♪[theme music]
>>teacher: I know that you usually do a small version with your groups every morning
as you look at your challenge problems. Today you're going to do the full form
version of a math circle. A math circle is a group of scholars,
typically I separate my class into groups of four.
The scholars will then work together to first of all determine what is the
question even asking.
So they are given a question prompt and as you can probably see I have a special
set of papers that I use for them that I stapled together so they have plenty of
room to complete each step.
They're given the prompt, they glue it onto the front, they discuss and annotate
the prompt. They have to determine their own language objective for the lesson.
They don't know what the math objective is yet because they're not sure which
skill they're going to use that's part of the process that they're trying to determine.
So they have a language goal of how they can discuss it and what they'll use.
What can we guess? What's another question? Destiny?
>>Destiny: What do we know? >>teacher: What do we know?
After they've annotated the problem together, they come up with the list of
assumptions. So what do they know? What don't they know yet?
and what could they guess if they looked at the context clues within the question?
>>student: The numbers we know are 1/3 divided by two, one. And we know it's division
because each pillar uses an amount of concrete
so we got-we gotta see they're distributing the-the concrete in each pillar.
>>teacher: The scholars will receive points for this
particular activity because group work is very
important. It's important that they can communicate with their peers.
It's important that they can present to me, and have a cogent argument as to why
their answer is either valid or invalid. So that will be point-assessed.
>>student 1: We can-we can guess that it's probably going to be multiplication
if it's times. >>student 2: No, if it has...
>>student 3: Well we don't know it's really-it's multiplication or division.
>>student 2: Yeah sure. Yeah because, yeah because of
sometimes means to multiply or divide.
>>student 1: Yeah, we need to find like key words in the prompt.
>>student 3: Yes. And then underline them.
>>teacher: After they've come up with that list of facts then they have their SLED.
Which is: sketch, label, estimate, and discuss.
So that's basically sort of a catch-all space for them where it's just get your
thought process out. If you were comparing it to language arts it would
be organizing your thoughts or filling in a graphic organizer.
I give them materials that they are able to select from
based on what they think they need. If the materials that I give them are
insufficient they are welcome to ask me, hey, we also need a protractor or a ruler
or whatever else it is they think.
>>student 1: When you multiply,
1/3 to a number, it could be like one of-one of those answers.
So it's a great idea.
>>student 2: So instead of one half, we could cut right here and make the two halves.
>>teacher: After SLED they head into calculate.
Calculate is the area where they are expected to
solve the problem in usually more than one way. Most of the problems that I give
them will have more than one solution or more than one way to find a solution.
My role as a teacher during math circles is largely one of facilitation.
By the time I get to a math circle I have at that point already taught the
math skills that lead up to it, so there are days where it's, you know, the sort of
traditional my turn, our turn
lecture style of math implementation where they're learning new skills and
concepts. But as a culminating activity every one to two weeks once that set of
skills is firmly established, uh that's when I give them the math circles. And really
that's when I need to step back.
The math circles are actually about them figuring out on their own if something
is valid or not. And why if it's invalid they've reached that conclusion.
And beyond that even being able to defend and justify why something is
valid or invalid.
So I walk around class. I make sure that everybody's on topic, everybody is
speaking in academic vocabulary,
I often just offer praise when I see something happening that's good and give
them sort of positive feedback so that they're willing to continue to try.
Because that's something that our scholars really need to learn is to
persevere, to solve the difficult problems and to not give up.
And if you get it wrong, that's fine. But why, why was it wrong?
Don't just accept, oh well, I got it wrong.
>>student 1: Wait, you caught up? Alright, we convert the fraction.
>>student 2: Clean up the number. >>student 1: Oh, yeah. The whole number.
>>teacher: Once they have calculated, again as a group, they need to
be working with all 4 team members, they write their articulation.
I give them the option of writing the articulation independently or as a group
because they did solve it as a group, so their articulation should be fairly similar.
If they've worked together then they all follow the same steps they should be
writing those steps down. But if they just prefer to work independently at
that time and sort of gather their thoughts and organize them on the paper
that's fine by me too.
During math circles when my scholars are off task, it does occasionally happen, I
have the same mix-up of group as everybody else, uh
it's fairly easy for their teammates first to redirect them. So I rely
initially on teammates to redirect. So teammates are sort of the first line of
defense. And if I notice that-or if another scholar reports to me that
there's an issue at a table then I'll come over, and I think redirecting has really
worked very well.
Also I found proximity works quite well if somebody's being goofy in their group
they will not be goofy when you're standing right next to them. [laughs]
I heard a lot of really great conversations happening.
Uh, I noticed that my scholars were all on task, and even the kids who were taking
the wrong path to solve the problem were using the proper vocabulary. They
had the skills, they just chose the wrong one.
>>student: When we checked for validity,
we drew a picture and still got 2/3 as our product. Finally we simplified...
>>teacher: After they've completed solving the entire problem
then they do the presentation portion which is
almost always on a second or third day because math circles
are not a quick process they take quite a long time.
>>student 1: SLED: sketch, label, estimate, and discuss.
We put 1/3 because it says 1/3
to support- 1/3 of concrete to support a pillar.
The problem will be 1/3 divided by 2 halves-2 wholes because it is division.
>>teacher: The idea of the presentation is that when you teach you learn even stronger,
and the presenter needs to be learning this material very solidly by sharing it with
the rest of the class. But the rest of the class also needs to be absorbing and
understanding what they're trying to say.
>>student: The shaded part is the numerator of the
concrete the engineer used for the pillars. Here we cut out a circle. We shaded the
the part to know-so to figure out what the shaded part is. The shaded part is
numerator.
>>teacher: Math circles will help with the Common Core implementation because
often during Common Core and with the new tests they're asked to-they're given
a problem not given any indication of what they need to do to solve it.
They are asked to come up with their own solution based on the knowledge they
already have. And math circles are sort of a lower stress version of that
because they have these other resources of teammates who they can say, hey I'm
thinking about multiplying here or I'm thinking about dividing. And another
teammate might say well I was going to divide until I noticed that
such-and-such was happening. And again it's just sort of a lower stress way for
them to work that thought process out until it becomes second nature. And
hopefully with enough practice they'll be able to internalize that and do it
independently so that when they're working on their own papers at home or
at school or they're taking a test, they have those skills already and
that set of ideas of what they need to do to proceed is established.
Alright so what I have in my mind is this construction engineer who has to
make two pillars. So here's pillar number one that he has to make,
and here's pillar number two that he has to make. It doesn't need to be perfect a
sketch is exactly that, it's just a quick sketch.
So here are the pillars that he has to make. How much
concrete to see order to make those two pillars?
>>class: 1/3 of a ton. >>teacher: 1/3 of a ton.
So he orders 1/3 of a ton of concrete. That 1/3 of a ton of concrete has
to go to each pillar. The pillars are the same size so they each get half.
They each get half.
♪[theme music]