A group of young women who had graduated from high school between 1997 and 2006 sat at the front of the room crying and laughing about their experiences learning math at Railside High (a research pseudonym for the school). This session of the National Council of Teachers of Mathematics annual meeting didn’t focus on any specific mathematical practice and yet it was enlightening -- with the right approach, teachers can help kids who hate math feel like it’s their best subject.
One after another, these young women, who had all graduated from an urban high school serving many kids living in poverty, described how math class made them feel safe, heard and able to express their ideas without fear.
“I felt like they cared for me,” said Martha Hernandez, who graduated in 2002 and is now a social worker. “They cared for my education and they wanted me to succeed.”
Hernandez was designated an English language learner in high school and was the first in her family to go to college. She loved her math classes so much that almost 15 years later, in the NCTM session, she held out physical examples of her work as she cried about the impact the non-traditional math program at Railside High had on her confidence and future success.
“It changed what math meant,” said Maria Velazquez, who now studies education policy at the University of Wisconsin. “It was a process and it required other people. It wasn’t just you and your work and not talking.”
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Before high school, these young women, like many students in the U.S., experienced math as lecture, sitting at desks quietly. Many believed they weren’t good at math because they didn’t understand or compute quickly. But the math program at Railside High changed that for each of these women, showing them their strengths and allowing them to bring all of themselves to the pursuit of mathematics.
But what was so different about how these women learned math in high school? How did their math teachers form bonds so strong that years later they were attending students’ weddings in Mexico?
The answer: Complex Instruction. This pedagogy is not specific to math and has been in the literature for decades, originally researched by Elizabeth Cohen and Rachel Lotan at Stanford University. Teachers at Railside High discovered the methodology when they were undergoing an accreditation review and were told they needed to drastically change something to improve their results. The ultimatum prompted teachers to try something different -- heterogeneous classes, high expectations for all students and, above all, approaching math with an eye to students’ strengths.
Courtesy of Yuka Walton
The three main tenets of Complex Instruction are that learning should have multi-ability access points, norms and roles that support interdependency between students, and attention to status and accountability for learning. In most Complex Instruction classrooms the majority of class time is spent with students working in groups of four on a rich task that has multiple entry points and ways it could be solved. If one student can solve the problem in his or her head, it’s not a rich task.
Each student in the group has a role: team captain, resource manager, recorder-reporter and facilitator. While these roles might sound cheesy to some students, they are important for helping groups to work equitably, ensuring that every group member has a crucial and intellectual task. The roles help students learn how to effectively participate and, because each role is necessary to solve a task, everyone must share their ideas.
“Participation leads to more learning because learning is a socially constructed activity,” said Lisa Jilk, program director of Reculturing Math Departments for Excellence & Equity, part of the Mathematics Education Project at the University of Washington. Jilk taught at Railside High, and when she left to get her doctorate she studied how and why Complex Instruction worked for so many students from various backgrounds. Now she’s dedicated to helping other math departments around the country “reculture” themselves to think about what learners bring to math that will help them, rather than only about the information they are missing.
When the three tenets of Complex Instruction are all working together simultaneously it can feel like a magical experience. But getting there takes a lot of work. When Jilk starts training teachers, one of the first things that must be discussed is the idea of status in the classroom and how to break that down. Teaching with Complex Instruction is intimately tied to research in educational psychology, which says that to succeed students need more than content knowledge -- they need to see themselves as efficacious learners.
That is particularly hard in math, where many students believe they are dumb or incapable because of past math learning experiences. To combat that, a core part of Complex Instruction is to teach with a strengths-based approach, rather than only seeing student deficits.
“Every person who walks through our doors has mathematical strengths,” Jilk said. “They also have mathematical needs or weaknesses, things they have yet to learn. So we need each other.”
The Complex Instruction model works because when students work in groups to grapple with a rich math task (Jilk says College Prep Math is a good place to look), they are each encouraged to bring their full personality and ways of seeing math to the task. The teacher’s job is to observe what’s going on within groups and assign status when she sees a great idea, technique or way of thinking.
“You definitely can’t fake these moments,” said Yuka Walton, a seventh- and eighth-grade math teacher at James Denman Middle School in San Francisco. “You can’t assign competence or publicly acknowledge kids for things that aren’t meaningful because then it feels super fake.” Kids are great at detecting inauthentic praise, which ends up sounding condescending.
But when a teacher recognizes competence in students who don’t often feel like they have much status as a math learner, it can make a huge difference. Walton remembers one student, Alexis, who would often push the limits in class and consistently referred to herself as bad at math. One day in group work, Walton’s Complex Instruction coach noticed that Alexis was using a really smart, unique technique to organize the numbers in the problem, and her method was propelling her group’s thinking forward. Walton publicly acknowledged how smart that specific technique was and why it was adding value to the group. From then on, the whole class started calling that technique the “Alexis Method.”
“It helped her feel ownership over her own learning and her own smartness and power,” Walton said. Over time, Alexis built an identity as a math person, and as she had more confidence in her ability to contribute to her group, other students started assigning her status on their own by asking her for help. In order for teachers to assign competence well, they need to be open to many ways of solving the problem and many kinds of “smartness.”
