S6-02: Assessing fluency

I think assessment and evaluation are two different things. Evaluation is often where we put a number to something and we try and give it a grade. Assessment is where we're trying to understand what students are thinking and I think they're very different animals. Hi and welcome to another episode of Math Teacher Lounge. I am Bethany Law-Card Johnson. And I am Dan Meyer. Dan, we're in fluency land. How you doing? How you doing? I'm getting more and more interested in it. Every new guest we talk to gives me some new angle on fluency that helps me see. What an important part of it is of a student's development of new ideas and I'm also in my own personal life getting excited to see fluency kind of bloom with that. Wait, wait, say more about back that up. I'd be happy to thank you for asking. Yeah, so I've been noticing one of my kids does direct counting no matter what the sum is. You know, like four plus three. I'm going to start at one, two, three, seven, or ten plus twelve. It's like I'm going all the way back to one. I'm going to direct count that thing the first ten, the next twelve. I'm like I'm just like I find it more fascinating now. So like what is it? What are the experiences that he needs to be able to see the value of just like not just say, here's ten. I'm here at ten and now count up twelve more, let's say. And I've seen the limitations of just like saying, hey, do this. Like you should do this thing. It's like, wow, now kids ideas just take longer. You're not doing that, Dan. You math teacher Dan are not telling your child, no, no, no, solve it this way. No, there's no way to do that. I just I haven't tried it, but okay, okay. There's just futility where the kids is like not ready for it. Like whatever's going on in his brain is so much more powerful and durable than any words I would have to offer. However, I have been offering various experiences like for instance this game that I don't know we call it garbage that has like has five cards on top in a row and five cards on bottom on a row. And the kids got to find seven. And so at first he'd count one, two to five, six, seven with his fingers, which are counting, but recently we've had enough of those experiences where he just starts at six. Like he just says that first row is five. I know this now or he's even started it 10 and gone backwards. And so I just, to me, like it's a mystery. Like it is a mystery. I love a good mystery. Love a movie mystery, a book mystery, love a math mystery. Like how are these ideas taking root in his head? That's where I'm coming from with fluency this week and kind of excited to talk more today about it with you. I love hearing that and sorry I jumped on you a little bit because I got, I thought you were saying, you know no matter how many times I tell him that's not how you do it, he keeps doing it. I'm like, who are you? I'm like you won't get dinner. There's no dinner tonight for you. Counting on if you want to treat. Yeah, you know me. Let me tell you, but what I love is that you're giving him repeated experiences to practice building that relationship with those numbers because that is exactly what, you know, we celebrate in our classroom, right? You, yeah, oh, what if we do this and now he gets it, he sees that five, right? Eventually, well sure, you can keep counting up to five, but eventually he won't need to. He's like, okay, five, six, seven, or you know, what if you give him like some larger number, something like 32 plus two? You know, he could, he may start at one, I've seen it and go all the way up, but maybe he would hold that number, that large number and then count on, but you know, I could sit here and tell you, you can't help yourself, Ken, I can't help myself. You're like, what's the next thing? So much, I love the way students think I love, but you know, I've been talking, my kiddos two and a half and I'm not forcing the counting, but I do give ample opportunities for counting. I love counting with my kiddo and exploring different concepts and math, but I think we need more of this Dan. We need more of you sharing what is going on in your household as your kiddos are beginning to develop fluency. Oh, I am game. I'll take a daily report. The real win of it all is that they ask to play this game. They don't know that they're learning math. See? So yeah, I love talking about this with you. It's grown on me and I love the guests that we bring on and how the perspectives they bring to bear on fluency and none more so than Dr. Val Henry today. Yeah, if you love talking to our guests, you are really going to love talking to Dr. Val Henry again. We spoke with Val a few seasons ago about fluency in a shared episode with Tracy Zager and Graham Fletcher getting a couple different perspectives on fluency. But today we are talking to Dr. Val Henry specifically about assessment, but we will ensure the conversation will run the gamut. She is an amazing, dare I say expert on fluency? I mean, she's been thinking about this for decades and she's done research about it and developed a program called FaxWise that I've used in my own classroom and she also is a university professor at the University of California Irvine and teaching pre-service