Rethinking the Definition of High-Quality Instructional Materials for Math

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In many states and districts, post-pandemic learning recovery began with literacy. Not only had students fallen behind in reading, but a new body of research pointed to deep flaws in the way reading had been taught for decades. 

Now, policymakers and education leaders are beginning a pivot to math, where drops in scores on both the PISA and NAEP exams have been far more acute.

What’s the plan?

One strategy states will assuredly consider is to focus on the continued adoption of High Quality Instructional Materials — curriculum aligned to college- and career-ready standards. The trend toward these materials in both reading and math accelerated when troubling evidence emerged that disadvantaged students were not getting equitable access to high-quality teaching. Federal recovery dollars then helped to turbocharge adoption across the country.

These materials have been a major step forward for teachers who, for decades, were provided with low-quality textbooks or online resources that didn’t reflect high standards or research-based teaching practices. Introducing an objective quality rating into the textbook adoption process disrupted the K-12 publishing industry for the better and helped to ensure that all students had access to educational programs rooted in high expectations.

But before going all-in on HQIM in math, state and district leaders should consider the implications of an important nuance in how instructional materials are evaluated by EdReports and other ratings agencies: to qualify for an acceptable rating, the materials must focus on grade-level work.

In reading, most students can benefit from grade-level instruction so long as they have passed the decoding threshold. They become better readers when they build knowledge and vocabulary, learn to navigate more complex texts and exercise critical thinking — all of which can happen regardless of the students’ starting point. A seventh-grader at a fifth-grade reading level can grapple with seventh-grade content and become a better reader. The struggle can be productive.

But in math, specific topics that are taught during one school year are foundational for what’s taught in the next. If students fall behind, gaps in learning can quietly accumulate, making it harder to catch back up. A student who didn’t quite grasp enough about the concept of decimals in elementary school can struggle to understand percents in sixth grade and then to apply them in seventh. Teachers can have a hard time addressing unfinished learning when their materials are focused largely on grade-level content. Math is cumulative — a fact that doesn’t change when a student happens to move on to the next grade level.   

Each day, we see a clear relationship between foundational concepts and grade-level mastery in the data we gather within our supplemental math program, Teach to One Roadmaps. For example, when students attempt to learn the Pythagorean Theorem having already understood concepts such as estimating square roots and classifying triangles, they have a 72% chance of achieving mastery. When they don’t know these predecessor concepts, that success rate drops to 32%. Similar rates exist for nearly all the topics in the program. 

The importance of addressing unfinished learning in math proficiency is also consistent with learning science. Among the most foundational principles of cognition is that students have limited working memory capacities, which can be overwhelmed by tasks that are too cognitively demanding. Once students memorize information and master skills, their brain is free to use their working memory on other, higher-order tasks. But if they don’t master those lower-order skills, their working memory strains and their understanding of new ideas is impeded. 

Does this mean that students should instead spend all their time addressing every learning gap from previous grades? Of course not — instructional time is too limited. If students spend an entire school year working only on unfinished learning, they finish the school year behind again, having missed out on grade-level content that’s foundational to the next year. The cycle continues, year after year, making it nearly impossible for them to ever catch back up.

But it also doesn’t mean that instruction can ignore those gaps. As Dan Weisberg and I argued in 2019, teachers need strategies to both maintain high expectations and address unfinished learning from prior years. Advances in technology, and especially in artificial intelligence, make both objectives more achievable than ever. However, a curriculum that does both would have a hard time qualifying as High Quality Instructional Materials, since it would not focus on the major work of the grade.

Teachers clearly recognize that students are behind. So do advocates for HQIM, many of whom guide schools to access resources that help teachers better understand predecessor relationships. But guidance documents aren’t the same as instructional materials that could actually help teachers address foundational learning gaps. And since those materials don’t fit a grade-level-only definition, teachers often need to source their own materials to diagnose and address foundational learning gaps and then somehow integrate it into their classroom workflow. Not only is this difficult to do, but it’s what HQIM was supposed to avoid.

What can be done to ensure students have access to both grade-level content and pathways to proficiency?

Some states are broadening their definition of HQIM to allow for more than just grade-level content. Texas recently launched a curriculum review process in math that allows publishers to include both on- and off-grade material so long as the grade-level standards are fully covered. California seems to be on a similar path, as its new math framework is now more focused on grade bands (i.e. grades 6-8), as opposed to individual grade levels. (Most states use grade-level bands in their science standards.)

Others who prefer to hold tight to grade-based core instruction can consider changing the definition of HQIM when it comes to evaluating supplemental resources. Rather than simply applying the same grade-level-only filter, evaluation criteria for intervention solutions can focus on the ability to accurately diagnose relevant skill gaps (no matter how far back), embed rigorous content and assessments, develop custom learning pathways, activate student engagement and integrate with core instruction.  

High-quality instructional materials help to ensure students have access to an academic trajectory that’s aligned to college and career-readiness. But access alone is not enough to unlock social mobility — mastery is what matters. For as long as the nation’s schools have taught math, they have struggled to serve students who, for whatever reason, are not performing at grade level. That’s been true regardless of the quality of the curriculum or the training of the teacher. 

Instructional materials are the most important tool an educator can put to use in the classroom.  But as with any tool, quality should reflect both an aspirational vision for what it can do and the science to make sure it can deliver. 

The current definition of HQIM sets an appropriately high aspirational vision. But for students to meet that bar in math, their teachers need more than what HQIM — as currently defined — can offer.

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