Unknown: Music. Hello and welcome to tier one
interventions Podcast
with your hosts, jonily Zupancic
and me, Cheri Dotterer And I like that you interrupted me
there because sometimes their understanding of number and
their understanding of visual perception are not aligned.
Hello and welcome to tier one interventions podcast where we
share with you tips, techniques and strategies to strengthen
your core. The core classroom that is in the last episode of
tier one interventions, John Lee was training on number sense and
how dots relate to number at the end of what we've shared last
time, we're going to continue that conversation with a
question that she asked me. So tune in and find out what she
asked.
Sherry. I don't even know what question I have for you, but
what are your thoughts on all of that? What are the struggles
that kids have. What are the deficits that kids have with
visual perceptual What are many of the positive aspects of
classroom teachers using visuals to gain access to the
curriculum, and specifically the math curriculum? What is
happening in the brain that is going to support what we're
trying to teach in tier one interventions. I'm going to let
you take it away a little bit and make some of these
connections for us through cognitive science and
neuroscience.
And there's another thing you said, I'm giving you a lot right
now. I know that you always talk about what the brains crave and
what toddlers naturally do like, I'm asking you, like, 52
questions at once, but you just take it away and give us your
insight on how cognitive science matches what we're talking
about. Constantly, we were having pre discussions about
what we were going to talk about today. We've had discussions
about dots for a long time, you and I, we've had conversations
with some of our students in the past about dots, one of the dots
patterns that you utilize to represent equation. We have some
samples from kids that we have looked at in the past. But one
of the things that triggered me earlier this week, we were
talking about representation of dots in a different form. We
were looking at it with a board, and one of the things that I was
thinking about was representing dots on a pegboard.
We have these different dots available. What I don't have is
one of those foam boards. I just don't have any in stock at the
moment there at school, and you know how that is. But they often
have this big knobby peg that's three times this size. It has
that knob on the end, like this one
was it? Those big knobbies are going to be better for kids who
are struggling with fine motor skills. What's nice about foam
is you can pop it in and out, because looking at different
ways that we represent dots. The other way is really a bigger
dot, but parketry also creates patterns like dots. For those of
you listening to the podcast, I suggest that you pop over to the
YouTube channel and look at this segment so that you can see what
we're talking about, because the dot representations and how the
kids represented the pattern that they were copying is really
impactful.
These dots represented on a piece of grid paper. I don't
know if you can see the dots in here, but she was trying to
mimic an image that she had seen earlier that day.
Jason was trying to mimic the image. Was a bit of a shot. We
can see the dots a little bit better on on this image.
You need to know what the image was, to know whether he's doing
a good job at representing that the images, but he's keeping his
circles inside the dots. He's doing a pretty nice job of
representing the fine motor skills.
This little one, Lacey, she made circles out of it. She got
started, but got stuck on expanding Lane looks like the
top part of it is formed nice. It's got nice circles, and the
nice hand form on the pencil looks like he's got a pretty
nice pencil grip. And we come up with something like this that
Zane did, and he knew he.
Was trying to make an X, but had no idea how to represent the
blocks and the dots. Karen, it's almost there's a left side and a
right side. They're all separate. They're not blended.
She had the idea, but could not
write it and represent it. This is what happens with a lot of
kids with writing skills, the there's a disconnect between
what they see visually and what they can put on paper. One of
the reasons that John Lee and I really meshed when we first met
is we have in mathematics a need to understand and relate some of
the disconnects there are neurologically with what they're
seeing in the math classroom.
Chris is working. He's got an okay pencil grip. He looks like
his. He could be doing a little bit better with his grip. He's
loose on there, but he's making circles. He started at the
outside, so he knew he had to start wide and come to the
middle.
He may be processing it a little bit slower than some of the
other kids. Then we have this one. She knew she was making an
X, but that's all that she can manage.
