Latest / Rounding Up / Assessment in the Early Years with Shelly Scheafer

Transcript

Assessment in the Early Years with Shelly Scheafer · Rounding Up

0:03
How is the work of assessing young children different from assessing students in
0:07
upper elementary grades or in grades six through 12?
0:10
And what actions can we take to ensure we understand our youngest learners'
0:14
thinking? Today we're talking with Shelly Schafer,
0:18
senior manager of Content Development with the math Learning Center about the
0:22
ways educators can understand and advance the mathematical thinking of our
0:27
youngest learners. Welcome to the podcast, Shelly.
0:32
Thank you so much for joining us today.
0:34
Thank you, Mike, for having me.
0:36
So I'd like to start with this question.
0:38
What makes the work of assessing younger children,
0:41
particularly students in grades K through two,
0:44
different from assessing students in upper elementary grades or even beyond?
0:49
Wow, there's a lot to that question, Mike.
0:54
I think there's some obvious things.
0:58
So effective assessment of our youngest learners is different
1:03
because obviously our pre-K, our first,
1:06
even our second grade students are developmentally different from fourth and
1:10
fifth graders.
1:11
So when we think about assessing these early primary students,
1:15
we need to use appropriate assessment methods that match their stage of
1:19
development. For example,
1:21
when we think of typical paper pencil assessments and how we often ask
1:26
students to show their thinking with pictures, numbers and words.
1:31
Our youngest learners,
1:34
our just starting to connect symbolic representations to mathematical
1:38
ideas, let alone put letters together to make words.
1:42
So we need to take into consideration that primary students
1:47
are in the early stages of development with their language, their reading,
1:52
and their writing skills.
1:53
And this makes it challenging for them to fully articulate,
1:58
write, sketch,
2:00
any of their mathematical thinking. So we often find that with young
2:04
children, interviews can be really helpful,
2:07
but even then there's some drawbacks.
2:10
Some children find it challenging to show in the moment what they
2:15
know.
2:16
Others just aren't fully engaged or interested because you've called them over
2:20
from something that they're busy doing,
2:22
or maybe they're not yet comfortable with the setting or even the person doing
2:26
the interview. So when we work within children,
2:30
we need to recognize all of these little peculiarities that
2:35
come with working with that age.
2:38
We also need to understand that their mathematical development is
2:42
fluid, it's continually evolving,
2:45
and this is why they often or some may respond differently
2:50
to the same prompter question,
2:52
especially if the setting of the context has changed.
2:56
We may find that a kindergarten student who counts to nine on Monday may
3:01
count to 69 or even a hundred later in the week,
3:04
depending on what's going on in their mind at the time. So
3:09
this means that assessment with young children needs to be frequent,
3:13
formative, and ongoing.
3:15
So we're not necessarily waiting for the end of the unit to see, aha,
3:19
did they get this? What do we do?
3:21
We're looking at their work all of the time.
3:25
And fortunately,
3:26
some of the best assessments on young children are the observations in their
3:31
natural setting,
3:33
like times when maybe they're playing a math game or working with a center
3:37
activity or even during just your classroom routines.
3:41
And it's these authentic situations that we can look at
3:46
as assessments help us capture a more accurate picture of their
3:50
abilities because we not only get to hear what they say or see
3:55
what they write on paper, we get to watch them in action.
3:59
We get to see what they do when they're engaged in small group
4:04
activities or playing games with friends.
4:08
So I want to go back to something you said and the way that you said it.
4:11
You were talking about watching or noticing what students can do and you really
4:16
emphasize the words.
4:17
Do talk a little bit about what you were trying to convey with that Shelly.
4:22
Young children are doers when they work on a math pass,
4:25
they show their thinking and their actions with finger formations and objects.
4:30
And we can see if a student has one-to-one correspondence when they're
4:35
counting, if they group their objects, how they line 'em up, do they tag them?
4:39
Do they move them as they count them?
4:42
They may not always have the verbal skills to articulate their thinking,
4:46
but we can also attend to things like head nodding, finger counting,
4:51
and even how they cluster or match objects. I'm going to give you an example.
