Welcome fellow recovering traditionalists to Episode 78. Today, we are talking about Looking for the CAN-DO’s in Math.
Christina: In today’s episode, you get to listen in on a conversation I got to have with an alumni of my online course, Amy Warren. Amy is an elementary special education teacher. We discuss all kinds of topics from looking for the things kids can do, to how to do assessments with young kids, even if you are doing virtual school.
Christina: Now, before we hop into that discussion, I wanted to let you know that my online course for elementary teachers is open right now for enrollment. The Flexibility Formula is a completely online PD course for elementary teachers. Flexibility with numbers is something we cannot directly teach to kids. It comes from the experiences they have with numbers, and the connections they see between numbers. The Flexibility Formula helps elementary teachers learn how to help kids catch flexibility, so you can build math minds, not just create calculators. It is only open for a few more days, so head over to buildmathminds.com/enroll, to learn more about the courses. There is one for PreK to 2nd grade teachers, and one for 3rd through 5th grade teachers.
Christina: Okay. Let’s get into the discussion with Amy Warren. All right, Amy, let’s start off with having you tell us a little bit about your role in education and what you’re currently doing, and how you got to that spot, I guess.
Amy: Okay, sure. I am a special education teacher. I am working in an elementary school that is K through 6, because our county allows for some of the overflow from middle school. The children can stay in their elementary school for a year, and that helps with the crowding issues in the middle school. Almost all of the kids-
Amy: … at our school. This year, I’ve been working with the 6th graders, but I had them last year as 5th graders. We had the San Francisco Curriculum recently at K-5. I was watching them struggling with this, because it expected them to have had the San Francisco Curriculum since kindergarten, first grade, and they didn’t. They had teachers who taught them the old fashioned methods, and then we’re teaching the Merriam-Mutton method for multiplication, and they’re looking at us like, “What in the world are you doing,” and they don’t understand. My students in particular, had some crises in, everything was getting harder, faster. So, they already knew they were behind their peers in a lot of stuff, but this year the gap was tremendous. So, they were being emotionally overwhelmed with it.
Christina: That’s because you’re special education?
Amy: Right. I am special education, yes. But, even the typical kids in the school were also struggling with I’ve had. As an aside, my daughter tutors one of my former students, who ended up going to a different school, who I was thinking, “Wow, she really didn’t have an easy time understanding area model,” and Natalie’s like, “Yeah, but she can do the other ones, so who cares,” and I’m like, “Oh, well, if she knows how to multiply multi-digit numbers, and is satisfied that she thinks she knows what she’s doing, and she’s not asked to prove that she can break it down that way, then she’s fine.” That’s just like being able to use a calculator.
Amy: But, we were trying to get her to understand why you break them into tens, and ones, and multiply them out, and how it works, and how that applies to division, because that’s not a reason for her. My daughter wouldn’t have any of it, because of course she’s a traditional learner. So, even the typical kids who thought that they already had it, were flummoxed by the new ways of thinking, the new ways of doing things.
Christina: Yeah. I think that’s true with any new curriculum you get. Every curriculum series assumes that children have been in that series from kindergarten, on up through. But, it becomes especially difficult if the students haven’t been focusing a lot on number sense, and building strategies. Then all of a sudden in sixth grade, it’s like, “Oh, you use so-and-so strategy,” and they haven’t ever had any exposure to them. It makes it even more difficult for all the kids.
Amy: Right. And, it’s funny because, even before I took the course with you, we do collaborative planning every Wednesday. The teachers who all teach math from K-6 get together, and we’re usually analyzing data, but we’re talking about things. We’ll get examples, and we’ll all look at each other’s grade level work, and we’ll see where they are. So, we see the progression, we see what they’re supposed to be doing. I’ll say, it is, it’s awesome. But I’ll say, that that child doesn’t seem to have the number sense to understand going on. They all look at me, and they say, “What is number sense?” I’m like, “Well, it’s understanding how numbers work, and there are factors.” I was trying to explain certain things, but I, even as a special education teacher, didn’t have all the bits and pieces.
Amy: So, one of the things that you have to do as a special education teacher is task analyze. You have to break things down into pieces so that they can show what they can be successful with, and take it step, by step, by step, to get to the major point. I knew, back when I got my masters and taught. Okay, so I taught for seven years, and then I took 14 years off, and worked another master’s degree, and a doctorate, and then raised my kids. Now I’m back in those schools for seven years. So, there was a huge break between learning about how to teach math, and coming back into it at the elementary level. There are things that have happened, and I knew it from having my children go through school, but I didn’t see the breakdown.
