Assessment in the Early Years Guest: Shelly Scheafer
ROUNDING UP: SEASON 3 | EPISODE 13
Mike (00:09.127) Welcome to the podcast Shelley. Thank you so much for joining us today.
Shelly (00:12.956) Thank you, Mike, for having me.
Mike (00:16.078) So I'd like to start with this question. What makes the work of assessing younger children, particularly students in grades K through two, different from assessing students in upper elementary grades or even beyond?
Shelly (00:30.3) There's a lot to that question, Mike. I think there's some obvious things. So effective assessment of our youngest learners is different because obviously our pre-K, first, even our second grade students are developmentally different from fourth and fifth graders. So when we think about assessing these early primary students,
we need to use appropriate assessment methods that match their stage of development. For example, when we think of typical paper pencil assessments and how we often ask students to show their thinking with pictures, numbers and words, our youngest learners are just starting to connect symbolic representations to mathematical ideas, let alone, you know, put letters together to make words. So
When we think of these assessments, we need to take into consideration that primary students are in the early stages of development with respect to their language, their reading, and their writing skills. And this in itself makes it challenging for them to fully articulate, write, sketch any of their mathematical thinking. So we often find that with young children in reviews,
you know, individual interviews can be really helpful. But even then, there's some drawbacks. Some children find it challenging, you know, to be put on the spot, to show in the moment, you know, on demand, you know, what they know. Others, you know, just aren't fully engaged or interested because you've called them over from something that they're busy doing. Or maybe, you know,
they're not yet comfortable with the setting or even the person doing the interview. So when we work with young children, we need to recognize all of these little peculiarities that come with working with that age. We also need to understand that their mathematical development is fluid, it's continually evolving. And this is why
Shelly (02:47.42) they often or some may respond differently to the same proper question, especially if the setting or the context is changed. We may find that a kindergarten student who counts to 29 on Monday may count to 69 or even 100 later in the week, kind of depending on what's going on in their mind at the time. So this means that assessment with young children needs to be frequent.
informative and ongoing. So we're not necessarily waiting for the end of the unit to see, aha, did they get this? You know, what do we do? You know, we're looking at their work all of the time. And fortunately, some of the best assessments on young children are the observations in their natural setting, like times when maybe they're playing a math game or working with a center activity or even during just your classroom routines.
And it's these authentic situations that we can look at as assessments to help us capture a more accurate picture of their abilities because we not only get to hear what they say or see what they write on paper, we get to watch them in action. We get to see what they do when they're engaged in small group activities or playing games with friends.
Mike (04:11.832) So I wanna go back to something you said and even in particular the way that you said it. You were talking about watching or noticing what students can do and you really emphasize the words do. Talk a little bit about what you were trying to convey with that, Shelley.
Shelly (04:27.548) So young children are doers. When they work on a math task, they show their thinking and their actions with finger formations and objects. And we can see if a student has one-to-one correspondence when they're counting, if they group their objects, how they line them up, do they tag them, do they move them as they count them. They may not always have the verbal skills to articulate their thinking, but we can also attend to things like head nodding,
finger counting, and even how they cluster or match objects. So I'm going to give you an example. So let's say that I'm watching some early first graders, and they're solving the expression 6 plus 7. And the first student picks up a number rack or a rec and rec. And if you're not familiar with a number rack, it's a tool with two rows of beads.
And on the first row, there are five red beads and five white beads. And on the second row, there's five red beads and five white beads. And the student solving six plus seven begins by pushing over five red beads in one push and then one more bead on the top row. And then they do the same thing for the seven. They push over five red beads and two white beads. And they haven't said a word to me. I'm just watching their actions.
And I'm already able to tell, hmm, that student could subitize a group of five, because I saw him push over all five beads in one push. And that they know that six is composed of five and one, and seven is composed of five and two. And they haven't said a word. I'm just watching what they're doing. And then I might watch the student, and they see it.
I see him pause, know, nothing's being said, but I start to notice this slight little head nodding.
