David speaks: Out in the world if you’re a

kid learning, you really like to learn by playing with stuff, right? We like throw balls around when we’re toddlers,

we catch things, we pour sand back from one bucket to another. We learn how sand works. But in algebra we expect students to play

with the algebraic representations and remember all the rules that instantiate the world. So Graspable Math is a way to let the algebra

respond to us, to let us play with the algebra. Erik speaks: Graspable Math turns algebra

into something like a real thing you can interact with. And that’s something fantastic for students

which can actually now go and explore algebra. David speaks: Graspable Math, for the student

and the teacher, is a way to pick up the symbols and move fluidly. Erik speaks: So we can see Graspable Math

being used as a teacher presentation tool where a teacher is standing in front of a

smart board or a projector and explaining things more clearly to the classroom. David speaks: The sidebar that lets you pull

in equations from Wikipedia or a lot of other sites. Erik speaks: A homework tool where students

get immediate step-by-step feedback. David speaks: Graspable Math came specifically

out of a Department of Education-funded project to develop interventions that would help students

see the dynamic properties of algebra. See this dynamic algebra the way that experts

do. And we’re working with schools in Massachusetts,

in Virginia, in Indianapolis to study how kids learn, and our commitment is to make

sure that it’s always free for teachers and students. Erik speaks: So the state of the art in algebra

assessments is that you give students a problem and then they type in the final answer. David speaks: Often we say, okay, well the

student got the problem, check. Erik speaks: But they’re still doing all their

algebra with pencil and paper. David speaks: What we can get is a very different

insight into how students are succeeding. Erik speaks: In Graspable Math, students really

trigger each algebraic step by a gesture. They really control how they go through a

derivation. And Graspable Math will record all of these

steps. David speaks: In a usual experimental context,

all you get is the answer the student gives, or you have to hand code all the steps that

they did. But we get everything the student did, and

everything the student tried to do and failed. And so we can find out what kinds of things

students think are a good idea as they’re struggling to learn these algebraic concepts. Erik speaks: The student can look at them,

the teacher can look at the steps, you can compare different ways of solving a problem. David speaks: And that gives us, I think,

a unique access to misconceptions students have, and the struggles that students have,

and then just the ways that they succeed. Erik speaks: There’s certain types of mistakes

you can still make in the system, which are the strategic mistakes, which are going off

in the wrong direction, without breaking the rules of math. These kind of mistakes are incredibly important

for learning, and you can still make them in our system. David speaks: One way that it gets used is

for research, and then the other place it gets used is by teachers who just find it. Erik speaks: It ensures that you play by the

rules and creates this safe space. David speaks: Graspable Math helps support

whatever algebra a teacher’s teaching. [MUSIC]