# From Concrete to Abstract—The Montessori Math Approach

>>Teacher: Well, the thousands cube
represents our thousands place. So let’s put that right here.>>Amanda: The Montessori Math approach
works, because it really helps the kids on each level that they’re on. There is a material made for
kids who can’t even count yet, kids who can’t recognize numbers,
and then also for kids who are ready to read four-digit numbers.>>Student:
Two-thousand-four-hundred-and-fourteen.>>Dollie: Montessori Math puts
children on a continuum of lessons and the children go from
concrete to abstract. It starts with the lower-level
math lessons, and it progresses to the most difficult.>>Amanda: So what do you have to do? You have to put these numbers in
order, and what are you counting to?>>Amanda: They have a Control Board that
they use, and they put the little tiles in order from one to one-hundred. And then if a child’s really
ready, we have an extension to that where they write one to one-hundred.>>Dollie: In a traditional classroom, even though you differentiate
instruction, the teacher has to teach to the group. In a Montessori classroom, you’re able
to provide lessons to those children on exactly the level that they’re on.>>Diana: We’re just going to focus
on our multiplying by units first.>>Diana: Every child
has their own workplan, which means that they’re all
working on different things at different times in the classroom. There might be some similarities,
for example, many second years might be learning
multiplication at the same time. But for the most part,
it’s very individualized.>>Diana: That’s right.>>Bella: Here’s our Math Shelf. We could count by sliding the beads.>>Phyllis: I believe that
kids can grasp it much easier, because we use concrete
materials to teach math.>>Phyllis: Two, three,
four, five…>>Phyllis: The Golden Bead lesson
begins with “This is a unit. And then this a ten. And a ten is ten of the units.” And then we build the hundreds square,
and we build the thousand cube, and they get that understanding
of what those numbers mean, and not just saying those numbers.>>Rachel: One of the things
that Montessori does so well is that it teaches conceptually. It doesn’t just teach a bunch of fact, it doesn’t just teach you
how to remember something. It teaches you the base concept, and
then you go and apply those concepts.>>Student: This is a
five long bead chain. A six long bead chain.>>Diana: When it comes to place
value, our ones, or we say units, are color-coded in green,
and then our tens are blue, and our reds are hundreds, and then we
say, “There’s a new family started.” And then it goes to the
thousands, which are green again, and then the ten thousands are blue.>>Teacher: So my answer’s
going to be down here, okay?>>Amanda: You’re going to
count to eight seven times, and then we’ll count the total, and we’ll find out what eight
taken seven times is, okay?>>Amanda: Instead of saying
“plus” in Montessori, we say, “Two together with two is four.”>>Amanda: One together with six.>>Amanda: And the same thing
when we do multiplication we say, “Taken so many times.” When we do subtraction,
we’ll say, “Take away,” because “subtract” is a really big word. But they know what it means
to take something away. They take away toys from
their friends all the time.>>Teacher: We are going
to share out the number–>>Amanda: And then when we do
division, we do “shared out.” And those words just
make more sense to them. Once they get the concept, we do
teach them the math vocabulary that is actually what you use.>>Dollie: As a public school,
you have to find that balance. You have to stay true to the
Montessori Continuum, but you also have to implement State Standards
on every grade level.>>Teacher: And we’re still trying
to make that magic number seven.>>Diana: If you look at the
curriculum and how it progresses, then you see that Montessori
covers everything. And in some ways, it covers more than
what the standards have offered to us.>>Rachel: I feel like Montessori Math
really increases their confidence, and helps them to understand
that there’s that “try” mentality involved with it. It’s not that, “Oh, you got a bad
grade on this, and we’re moving on.” It’s, “How can we work
towards that mastery, and how can we really
fully learn this concept?”