4:57
Let's say that I'm watching some early first graders and they're solving the
5:01
expression six plus seven,
5:04
and the first student picks up a number rack,
5:07
and if you're not familiar with a number rack,
5:10
it's a tool with two rows of beads.
5:13
And on the first row there are five red beads and five white beads. And on the
5:16
second row there's five red beads and five white beads.
5:20
And the students solving six plus seven begins by pushing over five red
5:25
beads in one push and then one more bead on the top row.
5:30
And then they do the same thing for the seven.
5:32
They push over five red beads and two white beads,
5:36
and they haven't said a word to me,
5:38
I'm just watching their actions and I'm already able to tell, hmm,
5:44
that student could subitize a group of five because I saw 'em push over all
5:48
five beads in one push.
5:50
And that they know that six is composed of five in one
5:55
and seven is composed of five and two,
5:59
and they haven't said a word. I'm just watching what they're doing.
6:03
And then I might watch the student and I see 'em pause,
6:08
nothing's being said,
6:09
but I start to notice this slight little head nodding. And then they say
6:13
13, and they give me the answer and they're really pleased.
6:18
I didn't get a lot of language from them,
6:20
but boy did I get a lot from watching how they solve that problem.
6:25
And I want to contrast that observation with a student who might be solving the
6:29
same expression, six plus seven, and they might go, Hmm,
6:34
six.
6:36
And then they start popping up one finger at a time while counting
6:40
7,
6:45
8,
6:45
9,
6:45
10,
6:45
11,
6:45
12,
6:45
13.
6:45
And when they get seven fingers held up, they say 13. Again,
6:51
they've approached that problem quite differently, but again,
6:54
I get that information that they understood the equation they were able to
6:59
count on starting with six,
7:02
and they kept track of their count with their fingers and they knew to stop
7:07
when seven fingers were raised.
7:10
And I might even have a different student that might start talking to me and
7:15
they say, well, six plus six is 12,
7:18
and seven is one more than six.
7:22
So the answer is 13.
7:25
And if this were being done on a paper pencil as an assessment
7:29
item or they were answering on some kind of a device,
7:34
all I would know about my students is that they were able to get the correct
7:37
answer.
7:38
I wouldn't really know a lot about how they got the answer,
7:43
what skills do they have? What was their thinking?
7:46
And there's not a lot that I can work with to plan my instruction.
7:50
Does that kind of make sense?
7:52
Absolutely. I think the way that you described this,
7:56
attending to behaviors, to gestures,
7:59
to the way that kids are interacting with manipulatives,
8:03
the self-talk that's happening, it makes a ton of sense.
8:07
And I think for me, when I think back to my own practice,
8:11
I wish I could wind the clock back because I think I was attending a lot to what
8:15
kids were saying and sometimes their written communication.
8:19
And there was a lot that I could have also taken in if I was attending to
8:24
those things in a little bit more depth.
8:26
It also strikes me that this might feel a bit overwhelming for an educator.
8:30
How could an educator know what they're looking for?
8:33
I do think it can feel overwhelming at first,
8:37
but as teachers begin to make informal observations,
8:41
really listening and watching students actions as part of just their daily
8:45
practice, something that they're doing on a normal basis,
8:49
they start to develop these kind of intuitive understandings of how
8:54
children learn, what to expect them to do,
8:57
what they might say next if they see a certain action. And after several years,
9:02
let's say, of teaching kindergarten,
9:04
if you've been a kindergarten teacher for four or 5, 6,
9:08
20 plus years,
9:09
you start to notice these patterns of behavior,
9:12
things that five and six year olds seem to say and think and do on a
9:17
fairly consistent basis. And that kind of helps you know what you're looking at.
9:22
And fortunately, we have several researchers that have been, let's say,
9:27
kid watching for 40 years,
9:29
and they have identified stages through which most children pass as they develop
9:34
their counting skills or maybe strategies for solving addition and subtraction
9:38
problems. And these stages are
9:43
laid out as progressions of thinking or actions that students exhibit
9:48
as they develop understanding over periods of time.
9:52
And listeners might know these as learning progressions or learning
9:57
trajectories.
9:58
And these are ways to convey an idea of concept in little bits of
10:03
understanding.
