Yeah no.
Okay. Alright everybody. Good evening.
Thank you for joining us tonight for this quick parent workshop
on bringing on bridging mathematics and the home.
Um We're so honored and lucky to have dr Sarah Powell here with
us tonight.
Um Sarah and I have worked together in the past in my previous
position when I was working at central offices and um she is a
far known expert of um just how to incorporate language within
mathematics and as and as we all know our our math curriculum
with envisions has has a preponderance of language within it.
Um So I do believe that some of the quick strategies that should
be able to discuss with you uh today um we'll showcase how you
can help your child at at home with bridge and the math and um
within home instruction as well.
So without further you dr Powell. Welcome.
Alright thank you so much jordans and it's so nice to see all of
you. Um So as Jordan's said my name is Sara and I'm an associate
professor at the university of texas at Austin and all of my
teaching and research is focused on the area of mathematics.
So we're gonna briefly talk here tonight but I do give you my
contact information.
Um I have put this entire presentation on my website so if you
go to Sarah paul PhD dot com you can download that if you wanna
look through it again or share it with other people and then I
also share my email with you and my twitter with you if you want
to contact me in other ways and I'll share that again at the
very, very end.
So I'd like you if you are okay with it in the chat,
just say hi and describe some of the math that you maybe work on
with your child or with your Children.
And that will give me a chance to know a little bit more about
you.
So if you want to open up the chat and go ahead and tell me on
some of the math that you're working on in the home and I'm not
gonna spend a lot of time here. I'm gonna move on.
But as you drop those in the chat,
I'll be able to see a little bit more about you.
So there's two things that we're going to talk about here
tonight. The first is math vocabulary.
So this here is a snapshot from grades K through eight of the
number of math terms that students are typically expected to
know at any grade level.
And we came upon this listing by looking in several math
textbooks and going to the end of those textbooks and looking at
the glossaries and counting all of the different terms and those
glossaries, then we removed all the duplicates and we would say,
oh this is how many terms a student at a grade level uh,
is expected to know.
So if you have a kindergartner or a first or second grader at
home,
Their math classroom and the math that they're talking about,
they probably are using anywhere from 110-140 different math
terms. So they might be talking about adding that's a math term.
They might be talking about share, that's a math term.
They might be talking about a number sentence or a square lots
of different math terms that you would be talking about at home.
Now if you teach grades 34 and five,
that number goes up quite a bit.
So an average third through fifth grader is going to be using in
math anywhere from 300 to almost 400 different math terms.
We see a big jump up from second grade to third grade because if
any of you are helping your third grader,
you know that a lot of new things come into play in third grade,
specifically multiplication, division and fractions.
There's a whole host of vocabulary that's associated with
fractions.
So you can see why the number of math terms increases.
And then if you are working with middle schoolers,
that number of math terms ranges anywhere from 400 to over 500
different math terms and lots of new things in middle school
specifically.
Language related to ratios and rate and proportional reasoning.
And a lot of new language related to algebra.
So what we know about math language is that students have to use
math language,
they have to listen to the language whether that's listening to
you or their teacher or peers or video.
They have to talk a lot about math.
So they have to speak in the language of math,
they have to read a lot in math and they also have to write in
math.
And all of this involves a really strong understanding of math
vocabulary. So if you are in the chat and I hope you'll,
you'll open it up and drop this in.
But if you'd like to tell me which of these areas is easiest for
your child and which is most difficult.
I'd love to know what you think. Um, for some Children,
it's easier to listen to math language than it is to speak it.
It's easier to write it than to read it.
Um, but for many other Children,
those profiles might be different.
So, um, so it's so nice if you can drop those in the chat,
I'll learn a little bit about you and your kids.
So why is math vocabulary difficult?
So first of all, there's a lot of it,
but it also causes a lot of complications for kids.
And if you don't understand math vocabulary,
you're not able to access the math that you are working on in
the home or at school. So why is math vocabulary so difficult?
I'll show you quickly? 11 reasons why quickly. There we go.
So some of the math terms that your kid may be using,
they they hear those in their math class and then they hear
those in different areas besides math.
