Do you have a makeup budget? Yeah, I was
wondering about that. Do you have an airbrush?
Mhm. is this good? Yeah, it's on. Okay.
Alright. Could you say your name? Steven Boyce.
All right. What kind of research do you
do? Look at me also. Oh, look
at you? Okay. What kind of research?
Well, I guess you would say it's mathematics education
research. Specifically, I'm interested in understanding how students understand
fractions. Um I don't know if you personally are aware
of it, but uhh it's a pretty big problem in
schools right now. Like for instance, I used
to teach high school, I taught in Pulaski County,
which is just west of here. And I
would I could say that probably most of the students
that I taught like in algebra two geometry or even
calculus didn't really have a very understanding of fractions. And,
we there's been some research as to why that is
and but it's not, it's by no means finished.
It's one of those areas that it's really important.
It's um fractions are sort of a building block
for understanding um higher level mathematics like limits or calculus,
that kind of stuff or even just algebra
one. And we're making progress into uncovering why it is
that we have difficulty because if we don't know why
the difficulty is happening, then it's hard to try
to see if we can fix it. Did you work at the Candy Factory? Oh yeah
yeah, yeah I worked on the Candy Factory. Can you tell us about it? Oh, yeah, sure. Candy
Factory is the first in a sequence that will be
at least three apps, umm that's trying to basically,
It's trying to find a way that we can um
try to help students build the necessary ways of thinking
that they need to do in order to understand fractions.
So the Candy Factory app, basically what it
does is it takes students through a a sequence in
each each task that they're given, they have to
be given a customer order of a candy bar.
So something like this and they're they're asked basically to
make that custom order from a given whole and what
it what it really requires of them is to think
about fractions in a fundamentally different way than is usually
taught. Um usually with fractions, we think about
fractions in the United States, at least, as primarily
being sort of a part out of the whole relationship.
And a lot of times for students, they
don't they don't ever get to the place where they
see a fraction as being a number itself, where
they think of a fraction like 2/3 as being a
number. They think of it as being a relationship
between two out of three and so what we're trying
to do with the Candy Factory is seeing if we can sort
of transform the way that they're thinking about fractions so
that it will enable them to be able to do
the operations with fractions later on like addition or multiplication
or division or whatever equivalent fractions, all those types
of things right now a lot of times students are
learning those things sort of like an algorithm. They're
just memorizing the steps and the procedures, you know?
It's hard, it's hard, it's really hard
for us as educators or mathematicians sometimes to explain that
because all of us we were able to come to
that understanding despite the way that we were taught,
it's sort of like the reason we like math and
the reason that we we can do math is because
we were part of the people that were able to
sort of abstract that despite it. So what we're
trying to do is trying to make it more accessible
to everyone really and and so that we don't have
people that are that are not making it through algebra,
or basically just going through the motions and not really,
it's like pulling teeth to get through algebra.
And then they don't even want to go any farther
with math because they don't really understand what's going.
They're just trying to memorize the procedures. So Candy
Factory is the first one. The procedures basically you've
given a whole candy bar and you're given a customer
order. Well you're giving a customer order, you
choose the whole candy bar and then you have to
make that candy bar by partitioning the whole into so
many pieces that could be between two, between two and
12 in the original Candy Factory version, and then
you have to decide how many iterations of that piece
that you need to make. So how many repeated
copies you have to make of that piece that you
made. And so that's sort of thinking of fractions
in a different way where you're thinking it more of
a measurement then thinking that as a part out of
a whole. So basically the idea of the Candy
Factory and the other games that we're doing is that
we have something that's that students enjoy. It's engaging
for students but actually is involving meaningful mathematics. So
it's not something where they learn in the classroom how
to do something and then they're just practicing it by
going through this game. By going through the process of
doing the partitioning and then doing the iterating, eventually
we hope that those things will become almost automatic for
students of what we called interiorized, where they
understand or they think of a fraction as being and
iteration of a partition instead of it being something that
they have to go through the process and procedure to
do, they eventually get to the place where that's
just the way that they see the world, the
way they see a fraction. That's the idea of
what we call transformative research app. The other two apps
we got another one we're working on, it doesn't
have an official name yet, but the temporary code
name is Candy Warehouse and it's actually working with building
unit coordination, where you can understand um basically we
want to get students to be, where they can
understand three levels of unit coordination. So they can
do basically the game is trying to pack um candy
bars into bundles and then into boxes and then they
have to ship them off and be able to coordinate
how many bundles are in a box, how many
bars are in a box? How many boxes would
be in one bundle, that kind of thing. So the same
kind of thing with fractions, but focusing on the
units coordination, which is another thing that we've identified
as being important um for for understanding fractions and also
algebra, algebra is really where we're heading. Good.