10:05
So when I was sharing the thinking and actions of three students
10:10
solving six plus seven listeners familiar with cognitively guided
10:14
instruction, CGI,
10:16
they might've recognized the sequence of strategies that children go
10:20
through when they're solving addition and subtraction problems.
10:24
So in my first student,
10:26
they didn't say anything but gave me an answer was using direct modeling.
10:30
We saw them push over five and one beads for six and then five and two beads for
10:35
seven, and then kind of pause at their model.
10:39
And I could tell with their head nodding that
10:43
they were counting quietly in their head counting all the beads to get the
10:48
answer. And that's one of those first stages that we see and recognize with
10:52
direct modeling.
10:53
And that gives me information on what I might do with a student
10:58
coming next time.
11:00
I might work on the second strategy that I conveyed with my second
11:04
student where they were able to count on,
11:08
they started with that six,
11:10
and then they counted seven more using their fingers to keep track of their
11:14
count and got the answer.
11:17
And then that third kind of level in that progression as we're moving of
11:21
understanding was shown with my third student when they were able to use a
11:25
derived fact strategy. The student said, oh,
11:27
well I know that six plus six is 12. I knew my double fact,
11:33
and then I use that relationship of knowing that seven is one more than six.
11:37
And so that's kind of how we move kids through. And so when I'm watching them,
11:42
I can kind of pinpoint where they are and where they might go next,
11:46
and I can also think about what I might do.
11:48
And so it's this knowledge of development and progressions and how children,
11:53
number concepts that can help teachers recognize the skills
11:58
as they emerge, as they begin to see them with their students,
12:01
and they can use those to guide their instruction for that student or look at
12:06
the class overall and plan their instruction or think about more open-ended
12:10
kinds of questions that they can ask that recognize these different levels that
12:15
students are working with.
12:18
As a K one teacher,
12:19
I remember that I spent a lot of my time tracking students with things like
12:23
checklists.
12:24
So I note if students had or didn't have a skill,
12:30
and as I hear you talk,
12:33
that feels fairly oversimplified when we think about this idea of developmental
12:37
progressions.
12:39
How do you suggest that teachers approach capturing evidence of student
12:43
learning, Shelly?
12:44
Well,
12:45
we have to really think about assessment and children's learning is something
12:49
that is ongoing and involving, and if we do,
12:52
it becomes part of what we can do every day.
12:56
We can look for opportunities to observe students' skills in authentic settings.
13:01
Maybe it's something that we're having them write down on their whiteboard,
13:05
or maybe it's something where they're showing the answer with finger formations
13:08
or we're giving a thumbs up or a thumbs down to check in on their
13:13
understanding. We might not be checking on every student,
13:18
but we're capturing a few and we can take note because we're doing this on a
13:22
daily basis of who we want to check in with, what do we want to see?
13:26
We can also do a little more formal planning when we draw from what we're going
13:31
to do already in our lesson.
13:33
Let's say for example that our lesson today includes
13:38
a.talk or a number talk,
13:40
something that we're going to write down. We're going to record student
13:43
thinking. And during the lesson,
13:46
the teacher's going to be busy facilitating the discussion,
13:49
recording the student's thinking and making all of those notes.
13:53
But if we write the child's name,
13:56
honor their thinking and give it that caption on that public record at the end
14:01
of the lesson, we can capture a picture, just use an iPad quickly,
14:05
take a picture of that student's thinking,
14:07
and then we can record that where we're keeping track of our students.
14:12
So we have, okay, another moment in time.
14:15
And it's this collection of evidence that we keep growing.
14:20
We can also by capturing these public records note,
14:24
whose voice and thinking we're elevating in the classroom.
14:27
So it gives us how are they thinking and who are we listening to and making sure
14:31
that we're spreading that out. And hearing everyone,
14:34
I think like you mentioned checklists that you use.
14:38
I did.
14:39
Yeah.
14:39
And even checklists can play a role in observation and assessments
14:44
when they have a focus and a way to capture students' thinking.
14:49
One of the things we did in third edition is we designed additional
14:54
tools for gathering and recording information during workplaces.
14:58
That's a routine where students are playing games and or engaged with partners
15:02
doing some sort of a math activity.
