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The math wars are raging again.

In statehouses, school board meetings and academic journals, a familiar debate has resurfaced: Should math be taught through clear, repeatable algorithmic steps or with a focus on why the numbers behave the way they do?

This fight has flared up repeatedly for more than a century, with the tide turning back and forth through the years. Today, with and still haunting the nation’s classrooms, many in education are hoping that a resolution can herald a science of reading-type breakthrough that brings clarity and results.

Why does neither side ever win the math wars? Perhaps it鈥檚 because they鈥檝e been fighting on the wrong battlefield.

The math wars focus on how to teach 鈥� the specific methods used to deliver a lesson. But to make serious improvements to math education, it is necessary to stop obsessing over the “how” and start focusing on the 鈥渨hen.鈥�

In nearly every American math classroom, what students learn depends largely on their birthday. Ten-year-olds in fifth grade study decimals; the following year, they move on to percentages. The underlying assumption is that all students move in lockstep, mastering each year鈥檚 content on a rigid, chronological schedule.

This approach can work fine so long as students stay on track. But if they fall behind for whatever reason, the results can be devastating. That鈥檚 because math is, as Harvard cognitive psychologist Steven Pinker , 鈥渞uthlessly cumulative.鈥� Each new skill builds on previous learning. There are no shortcuts. If students haven’t mastered , like multiplication, they will struggle with higher-level concepts like exponents. And once students have holes in their understanding, the traditional school structure 鈥� one teacher, 30 same-aged students, one lesson 鈥� makes it nearly impossible to catch up.

This isn鈥檛 a failure of teachers, or instructional materials. It is a failure in the design of the math classroom itself. It’s one reason why in every state, are lower in eighth grade than they are in the fourth 鈥� a trend that does not hold true in . As the content becomes more advanced and the prerequisites more demanding, those holes in the foundation eventually cave in.

To see why the “how” matters less than the “when,” consider an eighth-grade teacher introducing the Pythagorean theorem, the familiar formula for calculating the lengths of the sides of a right triangle.

One camp leans more toward a conceptual approach to teaching math: Students should consider the relationship between squares and right triangles, visualize why the relationship holds true and explore geometric proofs.

The other camp takes a more procedural approach. The teacher walks through the steps for solving a problem using the Pythagorean theorem, students practice, and the goal is that they can consistently find a missing side of a triangle on their own.

Both sides believe their approach is superior. But both sides are ignoring the most important question: Are the students ready for the lesson at all?

The Pythagorean theorem, like other math skills, builds on knowledge acquired over multiple years. Two of the most important prerequisite skills are classifying triangles and using exponents. Using more than a decade of student data from our work with schools across the country, our organization, , has found that if students know those two skills, they have a 72% chance of mastering the Pythagorean theorem. If they don鈥檛, the likelihood is just 32%.

In other words, both sides in the math wars assume students are prepared for grade-level content. In reality, if eighth graders enter the year with unfinished learning that prevents them from accessing that eighth-grade content, the debate is moot.

In , a study my organization published with TNTP, researchers found that students are far more likely to succeed in algebra when grade-level instruction is paired with targeted support that addresses key lessons from prior grades. By implementing that approach, schools can more efficiently use instructional time 鈥� and, ultimately, better prepare students for grade-level content. This requires rethinking how schools organize math instruction in three key ways:

1. Map the progression of skills 

Math is less a checklist of grade-level standards than a web of interconnected skills. Teachers need a clear, shared understanding of how math skills build on one another across grades. Without that map, it鈥檚 impossible to know which unfinished learning actually matters for upcoming content and which gap is less urgent.

2. Use a diagnostic assessment to pinpoint where students are on that map

With that progression in place, diagnostic tools can identify the specific skills students are missing and how they connect to what they鈥檙e about to learn. That is far more useful for teachers than broad labels like 鈥減roficient鈥� or 鈥渂elow grade level.鈥�

3. Deliver intervention that connects unfinished learning to grade-level work

Finally, schools need to make time and use the right instructional tools to help students coherently address their unfinished learning so they can access grade-level content rather than fall further behind. Approaches rooted in either procedural or conceptual understanding may play a role in that process.

The path forward isn鈥檛 choosing a side in the math wars. It鈥檚 recognizing that the real obstacle to progress is an instructional system that ties learning to a calendar instead of what a student is academically ready to learn. 

Until policymakers and systems leaders rethink the “when,” the debate over the “how” is just academic 鈥� and the math wars will never end.

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