teachers and helping them develop their relationship with math as they dive into their first classrooms. So I hope you folks, yeah, enjoy this interview as much as we did with Dr. Val Henry. We are so thrilled to have you back, Dr. Henry. Welcome so much again to the lounge. Thank you so much for joining us again. Thanks Bethany and Dan. Thank you both for inviting me. Oh, did you hear that? That was kind of. It was like a dot dot dot. It was a very short pause. I'm happy with how that went, honestly. Yeah, welcome back, Dr. Henry. Thank you. It's actually kind of appropriate because we recently chatted with Jason Zimbabwe who we were really excited to kind of get a peek into his brain and how he thinks about fluency and mathematics in general. And we also kind of worked on. Well, we, I worked on Dan a bit because Dan's been a little less than enthusiastic about fluency, but I'm telling you ever since we had you on the show, we've had these questions buzzing around about fluency and it keeps coming up and we knew we had to have you back. And in fact, you're really the inspiration for this whole season. Wow. Right? Dan, before we ask any questions, share a little bit just to give a little framework about your perspective because I think it's good. She knows what she's getting into. Yeah, sure. That's fair. I do feel like you're asking me to share with Val what it is I find uncomfortable about the work of fluency that she's into, but I'll just go with it. And that's just that like as a math educator, I've always been really excited about introducing the new. I've been a little bit less excited about fluency and especially because I think a lot of the way fluency is developed in students nowadays, like it constitutes a lot of people's like really negative memories of math class. I don't want to associate fluency like completely with those bad vibes, but you know, like thinking about like the endless worksheets or mad minutes or just those kinds of traumatic experiences. A lot of them have been in the fluency realm. And so I've been a little bit a little bit kind of cold to it. Let's just say Bethany is warm to fluency. I would say warm to hot. I've really enjoyed talking with Bethany about how to develop math fluency in kids, especially as we both have really young kids and thinking about how they develop those ideas. So I want to believe I want to be a believer here. So I'm excited about this season. Excited to have you on the show. Well, Dan, I have to tell you I was cool to cold about fluency 20 years ago. So I'd been doing a lot of professional development, a lot of it around algebraic thinking back in those days. And I'd go out and work with teachers and with students. And the teachers would say, but we can't do algebraic algebraic thinking with our kids because they're not fluent. They don't know the basics. Or I'd work on problem solving. And they'd say they can't do that because they're not fluent. And I go in and I sort of show them that kids can do a lot of great math thinking even if or before they're fluent. So I was really resistant to this, but every single upper grade teacher that I talked to brought up fluency as a roadblock. So when I went back to school to get my EDD, I decided that I would really investigate this. What is going on with this? And so by learning about how other countries really do a better job often with fluency, teaching and learning, I decided maybe it was worth looking at from a different perspective, than worksheets or time tests, that kind of thing. So that we could get away from those negatives. I appreciate that background. And enormously, I feel like we have a new kinship you and me here. I also do, it does resonate with me that the new stuff that excites me is often much more challenging to students. If they struggle with some of those basics, if they struggle, I don't know, I feel like we're at the same basics. But prerequisite skills, foundational skills, I don't know what word would be most appropriate here. But that as a mission, as a, you know, your desire to understand those skills because they support these other skills that also interest you. That is, that's a helpful route in for me in this conversation. That's worth. Thank you. Cool. I'll also say one more thing that has really stuck with me over the years, I had a teaching assistant who grew up in China, I believe, and so learned her early mathematics in China. And so very fluent in English. So she was helping me with a graduate course. And I said, one of the things we're going to be looking at is basic facts fluency. And she said, well, what's that? And I thought, okay, well, maybe she doesn't understand the word fluency. So I explained that and she said, yeah, yeah, yeah, I get that. And then I said, basic, you know, like between one and 20. And she said, yeah, I get that. But why are you calling them facts? And I said, well, because, and she said, well, let me explain. In China, when we grew up, we learned that one plus one was two. And then everything else was a relationship that was built off of one plus one is two. They aren't facts. They are relationships and are provable. She said, facts are things that you can't really know unless somebody tells you. So I'll just