And here we have one is, oh, this is wrong. Oh, this is
wrong. And doing a lot of erasers. That's what happens
with kids with memory issues. They'll do a lot of erasers. And
perfectionists also want to do a lot of erasers and crossing out
and redoing things. Sherry, I'm gonna say something here about
Jeb, that last one that you did in looking at just without
knowing the context, you might think that Jeb has a lot of
deficiencies and gaps. Jeb does have some interesting brain
disconnects,
but from this picture, you can't tell this. And I know who this
student is. He actually, conceptually, is very high
achieving mathematically. Sherry, this proves, on this
one, the disconnect between what kids are seeing, what's in their
brain, what they can analyze mathematically, which sometimes
is a higher level than the teacher. And these kiddos were
in kindergarten at the time, and he was actually teaching me
things about mathematics, but then to show that on paper, it
is a huge struggle for him and pushing on the pencil very
heavily. So he's got some other issues. I'm going to say,
however, they're not with math content. So I wanted to point
that out on this picture.
Then we have somebody like Ray, who is not
maybe the fine motor, and making the dot wasn't good, but he's
still doing three by three squares that he's coloring them
in. Somebody Melissa thought she did a fantastic job. Our friend
Randy. Randy had a real difficult time with his visual
perception.
Whether he had initiation of tasks, those executive functions
were getting in the way, or he really had no concept, but he
knew he had to do something on paper. I hope that represents
and answers a little bit about where you wanted me to go.
Generally,
look at visual spatial dysgraphia. Dots are they
staying within the lines and the bottom lines, are they able to
see the overlaps of the dots? Are they able to
represent what they see visually? And that's one of the
reasons I've like your what do you see? Question, because if we
can have them verbalize what they're seeing first before we
write it down, we can more
differentially analyze where the disconnect is. Is it the visual?
If it's the visual, we need to start there. Is it what they're
writing? Is it that motor skill, is there some disconnect with
their memory? It's breaking it down into its parts, looking at
it from a visual, a motor and a memory standpoint,
we're looking at it to try and differentiate where the
neurological gap is you're looking at and then how do they
represent their understanding of number?
And I like that you interrupted me there, because sometimes
their understanding of number and their understanding of
visual perception are not aligned. And.
Yeah, I like that you interrupted me there, because
sometimes their understanding of number and their understanding
of visual perception are not aligned, that what you just
said, they're not aligned creates, and I haven't talked
about this yet, but that false negative kiddo, I'll explain
what I mean by that. Earlier I talked about the false positive
kiddo that is appearing to achieve high does well on tests,
can mimic the notation, but doesn't have this deep sense of
conceptual understandings when given something out of context,
or a more comprehensive test, like an A CT, they don't score
well there, and we're confused as the adults, because it
doesn't match what we typically see from them in school. On the
flip side of that, we get these kiddos that what Sherry just
said, the mathematics and the visual perception, they don't
align. So we get a false negative reading on kids when
we're asking kids to replicate or use the visual to figure out
the mathematics. Many of them struggle to do that on paper.
That's that misalignment that Sherry's talking about. When
that misalignment happens, I can't use that paper form to
truly assess what the kids understanding is in that
specific example that she had just shown we have to be really
savvy as the adults to know if this is a misalignment, and not
falsely
target a child for math intervention that actually has a
separate issue, and it's not the mathematics. This is how we
expose conceptual understanding in mathematics by using these
dots, and that's what I mean by assessment of watching these
kids work. We had a session not too long ago where one of our
participants, one of our teachers on the session, said,
is what you're talking about, like, when kids know the answer
but they don't show their work. And that's absolutely what I'm
talking about here. Kids that can look at DOT images or look
at mathematics and they're accurate, they can actually
solve, they can actually count, they can get the answer. And we
demand that they show their work. This sometimes is a demand
that the kiddo is just not capable of. They just physically
can't now that's what they need the intervention for. But what
happens is, oftentimes, we give them this lecture. If you don't
show your work, I can't give you partial credit, so I have to
take all the points away. What we're doing is we're reducing
the number of points they get based on something they're not
even capable of doing. When we're thinking about
intervention, whether it's math intervention or therapy
intervention, we need to be able to analyze and work with as
classroom teachers and educators, be able to work with
our direct service providers to make sure that we're assessing
the correct thing. If you have a kid that's not showing their
work in mathematics, it's probably because that is where
they need the intervention to help them show on paper what
they're getting accurately. Because, again, they probably
know more mathematically than we do as teacher,
but where their deficit is being able to articulate that and
those false negative kids, which means they know more mathematics
than what we're giving them credit for. Those are the kids
that we sometimes say, Oh, they just don't test well, no, they
just aren't seeing the notation and symbol, and they're just not
able to replicate that. And that's where we need to provide
the intervention, which one of the interventions is giving them
more experiences on creating mathematics using dots. Picture
is not 1000 words. Go ahead, Sherry, one of the things that I
want to emphasize to the occupational therapists that are
listening to this is, please include the symbols, math
symbols in your therapy sessions, explain why a
parentheses goes to the right versus goes to the left. Explain
it, and not just in literacy terms, but also explain it in
its connection to mathematics. What are three ways that you can
represent the divide sign. You have the dots on the top and the
bottom. You have a fraction which just has the line, and you
have a horizontal equation. You can have it with the thing
almost looks like a square root that line, you've got the dots,
you've got just a line. And what are some of those other ways
that you can talk to your students about the
representation of those symbols and make connections for
mathematics? I think I just in my brain, created a new
worksheet for my.