Amy: So, I had like my Ginsburg, and Baroody, and my team of two, and my math lessons. They went as far as recognizing one, and two, and more, oral counting, counting cardinality, and that’s pretty much where my understanding of early math was. Now, I’m trying to help the kids solve word problems. There are, as you have in your class, 8 steps, and I only had three of them. So, tasking without knowing what those steps were, was really hard. We had a math coach, and she was showing us, “Well, you need to show them benchmarks,” and I’m like, “Well, what the heck is a benchmark? Because, I haven’t been teaching this way for forever, and I need to know.” So, now I see all the little pieces that you can build up with, and I’m so excited. Even though the course is for through 5th grade, my 6th graders still need it. So, I’m excited.
Christina: You mentioned it very quickly, but Ginsburg and Baroody are foundational research of early numeracy. So, you have that base foundation already before you ended up taking the course. Then you said the course gave you even more of those pieces to be watching for, with your kids. I loved how you talked about it as looking for the things that they are able to do. So hopefully through that, because if we only know some big rocks of the things that our students are supposed to be able to do, but we don’t know all the layers that it takes to get those big rocks in place, all we end up seeing are that they don’t have this thing, that they can’t do this piece. But then, once you learn all the underlying things, then you can finally see, “Oh, they do have this,” and I can build upon that to help them get to that final point of the big rock that I’m needing them to know.
Amy: Yeah, exactly. For each of my students, because if they have special needs, their processing problems are all different. So, you’ve got the children with the visual problems where visual spatial is going to be a real problem. You use their auditory and their understanding of number sense, if they’ve gotten to that point, to help them with the visual stuff. And, you’ve got the kids who are having just global problems processing things, and the language is hard. I have one child who doesn’t get that sometimes the answer can be called a different thing. So, it could be the sum, or it can be… They just look at you like, “You’re asking me a different question than you just asked me. You used a synonym.” So, you have to pay attention to those pieces as well.
Amy: You have to have a full understanding of all of it, so that you can say, “Well, this one child doesn’t get decimals, but he sure does know how to count money. So, let’s turn all the decimals into money for now,” and make it what they’re interested in. With universal design that we need to do, we need to have all these bits and pieces, and we have to look for the candidates. We have to look for the things that they can attach something to. If you start with an assumption that they know that when you’re rounding, you want to go either down, or up to that decade, if you’re doing tens.
Amy: So, you either need it to make it go to 0 or the next one, then that idea that there’s a middle ground, that we need to pick which one in they’re on. For me, it was hard to explain why you go up when it’s 5, and not when it’s 4. Now I have skills that I didn’t have before that I can use, and I can use the words, and I can use the number line, and I can use the blocks, and I can use Cuisenaire rods, but I have the vocabulary of the benchmark. We’re going to look for the benchmarks, and we’re going to see. We just started doing that this week, with our number lines actually.
Christina: That’s awesome. You had said that you’ve been in school for about five days. Are you guys face-to-face? Are you virtual? What’s your setup so far for 2020?
Amy: We’re virtual and, we have a CEO, not a superintendent. It’s a very big district. Prince George’s County surrounds D.C., it’s huge, and we have a CEO. I think what she wants us to do, is to rethink education, and be in the forefront of how it’s changed. So, she wants us to do a whole semester this way, so that we don’t just learn how to do it, and then all a sudden switch, and go hybrid. So, around December 1st, we’ll decide what happens in the second semester, from February to June. But, for now we’re pretty much fully distant, same school hours as before. We have our kids come in at 9:30, and they leave at 3:40. But, we have breaks built in, and we have chunks of direct instruction, and then chunks of independent work, and chunks of break, and then chunks of lunch, and chunks of extension, or small group work. A lot of stuff that happens on Wednesday.
Christina: What have you, I guess, taken from the course and implement… I know it’s only been a few days of getting going, so you can either say something you have done, or what you plan on ensuring that you do this school year. What was something you were like, “I am going to make a point of doing this thing?”
Amy: Well, I learned about numberless word problems, and bet lines, and that was the whole reason I wanted to take the course, because I couldn’t figure out why, if they had what I thought they had enough number sense to do, they couldn’t work the word problems. Because, we do the reading comprehension and get the stories right, and we do a three read protocol with San Francisco. So, the first time you read it, you just figure out what’s going on, and then you put the numbers in. I started to do it at the end of the year, when we had our continuity of learning, just 4 hours lessons.
Amy: Some of the kids really hooked onto that, and some of the kids were still a little mehh about it. So, I need to do more conversations with the kids who are on pulling from them what they’re seeing, when I’m talking about, “Some girls went into a class, what do you see? What’s math?” Then we go from there, and some of the kids got to the point where it says, “Some girls,” and it says, “Girls,” with an S on it, so that’s got to be more than one. So, it can’t be 0, and it can’t be one, it’s got to be at least 2. And then the others were saying, “well, maybe it’s 10,” and it just came this organic conversation. Then the guys that were reluctant to participate had something to add. It was good to have them do that, but it was all the numberless word problems, and I’m going to implement that lines with it. What do you think? What’s your bet?
