The Retention Problem Isn't Really About Retention

One of the most common concerns I hear from teachers is that students don't retain what they've learned. The frustration is understandable. Students seem to grasp a concept during instruction, perform reasonably well on an exit ticket, and then, a week or two later, struggle to recall the very ideas they appeared to understand. By the time a related concept appears later in the year, it can feel as though the learning has disappeared entirely.

The natural response is to ask how we can help students remember more. We add spiral review, retrieval practice, warm-ups, and cumulative assessments, all of which are valuable instructional practices. Yet I wonder if the question itself is incomplete. Rather than asking why students forget, perhaps we should first ask what kind of understanding they developed in the first place.

As I prepare for HIVE this summer, I've been thinking deeply about surface, deep, and transfer learning. Surface learning is an essential beginning. Students need vocabulary, procedures, and foundational knowledge before they can reason about mathematics. The problem isn't that surface learning exists. The problem is that too many students never move beyond it. They learn enough to complete today's assignment but not enough to connect today's learning to tomorrow's.

When learning remains at the surface level, forgetting shouldn't surprise us. Surface learning is often tied to isolated facts, disconnected procedures, or rules that make sense only within a single lesson. Without opportunities to make connections, students have very little to anchor that knowledge to. It simply floats until time causes it to fade.

Research on memory has long shown that forgetting is a natural part of learning. Hermann Ebbinghaus demonstrated that we lose a significant amount of newly learned information unless we intentionally revisit it over time. His work gave us what we now know as the Forgetting Curve, reminding educators that retrieval and spaced practice are essential if we want learning to last.

While I value those practices, I don't believe repetition alone explains lasting learning. Students remember ideas more readily when those ideas become part of a larger network of understanding. Mathematics is not a collection of independent skills. It is a connected system of relationships. The more opportunities students have to discover those relationships, the more durable their understanding becomes.

This is where the idea of mathematical generalizations becomes so important. Generalizations are not rules teachers hand to students. They emerge when students notice patterns across multiple examples, test their thinking, revise their conjectures, and eventually recognize an idea that holds true beyond a single problem. Bush, Karp, and Dougherty describe this process as identifying commonalities across examples, extending reasoning, and deriving broader mathematical ideas from specific cases. Importantly, these understandings develop through students' experiences rather than through memorization alone.

That distinction matters because generalizations transfer while rules often expire.

Consider how often students are taught procedures without understanding the relationships behind them. A rule may help a student solve ten nearly identical problems, but the moment the context changes, uncertainty returns. By contrast, a student who understands the underlying structure is equipped to adapt that knowledge to unfamiliar situations. The difference isn't intelligence. It's the depth of understanding that instruction made possible.

This perspective has changed the way I think about planning. Rather than asking whether students will remember today's lesson next month, I find myself asking a different question: What relationships will students discover today that they can use again tomorrow? That question naturally shifts instruction away from isolated objectives and toward coherent learning experiences where concepts build on one another over time.

It also changes how we think about review. Effective review is not simply revisiting old problems. It is intentionally reconnecting ideas. When students use ratio reasoning to understand percentages, recognize proportional relationships within slope, or represent geometric relationships with algebraic expressions, they aren't just practicing previous content. They are strengthening the threads that hold mathematical understanding together.

Perhaps retention has become the wrong goal. What we really want is transfer. We want students to encounter a new problem and recognize familiar structure. We want them to draw upon previous experiences without prompting. We want understanding that endures because it is connected, not because it was rehearsed one more time.

Students rarely retain ideas they merely memorize. They retain ideas that become part of the way they think.

Listen to Fighting the Forgetting Curve: Building Generalizations That Last