Shelly (06:26.748) And then they say 13 and they give me the answer and they're really pleased. I didn't get a lot of language from them, but boy, did I get a lot from watching how they solve that problem. And I want to contrast that observation with a student who might be solving the same expression six plus seven and they might go six and then they start popping up one finger at a time while counting seven, eight.
9, 10, 11, 12, 13. And when they get seven fingers held up, they say 13 again. They've approached that problem quite differently. But again, I get that information that they understood the equation. They were able to count on starting with six. And they kept track of their count with their fingers. And they knew to stop when seven fingers were raised.
And I might even have a different student that solves the problem by thinking, hmm, and they talk to themselves or they know I'm watching and they might start talking to me. And they say, well, 6 plus 6 is 12 and 7 is 1 more than 6. So the answer is 16 or 13.
And if this were being done on a paper pencil as an assessment item or they were answering on some kind of a device, all I would know about my students is that they were able to get the correct answer. I wouldn't really know a lot about how they got the answer. What skills do they have? What was their thinking? And there's not a lot that I can work with to plan my instruction. Does that kind of make sense?
Mike (08:20.84) Absolutely. I think the, the way that you described this really attending to behaviors, to gestures, to the way that kids are interacting with manipulatives, the self-talk that's happening. It makes a ton of sense. And I think for me, when I think back to my own practice, I wish I could wind the clock back because I think I was attending a lot to what kids were saying.
and sometimes they're written communication, and there was a lot that I could have also taken in if I was attending to those things in a little bit more depth. It also strikes me that this might feel a little bit overwhelming for an educator. How do you think about what an educator, let me back that up. How can an educator know what they're looking for?
Shelly (09:17.5) to start, Mike, by honoring your feelings, because I do think it can feel overwhelming at first. But as teachers begin to make informal observations, really listening to you and watching students' actions as part of just their daily practice, something that they're doing, you know, just on a normal basis, they start to develop these kind of intuitive understandings of how children learn, what to expect
them to do, what they might say next if they see a certain actions. And after several years, let's say teaching kindergarten, if you've been a kindergarten teacher for four, five, six, 20, you know, plus years, you start to notice these patterns of behavior, things that five and six year olds seem to say and think and do on a fairly consistent basis. And that kind of helps you know, you know, what you're looking at. But before you say anything,
I know that isn't especially helpful for teachers new to the profession or new to a grade level. And fortunately, we have several researchers that have been, let's say, kid watching for 40, I don't know, 50 years, and they have identified stages through which most children pass as they develop their counting skills or maybe strategies for solving addition and subtraction problems. And these stages are
laid out as progressions of thinking or actions that students exhibit as they develop understanding over periods of time. listeners might, you know, know these as learning progressions or learning trajectories. And these are ways to convey an idea of concept in little bits of understanding. So.
When I was sharing the thinking and actions of three students solving six plus seven, listeners familiar with cognitively guided instruction, CGI, they might have recognized the sequence of strategies that children go through when they're solving addition and subtraction problems. So in my first student, they didn't say anything but gave me an answer.
Shelly (11:40.068) was using direct modeling. We saw them push over five and one beads for six and then five and two beads for seven and then kind of pause at their model. And I could tell, you know, with their head nodding that they were counting quietly in their head, counting all the beads to get the answer. And, you know, that's kind of one of those first stages that we see and recognize with direct modeling. And that gives me information on what I might do with a student.
coming next time, I might work on the second strategy that I conveyed with my second student where they were able to count on. They started with that six and then they counted seven more using their fingers to keep track of their count and got the answer. And then that third kind of level in that progression as we're moving of understanding.
was shown with my third student when they were able to use a derived fact strategy. The student said, well, I know that 6 plus 6 is 12. I knew my double fact. And then I used that relationship of knowing that 7 is 1 more than 6. And so that's kind of how we move kids through. And so when I'm watching them, I can kind of pinpoint where they are and where they might go next. And I can also think about what I might do.