Christina: Yeah. I love the combination of those together, of when you only give the story problems a line at a time is called a bet line. There was a study done by a group in North Carolina, we’ll link to the study that was published by the NCTM. So, I’ll make sure I link to this when people are watching or listening to this, to that article that talked about how it helps our English language learners. But, I’ve found it is so helpful for all of our learners, to only give them a line at the time, and say, “What do you bet is going to happen next,” and just helping them learn that structure of how story problems actually are supposed to sound.
Christina: They get, I think it was Graham Fletcher who called them number pluckers, where they will just pluck out the numbers, and try to operate. So, the numberless where you don’t even give them the numbers, but then you also only reveal a line at a time, those two things combined really make the kids have to slow down, and think about the situation that’s actually happening, and not just pulling out numbers to operate with them. So, it does, it helps with the story problem stuff, but also is building a lot of number sense as you go through it, too.
Amy: Right? The thing is, a lot of our kids need chunking when they’re doing reading, because too much information at a time is overwhelming for them to process. Well, this is chunking in math, and I love it. I can’t wait, and you’re right. When they’re number plucking, they pluck the numbers, and then they add them, because they know adding.
Christina: Absolutely, yeah. Or, they’ll just pluck and do whatever operation you’ve been doing. If you’ve been doing a lesson on multiplication, and then there’s a story problem, they just assume you’re going to multiply, because that’s what we’ve been working on. So, they just grab the numbers, and multiply. It’s crazy how they get trained into finding those little tricks. Even if you don’t try to teach those tricks to kids, they will naturally try to pull those out, and so instead of them trying to find those tricks, one of the big pieces that we talk about through the course and stuff, is to help those kids start to notice relationships and patterns. That’s the biggest part of mathematics that helps you be able to think through mathematics, not just do mathematics.
Amy: Right. I remember the stern blocks, from, what are they from, the 40s? Maybe the 60s. There’s a four in it, it’s either 46, or 64. There were stern blocks that I learned about in my first master’s program, which were to teach number sense, but they basically turned into base 10 type cubes and sticks and flats. They also had the old wooden base that you filled the blocks in, and it would be one, and then two. You would put them in, you would say one, and.., And fill them in and go all the way to 10, and I am dying for a set of those, because I have so many kids that I need that kind of background, before we then do a 10 frame. Which they also have three-dimensional that you put things in.
Christina: So Amy, I’m not familiar with stern blocks, but it sounds like the Montessori beads. So, you might look into that, Montessori beads. I’ve seen wooden things, where you put one bead in for the one, and then two for two, and three for three. It really does help kids see that you build on top of each other, that the two does include a one. That’s one of the things that kids really do struggle… Like, “5 includes 4.”
Amy: And one, and, exactly.
Christina: Yeah. It’s all inclusive. I’m not sure if that’s exactly it, but you’re going to have to tell me when you look at it after this, if that’s the same thing. I’ll look, too.
Amy: I actually just printed it out an article that I haven’t read today. I looked up Baroody again, to see what he was up to, and he gave a history of the base 10 blocks, basically, included the stern stuff. I was like, “Oh, there it is.”
Christina: That’s awesome.
Amy: You really got me thinking about learning more, which is the best thing.
Christina: That’s excellent, that’s excellent. I don’t know if this is the same thing, but what we tend to end on here, is for those who are listening, you did talk a lot about things. We’ve talked about that struggle of moving into a new curriculum, the struggle of being online. You didn’t say this was a struggle, but one of the things you did talk about was doing a lot more of the visuals with your kids, looking for the places where they can do things, and then building on top of that, the numberless word problems. You’ve given us a lot to think about, so to end it, for those who are listening, and this is a trying time this year, my question is, the one thing that you suggest people try. I know that, that might be different if you were face-to-face, versus in a virtual setting, but for your specific situation, and for people who are out there doing the virtual stuff, what is your one thing that you want people to take away with and try out, maybe this coming school year?
Amy: My bet is always in assessment, and assess means, “To sit next to,” and we can’t be the way we want to be, where we can walk around and look at the kids, and see the kids, and see what they’re doing this year. So, we have to come up with another way to virtually sit next to the kids while they’re working. Finding the things that they’re doing, finding the bad example, the one that didn’t work, and having the kids explain without letting them know which kid in the class did it, apparently.