share that as a, as an insight that I have into this whole language of basic facts fluency. I hate to call it that now, but that's what I think a lot of people understand what we're talking about when we reference it that way. This is really a helpful perspective out. And I'm saying that that's fine. Diane, you continue to call her Dr. Henry. I'm more and more comfortable with that. You know, it was my joy to get to learn from you at University of California Irvine. And I felt like the way that you approached your pre-service teachers was the same way with like you were helping us to like kind of heal our relationship with math. And something that I learned from you was really a new way to think about assessment. And when we think about fluency, people have been jumping in with like, well, time tests, right? Or we gave the example of like teachers pay teachers, they pull up like a themed time test. And therefore, if I give it to you every Friday, you're going to get it. And I know some of your research has been specifically why time tests are problematic, why why they don't work, right? They aren't enough. But you had a bigger picture of assessment. And I'm wondering if you could share a little bit about that. So what I was growing up teachers often thought that assessment would drive students to become fluent without really anything else happening in the classroom. Maybe an occasional worksheet, maybe an occasional around the world kind of game or something. But most of the time, it was assumed that you would go home, you would somehow learn those basic facts on your own. And the testing would compel you to keep working at it at home. And so assessment was sort of seen as a I don't know a force that would require kids that would compel them to to make sense and become fluent. My theory is, and this is what we do in every other subject is we teach the subject to the students. We work with them. We give them learning experiences. And then we assess to find out how far they've come towards meeting the learning goals we have. And the assessment doesn't happen without the learning experiences in the classroom. And I often talk with my student teachers about this that we would never think about saying go home and learn how to read. And we'll just test you every Friday. And therefore, you will learn how to read. So I don't see why we're doing that with math back fluency. It's so foundational to mathematics. And it gives everybody such a sense of confidence and number sense that why are we assuming that we shouldn't be teaching it. And so when I say teaching, I don't mean lecturing. I mean providing learning experiences. You're describing a diminished sense of what fluency is if it is possible to teach it just through assessing it. Like that implies a definition of fluency that I think the rest of your work speaks to the opposite idea that it is rich, requires persistent development on the part of a teacher, work from the student. That's just an interesting dichotomy that now we are moving into this other way of thinking about fluency. Yes. And I think it goes directly back to the idea that if we thought of fluency as learning facts, things that could be put into a song or things that could be chanted and that could be learned just through verbal memory, then we thought of it as something that you could just test over and over. But if we think of fluency as these relationships and finding strategies that can make connections between something that we know like I know 2+2 is 4. So therefore I can use that to help me figure out that 2+3 is 5 without having to memorize 2+3 is 5 on its own without without making connections. I'm curious if you can talk about what has assessment looked like to you in your research where you were able to really see those relationships or students were building with these numbers with these facts. And how is that maybe different than what we want to get away from? Absolutely. So when I first started reading the literature about fluency, one of the things I realized was that the psychologists who actually specialize in studying the challenges of fluency in mathematics do one-on-one assessments so that they can really hear students not only say the answer correctly or incorrectly and they can get a sense of how long it took them to come up with their answer. But they also get to ask them this really important question which is how did you get that answer? And so one-on-one assessments are so different than time tests in a couple of different ways. The first one is that you actually find out how fluent I'm going to I'm going to move away from whether or not they're fluent but sort of how fluent they are with the fact, with the math problem. As opposed to on a time test which typically has you know 20 or 50 or 100 problems and students completed and you have no understanding of how they completed it, whether they were skip counting on their fingers, whether they were jumping around and kind of going okay five times seven is 35 so now I'm going to look for seven times five because now it's in my short-term memory and then I'm going to do 35 divided by seven and 35 divided by five all without really having been fluent with any of those but just capitalizing