15:05
And we designed these based on what we might see
15:10
students do at these different games and activities.
15:15
And we didn't necessarily think about this is something you're going to do with
15:18
every student or even in one day because these are spanned out
15:23
over a period of four to six weeks where that they can go to these games
15:28
and we might see the students go to these activities multiple times.
15:33
And so let's say that kindergarten students are playing
15:37
something like the game beat you to 10 where they're spinning a spinner,
15:41
they're counting cubes,
15:42
and they're trying to race their partner to collect 10 cubes. And with an
15:46
activity like that,
15:48
I might want to focus on students who I still want to see,
15:52
do they have one-to-one correspondence? Are they developing cardinality?
15:57
Are they able to count out a set?
16:01
And those might be kinds of skills that you might've had typically on a
16:05
checklist, right, Mike for kindergarten.
16:08
But I could use this activity to gather that note and make any comment.
16:13
So just for those kids I'm looking at,
16:15
or maybe first graders are playing a game like sort the sum where they're
16:19
drawing two different dominoes and they're supposed to find how many they
16:24
have in all. So with a game like that,
16:26
I might focus on what are their strategies? Are they counting all the dots?
16:31
Are they counting on from one set of the dots on one side and then counting on
16:35
the other?
16:37
Are they starting with the greater number or the most dots? Are they starting
16:40
with the one always on the left?
16:42
Or I might even see they might instantly recognize some of those.
16:46
So I might know the skills that I want to look for with those games and be
16:50
making notes, which kind of feels checklist,
16:54
but I can target that time to do it on students.
16:57
I want that information by thinking ahead of time,
17:01
what can I get by watching observing these students at these games? I mean,
17:05
as you know, young children love it.
17:08
Older children love it when the teacher goes over and wants to watch them play
17:11
or even better wants to engage in the gameplay with them.
17:15
But I can still use that as an assessment.
17:19
That's helpful, Shelly, for a couple of reasons.
17:22
One of the things that you said was really powerful is thinking about not just
17:26
the assessment tools that might be within your curriculum,
17:28
but looking at the task itself that you're going to have students engage with,
17:32
be it a game or a project or some kind of
17:37
activity and really thinking,
17:39
what can I get from this as a person who's trying to make sense of students'
17:43
thinking?
17:44
And I think my checklist suddenly feels really different when I've got a clear
17:48
vision of what can I get from this task or this game that students are playing
17:54
and looking for evidence of that versus feeling like I was pulling kids over
17:58
one-on-one,
17:59
which I think I would still do because there's some depth that I might want to
18:02
capture,
18:03
but it changes the way that I think about what I might do and also what I might
18:07
get out of a task that really resonates for me. The other thing that you made me
18:11
think about is the extent to which I remember thinking is I need to make sure if
18:16
a student has got it or not. Got it.
18:19
What you're making me think can really come out of this experience of observing
18:23
students when they're working on a task or with a partner is that I can gather
18:28
more evidence about the application of that idea.
18:31
I can see the extent to which students are doing something like counting on in
18:35
the context of a game or a task,
18:38
and that adds to the evidence that I gather in a one-on-one interview with them.
18:42
But it gives me a chance to see,
18:43
is this way of thinking something that students are applying in different
18:47
contexts or did it just happen at that one particular moment in time when I was
18:51
with 'em?
18:52
So that really helps me think about how those two different ways of assessing
18:57
students be it one-on-one or observing them and seeing what's happening,
19:02
support one another.
19:04
And I think you also made me think it really hit on this idea that
19:08
students, like I said,
19:10
their learning is evolving over time and it might change with the
19:15
context so that they show us that they know something in one context with these
19:19
numbers or this scenario,
19:22
but they don't necessarily always see that it applies across the
19:26
board. They don't make generalizations.
19:29
That's something that we really have to work with students to develop.
19:32
And they're also young children.
19:34
Think about how quickly a three-year-old and a four-year-old change
19:40
the same five to six, six to seven, I mean, they're evolving all the time.
19:44
And so we want to get this information for them on a regular basis.
19:49
A unit of instruction may be a month or more long,
19:53
and a lot can happen in that time.