So if I asked you what the word degree meant.
Some of you might talk about temperature,
some of you might talk about the degrees of an angle and others
might talk about a degree that you get when you graduate from
high school.
And I know a few of you would tell me about deodorant that is
called degree.
So a lot of times when you might be saying a math word to your
kid,
they might know not understand what you're talking about because
they know a different interpretation for that word.
Math vocabulary is difficult for a lot of kids because sometimes
there's a math term where it's also shared with general english
and they have similar meanings but they don't know exactly the
the differences between these meetings.
So for example with difference you might ask about,
well let's compare numbers.
What's the difference between eight and three.
So the difference between eight and three is five.
But you might also ask a question of like what's the difference
between fall and spring and lots of interpretation for what that
might mean.
So make sure that your students understand what you're talking
about. Another reason.
Math vocabulary might be difficult is that there's a lot of
terms that are only used in math.
So before you and your kids started working on this math work,
whether it's related to factions or money or coins.
They have never heard this word before.
So you have to make sure that they know it and not only that
they know it by hearing it but they know it by reading it and
often that they know how to write it.
So have you talked about this word trapezoid?
If you're doing some homework on quadra laterals when you get to
fractions,
have you talked about this word numerator and how that's
different from denominator?
Another reason that math vocabulary is hard for kids is that a
lot of math terms have more than one meaning.
So if I said the word square some of you probably would think
about a shape but some of you might also think about to square a
number. So three squared. So what are you talking about?
We have to be really clear.
There there are some math terms that your kid might use in other
classes at school.
So are there terms that they might hear in science class and
math class or their terms that they might hear in reading or L.
A. And math. So you've got to clarify those terms as well.
There's some math terms that are hama graphs.
So if you say I'd like you to write the sum which is what
happens when we add two numbers together.
Your kid might say well I only have some of these so s.
Um is different than S. O. M. E.
But it sounds the same and so that could cause confusion.
Other reasons that kids struggle with Math vocabulary is that
there are math terms that are related but they have distinct
meanings.
There are math terms that in english may translate into another
language and have a different meaning.
Math vocabulary might be difficult because sometimes we have
spelling irregularities. So why is it F. O. U. R.
But it's F. O. R. T. Y.
Math vocabulary might be difficult because you might hear math
the same math things talked about in different ways.
So maybe you're telling your kid about skip counting but their
teachers using the word multiple,
but in reality you're talking about the exact same thing and
then there's some math vocabulary where many times we use more
informal terms than those formal math terms.
So again you might be saying one word and maybe their classroom
teacher is saying another word and you're talking about the
exact same thing,
but because you're using different words it may cause confusion
for the kids.
So this is just 11 reasons why Math vocabulary might be hard for
you and your child or you and your Children,
but there are some things that we can do about this.
So what are some of the ways that you can use your math language
appropriately if kids have a good math language model then they
typically have stronger math language.
So let's look at one of the ways we can do that.
So one way is for us to take our informal math language and make
that more formal. So here on the left,
I have a little red person and they're going to use informal
math language.
And my green person is going to use more formal math language.
So maybe my red person says,
well what number is in the tens place?
If I'm looking at this number, 135.
But in reality the number is 135.
But you could ask what digit is the tens place.
So we could talk about the three is the digit in the 10th place.
Ah, here, my red person might say, oh,
I'm going to carry the one or I'm going to borrow if we're
working on subtraction problems.
But that's informal language these days, more formal language.
We'd be talking about regrouping or maybe trading or exchanging
another informal way to talk about fractions is to talk about
the top number and the bottom number.
That's informal and really just describes where numerals fall in
a fraction.
Instead we could be talking about the numerator and the
denominator when you ask your Children.
I know some people are working on fractions.
I see that in the chat to reduce the fraction that might
indicate that you're actually changing the value of the fraction.
But instead you could ask,
let's rename this fraction or let's simplify fractions here.
If I was going to read these decimals instead of saying 4.7,
I should say four and seven tents.
And instead of saying four point oh seven or 07,
we could talk about that as four and seven hundreds.