on skip counting in short-term memory. So one-on-one assessment taught me a lot about how to really understand what's happening with students. I'm going to stop there because there's a whole other picture which is one-on-one assessment practical in the in the average classroom on a regular basis. Something I want to say I love about the one-on-one assessment idea is that I think it's been so radicalizing for a math teacher to become aware that students have interesting ideas all the time. Even those ideas don't fit into you know really precise boxes like the sort that are expressed on a time test and it sounds like these one-on-one assessments for you that a lot of work on you to help you see that oh what's going on in the development of fluency is much more sophisticated than a lot of the the timed test assessments I gave credit for. I'm just curious like what were a couple of the of the big takeaways that you had as you did these one-on-one assessments. So I've done thousands of one-on-one assessments with students from kindergarten all the way through eighth grade and well actually even higher and one of the things that has really resonated with me is that students do come up with fairly similar strategies either because they've invented them themselves or because they've had learning experiences that have helped them develop these relational ideas. So when I ask a student what six plus nine there's usually a small handful of different strategies that students will tell me about one is they just know it another is that they counted on their fingers or in their head which is not quite at fluency level for me yet but then the others are things like well I gave one for from the 6 to the 9 and that made 10. So now I have 10 plus 5. Another is, well, I just temporarily added 10 to 6. That was one too many. So then I subtracted one. It's a little bit different strategy. Another is, I might have thought of it as 7 plus 7 plus 1. And then I've had one first grader ever say that he knew that 4 plus 9 was 13 and that he just needed to add two more to get to 15. Nobody else has ever come up with that idea. Just that one little guy. So yes, you do have a lot of students capitalizing on making tens, sometimes using doubles and sometimes using a fact that they knew that just helped them build relationships even if it wasn't one of the standards. So these are just really interesting ways of thinking that aren't visible to teachers from a worksheet or printed time test where there's a number and maybe some scratches where students carried something or something like that. And you're describing like what's visible to you. What's present in these one-on-one interviews. I wonder what's possible though in the logistics of a classroom. Like you're able to do this as a researcher or a consultant and I'm curious how you'd help teachers who have different logistical demands than you doing your role. How can they capture the best of your one-on-one assessments within the constraints of a classroom, the time constraints, the student constraints? So there are a couple of different ways that I think about this. One is when I wanna understand what students, what strategy students are using. I ask them to share their thinking either in the small group setting or in the whole class setting. I usually alternate a little mini lesson where we do something usually with manipulatives or some kind of visual on the board with games. And even when the kids are playing the games, I will often ask that the students share their strategy thinking as they're responding with their answers. So they might be playing a little card game where they have the nine face up on the table and they'll pick up another card and it'll say four plus nine. And so they'll say the answers 13 and then their next job is to explain to their partner how they got 13. And so that's one way that as I'm circulating the room, I get to feel like I'm hearing what's inside their head. Even though I'm not doing a one on one assessment with them. And I work with teachers then to use that same kind of approach for hearing students' strategy thinking. Sometimes they're actually showing it with a manipulative in addition to or instead of verbalizing it. So we often have them use number racks or 10 frames, depending on whether we're doing add subtract or multiply divide. The manipulatives change a little bit but they're sharing their thinking either verbally or with the manipulatives. - I love that that you're talking about teachers becoming sensitized like through all their senses to the different ways that students are developing fluency. Even verbally, nonverbaly through manipulatives and there's something that's so special about that where a teacher becomes like a fine tuned antenna for all the different ways students are being smart and fluent in a class. I don't want to diminish that by asking but what about the logistics? But I'm kind of curious, as the teacher is moving around and is assessing students in a very real way while students aren't even really aware that they're being assessed, how should the teacher make good use of that data to support the students development? Like I know what to do with the time test that has 19 out of 20. Like