19:55
So we want to make sure that we continue to check in with them and help them to
19:59
develop if needed or that we advance them,
20:03
we nudge them along, we challenge them with maybe a question,
20:07
will that apply to every number?
20:09
So a student discovers when we add one to every number,
20:12
it's like saying the next number, so six and one more,
20:16
seven and eight and one more is nine. And you can challenge them. Ooh,
20:20
does that always work? What if the number was 22?
20:25
What if it was 132? Would it always work?
20:28
So when you're checking in with kids,
20:30
you have those opportunities to keep them thinking, to help them grow.
20:35
I want to pick up on something that we haven't necessarily said aloud,
20:38
but I'd like to explore it.
20:40
Looking at young students' work from an asset-based perspective,
20:44
particularly with younger students,
20:46
I've had points in time where there felt like so much that I needed to teach
20:50
them, and sometimes I felt myself focusing on what they couldn't do.
20:55
Looking back, I wish I had thought about my work as noticing the assets,
20:59
the strategies, the ways of thinking that they were accumulating.
21:03
Are there practices you think support an asset-based approach to assessment with
21:08
young learners?
21:10
I think probably the biggest thing we can do is broaden our thinking about
21:14
assessment.
21:16
The National Council of Teachers of Mathematics wrote in catalyzing change in
21:20
early childhood and elementary mathematics that the primary purpose of
21:25
assessment is to gather evidence of children's thinking,
21:30
understanding and reasoning to inform both instructional
21:34
decisions and student in teaching learning.
21:38
If we consider assessments and observations as tools to inform our
21:43
instruction,
21:45
we need to pay attention to the details of the child's thinking.
21:50
And when we're paying attention to the details,
21:53
what the child is bringing to the table, what they can do,
21:57
that's where our focus goes. So the question becomes,
22:02
what is the student understanding?
22:05
What assets do they bring to the task?
22:08
It's no longer can they do it or can they not do it?
22:12
And when we know,
22:14
when we focusing on just what that student can do and we have some
22:18
understanding of understanding learning progressions,
22:22
how students learn,
22:25
then we can place what they're doing kind of on that trajectory
22:29
in that progression,
22:31
and that becomes knowledge. And with that knowledge then we
22:36
can help students move along the progression to more
22:40
developed understanding. For example, again,
22:43
if I go back to my six plus seven and we notice that a student is direct
22:47
modeling, they're counting out each of the sets and counting all,
22:51
we can start to nudge them toward counting on.
22:55
We might cover, they're using that number rack.
22:58
We might cover the first row and say, Ooh,
23:00
you just really showed me a good physical representation of six plus seven,
23:05
and I noticed that you were counting the beats to see how many were there.
23:08
I'm wondering if I cover this first row, how many beats am I covering?
23:13
Six. I wonder, could you start your counting at six?
23:18
We can work with what they know,
23:21
and I can do that because I've focused on where they are in
23:26
that progression and where that development is going.
23:30
And I have a goal of where I want students to go to further their thinking,
23:35
not that being any one place is right or wrong, or yes, they can do it. No,
23:38
they can't. It's my understanding of what assets they bring that I can build on.
23:44
Is that kind of what you were after?
23:46
It is. And I think you also addressed something that again has gone unsaid,
23:51
but I think you unpacked it there,
23:53
which is assessment is really designed to inform my instruction.
23:57
And I think the example you offered is a really lovely one where we have a
24:01
student who's direct modeling and they're making sense of number in a certain
24:05
way, and their strategy reflects that.
24:08
And that helps us think about the kinds of nudges we can offer that might
24:12
shift that thinking or press them to make sense of numbers in a different way.
24:17
That really the assessment is it is a moment in time,
24:21
but it also informs the way that you think about what you're going to do next to
24:25
keep nudging that student's thinking.
24:28
Exactly. And we have to know that if we have 20 students,
24:32
they all have 20 little plans,
24:34
that they're on 20 little pathways of their learning.
24:37
And so we need to think about everybody.
24:41
So we're going to ask questions that help 'em do 'em,
24:43
and we're going to honor their thinking. So again,
24:45
I'm going to go back to doing that.talk with those students.
