Book #3 in this series, Mathematics for Equity: A Framework for Successful Practice, edited by Na’ilah Suad Nasir, Carlos Cabana, Barbara Shreve, Estelle Woodbury, and Nicole Louie, is one that got me very exited about Math instruction. As a former English teacher, that is not a sentence I ever thought I’d type, but the instructional model presented in the book embodies all the things we tell districts to do if they want to improve learning for students. To see it lived out in classrooms and to see the effect it had on students both academically and personally, and to see how it impacted equity, was — and I am not being facetious here — thrilling.
The model was the brainchild of a high school in California (dubbed “Railside” to protect student and teacher identities) and became the subject of a university study in which it was compared to two other high school math programs in two other high schools near by, both in suburban settings. Railside High was an urban school, culturally and linguistically diverse with many language learners and students whose families had few financial resources. In fact, if you look at the demographics of Railside High, you would immediately see risk factors for lower achievement: high population of ELL students, low percentage of parents with college education, high population of minority students (80%), highest proportion of FRL among the schools compared, and so on. At the beginning of the program, 9th grade students were achieving at significantly lower levels than the students from the other, suburban schools in the study. By the end of the first 2 years, Railside students were consistently outperforming students from the other two schools and achievement differences between ethnic groups were reduced in all cases and eliminated completely in most. Not only that, the Railside students were more positive about math, took more math courses in high school, and more of them planned to pursue mathematics in college than the other two schools. Stop and take that in: they were so dialed in to their math classes that they wanted to keep studying math. MATH. I think it’s fair to say that this is not generally the response from your average high school student, and it’s definitely not the response from traditionally low-achieving kids. How did they get these results?
Reading the book will give you the most detailed explanation, but here are a few important tenets of the model.
- The program completely redefined how math was learned. In a traditional classroom, math is demonstrated by the teacher and practiced by the individual students. Achievement in such classes is individual and positional: Jen is better than Calvin, Ari is doing worse than Na’isha, etc. If a child does poorly in the course, the responsibility rests with the child and the perceived effort s/he is putting forth towards learning. Railside took this paradigm and upended it completely. At Railside, students worked in groups most of the time and the group was responsible for everyone’s learning within the group. The ways in which kids were assessed supported this model: one member of the group could be chosen to take a mastery quiz and all members get a group score based on his/her performance. BUT students had agency in the assessment. If the group didn’t feel they were ready to be assessed, they could delay the assessment until they all understood the concepts. Students were also assessed individually, but the group assessments were a key strategy.
- Teachers upended traditional classroom practices. In a traditional math class, teachers lectured 21% of the time and questioned students 15% of the time while students worked on practice problems in their books 48% of the time and presented work 2% of the time. The problems students completed were all short, “closed” problems meant to offer practice of a particular method. Average time spent on problems was 2.5 minutes, for an average of 24 problems per class period. At Railside, students were given long, complex problems with no set method. Teachers rarely lectured (4% of the time) and only questioned students as a whole group 9% of the time. The bulk of the class was students working in groups (72% of time) while teachers circulated between groups and demonstrated methods or questioned groups on their thinking. Students presented their work 9% of the time. Average time on problems was 5.7 minutes — more than double the traditional classroom — for an average of 16 problems per class period. That’s a lot of numbers, so I’ll summarize: students at Railside approached concepts at depth rather than at speed as in the traditional classrooms. Another indicator of depth? Introductory algebra was taught over the equivalent of two years, in effect spreading out the concepts so that they could be covered more deeply. Also notice how the teacher is decentered here: students are the focus and the teacher is the facilitator.
- Tasks for students were carefully designed to promote critical thinking and to require the
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collective resources of the entire group. The word Railside teachers used for these tasks was groupworthy. A groupworthy task was complex and allowed for multiple representations and solution paths; there was no one “right” method for solving the problem. Underlying these tasks was the mandate to justify their solutions — explain why your solution works, defend your answer. There is a lot more to task construction but suffice to say that it is foundational to the entire pedagogical program. Without these complex tasks, the group work would have likely fallen flat.
- Teachers flipped the paradigm of why a student needed to individually know the content. In traditional classrooms, the purpose of individual knowledge is to do well on an assessment. At Railside, the purpose of individual knowledge was to help others in your group understand the concepts better. This shift is profound: instead of competing with each other, the work and the understanding becomes collective. Individual knowledge becomes a resource for group success. What struck me here was that this is essentially how business operates. This paradigm-flip had the effect of easing tensions between groups in the school; in math class, everyone worked toward a common goal. It also supported the often-expressed belief that everyone could “do” math if they kept trying.
- The program had high expectations for all students. Tracking was eliminated at Railside and all students were required to take Algebra I at the same time. The curriculum at Railside was more cognitively demanding than at the other schools in the study and teachers expected not just minimal competence but high achievement from students. In one interaction, a teacher told a group “I can’t quite give you an A+ yet — call me when you think everyone can explain. It’s really important that you all understand.” Additionally, it wasn’t enough to arrive at a solution; students needed to understand and communicate the thinking behind the solution. The focus was not on correctness but on making meaning. The curriculum was built around Big Ideas — overarching concepts that connect across mathematical disciplines. Those connections were part of what encouraged and enabled kids to go on to higher level math.
- There was deliberate emphasis on relationships with students to help them construct identities as math learners, and deliberate emphasis on student agency in a number of arenas. Teachers emphasized and supported intellectual risk-taking and encouraged diverse styles of thinking. There was no “wrong” method, though some methods were less efficient. All this was meant to counter the negative baggage students brought with them from prior math classes.
- Hiring was driven by the model. New hires had to share the philosophical beliefs of the program and the other teachers and be willing to engage with both the model and the students as whole people.
I could write on this book for days; what I’ve written here doesn’t begin to do it justice. It’s packed with information and ideas and the model is clearly delineated for those who want to follow it. What’s most encouraging are the results, especially the results between ethnic/racial groups, even though the program was not built around race/ethnicity in any way. Instead, it committed to raising the bar for all kids and redefining what it meant to “do math,” turning a mostly individual activity into a collective, inclusive process. It’s not hard to see how the model could be replicated in other content areas and at other grade levels, so long as the philosophy holds constant and groupworthy tasks are carefully constructed.
If you’ve wondered how to practically enact academic equity, this is your guidebook.