I put the 19 in my grade book or something. But what are some productive ways to use all of that sensory data almost to support a student? - Great question. And my top recommendation for that is to take a class list, make some columns on your class list and start writing in some things that you are interested in looking for or looking at. And so if I were working on adding nine's, let's say, I might write in student uses plus 10 or student makes a 10. Or student uses a doubles approach or student counts with their fingers, student counts in their head. I might list all of those at the top of those columns. And so as I'm walking around, I'm able to just start making a quick check mark, maybe having some room over on the side so that I can write a note if it's something unique that I want to attend to. And I can start then looking, after that one 10 minute session or a few 10 minute fluency sessions, I can now look at my chart and see, wow, a lot of students are using plus 10. But I've got three that are still counting on their fingers. So now I know that there are three students that maybe need some extra support, maybe need some extra time with a manipulative to help with that. I can also see that the majority of my students are building fluency quite easily with their plus 9s. So we can start moving on to the minus 9s if that's the approach we're taking. - I want it to say, Val, just how much I respect and appreciate the way that you listen to students. And for me, that is what this assessment kind of all boils down to. You are teaching students to think flexibly about numbers. You're doing these routines and these games and these shareouts and spending time supporting students in like having experience working with these numbers. And the assessment is just a piece of that. The assessment comes, like you said, during the games as you're walking around or during a share out after the students are playing the games. But really, I hope that our listeners are taking from this, like Dan said, using your senses as a teacher, how much you are listening to students. I know you did this as your research, but you just so respect students thinking. And that is something that I think is so powerful. And so assessments weren't just something to squeeze in there and then you kind of don't do anything with what you find. You're really listening to them and valuing their thinking. - I think that's such an important perspective about assessment because I think assessment and evaluation are two different things. Assessment is where we're trying to understand what students are thinking and able to do, what they need support with, what they're ready to move on from. And I think they're very different animals. And so putting a number on a piece of paper doesn't help me know what to do next with my students, but listening and engaging with them does let me know what's the next thing that I can do to help them. - Yeah, what you're describing to me has much more in common with my asking, a friend, how is your day to day than any kind of math assessment I think a lot of us are familiar with. Like you're seeking to understand, it's conversational. I like that distinction between assessment and evaluation. When I ask, how was your day? I'm not trying to evaluate your answer anyway. Just understand you a little bit better. - Definitely. So I have had teachers ask whether this writing things on a chart as I'm listening or as we're circulating around watching students is good enough to put on a report card. And so I've asked a few principles, what would you think if your teacher stopped giving time tests or stopped grading worksheets and did this approach of listening in and understanding where students are in their thinking and kind of marking it down on a piece of paper, would that be good enough in terms of reporting back to parents? How students are doing on a report card? And at least the principles that I've talked to have said absolutely, that's a completely responsible way of grading fluency if you have to grade it. - Val, I was in an Uber in Colorado and I thought of you because the Uber driver was like, "Oh, what do you do?" We were talking, I was there for a math conference and her first reaction was like, "Oh, she's like a conference where you just talk about math that you know whatever." And then she immediately launched into, "Oh, I hear those standards, "I hear they're really asking kids, "it's not even how kids think." And she went into kind of this whole thing and she's like, "What is it even all about?" And the first thing that came to mind, I said, "Well, if I asked you to add, what's 9 plus 7?" And she said, "16." And I said, "Well, how did you get that?" You got that pretty fast. And she said, "Well, I don't know, "I guess I took something from the 7 to make it a 10." And I made 10. 