How many ways can you represent the divide sign? I remember,
gosh, we were working together. Maybe this was back in 2019
it was, I'm pretty sure it was before covid, and you put up
something that to this day, I still go, I
she went off on a crazy tangent, and I still don't know that I
fully understand it, and I represent it often, because it
made that much of an impact on me. And you asked me, How many
ways can I write eight over 12? And I looked at you and I went,
give me a calculator, because to me, I automatically know what
the procedure is. I know how to get the answer on the
calculator.
Don't ask me, How many ways to represent it. You did this thing
called 20 ways, and one of the ways that you did it was with
dots, and that was different ways to represent that
particular number, and I just sat back
and I went, I have a long way to go with understanding
mathematics. And I thought that I understood mathematics until I
sat with you for a day.
But that really sums up my story as well. I was that I'm going to
say false positive kid in K 12, I achieved high I was always
told I was good at mathematics. I always had this perception
that I was good at mathematics. Got good grades in mathematics.
So I decided to actually major in a mathematics area in
college, I started in Actuarial science, but as a sophomore in
college, I failed my first math class, and it really made me
question my own understanding, just like Sherry said she came
to that realization at some point that, wow, do I really
even know anything at all about mathematics. So I failed that
math class, switched out of actuarial science. That's how
much it affected me. Majored in just pure math in college. Took
me five years to get the four year degree, and then decided to
go on and get my certification to teach. And I thought, oh, I
can teach eighth grade mathematics because I at least
know enough to teach eighth grade mathematics. What happened
was, in the first two or three weeks of my first year of
teaching, I I thought, I'm a brilliant teacher, and I would
give my quizzes and my tests, and about half of my students
were not able to do what I taught them. I was really
questioning where that disconnect was, and the
realization I came to was I really don't know math well
enough to be able to give access to this mathematics. We did
almost full inclusion. We still had some resource room for math,
where we had, like, pure tier 300% pull out for mathematics,
but we were trying to really get full inclusion tier one core
classroom, and my we're recording this live today, and
my intervention specialist who helped guide me through this
realization of, do we really even know the mathematics to
better support our students is actually here. Live with us
today. You know who you are. Thank you for being here. Would
you like this morning? Hello.
This is, this is a fun story. Take us back, Christy, 1999
you saw this very young, early, 20 year old girl come in and
over the next five or six years, as we collaborated and worked
together, you as intervention specialist, me as math classroom
teacher. Give me your perspective of this journey that
we actually took together, I feel like I was in the same boat
as you, as a student, where I always got great grades. I was
not necessarily a straight A math student, but I could play
the math student. I could do the math. Just show me what to do,
and I can follow the steps and I can get the right answer. I feel
like when we first started teaching together, we were like,
Okay, if I can give these kids tricks and mnemonics to remember
how to do long division and how do subtraction and how to do
different procedures, that it's okay the kids have it. If I
write those mnemonics out and I write the steps out, the kids
can go home and they can do it for homework. Then in two weeks
from now, I give them a problem again, and they have no idea.
How do we even start? I feel like what we learned together is
that a lot of times we have kids that can play the math game and
they can do the procedures, but in the end, they have absolutely
no idea what they're doing and why. They didn't really
understand the math. They didn't have the.
Number Sense, that's the biggest thing I felt. Was our journey
working together was, how do we get kids to understand what
they're doing and why? Which is that whole importance of number
sense? And how can we improve number sense in kids? That's
exactly the neurological philosophy neurodevelopmentally
gifted students will be able to figure things out and understand
them in a few sessions, typical kids a couple more, but kids
with disabilities and kids who are truly struggling.