And so it's this knowledge of development and progressions and how children learn number concepts that can help teachers recognize the skills as they emerge, as they begin to see them with their students. And they can use those, you know, to guide their instruction for that student or, you know, look at the class overall and plan their instruction or think about more open-ended kinds of questions that they can ask that recognize these different levels that students are working with.
Mike (13:39.17) You know, as a K-1 teacher, I remember that I spent a lot of my time tracking students with things like checklists. You know, so I'd note if students quote unquote had or didn't have a skill. And I think as I hear you talk, that feels fairly oversimplified when we think about this idea of developmental progressions. How do you suggest that teachers approach capturing evidence of student learning,
Shelly (14:09.604) well, I think it's important to know that if, you know, it takes us belief. We have to really think about assessment and children's learning is something that is ongoing and evolving. And if we do, it just kind of becomes part of what we can do every day. We can look for opportunities to observe students skills in authentic settings. Many in the moment.
types of assessment opportunities happen when we pose a question to the class and then we kind of scan looking for a response. Maybe it's something that we're having them write down on their whiteboard or maybe it's something where they're showing the answer with finger formations or we're giving a thumbs up or a thumbs down, know, kind of to check in on their understanding. We might not be checking on every student, but we're capturing the one, you know, a few.
And we can take note because we're doing this on a daily basis of who we want to check in with. What do we want to see? We can also do a little more formal planning when we draw from what we're going to do already in our lesson. Let's say, for example, that our lesson today includes a dot talk or a number talk, something that we're going to write down. We're going to record student thinking.
And so during the lesson, the teacher is going to be busy facilitating the discussion, recording the students thinking, you know, and making all of those notes. But if we write the child's name, kind of honor their thinking and give it that caption on that public record, at the end of the lesson, you know, we can capture a picture, just, you use our phone, use an iPad, quickly take a picture of that student's thinking, and then we can record that.
you know, where we're keeping track of our students. So we have, OK, another moment in time. And it's this collection of evidence that we keep kind of growing. We can also, you by capturing these public records, note whose voice and thinking were elevating in the classroom. So it kind of gives us how are they thinking and who are we listening to and making sure that we're kind of spreading that out and hearing everyone.
Shelly (16:31.728) I think, Mikey, you checklists that you used. Yeah, and even checklists can play a role in observation and assessments when they have a focus and a way to capture students' thinking. So one of the things we did in Bridges 3rd edition is we designed additional tools for gathering and recording information during workplaces.
Mike (16:35.501) I did.
Shelly (16:56.208) That's a routine where students are playing games and or engaged with partners doing some sort of a math activity. And we designed these based on what we might see students do at these different games and activities. And we didn't necessarily think about this is something you're going to do with every student. You know, or even, you know,
in one day because these are spanned out over a period of four to six weeks where they can go to these games. And we might even see the students go to these activities multiple times. And so let's say that kindergarten students are playing something like the game Beat You to 10, where they're spinning a spinner, they're counting cubes, and they're trying to race their partner to collect 10 cubes. And with an activity like that,
I might just want to focus on students who I still want to see, do they have one-to-one correspondence? Are they developing cardinality? Are they able to count out a set? And so those might, you know, of objects, you know, based on the number, they spin a four, can they count out four? And those might be kinds of skills that you might have had typically on a checklist, right, Mike, for kindergarten? But I could use this activity to kind of gap.
gather that note and make any comments. So just for those kids I'm looking at or maybe first graders are playing a game like sort the sum where they're drawing two different dominoes and they're supposed to find how many they have in all. And so with a game like that, I might focus on what are their strategies? Are they counting all the dots? Are they counting on from the dot? And if one set of the dots on one side and then counting on the other.
Are they starting with the greater number or the most dots? Are they starting with the one always on the left? Or I might even see they might instantly recognize some of those. So I might know the skills that I want to look for with those games and be making notes, which kind of feels checklist-like. But I can target that time to do it on students I want that information by thinking ahead of time.
Shelly (19:18.684) What can I get by watching, observing these students at these games? trust, I mean, as you know, young children love it. Older children love it. When the teacher goes over and wants to watch them play, or even better, wants to engage in the game play with them, but I can still use that as an assessment.