Tracy Thompson teaches math at George Washington High School in San Francisco. Her math department was one of the first in the district to take on Complex Instruction seven years ago, before San Francisco made the decision to detrack math classes through sophomore year of high school. When Thompson started trying this approach, she had a group of juniors taking a class called “Applied Math,” an alternative to Algebra II that mostly low-performing math students chose to take. The class counted for graduation credit, but many students couldn’t wait to finish and be done with their math requirements.
By the end of that year, students had changed their tune. “Most of the kids that were juniors told me on their own that they wanted to go to Algebra II now,” Thompson said. Even though these students came from 10 years of school where they felt bad at math, with one year of strengths-based instruction that focused on kids working together to figure out interesting problems, they wanted to take on more challenging math.
Both Thompson and Walton were clear that this is difficult work and that it doesn’t happen overnight. It can be overwhelming for teachers to balance all the elements: designing or choosing a rich task for every lesson, monitoring status issues, holding students accountable to the norms and roles of group work, and not helping too much when students struggle. It doesn’t always go perfectly. But both teachers say they’d never go back to teaching any other way.
“The most important thing is it makes you see so much more clearly,” Thompson said. “Even though things aren’t perfect, it gives me these tools to work with and it just becomes part of the lesson planning process.” Now, when a student is unengaged in the lesson she doesn’t assume he’s lazy. Instead, she tries to find ways to make the classroom a dynamic, comfortable place for him to share his ideas and to participate.
“It has expanded my thinking about what makes you smart at math,” Thompson said. “It’s really helped me understand that there are different strengths that people have and that also the fastest calculator is not the best math student always.” Thompson now teaches both Algebra II (which all juniors take) and Calculus BC, one of the few tracked classes for high achievers. She says she has more trouble getting her calculus students to explain their thinking because they believe the best students are godlike and don’t push on their thinking.
RECULTURING MATH DEPARTMENTS
San Francisco has been training teachers in Complex Instruction for seven years. The district started by focusing on high schools, bringing in cohorts of teachers who worked at the same school in order to build a community that could collaborate on this difficult and transformative work.
“We’re broadening this idea of smart,” said Angela Torres, high school math content specialist for SFUSD. She and Ho Nguyen have championed the Complex Instruction program within the district, slowly broadening its reach as teachers heard about the program and expressed interest.
“We literally have to reculture these spaces so we are providing people with a new message and a new narrative about what they bring, the strengths and smartness they bring, and redefine what they’re capable of,” Jilk said.
Just a few years after San Francisco began dabbling in Complex Instruction, California adopted Common Core standards, which require more focus on the conceptual underpinnings of math, explaining thinking and reasoning, and less focus on procedural quickness. The SFUSD math department responded to the new standards by inviting teacher leaders to help them write the new math curriculum, pilot test it and offer feedback. They’re still iterating on that work, but the result has been a more engaged math team throughout the district, and more interest in strategies like Complex Instruction that can help teachers get students where they need to go.
“It took us really about four years to really understand what it takes,” Nguyen said. “And it wasn’t just about teacher change. It was really about reculturing the math department. We had to go through our own struggles.” SFUSD teachers have received training from Lisa Jilk’s organization, including classroom coaching.
The district has also been working to build up its own capacity to coach teachers through Complex Instruction so they can continue sustaining and broadening the program’s reach throughout the district. Coaches watch teachers as they teach and often provide on-the-spot feedback when they notice a student displaying a strength that the teacher missed. The coach will often nudge the teacher to acknowledge that student, sometimes to the whole class, as a way of breaking down some of the status issues in the classroom.
Torres and Nguyen have strategically tried to build teams of teachers at school sites who have incubated the ideas and continue pushing each other. As with students, teachers each have their own strengths and issues of status. Working together to develop rich math tasks, align assessments and discuss strategies has helped them experience the kind of learning environment they are trying to create. And there are meetings to connect educators across the district doing Complex Instruction, as well as a "video club" to practice identifying and assigning competence to different students.
“When grading we see students are able to think in this critical way that they weren’t able to do before,” Walton said. She used to teach in a district that used direct instruction, a type of teaching that came naturally to her. But she noticed that her students struggled as soon as a problem involved something that had not been explicitly taught.
“After doing Complex Instruction, it didn’t matter how complicated the problem was. Even if kids hadn’t seen it before, they would dive right in and get started,” Walton said. Even better, “you see these moments where these kids who before were so discouraged, brighten up and engage and feel more empowered. It has made it so much more meaningful.”
All the teachers and coaches involved in Complex Instruction stress that like any other truly transformative teaching practice, getting good takes time. For this style of pedagogy to work well all three elements of the program must be in place and functioning simultaneously. Teachers have to have high expectations for all students, and a real belief that each learner is coming to the experience of learning math with strengths, not just gaps in learning. It takes time to get good at listening for authentic moments of brilliance in student work, and to help students create the interdependence on one another necessary for strong group work.
“If you do only one thing, and that is to create opportunities for kids to leverage their strengths in your classroom activities and then name those strengths for them, if you can create those strengths for them, you will already be changing things for most kids in ways that are otherwise not possible,” said Jilk.
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And when it all starts to come together, and every student is in the “sweet spot,” it’s like magic. That’s when students start to feel the connection and recognition that the graduates of Railside High were so grateful to have experienced.
