Why Step-by-Step Instructions Leave Your Students Lost
By Pamela Seda, PhD
I have a confession to make: I am directionally challenged. I rely on GPS for almost everything. So when I visited a school for the third time and still couldn’t find my way there without my app guiding me turn by turn, I wasn’t surprised – but I was annoyed with myself. After three visits, I should know how to get there.
That experience was fresh in my mind when I walked into a middle school math classroom later that same day. The teacher had everything that looks like a great lesson: standards posted on the board, students at computer stations, colorful anchor charts on the walls, an orderly and engaged class.
She was teaching students how to add and subtract decimals, walking them through exactly how to line up the decimal points. The students followed along dutifully and completed their problems correctly. On the surface, it looked like learning was happening.
Then it hit me: she was GPSing her students.
“When we give students step-by-step procedures without sensemaking opportunities, they are often lost – and they don’t even know it.”
It’s a pattern I named in Choosing to See (p. 172), and one I’ve watched play out in classrooms across the country ever since.
What Does It Mean to GPS Your Students?
When you use GPS navigation, it tells you exactly where to turn, step by step. You don’t need to understand the route, know your surroundings, or develop any internal sense of direction. You just follow the instructions. And it works – until the GPS loses signal, leads you astray, or you need to get somewhere on your own.
In the same way, when we give students a procedure to follow – “line up the decimal points, then add as you normally would” – we are acting as their GPS. The steps work in the moment. Students can execute them and get correct answers. But they haven’t developed any mathematical sense of why the procedure works, what it means, or how to apply it in an unfamiliar context.
The result? We have students who can follow steps but can’t think through the math. Students who are dependent on the teacher. Students who, the moment they face a problem that looks slightly different from what was modeled, are completely lost – and often don’t even realize it, because the GPS has always been there to guide them.
Why This Matters – and Who It Hurts Most
Mathematics education researchers have long documented what happens when students learn procedures without conceptual grounding. James Hiebert and Patricia Lefevre established in their foundational work that knowledge without conceptual connections is fragile and difficult to retain or transfer.
In practice, this means students who learned to line up the decimal points by following steps often fall apart when:
- the numbers appear in a word problem or real-world context
- the format is slightly different from what was practiced
- time passes and the memorized steps fade
And here is the deeper issue: this kind of instruction disproportionately affects our most vulnerable students. In too many middle schools, it is Black, Brown, and economically marginalized students who are most often subjected to low-rigor, procedure-heavy math – instruction that keeps them dependent rather than building their capacity to think independently. That is an equity issue, and it demands our attention.
The Landmark They’re Missing
Here’s what I realized about my own GPS dependency: the reason I couldn’t remember how to get to that school after three visits is that GPS never gave me anything to hold onto. No landmarks. No sense of how one road connected to roads I already knew.
Students need mathematical landmarks – conceptual anchors that help them make sense of what they’re doing and why. Take the decimal example. The real reason we line up the decimal point is not about the decimal point at all. It is about a much bigger mathematical idea: you can only combine things that are alike.
When we add decimals, we must align tenths with tenths, hundredths with hundredths, ones with ones – because you cannot meaningfully combine a tenth and a hundredth any more than you can add apples and oranges. The decimal point is just the landmark that helps us find that alignment.
When students understand this big idea, they have a mathematical anchor that travels with them: it applies to adding fractions with like denominators, to combining like terms in algebra, and far beyond. Without it, they have only a rule – and rules without meaning are easily forgotten.
Four Moves to Stop GPSing
Making this shift doesn’t mean abandoning students to figure everything out alone. It means changing the sequence and nature of your support. Here are four concrete moves to try:
►1. Let students make sense of the problem first. Before you teach anything, give students time to think and explore on their own. Ask: “What do you notice? What do you wonder? What would you try?” This positions students as mathematical thinkers, not procedure-followers.
►2. Promote collaborative discourse. Have students share their thinking with partners or the whole class before you share yours. When students articulate their reasoning out loud, they deepen their own understanding and often surface the conceptual connections you want them to have.
►3. Ask questions instead of giving answers. When a student is stuck, resist the urge to show them the next step. Instead, ask: “What do you already know that might help?” or “Does this remind you of anything?” Guiding questions help students find their own path rather than follow yours.
►4. Use student thinking as the foundation. When you do introduce or clarify new content, build from what students already produced. Show them that their thinking led somewhere meaningful. This validates their sense-making and reinforces that math is something they can do – not just receive.
For the decimal lesson, this might look like giving students two differently formatted decimal addition problems and asking them to figure out what goes wrong when you don’t align the places correctly. Or using base-ten blocks so students can see, concretely, why a tenth and a hundredth cannot simply be combined. The procedure can still be taught – but it comes after understanding, not instead of it.
The Deeper Issue: Expectations
At the heart of GPS teaching is a matter of expectations. When we give students step-by-step instructions without room to think, we are – often with the best intentions – sending a subtle message: “I don’t think you can figure this out on your own. Let me just tell you what to do.”
Expecting more means trusting students to grapple with problems before we provide answers. It means believing that confusion is part of the process, not a sign that we need to rescue students with a procedure. It means designing learning experiences that require and develop genuine thinking – especially for the students who have most often been handed the GPS instead of the map.
“The goal is students who can navigate mathematics on their own – not students who are lost the moment the GPS is turned off.”
A Question to Ask Yourself
Before your next lesson, pause and ask: Am I about to GPS my students? If you’re planning to open by showing students a procedure, consider flipping the sequence. Give students the problem first. Let them try. Let them talk. Let them be temporarily lost – because being productively lost, with support, is how we develop a real sense of direction.
The goal isn’t to never give guidance. It’s to make sure the guidance we give builds mathematical understanding rather than replacing it. We want students who, after leaving our class, can find their way – not students who are dependent on a voice telling them where to turn.
Reflection Questions
- In my recent lessons, have I been giving students the procedure before they’ve had a chance to think?
- What conceptual “landmarks” do my students have for the topics I’m teaching right now?
- When students are stuck, is my first instinct to show them the next step, or to ask a question?
- How might I restructure an upcoming lesson so that student thinking comes first?
Works Cited
Hiebert, James, and Patricia Lefevre (1986). “Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis.” In Conceptual and Procedural Knowledge: The Case of Mathematics, pp. 1-27. Lawrence Erlbaum Associates, Inc.
Seda, Pamela, and Brown, Kyndall (2021). Choosing to See: A Framework for Equity in the Math Classroom. Dave Burgess Consulting.
Dr. Pamela Seda is an educational consultant, author, and founder of Atlanta-based Seda Educational Consulting, LLC. She has held various positions in mathematics education including high school mathematics teacher, math instructional coach, college math instructor, and K-12 district math supervisor.
Pamela is the creator of the ICUCARE® instructional framework and co-author of Choosing to See: A Framework for Equity in the Math Classroom. She works with schools and districts to help teachers and leaders create math classrooms where all students are expected to think, reason, and contribute. Learn more at sedaeducationalconsulting.com.
