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“Students Using Their Minds Well”: Extreme Differentiation in the Math Classroom

“It’s my job to notice people,” quipped Dawn Crane as she offered a seat to the event photographer who had quietly stepped into the back of the room a few minutes into her presentation.

As a Math and Science teacher at the Francis W. Parker Charter Essential School in Devens, Massachusetts, Crane has become an expert at not only noticing, but also taking action on the strengths, challenges, interests, and learning styles she observes in her students. She shared her approach—which she describes as “extreme differentiation”— during a packed pre-conference session at the 2016 High School Redesign in Action Conference.

Tailoring instruction to meet the needs of diverse students is not a new concept in teaching, but Crane takes this principle to a new level. In her Integrated Mathematics classes, she has twenty-four to twenty-six students who range from 8th to 11th graders. At Parker, students are heterogeneously grouped, so her students’ proficiency on mathematics standards in any given class ranges from “beginning” to “exceeding.” In response to this broad array of student need, Crane must be creative, flexible, and highly data-driven.

Extreme Differentiation in the Math Classroom
Math educator Dawn Crane (middle) speaks with participants Stella Ross (left) and Heather Vonada (right).

Crane, a 22-year teaching veteran, says she first began deeply investing in differentiation and personalized learning about five years ago, when she realized how many students were coming in after school for help. “We were good at following up with students on an individual basis, but that’s not sustainable,” she said. To “move that learning back into the classroom,” she has infused her teaching with a variety of tools and practices that enable her to regularly monitor student learning. Based on that feedback, she adjusts assignments, opportunities for practice and extension, and assessments to reflect what students need—and what will motivate them. “It can’t be just more of the same,” she pointed out.

One of the most important elements in her approach to personalization, Crane says, is the way she builds an instructional unit. Before she introduces a unit’s core concepts and skills, Crane often invites students to wrestle with a real-world scenario or a hands-on puzzle, which sparks their curiosity and creates “a need to know.” For instance, to introduce exponential equations, she might ask students to try to figure out how many dominos it would take to knock over an Empire State Building-sized domino.

Crane also designs “stations” in hard copy and digital formats that offer students a variety of scaffolds and practice opportunities to ensure that they are gaining proficiency on content-area and interdisciplinary standards.

Math Photo 2
Crane’s stations for differentiated learning.

After checking student classwork, Crane helps guide each student to the station best suited for their needs. Students may select which stations they need and can move among them or seek out peer collaboration based on how well they are progressing toward proficiency. These independent decisions are supported by a culture of self-awareness and personalization that Crane intentionally builds in her classroom. “I work really heard to encourage kids to be wrong,” she says. “I thank kids for finding my mistakes and acknowledge that I make them, that it’s okay that I made them.”

Through the use of many different methods of formative assessment, Crane learns more about what each of her students needs. Exit tickets, data from digital programs, quizzes, and “problems of the week” also inform Crane’s understanding of her students’ knowledge and skills on a regular basis.

Crane uses information gained from assessments to determine which students need re-instruction and to coach her students’ next steps. She may direct struggling students to certain problem sets, stations, or technology-based supports for additional reinforcement, while pointing proficient students toward more complex problems or extensions. Sometimes, Crane says, students just need more time. She grinned as she shared the story of one student who spent an entire year at the “beginning” level of proficiency in Integrated Mathematics. Now, during her second year in Crane’s course, the student has volunteered a response twice in two weeks. “That never would have happened last year. I’m so proud of her,” Crane beamed.

Crane emphasizes that she constantly groups and regroups students according to their needs and strengths, enabling productive collaboration and conversations among them. “The [Coalition of Essential Schools] principle I most resonate with,” Crane explained, “is ‘student as worker, teacher as coach.’” As each unit draws to a close, students engage in summative assessments in diverse ways, choosing to present their learning through a video, poster, or a written piece, for instance, that is included in the school’s portfolio-based assessment process.

Reflecting on her journey toward deeper differentiation and more personalized learning, Crane is quick to point out how powerful it has been to collaborate with her colleagues. From exchanging creative instructional ideas to developing shared agreement on what constitutes proficient student work, she has worked closely with her peers over the years. (And she’s happy to pay it forward: check out these resources for examples of Crane’s unit introduction activities, stations, and differentiated assessments.)

She suggests that, when it comes to extreme differentiation, educators should start small: “You don’t have to change it all tomorrow. Just try one thing—and you can’t give up on it if it doesn’t work the first time.”

A keen observer, indeed.

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