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Oliver Miller teaches sixth grade at KIPP One Academy in Chicago. He wrote this column for the Chicago Tribune.
If ever we needed a wake-up call to improve math learning, especially for historically marginalized students, the latest scores from the Nation’s Report Card and Northwest Evaluation Association provide it.
They show math scores hitting the lowest level in decades and pandemic recovery efforts stalling. The trend lines are particularly worrisome for low-income students like mine, whose existing opportunities and learning gaps worsened during the pandemic. The need for a major shift predates COVID-19, but the learning lost during this time more acutely highlights the need for change.
I’m guilty of previously using failing instructional methods myself. My early approach to teaching math was a bit like teaching someone to shoot free throws. I thought repetition was everything. If students just practiced the same skills repeatedly and committed them to muscle memory, I figured they’d be ready come “game time.”
I modeled how to solve a math problem using a single procedural approach, then students worked silently practicing the method that made sense to me. I learned math this way, so I taught it this way. While some students could replicate my math, they didn’t understand it and weren’t learning how to communicate their strategies. Such superficial mastery left them unable to retain or build on their learning in subsequent weeks and years.
After my first two years as a teacher, I tried something new. I started teaching my students how to think more like a coach — to think strategically about the math and what choices they could make, to decide what models to use, to see the “game” as more than free throws. For a task such as solving percent problems, for example, instead of simply identifying the missing information and plugging it into a formula, I now prompt them to select from various strategies building on previous work they’ve done with ratios to solve the problem.
A question might be: How much money did you start with if you spent $7 and this was 35 percent of your money? Some students might solve it by drawing a double number line, while others might create a ratio table or use more conventional methods. That’s fine. By selecting a strategy that makes sense to them, they are connecting percentages to previous learning about ratios and improving their understanding and retention of both concepts.
The beauty of math is that, like life, there’s no single approach that works best all the time. This also allows for rich classroom discussions as students make connections between the models they and their peers select.
The way I taught math before didn’t encourage my class to make connections to their previous learning. I usually had around half my students show proficiency on lessons related to percentages, with that figure declining unless we did regular review exercises. By teaching the topic cohesively as an extension of students’ existing ratio knowledge, I now get closer to 80 percent proficiency that I can far more easily maintain over the year because now solving a percentage problem and solving a ratio problem involve the same thinking and tools.
Nowadays my classes typically start with me asking students what they recall from the previous lesson. It’s empowering for them to build on their knowledge. Students talk constantly in class and solve problems collaboratively, rather than working silently. The learning process is noisier (and messier), but students are truly thinking and making decisions that make sense to them.
This type of instruction will improve math learning and help lift those low scores. Equally important, by giving my sixth-graders a chance to think, talk, execute a plan and compare their strategies to those of other students, I’m no longer teaching my students to simply and thoughtlessly follow the instructions of whoever happens to claim a position of authority. Instead, I’m helping them sharpen the life skills that mathematicians, CEOs, doctors, engineers and other professionals use every day.