And then these look like boxes and balls but they were actually
squares and circles and this looks like a point here on our
three dimensional figure.
But our formal math language is that this is a vertex.
Now, those were a lot of examples there. Um,
here's one more about flip slides and turns versus reflections,
translations and rotations.
Now go back here. Sorry, muting someone. There we go.
But I want you to think about, are there any examples of?
Well instead of saying this, I could say that.
So I'll drop one in the chat and I'll say it out loud but
instead of um saying answer,
maybe I ask about the sum or the difference or the product or
the quotient.
So can you think of any examples where you could help your
students improve their math language by instead of talking about
it informally, you could use a more formal math term.
So if you have any suggestions,
please drop them in the chat and I will share them with everyone.
But some of the ones that I shared with you are more,
more of the common ones, especially top number. Bottom number,
please say numerator and denominator now I'm gonna think about,
well what are some of the ways that we could now help our
Children with math language in the home.
So we know a little bit about how to formalize our math language.
So here are a few activities that you might think about using
one is if you get to a math word where a student is like I don't
really know that word.
Um there are different organizers that you can use to explore
these math terms. So here's an example for the word reflection.
So these are different graphic organizers that you could draw
and and fill out with your kid.
Um and so here you write a definition, they do a drawing,
they do an example and a non example.
So this would be a way for you to really dig deep into a word
that is causing confusion. Here's another graphic organizer,
there's actually many of these available,
but really you would just draw here four quadrants and write the
word, the lightbulb word is,
what is the word that helps you remember this word,
what's the definition and draw a picture And when students do
these graphic organizers,
it really helps them remember the different words.
Now, you could also have your kids create vocabulary cards.
These are ones that have been created with um computer programs,
but you could also draw these.
One of these is from middle school.
One of these is from elementary school.
Um but if there's a term or several terms that you see that your
kid doesn't really understand,
you could develop some vocabulary cards to help them with that.
You could also create glossaries.
I did this with my nephews when they were in grade three. Um,
I was doing a lot of their covid schooling where we were doing
stuff via zoom and we actually created a glossary of math terms
together. So we would come up with the word,
we would come up with their definition of that word and then
they would do a little drawing next to that definition.
You could also create a word ball.
I've seen a lot of these created by teachers and kids and I've
seen some of these created by caregivers and kids,
but maybe there are 10 or 20 words that you see that your child
need help help with,
go ahead and just put these on cards and you can print these out
and put them in their,
their home workspace or above their desk or wherever you may
work on math. And then there's also lots of cool games.
Um, these are word games.
These are both examples that you can print out from.
Um, your favorite search engine. Uh,
there's a seek and find and there's a ton of math crosswords.
So you could practice the math vocabulary in that way and then
you can also use a lot of technology.
There are quite a few different free and sometimes they cost a
little bit of money, but vocabulary math practice games.
So here on the left is one from the Math learning center that is
available in both english and spanish and here on the right,
this is an example from Houghton mifflin math or what they call
math lingo.
So math vocabulary is really important and that's something that
you could work on with your kid at home.
But the second thing that you could also work on is how to help
your kid set up and solve math word problems.
And I already saw a comment in the chat that says you are
working on multi step questions and I'm assuming that's probably
multi step word problems and I agree with you.
Those multi step questions start to really cause a lot of
difficulty for many kids.
So this is something you can also work on when homework comes
home and you're interested in figuring out how to help your
student with those word problems.
So here is a word problem and I just want you to read through
this very quickly.
So notice that the first thing I asked you to do was to read
through this problem.
So I'm going to emphasize today that the reading of problem math
problems specifically word problems is going to be something
that you can do with your kid.
But notice what's going on in this story.
First there's a lot of words.
So if I looked at that and maybe your kid doesn't you know love
reading or maybe they struggle a little bit with reading,
they might be turned off by this problem,
but we can read it together and we can understand what this
problem is about?
But look at all of the different vocabulary terms in here.
There's a lot of general english vocabulary.
So what's a caramel apple? What does it mean to sell something?