Mike (19:39.32) think that's really helpful, Shelly, for a couple reasons. First, I think it helps me rethink, like you said, one, getting really a lot clearer on like, love the, I'm gonna back that up. I think one of the things that you said was really powerful is thinking about not just the assessment tools that might be within your curriculum, but looking at the task itself that you're gonna have students engage with, be it a game or a,
Shelly (19:39.356) and
Mike (20:07.96) project or some kind of activity and really thinking like, what can I get from this as a person who's trying to make sense of students thinking? And I think my checklist suddenly feels really different when I've got a clear vision of like, what can I get from this task or this game that students are playing and looking for evidence of that versus feeling like I was pulling kids over one-on-one, which I think I would still do because there's some depth that I might want to capture.
But it it changes the way that I think about what I might do and also what I might get out of a task So that that really resonates for me
Shelly (20:47.066) Yeah, and I think absolutely, you know, I didn't want to make individual interviews or anything sound bad because we can't do them. just, you there's the downfall of, you know, kids comfort level with that and ask them to do something on demand. But we do want more depth and it's that depth that, you know, we know who we want more depth on because of these informal types of observations that we're gathering on a daily basis in our class. You know, might, says something and
we take note I want to touch bases with that thinking or I think I'm going to go observe that child during that workplace or maybe we're seeing some things happening during a game and instead of you know like stopping the game and really doing some in-depth interview with the student at that moment because you need more information I can might I might want to call them over and do that more privately at a different time so you're absolutely on there's a place there's a place for you know both
Mike (21:42.466) The other thing that you made me think about is the extent to which, like one of the things that I remember thinking is like, I need to make sure if a student has got it or not got it. And I think what you're making me think can really come out of this experience of observing students in the wild, so to speak, when they're working on a task or with a partner is that I can gather a lot more evidence about the application of that idea. I can see the extent to which students are.
doing something like counting on in the context of a game or a task. And maybe that adds to the evidence that I gather in a one-on-one interview with them. But it gives me a chance to kind of see, is this way of thinking something that students are applying in different contexts, or did it just happen at that one particular moment in time when I was with them? So that really helps me think about, I think, how those two...
maybe different ways of assessing students, be it one-on-one or observing them and seeing what's happening, kind of support one another.
Shelly (22:46.268) think you also made me think, you know, really hit on this idea that students, like I said, you their learning is evolving over time. And it might change with the context so that they, you know, they show us that they know something in one context with these numbers or this, you know, scenario. But they don't necessarily always see that it applies across the board. I mean, they don't, you know, make these.
generalizations. That's something that we really have to work with students to develop. they're also, they're young children. Think about how quickly a three-year-old and a four-year-old change, you know, the same five to six, six to seven. I mean, they're evolving all the time. And so we want to get this information for them on a regular basis. You know, a unit of instruction may be a month or more long.
And a lot can happen in that time. So we want to make sure that we continue to check in with them and help them to develop if needed or that we advance them. know, we nudge them along. We challenge them with maybe a question. Will that apply to every number? So a student discovers, when we add one to every number, it's like saying the next number. So six and one more is seven and eight and one more is nine.
And you can challenge them, ooh, does that always work? What if the number was 22? What if it was 132? Would it always work? you know, when you're checking in with kids, you have those opportunities to keep them thinking, to help them grow.
Mike (24:23.426) I want to pick up on something that we haven't necessarily said aloud, but I'd like to explore it. You know, looking at young students work from an asset-based perspective, particularly with younger students, I think I often had points in time where there felt like so much that I needed to teach them. And sometimes I felt myself focusing on what they couldn't do. Looking back, I wish I had thought about my work as noticing the assets, the strategies, the ways of thinking.
that they were accumulating.
Are there practices you think support an asset-based approach to assessment with young learners?
