According to Yeh, these tests and other teaching techniques that rely on memorization give children a very narrow view of what math is. When math seems disconnected from everyday life, it makes it easy for students to claim it’s not their thing. Instead, highlighting math’s connection to concrete examples and students’ everyday context communicates that math is all over the place.
“There’s still a lot of work that needs to be done in the way of trying to make sure that people understand how critical math is because math really is everywhere,” says Vilson. “It’s just a matter of how we contextualize it in our society.”
Learning isn’t linear, it’s embedded
Math can be intimidating to students because it seems like if they fall behind it’s nearly impossible to catch up. On top of that, Vilson says that many teachers suggest that students drop classes if they are not keeping up with the pace of the curriculum. Instead, he encourages teachers to rethink how students learn.
“Learning is not linear,” says Vilson. “So much of how we discuss math assumes that everybody picked up every single standard along the way.” Most schools have students progress through math courses in stages – algebra 1, geometry, algebra 2 and trigonometry. However, Yeh says this means teachers are missing out on opportunities for students to understand how math principles naturally work together.
“Adding fractions is a fourth grade goal and multiplying fractions is a fifth grade goal. If they’re both doing it and you’re connecting across the two, that allows everybody access to grade level content. They get to see the integrated connection between these two operations.”
Yeh also relies on culturally sustaining pedagogy to help students see how math principles work together and are intertwined with their everyday lives. During the first week of school, Yeh encourages Chapman teachers to ask students to interview a member of their family in their native language about how they use math in their daily life. When children bring these answers back to school, Yeh and student teachers create math lessons that align how the parents used math with what students were learning in class.
Students were able to broaden their idea of who can be a mathematician and what mathematics can be. Yeh would even invite family and community members to come to co-teach math lessons from their authentic experience.
Using mini-scaffolds to build confidence
In order to meet students where they are at in their learning, Vilson uses a ground up approach to find where learners need support. When he gives an assignment based on a new concept, he’ll walk around the classroom to identify students that need help. Then, he’ll ask students questions starting with “Tell me what you know.” He calls this finding “mini-scaffolds.”
“The bottom is ‘I don’t get it at all,’” says Vilson of when he’s working with a student that isn’t yet able to fully grasp foundational concepts. “If that’s the case. Then I build from there. But I’m asking questions that continually go down until I get to that point,” he says. He walks away when students no longer need help so that students build confidence as they finish completing the problem on their own.
For example, Vilson has a favorite activity where students construct a model and calculate scale to figure out how planets are positioned in outer space. Students will start out by making estimates based on what they already know. After introducing some of the principles of scientific notation, Vilson will give students a few numbers to work from. As students rethink what the solar system looks like based on new numbers, he’ll guide students who need extra support with questions like “Are the planets all evenly spaced out?” and “How big are the planets compared to one another?”
“Kids can get closer and closer to the actual true right answer if we just keep working with them and allow them to get to that,” says Vilson. “You don’t hear things like ‘I don’t get it.’ You hear things like ‘Oh, we’ll figure it out together’
Additionally, Vilson is always trying to model how to react to wrong answers and mistakes. “If a kid tells you something like ‘Two thirds is equal to three fourths because I added one above and below.’ I say, ‘I see that you’re trying to make a pattern here.’ And then you start interrogating.”
He’ll ask the class questions about the problem that will lead them towards the right answer. In this case, he may even guide the students through making different representations of two thirds and three fourths, by drawing it out.
“It’s not like I told them it was wrong. I said, ‘Here’s a different path that you may consider.’”
Pathways for discussing math
Developing confidence in the math classroom helps students apply math principles anywhere they go. “I think those experiences allow for people to say math is wherever you need it to be. And is it exactly the same math? No, not exactly. But it activates the part of your brain that allows you to move around the world pretty quickly,” says Vilson.
It’s easy to dwell on bad experiences, but most people have felt the magical lightbulb moment in their brain when they’ve figured out how to solve a math problem. Vilson wants math educators to identify pathways that help math click for more students so that they no longer feel as if their race, class or gender has any bearing on their math ability.
When the subject matter starts to feel abstract, Vilson works with his students to identify models that can be replicated in other contexts. He tells students to take their geometry knowledge into looking at maps or navigating public transportation in new cities and encourages students to think of how many math principles they rely on to calculate a 20 percent tip.
Vilson says,“They’re able to participate in a whole different way. They’re able to articulate their answers in a different way. They feel empowered by the things that they’re doing.”
Yeh relies on real life examples to engage students. If she’s working on dividing by fractions with students, she won’t just ask, “What is two divided by one half?” Instead she might say something like, “The family has two loaves of bread and they only want to eat half a day. How many days would two loaves last?” Students appreciate this accessible entry point into what is sometimes a tricky math unit.