Initially, I had heard 60, but lately, I've been hearing more
like 300
times you you need to represent the number two, 300 times. How
do we get more interactions with kids so that it increases their
memory and retention, and that is through visuals. That's
really what the phrase a picture is worth 1000 words mean. And
one thing I want to connect to what Christy said is, and I'm
going to say this a different way, but it's what we learned in
our journey, is that oftentimes we can get kids to replicate
short term. Some of these kids, we can give quizzes and tests in
our classroom, and they could score very high, because it's in
that short term, they're able to retain the information just long
enough to produce on my quizzes and tests, but then we give a
midterm or a final exam, or the end of the year assessment or
the state test at the end of the year, where they have all of
these concepts all At once, where they have to pull from
their memory and things that happened five or six months ago.
That's where the breakdown is. We have some of these kids that
achieve very high they get A's and B's in math class, but then
they fail, or come close to failing that end of year test.
And we're like, oh, they're just not a good test taker. No, that
has nothing to do with it at all. Their brain has not learned
in the way that increased the memory of this content, and
they're not able to retain a lot of teachers talk about this.
Also, when kids move through the grades, they get to fifth,
sixth, seventh grade, and the teacher says, These kids don't
know this. And the third and fourth grade teachers are like,
Oh my gosh, we spent so much time on this. We did this with
kids. The problem was they were able to get it short term, but
without those visuals, we're losing that long term memory and
retention.
So let's jump more into the mathematics. If you want to hear
a little bit more about that conversation, go to tier one
interventions.com sign up for the workshop, and you'll get the
rest of the conversation. It is impact
inclusion. And when I talk about inclusion, I'm talking full
inclusion. How are we going to reduce
pull out sessions to zero? I know it's in it might not be the
perfect for all kids, but the full inclusion, if we're really
looking at the definition, it requires professional
development. It requires
pull in sessions for all disciplines. So inclusion is the
first one, metacognition, thinking about thinking. And
that's all of these words and all of these phrases and these
little nuances that jonily All the time. What do you see? What
do you notice? Tell me about
number three is perseverance. When we're toddlers, we're
running around, we're curious, we're doing all these wonderful
things. We're always trying to take the next challenge. How
often does it take a toddler to learn how to walk? A few weeks.
How long does it take an 83 year old, after they've had a stroke,
to learn how to walk again?
Not a few weeks. Takes much longer. When we're looking at
perseverance, we're looking at helping them create an innate
sense of drive and motivation to accomplish something.
When we're looking at a we're looking at adaptability.
Adaptability is more than just physically adapting the
worksheet, adaptability is also a change in a shift in your
mind.
When we're looking at See, we're looking at curiosity.
I mentioned the toddler a little bit ago, looking around and
doing all kinds of wonderful activities and being absolutely
curious about their surroundings. We put them in
kindergarten. Here you need to sit in this seat. We can find
them.
We teach them this structure that we've created.
It in the system so that we can get all kids learning at the
same time. I would love to see,
especially in middle school, kids on treadmills learning
math.
There's been a research study that talks about it, where they
were had in this special ed class of kids who were failing
math, they started putting they put treadmills in the classroom
for these this particular set of students. All six students, Aced
their state testing that year because every time they came
into math, they had the treadmill at a low rate of speed
so they could still hear the teacher,
and their math scores skyrocketed, and they got the
concepts
before you say the last one, I'm going to give the definition of
this last one before we say the word that he is a new path that
doesn't yet exist, that Sherry and I are Creating and hoping
that it catches on. This isn't in addition to, it's instead of,
it's the better way.
It's the path unpaved that we have all the research to back
it, and now we just need to take the step so Sherry, give it to
us. What's that last word that I've just transcendence. It's a
journey.
It's not transformation which happens instantly. It's
transformation that happens from this point all the way to this
point and beyond. It's that concept of lifelong learning.
It's a concept of what we learn today
we integrate into our base of knowledge so that we can use it
tomorrow.
All right, everybody. Have a great weekend, great end of the
school year, great summer,
and we resume these tier ones, September 21 the third, Saturday
of every month, I just go in, go into disability labs and
register for September, October and November, the date
that way you're registered in your login so that you get all
the emails and the links and everything.
Hello, everybody. Happy Summer. You.