Are you in the math department or the School
of Education? I'm in the math department? Um
That's interesting. We just kind of, I think there
was one student that was in the math department before
that did math education in the math department here at Virginia
Tech. And it's kind of a relatively unusual or you
know, it's becoming less than usual, but most
of the time people that study math education are in
schools of education or, something like that. Um And
so we're kind of starting that here in Virginia Tech.
It's, it's a pretty good opportunity to be able
to have, and it's one of the reasons that,
one of the things I think really makes Virginia Tech
stand out is you do have the opportunity to be
in the math department while researching math education. And that
has lots of benefits. I think you have definitely
a closer relationship with the mathematics that I wanted.
Um And it isn't that I'm interested in the I
take the same some of the same courses of the
people in the school of education would take in mathematics,
but it keeps you closer to the mathematics community
I would say, like umm you know, I
I'm taking a course right now, for example,
on undergrad, research in undergraduate mathematics education. So we're
researching um like how students understand differential equations, how
students understand calculus and teaching methods for those types of
courses. I think that being in the math department
really gives you those foundations that you need to be
able to do research in those areas. So while
my research is focused on maybe math that pertains to
middle school, I'm using in my research material that
I learned from graduate level math courses and part of
the, part of the perk of being in the
math department, especially at Virginia Tech, is that
you're getting that foundation in graduate level mathematics that you
might, that you can apply to math education.
So you have a broader base from which to look.
So that's one of the benefits of being in
the math department I'd say. What else drew
you to the program at Virginia Tech. Oh gosh,
personally, I don't know if I'm a great
example, but I'm a Hokie for life. I I
went to community college in Northern Virginia and then I
transferred to Virginia Tech to finish my bachelor's degree back
in 1999 and I have not left the area.
So for me it was sort of, you know,
I came back to graduate school in Virginia Tech
in Mathematics, I knew I wanted to go in
mathematics. I didn't know what necessarily. I want
to do that. I was a Virginia Tech because
I live here, this is my home and I
just love the area, the mountains, the rivers,
and it's summertime, here is just the best.
It's great. The community is just really,
it's just opening, it's a diverse area, you
know, but like I said, you just can't
beat the beauty of the scenery and, you know,
my wife's family is from, I met my
wife at Virginia Tech. And so we got married
actually, right near the duck pond. And so
we've stayed here ever since. So I would say
that it wasn't, it definitely was not the mathematics
graduate program in Math Ed that drew me here at
all. Um That's sort of something that came afterward
because we were just kind of starting the program.
What drew me here was the fact that I,
I wanted to be here back when I was an
undergrad and I just have stayed here since, you
know, I taught nearby and this is a place
where I could commute to nearby and you wouldn't have
to uproot our family to go to graduate school and
that kind of stuff, so. In your research,
do you have a lot of interaction with the students?
Um when you say the students who do you mean? Do
you mean the students who are researching or the other
graduate students for both? Okay let's start with I
guess the actual students. Yes. Yes. That's
that's the fundamental aspect of research in mathematics education.
