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Math and Inquiry: The Importance of Letting Students Stumble

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A Science Leadership Academy sophomore puts the finishing touches on a geometry project during her lunch period.
A Science Leadership Academy sophomore puts the finishing touches on a geometry project during her lunch period.

For subjects like math and foreign language, which are traditionally taught in a linear and highly structured context, using more open-ended inquiry-based models can be challenging. Teachers of these subjects may find it hard to break out of linear teaching style because the assumption is that students can’t move to more complicated skills before mastering basic ones. But inquiry learning is based on the premise that, with a little bit of structure and guidance, teachers can support students to ask questions that lead them to learn those same important skills -- in ways that are meaningful to them.

This model, however, can be especially hard to follow in public school classrooms tied to pre-set curricula. Class time, class size, assessments, resources, student buy-in, administrative pressures, and students' learned helplessness are just a few of the reasons why it can be challenging to create learning experiences that are deep, authentic, and driven by inquiry, according to participants at EduCon 2.6 hosted by Science Leadership Academy (SLA), a public high school in Philadelphia recently.

Science Leadership Academy, which has an established track record as an inquiry-based school, has just opened a second campus in Philadelphia called the Beeber school, whose teachers are still adapting to the inquiry model. With one freshmen class and a new crop of teachers still adjusting to project-based and inquiry driven approaches to learning, the school is a good model for learning how these complex ideas flesh out.

“You have to spend a lot of time and a lot of energy supporting kids to unlearn how they’ve been taught to learn for the majority of their lives,” said Marina Isakowitz, a ninth-grade math teacher at Beeber. Students at both SLA campuses come from public middle schools across the city and enter with varying levels of proficiency and very little experience with inquiry learning.

Isakowitz starts the year by asking lots of low-stakes, but complex questions as a way of scaffolding a new kind of learning for her students. Gradually, she says, they realize that this math class isn't going to be like others they've been in and they begin to understand and appreciate the freedom they've been given. It’s about providing just enough structure that the class holds together, but not so much that teachers are telling students what to do and how to do it.


Watching students struggle with how to ask good questions and discover answers can be hard. “I, as the teacher say, 'I’m going to let you bruise yourself, and that’s going to be hard to watch, but I’m not going to step in and help,'” Isakowitz said. That can feel like she’s not doing her job, she said, but she knows it's an important part of getting them to take ownership of their learning.

“It’s so terrifying as a teacher when you have this notion of what looks right, and they’re not doing it right and I’m failing as a teacher because of that,” Isakowitz said. She’s had to learn to hang back and watch what develops. She’s also had to challenge her own ideas about math education, including the notion that students must learn one skill in order to move onto the next one.

"How much of this hierarchy comes from the idea that they need to know A in order to do B," Isakowitz said. She’s constantly asking herself, “How can I let them explore something and let them learn the skills along the way?” For example, Isakowitz designed a project based on students' complaints over the unbearably high temperatures at the school in the summer. They are working to come up with a solution to a problem they are physically invested in by researching air conditioning systems, figuring out how many units their school would need based on its size and layout, and calculating costs. In the process, students are learning about things like systems of equations and slope.

“Sometimes that means letting them go down a dead end -- that I know is a dead end -- because they just need to figure it out,” Isakowitz said. Within the framework of research and discovery she is building in different ideas and units that the state requires ninth graders to learn. Even with the best of intentions, there are times when the class has to cover a topic that will be on the test but it doesn’t fit into a project. In those cases, Isakowitz tries to be honest about why the learning style has changed.

An SLA senior explains how he got interested in robotics during his senior engineering seminar.
An SLA senior explains how he got interested in robotics during his senior engineering seminar.

“As much as we can say it's okay for students to fail within the class, if they don’t pass the test at the end of the year it’s suddenly not okay,” one teacher said in response to the discussion. That mixed message is a challenge to many teachers who understand that learning from mistakes is an important part of a good education.

Isakowitz faces that challenge every year when her students have to take a test that determines if they graduate. “I’m wagering my students' ability to graduate high school on this teaching practice,” she said.

Using a project-based inquiry approach to learning math is not easier, but kids are learning the material in ways that are relevant to them. Consequently, there are some topics that Isakowitz knows she won’t be able to cover. She’s hoping that her students have learned the topics she covered deeply well enough to make up for any gaps in knowledge on the state tests.

“Parents are having a hard time watching their kids struggle,” another teacher participant said. “Especially kids who were successful learning the other way.”


Teaching a topic like math without the traditional sequencing can be hard for everyone in the community to understand and requires tolerance for failure. The payoff is when, for example, a student becomes a senior and chooses mechanical engineering as an elective because he loves solving problems and has been learning to do it all through high school.

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