Brittany Marshall
“I think what happens a lot is that people focus on what a child doesn’t understand. We like to look at it the other way: what does the child know how to do?”
About the article:
This post is a part of an ongoing series in which I interview educators and education researchers to supplement the articles on AJ’s Takes on Why. All speakers have my sincerest gratitude and are acknowledged below.
Speaker Bio
Dr. Brittany L. Marshall is an assistant professor in math education at San Diego State University. Her research focuses on disrupting traditional mathematics logics (assumptions about who and what belongs in mathematics spaces) that exclude students from intentionally-neglected communities. New to California, she received her Ph.D. in education from Rutgers University. Before Rutgers, she taught elementary, middle and high school mathematics in her hometown of Chicago. Brittany also holds both a masters and bachelors d’s degree in architecture, and practices in Chicago and Washington, DC. When she is not teaching or learning, you can find Brittany exploring new cities, trying new cuisines with her family and friends or relaxing at home watching Chopped and Love and Hip Hop with her pets, Cori and Brennan.
How have your research interests progressed, and what inspired each development?
I am a new faculty member at San Diego State, teaching for two years now. Well, I'm in the second year now. Prior to teaching at San Diego State, I was working on my PhD, and prior to that, I taught elementary, middle, and high school in Chicago, which is where I'm from.
One thing I thought a lot about, even based on my own experiences as a math student, especially in middle and high school, is that I was so excited and wanted to learn math and wanted to do well at it, but I was taught very little higher-level math. I was always taught to just memorize formulas and things like that.
Just follow these steps, don’t worry about anything else. It doesn’t matter why it makes sense, why we can keep-change-flip, none of the formulas were explained to us. We just got the rules to it. And the older I got, school got harder, math got harder, classes got harder, but there was still very little explanation. Then I stopped even being able to take certain math classes, just not having the resources to take calculus and things like that.
Then I ended up going to college and majoring in architecture for undergrad, and I had to take Calc I and II, and the engineering sequence—so AP Calc BC, then the engineering sequence after that. And I was placed into remedial math, even pre-college math, and just continued to struggle with it without any explanation of how to make sense of it.
After my career in architecture—I actually practiced as an architect for a while—when I switched to teaching, I noticed that children were having the same issues. Even my textbooks and things like that did not explain why things were the way they were, just rules and procedures. So that was really important for me to focus on: making sure that math made sense and that everybody had access to understanding it.
Whether they eventually wanted to take more math classes or not wasn't the important thing, just making sure that people could have access to it if they wanted it.
You’ve described math instruction as often being rooted in rote memorization. How do you work to change that in your own teaching?
I guess, personally, at San Diego State I’m a math education professor, so I teach pre-service teachers how to teach math to children. The biggest thing that I spend time talking to my pre-service teachers about is just letting children try on their own. Let them reason through problems.
First of all, the problem has to make sense to them. I know you’ve interviewed other people, and I don’t know if they’ve ever discussed CGI, which stands for Cognitive Guided Instruction. Essentially, back in the day, these researchers looked at the way children learn math problems—I mean, little kids, like kindergartners—and the biggest thing was exploration.
A child would end up doing division problems because they understood certain concepts like sharing and what we call fair share. So, let’s say you, I and a kindergartner were together, and we gave them a bag of Skittles and told them that everybody got the same amount. They could pass out candy to all three of us and make sure that we all got the same amount of Skittles. That’s division, right?
Essentially, it’s just letting a child reason through problems on their own and with each other, and then, as they are reasoning through it, we sit with them and ask questions like, “Where’d you get that from?” “How’d you do this?” “Tell me where that number came from.” And they’ll get there. That’s actually how we learn.
So, if you have any little siblings or just little children in your life, you can ask them how to solve certain problems, and if you give them the tools to solve it—meaning manipulatives—they can figure it out. A lot of times, they get confused once we teach them all of this rote memorization. Then it starts to confuse them. But there are tons of videos and tons of examples of very young children solving pretty complex problems.
So that’s what I’m focused on: questioning, getting out of children’s way and letting them solve things, and then, when they get stuck, using supportive questioning to help them get unstuck.
What projects are you currently working on, and what research questions are you exploring?
Yeah, there’s a few. I’m working with people at different universities right now.
One project looks at how our pre-service teachers examine children’s work and figure out what the child knows. The children answered fraction quiz problems, and we pulled several examples of their work. We want our pre-service teachers to look at those answers and first tell us what the children know.
I think what happens a lot is that people focus on what a child doesn’t understand. We like to look at it the other way: what does the child know how to do? Even if it’s just that they know how to count to 10, whatever it is, what does the child know? From there, what are some questions or things we can do to help the student get to the next level? So if a child is getting answers wrong, exactly what is wrong? Where does the breakdown in understanding come from? Once we know what they know, how do we bridge the gap from what they know to what we need them to understand, and how do we ask those questions?
That’s one thing. Our pre-service teachers’ classes start this week, so we’re going to have them analyze that data, and we’re going to write about the way they look at how children think about math. Another thing that’s really interesting to us is math autobiographies. We have our pre-service teachers write their own math autobiography—how they’ve come to see themselves as math learners and doers. I’m really interested in how those math autobiographies line up with the logics.
Like I was saying, those are the things we think about: that math ability is innate, that it’s all about the teacher telling and students following procedures. Another one is individualism and competition, where it’s all about being the best and the first. I’m interested in how their autobiographies, and the way they learned math, align with those traditional logics, and also where they see their own math classrooms going. Do they want to stay with those traditional logics, or have they considered alternative logics that would make it possible for more children in their classes to participate?
Essentially, my pre-service teachers write math autobiographies, and I want to analyze them to see how much of what they write aligns with traditional math logics and how much aligns with trying to make sure the children they teach are encouraged to participate in math, as opposed to just being like, “Oh, it’s not for me.”
A lot of elementary math teachers get nervous. A lot of times, they feel like math isn’t for them, or they’re the ones who were pushed out of math. That’s another thing I’m always trying to fight against with them. I want them to feel like they can do math, too.