What does it mean if something has a topping and then look at
all these different words, peanuts, chocolate chips,
coconut sprinkles and then the rest are covered with sprinkles.
That tells me a lot about what's going on in this story,
but it might not always be obvious that that is something we
should pay attention to. So we're reading through this,
talking about these different terms and what they mean.
And then making a plan to figure out well what caramel apples,
what number of caramel apples are covered with the sprinkles.
So this is a very typical multi step word problem and you could
see how this could be really complicated for a lot of kids.
And so when we think about problem solving,
there's typically seven areas where we see where we see that
students consistently have difficulty solving these problems.
The first as we just talked about is reading the problem.
So read these problems with your child, you can read them,
they can read them back to you, you can read them together.
But students need a lot of practice reading these problems.
And then the second area of difficulty for many kids is
understanding the vocabulary.
So we talked about the caramel apples and the sprinkles.
But what does it mean if they sold something or what does it
mean if the rest are covered with sprinkles?
So we've got to have some discussions about the vocabulary.
And then the third area of difficulty that many students
encounter is identifying. What information do I need?
Do I need all of these numbers in the problem?
Can I ignore some of them?
And that gets us to our fourth area of difficulty which is can I
ignore some of the information in this problem?
And then 1/5 area of difficulty is reading information from
charts and graphs.
The problem that we just looked at with the caramel apples
didn't have a graph or a chart but many problems do.
So maybe you want to label that graph and talk about the Y axis
and the X axis and what those mean.
That's gonna help students solve the problem better.
And you'll notice I haven't talked about these last two areas of
difficulty yet.
But most of the difficulty that students have with word problems
is in the setup of the problem and it's not always with the
solving of the problem.
But then we see the 6th and 7th areas of word problem difficulty
are so selecting your operation.
So are you going to add subtract multiply or divide or do some
combination of that and then actually doing the addition.
Subtraction. Multiplication or division.
So if you are working with your kid at home I would try to
address each of these seven areas.
So think about reading the problem and talking about the
vocabulary and then think about talking about well what numbers
do we need? What numbers can we ignore?
And if there's a charter graph,
how do we interpret this charter graph?
And then talk about well what are you going to do in this story?
Are you going to add subtract?
Are you going to multiply divide and then working through that
process.
So one resource that we use a lot with up there we go a lot with
kids.
Um and this is specifically from both the elementary grades and
the middle school grades is we use what we call an attack
strategy.
So every time you see a word problem you can say hey let's use
that strategy. Let's U. P. S. Check this.
So you read the problem.
So first you understand so that's where you read and explain.
So that's where you're talking about that.
The reading of the problem and the vocabulary that's in the
problem and what's going on in the story. Then you make a plan.
So you figure out what numbers am I gonna need,
what numbers can I ignore?
Is there anything from the chart or a graph that I need to
interpret and you think okay well what am I going to do?
Do I want to add subtract multiply or divide?
And then you solve the problem.
So that's going and doing the computation and then you should
talk to your kid about Well does your answer makes sense?
So you want to go back and check your work?
So using an attack strategy like this ups check um is a really
helpful thing to do.
There are also many other attack strategies out there.
You don't have to use ups check.
Um but some other popular tax strategies are the solved strategy
and some schools will use the cubes strategy.
I'm going to just show you a little bit about how we have
students set up and solve word problems.
Um This is a more advanced example but I want you to see where
students are moving as they move across the elementary grades.
So here we have the ups check strategy.
We've written that on the left hand side and then we've
underlined what this problem is about.
This problem is about inches.
We checked off 11 and 4/10 and three and 9/10 as we use those
numbers.
And we put these into an equation to help students understand
what the word problem means.
And then we solved that equation And you can do that for
problems where you may add or subtract but you can also do this
for problems where you may multiply or divide.
So here's another example we wrote out the ups check strategy.
So we remember to understand plan solve and check.
Um we underlined that this problem is about the stories about
fish and then we hear a graphic organizer,
you could also write an equation to set up four times question
mark equals 24.
And then we saw that there's six fish in each bowl.