24:48
And so I'm honoring all these different ways that students are finding the total
24:52
number of dots,
24:53
and then I'm asking them to look for what's the same within their thinking so
24:58
that other students also can serve to nudge
25:03
kids, have them let them try and explore a different idea or,
25:08
Ooh, can we try that Mike's way and see if we can do that?
25:12
Or what do you notice about how Mike solve the problem and how Shelly solve the
25:17
problem? Where is their thinking the same? Where is it different?
25:19
And so we're honoring everybody's place of where they're at,
25:24
but they're still learning from each other.
25:28
You have made multiple mentions to this idea of progressions or trajectories,
25:32
and I'm wondering,
25:34
what are some of the resources that helped you build an understanding of
25:37
children's developmental progression? Shelly?
25:40
Honestly,
25:41
I can say that I learned a lot from the students I taught in my classroom.
25:45
My roots run deep in early childhood. With that said,
25:49
I think I stand on the back of giants,
25:52
teacher practitioner researchers for early childhood who have spent
25:57
decades observing children and recording their thinking.
26:02
I mentioned cognitively guided instruction,
26:05
which features the research of Thomas Carpenter and his team and their book.
26:09
Children's Mathematics is a great guide for K five teachers.
26:15
Another teacher researcher is Kathy Richardson,
26:18
and some listeners may know her from her books,
26:21
the Developing Number concept series or number talks in the primary
26:26
classroom.
26:27
She also wrote a book called How Children Learn Number Concepts,
26:32
A Guide to the Critical Learning Phases,
26:34
which Targets Pre-Kindergarten through grade four.
26:38
And then I think also the work of Julie Sama and Doug Clement.
26:42
They have a website that looks at learning progressions
26:47
starting at birth all the way through grade three.
26:51
And this website is learning trajectories.org,
26:55
and it's one of those that is always evolving,
26:57
so it not only explains learning trajectories for all
27:02
early childhood math concepts,
27:05
but there are literally thousands of videos and lessons for teaching math
27:10
and new content is always being added.
27:13
So any of those would really give teachers some good ideas
27:18
on how children learn the progressions that they go for and
27:22
really help them notice and put a reference to what they're seeing kids do.
27:28
You mentioned Giants,
27:29
and those are some gigantic folks in the world of mathematics education.
27:34
I had a really similar experience with both CGI and Kathy Richardson in
27:39
that a lot of what they're describing are the things that I was seeing in
27:43
classrooms.
27:45
What it really helped me do is understand how to place that behavior
27:49
and what the meaning of it was in terms of students' understanding of
27:53
mathematics.
27:54
And it also helped me think about that as an asset that then I could build on.
27:59
Are there resources you would invite our listeners to engage with if they want
28:03
to continue learning?
28:05
I think if listeners are interested in learning more about developmental
28:08
progressions in math, the resources I mentioned, children's Mathematics,
28:13
cognitive guided instruction by Thomas Carpenter Al,
28:16
the How Children Learn Number Concepts by Kathy Richardson or SAMA in Clements
28:21
learning directories.org are good places to start. But honestly, Mike,
28:26
it's about teachers making purposeful observations,
28:30
understanding what they're seeing and hearing,
28:33
and then knowing what to do with that information.
28:37
The Latin root of the word assessment means to sit beside.
28:42
I would like to invite our listeners to sit beside their students. Listen,
28:47
watch, question, take note,
28:50
because developing the capacity to observe children in action,
28:55
listening to their thinking and then acting upon what they see in hear
29:00
takes practice, takes effort,
29:03
and once teachers become fascinated with children sitting in front of us,
29:08
we can become students of our students. As Alan Fisher would say.
29:12
That's when teachers really see the benefits.
29:16
They'll recognize that all their students have math abilities,
29:21
and that these math abilities are specific and actionable.
29:26
And when we nurture our students with what they know and what they need to know,
29:31
they will grow.
29:34
I think that's a great place to stop. Shelly Schaeffer,
29:37
thank you so much for joining us.
29:39
Thank you so much, Mike, for having me. It's been a pleasure talking with you.
29:47
This podcast is brought to you by the Math Learning Center and the Meyer Math
29:50
Foundation dedicated to inspiring and enabling all individuals to
29:55
discover and develop their mathematical confidence and ability.