10 plus 6, right? And I said, that's it. Yeah, exactly. That's it, right? You broke apart those numbers. You're thinking about those numbers flexibly. And that's what we want to happen in our classroom that our students feel like they can manipulate numbers and think about it in new ways and share their thinking. And I tell you, I was thinking of you and I asked her that. And I think she gave me a pretty good rating as a passenger. If not for that story, you know, no, but for reals though, she, it was a really good reminder for me that so many of us have these negative experience with fluency, with mathematics, with assessment, right? And when it's conversational and when it's just a part of like, let's talk about this. What went on in your brain? How are you thinking about it? It can be really positive. You know, what's really fascinating is that students love to talk about their thinking and they feel very special when the teacher listens to them individually. And so sometimes we can listen to them individually by doing a one-on-one assessment. Sometimes we can just interrupt the little activity or game they're doing with a partner and say, you know, I just would love to hear how you thought about that one. You know, I want to know. And so the logistics kind of back to Dan's question of one-on-one assessment versus this kind of circulating as students are interacting with the mathematics, usually with a partner, is that you can interact one on one with a student for 10 seconds and they get that same sort of validation and you get to hear what they're thinking or you can spend five minutes with them doing a full-on sit down with one student kind of one-on-one assessment. And the reality is most teachers are finding that those quick 10-second interactions are more viable in the classroom than the sit-down one-on-one with every one of your 30 students once a week kind of assessments. Val, before we go, I'm wondering, is there a final message or thought that you want to leave our listeners with? - So one of the things that I've been so impressed by over the last several years is common core instructional materials have become more available is how much more confident teachers have become with relationships related to tens. Because this is what we see from countries that really have very strong fluency programs is that they invest their time in tens. If it's adding and subtracting, they're making sure that their students know that one plus nine is 10 and two plus eight is 10. I have a Korean first grade textbook where students spend an entire chapter learning how to make all of the ways to make 10. Not one lesson, one chapter out of their 10 chapters. And then the next chapters are about how do you use tens to work with numbers? So for instance, seven plus eight, a lot of American teachers in the past have thought that well, we should teach kids to do seven plus seven plus one. But that's not what I've read and seen in other countries' approaches. They're constantly and consistently building making tens. So seven plus eight, the most likely approach of students from these other countries would be to give two to the eight and then have 10 plus five is 15. So I've been really impressed by the fact that teachers understand more strategies because their instructional materials are emphasizing that. The thing that I'd love for teachers to think more about is why other countries emphasize making tens and de-emphasize doubles. So I've done a little analysis and doubles and doubles plus one limit the number of facts you can solve within the up to 20. And they absolutely limit what you can do within 100. So for instance, how many problems beyond 20 really work with doubles plus one? You know, if I ask what's 38 plus 49, doubles plus one doesn't help me at all, but making a 10 helps. So I think that's one of the things I've been really impressed by is this shift towards tens thinking. - That's a great to get your perspective there Val. I know that as the Common Core first rolled out, a lot of parents were very uncomfortable as some of the changes especially around fluency. And it's really been a generational project as the students who were coming up in the Common Core are slowly becoming teachers. And it's just great to have your perspective on these two snapshots before and after and what has changed and the value of 10. So thank you so much for coming on with us again. Again, you inspire the whole season. And it's just been great to have a moment to dive deeper into fluency with you and trade ideas. Thank you so much. - You're welcome. And I look forward to hearing from teachers. It's maybe they get a chance to think more about assessment and fluency. - Thanks so much, Val. - Thanks so much for listening to our conversation with Dr. Val Henry, creator of Faxwise. - Check out the show notes for more information on Dr. Val Henry and Faxwise. Let us know what you thought of this episode in our Facebook discussion group, math teacher lounge community. We're still early in this new season. So let us know what you'd like to hear about when it comes to math fluency. You can share your questions, your ideas, your thoughts, your wonderings. And make sure you catch all the episodes in this new season by subscribing to math teacher lounge wherever you get your podcasts. And while you're there, we'd really appreciate it if you could leave us a review. It helps other listeners find the show. And, you know, if you're enjoying it, let a friend know about it. You can find more information on all of Amplify's great shows at our podcast hub, go to amplify.com/hub. Thanks again for listening.