Shelly (25:06.278) think probably the biggest thing we can do is broaden our thinking about assessment. The National Council of Teachers of Mathematics wrote in Catalyzing Change in Early Childhood and Elementary Mathematics that the primary purpose of assessment is to gather evidence of children's thinking, understanding, and reasoning to inform both instructional decisions and student and teaching learning.
If we consider assessments and observations as tools to inform our instruction, we need to pay attention to the details of the child's thinking. And when we're paying attention to the details, what the child is bringing to the table, what they can do, that's where our focus goes. So the question becomes, what is the student understanding?
What assets do they bring to the task? It's no longer, can they do it or can they not do it? And when we know, when we're focusing on just what that student can do, and we have some understanding of learning progressions, how students learn, then we can place what they're doing kind of on that trajectory, in that progression, and that becomes knowledge.
And with that knowledge, then we can help students move along the progression to develop more developed understanding. For example, again, if I go back to my six plus seven and we notice that a student is direct modeling, they're counting out each of the sets and counting all, we can start to nudge them toward counting on.
We might cover, you know, they were using that number rec, we might cover the first row and say, you just really showed me a good physical representation of six plus seven. And I kind of noticed that you were counting the beads to see how many were there. I'm wondering if I cover this first row. How many beads am I covering? Hmm. I wonder, could you start your counting at six? You know, we can kind of work with what they know. And I can do that because of
Shelly (27:31.928) I haven't, I've focused on where they are in that progression and where that development is going. And I kind of have a goal of where I want students to go, you know, to further their thinking. Not that being in one place is right or wrong, or yes they can do it, no they can't. It's my understanding of what assets they bring that I can build on. Is that kind of what you're after?
Mike (27:58.51) It is, and I think you also addressed something that again has gone unsaid, but I think you, you, you unpacked it there, which is assessment is really designed to inform my instruction. And I think the example you offered us a really lovely one where, we have a student who's direct modeling and they're making sense of number in a certain way and their strategy reflects that. And that helps us think about the kinds of nudges we can offer.
that might shift that thinking or press them to make sense of numbers in a different way. That really the assessment is, it is a moment in time, but it also informs the way that you think about what you're gonna do next to keep nudging that student's thinking.
Shelly (28:44.348) Exactly, and we have to know that if we have 20 students, they all might be, you know, have 20 little plans that they're on, 20 little pathways of their learning. And so we need to think about everybody, you know. So we're going to ask questions that help them do them, and we're going to honor their thinking. And then we can, you know, like so again, I'm going go back to like doing that dot talk with those students.
And so I'm honoring all these different ways that students are finding the total number of dots. And then I'm asking them to look for what's the same within their thinking so that other students also can serve to nudge kids, to have them let them try and explore a different idea or, ooh, can we try that Mike's way and see if we can do that? hmm, what do you notice about?
how Mike solved the problem and how Shelly solved the problem. Where is their thinking the same? Where is it different? And so we're honoring everybody's place of where they're at, but they're still learning from each other.
Mike (29:51.224) You know, you have made multiple mentions to this idea of progressions or trajectories, and I'm wondering if there are resources that have informed your thinking about assessment at the early ages. Is there anything you would invite listeners to engage with if they wanted to continue learning, Shelley?
Shelly (30:13.008) I think Mike, had that question earlier, so just pause this for a second. Okay. I know you will. I just know it's right here.
Mike (30:16.558) That's okay, no worries. We'll cut every single bit of this out and it will sound supernatural. Yeah, yeah.
Mike (30:39.854) Brent's over here multitasking.
Shelly (30:41.85) OK. OK, I'm just making sure that I'm not going to blow it. I think you're spot on. I think I thought we skipped something. No, it's up here.
Mike (30:53.132) Okay, just pick up whenever you're ready.
Shelly (30:55.108) Yeah, I just have too many notes here.
Shelly (31:10.084) OK, I've got it. Do you want to ask the question again?
Mike (31:12.258) Go for it. Absolutely. Yep. Are there resources you'd invite listeners to engage with if they wanted to keep learning, Shelly?
Shelly (31:28.368) You phrased that a little bit different. What I answered was, what are some of the resources that helped you build an understanding of children's developmental progressions? Do you have that question? Or I can jump on from what you asked, too.