Amy: Nobody needs to see this, but being able to show them the negative example, but what were they thinking, and how is this focusing on the thinking behind, and having the children and explain more of their thought process, because that in turn, turns around and helps you know what you need to do. Because, you can see how far they got toward the answer, but you can also see where they turned off in the wrong direction, and you can go back and work on that. The other kids can work through it, and talk with them too, and everybody can get something out of that. Looking at the not quite right examples and talking through them.
Christina: That’s awesome. There’s a great video out there by The Teaching Channel that’s called, “My Favorite ‘No’,” and goes into detail of how this one teacher does it. Of course, it was face to face, but you can modify how you do that. That is a concern that I hear a lot is, “How do we actually assess kids, and sit next to them?” I’ve heard some districts that say they are all asynchronous, so they’re never online at the same time with kids. So, to be able to hear kids thinking, and know that it’s kids thinking, I think that’s a big concern for everybody. Was the parent there helping them, or an older sibling, and how do we know? All of those concerns are coming up? So, what kinds of tools or ideas do you have to help you with that?
Amy: So, you’re actually going into what my doctorate was about. I’d worked with dynamic assessment. Of the different types of dynamic assessment, one of them actually came from Ginsburg and Baroody’s test of early mathematics abilities, a team of two. It’s basically called the interview, the post-testing interview. So, you give the test the way it’s supposed to be done to fidelity, so that the norms give you what you need, but then you go back, and you ask them not just about the no’s, you ask them about how they got the yeses. Especially if you see a connection between, “Well, this one seems harder than that one, and it got the harder one right, but they got the easier one wrong, in the same vein. To be able to spend individual time, we still can do that, even asynchronously. If you have an asynchronous set up, you’ve got office hours, your kids are supposed to come to you for help.
Amy: You can also invite them to come, and you can say, “Hey, I’m looking at your work here. This is what you’ve got,” and you show it up on your Zoom, or your Google screen, your Meet screen, or whatever you’re using, and you say, “Can you talk me through that? Just tell me what you did,” and that post-work, or post-test interview, is an actual dynamic assessment. For my doctorate, I actually studied teachers doing math assessments with the kids that were based on interaction, and finding where the child was, and using the language to bring them up. So, you would ask a question up high, and the child would answer down low, and you would adjust your questions to meet where they were, and then build them up a step at a time.
Amy: That was a pretty awesome thing. So, being able to work with the kids during those one-on-one interviews, I think, sharing their work with them, and talking about it, directing them through the next steps. It’s going to take time, and it’s going to take organization, but it happens. It can’t happen.
Christina: I love that. I really love that, Amy. I’m so glad you brought that up, as your one thing, because it is… Our assessment in education has been not what assessment should really be. It is not the sit-beside, and learn what our kids are thinking. So, no matter if whoever’s out there listening is in a virtual setting, or face-to-face, that really is what true assessment is. So, rewind this, re-listen to it, what Amy just talked about there. About all of the questioning, and digging in the post-interview pieces. Those were all fabulous ideas, and can be done if you are virtual or not, and are really, truly, the thing that we should be doing for assessing, and really getting to the root of what the kids know, and are able to do. That was fabulous. So Amy, thank you so much for taking time to hop on here with me. I really do appreciate it, especially for your insights about assessment right there. That was fabulous. I didn’t know that’s what your doctorate was all about.
Amy: Well, I actually have a Reuben assessment called math plan, that’s based on balanced assessment from Harvard, that I got my copyright back from, that sitting downstairs, but I haven’t done anything with. So, I’ve been thinking about how I actually need to get that out there, and self-published, or something. So, I’m going to be sharing with you pieces of it, I need your advice on how I’m going to go ahead and do that, because I think it’s a useful tool that we can use these days.
Christina: Absolutely. Yes, yeah. We’ll chat more.
Amy: All right. Thank you so much. I have other interviews to get to.
Christina: Yes. Thank you so much, Amy. I really do appreciate it.
Amy: All right, you’re welcome. Thank you for having me.
Christina: Now, a reminder, that if you want to learn more about the things Amy and I discussed, come join me inside The Flexibility Formula at buildmathminds.com/enroll.
The Build Math Minds podcast is brought to you through the work I do with online courses, for elementary teachers. For the past five years, I’ve done online courses to help educators better understand how to build students’ number sense. Well, after thousands of teachers have gone through these courses, I’ve seen some things that need revised and I’ve learned new things along the way as well. So, the number sense courses have been reworked, and the new versions are called The Flexibility Formula. Inside The Flexibility Formula courses, we will take a look at how we build students’ flexibility with numbers. There’s a course for PreK to 2nd grade teachers, and a course that is for 3rd to 5th grade teachers. More information will be coming soon, but if you’d like to be the first to know about it, head on over to buildmathminds.com/courses to join the wait lists.
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