Is that what what we're trying to do is to
research students mathematics. We're not we're not focusing on
um what I think is happening, you know,
without without actually talking to a student or observing the
student working or trying to trying to get in basically
we're trying to do is trying to get in their
head, trying to figure out how they're thinking.
because that's the most important thing to do when you're
teaching is to have an understanding of what your students
know. If you in order to understand how you
can help them learn something new, you have to
know where they're at. So you have a very
very very heavily involved in getting to know students ways
of amazing in mathematics. So you definitely have a
lot of interaction with students in the, you know
, in the middle schools, what the methods that
we typically are using right now, our clinical interviews
were, it's a little bit different than what we're
doing because we would give students maybe a task or
two and have them interact with the task and then
ask them questions with based on the responses. Um
So it's sort of an interview setting, but you
have tasks that they have to do to try to
understand their reasoning and then um there's an extension to
that, which is developed by Dr steffie from university
of Georgia. And my advisor is actually a student
of Dr studies, so he knows this method very
well, which is called teaching experiments And teaching experiments
. There's basically one teacher researcher and the role isn't
just that of an interview, your role as a
teacher as well. And you are working with two
students usually appear students and you just, you know
, it's a longitudinal thing where you're working over maybe
a period of six months or so s semester at
least, and you're and you're really focused on what
those students are thinking, so you're very definitely interacting
with students. Um We also didn't, you know
, we did some stuff with the whole class,
we go into a classroom and we tried something with
the Candy factory with that. So we did some
interaction. There were students, we also a lot
of interaction with graduate students in the Math department in
Math education. We have seminars that we take um
each each semester there's a math education seminars to have
that close knit community where we can share ideas and
um you know, I had a presentation for a
conference and I could practice that presentation for that community
and we send each other our drafts when we're trying
to do presentations and give each other feedback. So
we have a very tight knit community in Math education
department here at Virginia Tech, both in the department
of Mathematics and in the school education, we all
come together and Coalesce is a larger group. Um
, definitely a lot of interaction. Do you enjoy
most about living in black? Oh gosh. Um
, most, well I already mentioned a couple of
things. I love the summers here. I mean
personally the, I'm from Washington D. C.
Area. Um, so I guess to me,
the biggest thing is the mountains, the rivers,
it's not crowded. It's the humidity. I mean
everything is just nicer here. I mean it's just
a nicer place to be and to interact with people
and you still have all those benefits that you maybe
not all the benefits, but most of the benefits
that you have from being in a big city because
you have the international community and you have the people
from, from all over the country coming to Blacksburg
. Um, you have the, you know,
the restaurant variety and the music and uh, and
the, you know, the types of things that
you might expect if you're in a larger place.
But then you go out a little bit and there's
national forests in adjacent to Blacksburg. So it's just
a beautiful place that people are very welcoming. And
I think in Blacksburg and it's just a nice place
to be. It's a nice place to raise a
family and have a daughter and the schools are great
in Blacksburg. It's just, it's just a place
that's nice for families as well as for students.
So if you're a graduate student and considering coming uh
mathematics education, you have, that's on her daughter
, I'd say this is a really great place to
be. Could you describe the partnership between the Department
of Math and the school of education and your own
words and how that works? Well? Um the
Department of State, that number, Could you describe
the partnership between the math department and the school event
in creating this math education program with the strength of
that? Um, Well, in the school of
education, the it is a school of education,
so it encompasses lots of different domains. It's not
, it's not just math science and goes to education
. It's family therapy and counseling. There's educational research
and methodology. It's very wide variety. So,
one of the real benefits of the partnership is that
I can really focus in on the content that's specific
to mathematics in my math mathematics department courses that are
, that are offered through the mathematics department. But
then when I go, when I'm taking courses in
the school of education, oh, which are much
less focused specifically in math, I get exposure to
a wide variety of perspectives um, in the classroom
, like maybe perspectives from more of a sociological perspective
, I guess. So, having that variety is
really important. I think that you're getting that those
courses from a different perspective. Um there's also in
the school education just within the teaching and learning,
there's a teaching and learning department which focuses on the
mathematics and they just have they have a different,
um I would say they have a different perspective maybe
on mathematics, it's maybe a little more focused on
um on research that is from a larger educational perspective.
So I think that's really the benefit is sort
of having them the content really coming from the from
the mathematics department and then the more broad educational courses are
coming from the school education, but as a