GPS teaching – Procedure-heavy math can teach students how to follow steps—without building understanding. Misryoum explores how to shift from “GPS” to “map” learning, and why it matters most for vulnerable students.
A middle school math lesson can look perfectly on track—until you realize students aren’t building a way of thinking, only a way of doing.
That’s the concern Misryoum highlights in a powerful argument about “GPS teaching”: instruction that gives students step-by-step directions so they can arrive at correct answers in the moment, but leaves them without the conceptual landmarks needed to navigate math independently later.
In the classroom, the pattern often appears subtle.. A teacher posts standards. runs an organized routine. and guides students through a specific process—say. aligning decimal places before adding.. Students follow along. compute accurately. and the lesson “lands.” But beneath the surface. the learning may be fragile: students can execute the procedure while struggling to explain what the procedure means or why it works.
The GPS analogy matters because it describes a dependency problem, not just a teaching style.. Real GPS navigation can get you to your destination when conditions stay familiar.. Yet it fails when the signal drops, the route changes, or you must find your own way without directions.. When classrooms provide math as a set of instructions to follow. students can become similarly reliant—confident in rehearsed tasks. lost when problems appear in unfamiliar formats. worded differently. or presented in new contexts.
Why this is more than a classroom skill gap is where Misryoum’s focus turns toward education equity.. Procedure-heavy learning without conceptual grounding has been shown to limit retention and transfer—students may remember the steps for a short time but struggle when the math shifts.. And the burden frequently isn’t shared evenly.. In many systems. the students who face the most limited access to high-rigor instruction are often Black. Brown. and economically marginalized learners.. When GPS-like teaching becomes the default for them. it can reinforce a harmful message: that they are supposed to follow. not figure out.
Misryoum also points to what students are missing when procedures replace understanding: “mathematical landmarks.” In the decimal example. the landmark isn’t the decimal point itself—it’s the underlying idea that you can only combine quantities that are alike.. Tenths align with tenths and hundredths with hundredths because those place values represent comparable units.. Once students grasp that larger reason. the decimal procedure stops being a memorized trick and becomes a portable mental model—one that can apply later to fractions with like denominators. like terms in algebra. and other forms of combining structures.
This is the heart of the editorial question Misryoum leaves readers with: what are we training students to do—navigate thinking. or react to instructions?. When students learn only the route, they can be successful right up until conditions change.. When they learn the map, they develop the flexibility to interpret new problems and decide how to proceed.. The difference can determine whether school becomes a place where students grow as independent problem-solvers or a place where they steadily lose confidence.
Misryoum offers a practical shift in instructional sequence, not a call to remove support. The alternative is to change the timing and purpose of guidance:
First, start with sensemaking. Before demonstrating a procedure, allow students to explore. Give them time to notice patterns, test ideas, and ask questions. When teachers position students as thinkers first, they’re less likely to reduce the lesson to a set of steps they must copy.
Second, elevate student talk.. Collaborative discourse—partners, small groups, whole-class sharing—turns private thinking into shared reasoning.. As students articulate their ideas. they not only clarify their own understanding; they also give teachers insight into what conceptual connections are taking shape and where misunderstandings are developing.
Third, lean on questions instead of next steps.. When students get stuck. the most helpful move may be to ask what they already know. what a problem reminds them of. or what patterns they observe.. Misryoum stresses that guidance doesn’t have to mean telling—questions can guide students toward their own reasoning.
Fourth, treat student thinking as the foundation for instruction. When teachers introduce new content, they can build from what students already produced—validating effort, correcting misconceptions through reasoning, and demonstrating that math is something students can do, not just receive.
Done well, these shifts can preserve the procedural accuracy students need while ensuring it rests on understanding.. For instance. a teacher might present two differently formatted decimal addition problems and ask students to predict what will go wrong if alignment isn’t handled correctly.. Or they might use base-ten representations so students can “see” why certain quantities can’t simply be combined.. The procedure still matters—but it becomes the result of sensemaking, not a replacement for it.
Misryoum’s closing concern is about expectations.. GPS teaching can unintentionally communicate that students can’t figure things out without an external voice.. High-quality instruction, by contrast, treats confusion as part of learning, not a trigger to rescue students from thought.. The goal Misryoum frames is clear: students who can navigate mathematics on their own—students who are not only accurate during instruction. but capable when the problem is no longer identical to what they practiced.
Before the next lesson begins. Misryoum suggests a simple self-audit: are you planning to open with a procedure because you believe students need it first. or because students are being denied the chance to wrestle with meaning?. If the lesson starts with students trying—talking. comparing. reasoning—then guidance becomes a bridge to understanding rather than a substitute for it.
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