Mike (31:35.5) Okay. Yeah, let let. No, no, no, let me let me ask the question that way.
Shelly (31:42.202) Okay.
Mike (31:45.774) Okay, how did we have it in the thing? Can you say it one more time and I'll say it back in the question?
Shelly (31:50.768) What are some of the resources that help to build an understanding of children's developmental progressions?
Mike (31:56.504) Perfect. What are some of the resources that helped you build an understanding of children's developmental progression, Shelley?
Shelly (32:05.34) Honestly, I can say that I learned a lot from the students I taught in my classroom. My roots run deep in early childhood. And I can also proudly say that I have a career-long relationship with the Math Learning Center and Bridges Curriculum, which has always been developmentally appropriate curriculum for young learners. And with that said, I think I stand on the back of giants.
practitioner researchers for early childhood who have spent decades observing children and recording their thinking. I briefly mentioned Cognitively Guided Instruction, which features the research of Thomas Carpenter and his team. And their book, Children's Mathematics, is a great guide for K-5 teachers. I love it because
I mean, the recent edition has QR codes where you can watch teachers and students in action. You can see some interviews. You can see some classroom lessons. And they also wrote young children's mathematics on cognitive-guided instruction in early childhood education. So I mean, they're just a great resource. Another teacher researcher.
is Kathy Richardson, and some listeners may know her from her books, the developing number concept series or number talks in the primary classroom. And she also wrote a book called How Children Learn Number Concepts, Guide to the Critical Learning Phases, which targets pre-kindergarten through grade four. And I love that Kathy writes.
in her acknowledgments that this work is the culmination of more than 40 years working with children and teachers observing, wondering, discussing, reading, and thinking.
Shelly (34:11.692) It is. So spot on to the observations and the things that I noticed in my own teaching, but it's also still one of the most referenced resources that I use. And if podcasts had a video, I would be able to hold up and show you my dog eared book with sticky notes coming out the all the sides because it is just something that.
just resonates with me again. And then I think also maybe less familiar.
Mike (36:38.958) I think you mentioned giants and those are some gigantic folks in the world of mathematics education. The other piece that I think really resonates for me is I had a really similar experience with both CGI and Kathy Richardson in that a lot of what they're describing are the things that I was seeing in classrooms. What it really helped me do is understand
how to place that behavior and what the meaning of it was in terms of students understanding of mathematics. And it also helped me think about that as an asset that then I could build on. Shelley, I think this is probably a great place to stop, but I wanna thank you so much for joining us. It has really been a pleasure talking with you.
Mike (37:28.95) Say thank you again, but definitively.
Mike (37:35.48) Brent, how do you feel about that?
Mike (37:41.966) do you want to jump in? Yeah, feel free.
Mike (38:04.194) is
Is there a question I could ask that would set you up?
Mike (38:14.574) can work that in to a new ending.
Mike (38:42.872) Do you, there something that you want to add though, Shelley? Cause we can, we can edit it, edit content in, and we can sequence content in too. So if there's something that mattered to you, we can absolutely add it.
Mike (39:14.542) Let's do a question like that then.
Mike (39:35.02) What if we see...
Mike (39:40.578) Why don't you, why don't,
Yeah, why don't you say it? Go ahead and say it the way that you you it was going to flow out and then we'll we can edit this in definitely.
Mike (39:59.191) Okay.
Okay, go for it. Yeah, yeah.
Mike (40:06.676) can I tell you this is one of the smoothest podcast recordings we have had? There's nothing to be sorry about.
Mike (40:18.562) There, okay, I was, can you ask the question again, Mike? So that it's clean.
Mike (40:29.752) Are there resources you would invite our listeners to engage with if they want to continue learning?
Mike (42:26.328) I think that's a great place to stop. Shelly Schaefer, thank you so much for joining us.
Mike (42:38.602) That was perfect. Yeah, fantastic. I'm gonna cut roll. No, there's nothing to be sorry about
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