to do this in my class, I’d be so jazzed. And I think my kids would love it. Why would they love it? You know, whatever it is. There’s so many good ideas that people are instantly blogging about publishing, um, slow reveal graphs. I love those two. I have like all these things. I was like, I would love to try these out, but I, I gotta do them with somebody cuz I need a sounding board about like how, what does it mean to do it well? And what does it mean to just do it at the surface level and do it a, you know, in a kind of a crappy way. And we don’t wanna do a crappy job. We wanna do a good job, but you have to start, you have to start sometimes in an awkward, crappy way. Like, you know, and get past that stage. Cause often we try a bunch of stuff, eh, and then we drop it. But like you gotta work on it to make it really

Bethany Lockhart Johnson (27:58):
Good. And if you’ve already tried it and it didn’t go so well it’s, this could be an invitation, like, you know, it doesn’t mean give up on the idea. It means like, Hey let, let’s let’s collaborate. Let’s you know, come into my class. Let’s co plan this.

Elham Kazemi (28:10):
So I would challenge people to think about the schedule. <laugh> try to do something just a little bit different. You know, like when we do learning labs, people are like, well, how do you do that? And there’s no money for it. Actually. We just use our money in a slightly different way to make or that everybody four people get a sub, which I know right now, sub shortages is crazy, crazy, but then combine your classes or do something different. Yeah. You know, um, involve people differently somehow in your, in your school environment to get that time,

Bethany Lockhart Johnson (28:43):
Really see this as a priority. This is a, this is there’s is intense value in this time to collaborate. Yeah.

Elham Kazemi (28:51):
Yeah. There’s so many side benefits for, I think for kids and teachers when you’re able to do this.

Dan Meyer (28:58):
Yeah. You’ve heard of folks. Uh, usually our, our math teacher challenge, our lounge challenge has been, uh, pedagogical in nature or a new CU. And uh, this is a different kind of one. This is, uh, go, go be a Rabel Razr go Rouse rabble at your, uh, front office and figure out the right way to get some funding or some time or shuffle a master schedule in such a way that you have collaboration, time to plan to co-teach to interrupt one another and uh, let us know how it goes. We are super excited and super interested in all of that. Thank you, uh, Elham for being with us here today and sharing all of your wisdom about how teachers grow.

Elham Kazemi (29:36):
Thanks for reminding me. You too loved

Bethany Lockhart Johnson (29:38):
It. We’re never done learning. We’re never done learning. Nope.

Bethany Lockhart Johnson (29:44):
Aha. Thank you so much for joining us in the lounge. I think all of us have sat through effective and ineffective professional learning sessions and just helping us to envision of how this can truly help PD can truly transform our classrooms. It is it’s exciting. It’s exciting. And I think we’ve all learned a lot from our conversation. So thank you. Thank you. Thank you. And don’t forget, you can connect with us in the lounge on Facebook at math teacher lounge or on Twitter at MTL show. Let’s keep this conversation going. Keep it going. Thanks so much for joining us. Thanks

Speaker 4 (30:20):
Everybody. <silence>.