Do Math and Grade-Level Instruction Need a Divorce?
As regular readers know, I’ve long held both that American education is overdue for a rethink AND that most “reform” is oversold. Finding the sweet spot, as Michael Horn, Julie Squire, and I note in our new book, School Rethink 2.0, requires focusing on rubber-meets-road change. Rethink 2.0 offers accounts from leaders doing that work, and I’m delighted to speak with one of them today. Joel Rose, a onetime 5th grade teacher who became convinced that grade-based math instruction puts teachers in an impossible bind, is the co-founder and CEO of New Classrooms. Whether or not you’re sold on his vision, I think you’ll be intrigued by his take. Here’s what he had to say.
— Rick
Dear Rick,
The future of math education will begin with the divorce of a very long-term marriage between math learning and grade-level instruction. “The Future of Math,” my chapter in School Rethink 2.0, imagines what’s possible after the divorce finally happens.
Why do I say this divorce is destined to occur? Well, ever since Massachusetts set up the nation’s first system of public schools, math education has inextricably tied what students should know to their date of birth: 3rd graders are taught multiplication and division, 5th graders are taught to coordinate planes, 8th graders are taught to graph linear equations, and so forth.
But this marriage between math and grade-level instruction has always rested on an unstable foundation. On the one hand, math, like most subjects, is cumulative. The skills students are taught in one year are foundational to what’s taught in the next year. For example, learning about ratios in 6th grade requires the ability to multiply with fractions and decimals, learned in 5th grade, and to compare fractions with different denominators, learned in 4th grade. Without those foundational skills, students will struggle to master ratios. On the other hand, grade-level instruction is sequential. A student’s age determines what grade level they are enrolled in, and each state determines the specific math standards that students are taught in each grade.
As long as students never fall too far behind, the marriage works well enough. But when some students inevitably do fall behind, there’s a conflict between what they are ready to learn based on their knowledge and what they are supposed to learn based on their grade level. And the winner of that conflict is always “what they are supposed to learn” because that’s what’s in the curriculum, what the teacher has been trained on, and what will be on the year-end assessment.
As a result, many students matriculate from one grade to the next without a complete understanding of the concepts they need to know. Those gaps make it harder for them to learn the next year’s concepts, which, in turn, makes subsequent years even more difficult and leaves many students discouraged. This vicious cycle of falling behind, and students’ resulting loss of confidence, is the product of this dysfunctional marriage.
This divorce will be inconvenient. But there’s no other choice. Policymakers and system leaders have tried nearly everything to improve math outcomes: raising standards, paying teachers more, reducing class sizes, providing better training, purchasing better curriculum, leveraging data, and more. There’s even been a declared “war” over math instruction. Despite agreement about the problem, meaningful improvements rarely follow. Instead, initiatives fade, and a new generation of leaders, legislators, and advocates commit to tackling math education with a set of reforms that are often merely a repackaged set of what’s been tried before.
Who benefits from this arrangement? Not the teachers, who are charged with the impossible task of teaching grade-level standards while also addressing foundational learning gaps. Not the students, who only fall further behind each year. And not the nation, which still has math scores in the bottom half of economically advanced countries in the Organization for Economic Cooperation and Development.
A shift away from grade-based math education and toward a new approach to math rooted in personalized, competency-based learning could deliver better outcomes. After all, in this kind of classroom, each student is on their own path to proficiency. Instead of all students of the same age focusing on the same concept, instruction is designed to meet each student where they are and to get them to where they need to be. Students learn through different modalities of instruction — from teachers, from technology, from real-world tasks, and from one another — so they can see how math is applied in different contexts and master new skills both inside and outside of the classroom.
The bar for success remains fixed: college and career readiness. However, the time that students have to meet that bar before they graduate is more flexible.
Let’s review the math of it all. From the time a student understands basic numeracy — counting, adding, subtracting, and the like — there are approximately 300 math skills they need to learn to be ready for college or a career. These skills include procedural, conceptual, and applied knowledge of basic numeracy through algebra. If a student begins the 5th grade knowing none of the 300 skills, which is rare, they could learn one per week and master just about all of them before graduating. At two per week, they’d be there by the end of the 8th grade.
That pace is eminently doable in a reimagined classroom because students spend their time learning new skills on a foundation of the skills they have already mastered. New Classrooms’ Teach to One Roadmaps — a supplementary online learning platform — assesses a student’s mathematical knowledge. Using that information, along with the content that is covered in their core math class, the platform creates a personalized “road map” for each student. Students can then use the platform to learn these skills through video lessons or, with their teacher’s support, collaborate with classmates working on the same material. When a student passes a short assessment, their road map updates, and they are allowed to move to the next skill. In the 2022–23 school year, when Teach to One Roadmaps was used as a supplement to a partner school’s core curriculum, students learned at an average pace of 1.4 skills per week. Those totals don’t include the skills students learned through regular classroom instruction — meaning their full annual pace was likely far higher.
This model also benefits students performing above their grade level. Rather than spending their time in school covering things they already know — a recipe for disengagement — students are challenged by content they otherwise wouldn’t interact with until they’re older. This can help them stay invested in school and set them up to take more advanced courses or even earn college credit.
What will this change take? For one thing, it will require a set of new state and federal policies, such as changing required annual state assessments to evaluate student growth rather than performance against grade-level standards. It will also require new investments in research and development to create and assess new methods, as well as professional development and other supports to help teachers make the transition.
Some will object to divorcing a student’s grade level from the content being covered. They may argue that ending the marriage is too messy or that another round of reforms is all that’s required. They may highlight specific increases in test scores in one place or another without acknowledging that these spikes rarely persist, and that even if they did, it would take decades, if not centuries, before the vast majority of students graduated with the ability to reason quantitatively, analyze data, apply mathematical concepts to real-world problems, and succeed in college-level math or technical training programs.
Divorce can be sad. But the courage to persevere through it can open up new opportunities for all involved. On the other side of this divorce is a new world where math classrooms are designed to meet each student’s needs, where teachers have a more sustainable and fulfilling role, and where families can become true partners in their child’s success.
This post originally appeared on Rick Hess Straight Up.