So that's some of the work that we typically encourage school
kids to do in the classroom,
but you could also do this at home but that tax strategy is
going to be really important there now um A few things that I
want you to think about are some other resources that you could
access to help you do some math in the home.
So one our virtual manipulative you probably have used these
already but if you haven't there are so many out there and they
are so great. Um If you follow this Q. R. Code,
I put together a collection of virtual manipulative that I've
just run across on the internet.
Um And there are virtual manipulative to help your kids with a
number and operations.
So how do you add subtract multiply and divide.
Uh There are virtual manipulators about place value.
Their virtual manipulative is you can use to show fractions and
there's stuff you can use for geometry or time and money.
I saw that some people are working on time and money so that you
have virtual manipulative that you can use.
So just because you don't have hands on tools to help your kid
with math you can have access to these virtual tools.
Um If you want more information about how to help Children
especially when they are having some math difficulty.
I worked with the National Center on intensive intervention or
what we call the N. C. Ii.
And they have a ton of amazing resources and all of them are
free for how to help students not only in math but also in
reading and writing. So here's an example.
We put together a free course that you can watch to figure out
how to teach math and improved ways.
And then they have lots of different free math worksheets and
flashcards and uh number lines and things that you can print off
for free that you could also use in the home.
And then finally I work with a group where uh many of you have
probably heard about the science of reading which is using
evidence based practices to teach reading but there's also
effort related to the science of math.
So using evidence based practices to teach math.
So if you visit the science of math dot com you can read about
some common misconceptions in math teaching and and some helpful
strategies for the teaching of math.
And they're always adding to this website.
So it's a good one to check in with periodically.
So it's 30 minutes past the hour and I was supposed to be
finished at that time. So I just did it.
Um but tonight we just talked about using math vocabulary and
helping students solve math word problems.
So with my vocabulary you want to talk about those vocabulary
terms and make sure that students know what they mean.
And then with math word problems you want to have that attack
strategy.
So help students maybe use the ups check strategy every time
they see a math word problem where they understand the problem
by reading it,
they make a plan they solve and they go back and check their
work and if you want this whole presentation you can visit the
website um and you can also email me,
I'm happy to talk to you or share more resources with you and if
you're on twitter please find me and we can tweet about fun math
things and I'll turn it back over to Jordan's and julie thank
you dr Powell. That was a great synopsis.
Probably a year's worth of research that you're doing.
Probably more than that actually.
But I think if we have time just to you know,
open up maybe for some specific questions.
Yeah I think also one thing that I wanted you to explain a
little bit is actually why finding keywords and associating them
with operations is actually not the best strategy when it comes
to problems if you can just briefly explain that.
Yeah so in word problems many times kids will use what Jordan is
talking about is key words so maybe they see the word total and
they think total always means to add Well usually in first grade
that might work out for you.
But in later grade levels total does not always mean that
they're going to add.
So I may give an example that Jordan and Julie have a total of
20 pencils. If Julie has 11 pencils, how many does Jordan have?
So there, if I added 20 plus 11,
I am not going to solve that problem, correct.
And so anytime a keyword works,
there's always a word problem down the road where it doesn't
work and we've done some research on this and we found that key
words in single step word problems work less than like 56% of
the time and in multi step problems keywords work less than 10%
of the time.
Thank you. So do we have any,
well let's open up the forum for a few minutes.
Um anybody have any burning questions that they would like to
ask.
Don't don't be shy.
All the questions will come after I finish after I sign off.
All right, well if we don't uh dr Powell,
I want to thank you for taking the time out of your day to do
this for us. Um I know it's a it's a busy time.
It's and then it's also a busy time of year for us as well as
the first E. L. A. State exam tomorrow.
So um with that being said,
if you have any questions feel free to email Dr Powell or you
can email me.
Um And yes the presentation will be available and so and
Michelle we've also accorded the uh presentation as well and it
will be posted on our website and also sent out.
Um Thank you um everybody um for joining us today and have a
wonderful night.
Thank you. Thank you Dr Powell. You alright?
Thanks bye bye George.
I think you have to stop because I change to you. Thank you.