Published: March 6, 2026
Question → Answer.
Question → Answer.
Question → Answer.
“My students don’t know how to problem solve. They don’t have any stamina when it comes to solving a complex problem. They can’t think their way out of a cardboard box!”
Okay. Let’s address the deficit mindset talk in another blog post…
In many math classrooms, the pattern is predictable: Question → Answer. We (and by we, I mean teachers) pose questions to students, students know they’re supposed to respond, and we anxiously hope their response lands on the exact response we had in mind.
In other words, most of the questions we ask are close-ended; we’re usually looking for the “correct answer.” Students internalize this, and years of this repetitive question → answer cycle don’t teach students how to think. Ergo, “my students are so focused on answer-getting” or “my students struggle with complex tasks that require critical thinking.”
Therein lies the problem: we’re asking the wrong questions.
Wasn’t it Einstein who said, “doing the same thing over and over again and expecting different results is the definition of insanity.” Well, if we want to change this answer-getting, complacent, sometimes lackadaisical behavior from students, we need to do something different: change the prompt. We need to ask better questions and support students developing critical thinking skills that allow them to be problem solvers who can productively struggle through a task.
Lately, I’ve been thinking about what this looks like in practice. Why is the questioning cycle “closed” and why is that our default?
In my own practice, I am a huge fan of Slow Reveal Graphs, Esti-Mysteries, and Three Act Tasks. In analyzing the patterns of those tasks, the script I keep coming back to sounds like this:
- What do you notice? What do you wonder?
- What do we know?
- What can we do with that information?
- What questions do you have? or What else do you want to know about?
- Now here’s a little more information: What did we gain insight about? How does that change your thinking?
- Here’s a little more: Adjust your thinking…
The value in a script like this one is how it mirrors thinking beyond the classroom walls. We constantly make decisions with incomplete information, act on what we know, and then revise as new information comes in. The ability to adjust thinking is fundamentally a life skill, not just a mathematical one. If we want students to be creative problem solvers - mathematically, socially, and emotionally - we have to give them repeated opportunities to refine their thinking, not just defend their first answer.
I don’t think a full overhaul of instruction is necessary. What I’m advocating for is a shift in what we normalize. Instead of rushing to complete, we create space for thinking to evolve. Too often, we offer complete problems and expect complete answers; the messier experience of revising with partial information and thinking gets pushed out.
Why this Matters for “Mathematical Proficiency”
In Adding It Up, Kilpatrick et al. (2001) describe adaptive reasoning as the strand of proficiency that lets students justify, connect, and revise their thinking (a.k.a the “glue that holds everything together”). The authors also note that students are typically strongest in procedural fluency and weakest in areas like conceptual understanding, adaptive reasoning, and productive disposition. That maps closely onto what many teachers see: students who can “do” procedures but struggle to adjust when a problem deviates from a familiar template.
Similarly, Frabasilio’s (2022) study explored how seventh graders used adaptive reasoning during inquiry-based tasks. Of the six adaptive reasoning indicators, the richest forms (i.e., pursuing alternative solutions or questioning legitimacy) were highly dependent on peer talk and task design. This work highlighted that when tasks unfolded in stages and invited reasoning with partial information, students’ adaptive thinking was cultivated and more visible.
A 2025 systematic literature review of adaptive reasoning found that approaches like Problem-Based Learning, STEM integration, and Creative Problem Solving consistently supported students’ adaptive reasoning, especially in middle grades (Nurlita et al., 2025). Research also highlights routine practice with non-routine problems as a critical component to the development of adaptive reasoning (Nurlita et. al., 2025). These approaches tend to launch learning with questions and contexts, allowing strategies to develop over time rather than front-loading procedures.
In short, when we design for staged information and non-routine problems, we’re actively building the very adaptive reasoning we say we want from students.
Where Students Start to Lose It
In elementary classrooms, we often see students noticing, wondering, and trying out ideas. Somewhere between those early grades and upper middle school, curiosity wanes, and “math” becomes synonymous with “getting the right answer quickly.” Coverage pressures and high-stakes assessments amplify that pull. Over time, product crowds out process. Sense-making feels like a luxury.
The National Research Council (2001) warns that when students are seldom given challenging problems that require reasoning, they learn that memorizing procedures is how you get through math, and students’ confidence as learners suffers. For students who no longer see themselves as “math people,” taking risks with their thinking is costly. But those risks - holding a tentative conclusion, testing it against new information, and adjusting - are the heart of adaptive reasoning. “Adjust your thinking” needs to become the standard prompt, not the exception.
What It Looks Like with Routines
This is why I am drawn to routines like Slow Reveal Graphs (SRG) and Esti-Mysteries (EM).
In a SRG, students only see part of some graph at first. They notice and wonder, information (e.g., axis label, title, shape, data point, etc.) is revealed one piece at a time, and students are prompted to consider how that information changes their thinking. Each new layer is an invitation to refine. Often by the time we have the full graph, students have constructed meaning collaboratively and expanded their thinking beyond anything a close-ended question could prompt.
In an EM, students start with a visual and make an initial estimate. Clues are used to prompt students to modify their estimates, narrowing the possibilities each round. The expectation is that thinking will change as information changes, and the “win” is not guessing perfectly on the first try, but using each clue to make a more reasonable decision.
Three Things These Routines are Quietly Building
In both routines, “getting the right answer” is diminished by the presumption that my current brain’s thinking is driven by the limited information I have, AND that thinking WILL change as I learn more about the situation. When used regularly, these short routines help students:
- Adjust cognitive effort to the task as it unfolds, instead of grabbing a single fixed procedure.
Cognitive Load Theory reminds us that working memory has limits and that dense, fully-loaded problems can overwhelm students. Answer-getting becomes a coping mechanism, not laziness.
The slow reveal structures counter this by offering information in manageable chunks. Each new piece of information is an invitation to ask, “Does my current idea still make sense?” - Build reasoning stamina.
These routines build productive disposition, not by assigning longer and longer problem sets, rather by offering repeated, short cycles of: make a claim, receive new information, adjust thinking. For students who tend to opt out as soon as a task feels hard, the shorter format lowers the cost of engagement while still asking for real thinking. Over time, the routine extends the length of time students are willing and able to stay in the work. - Develop awareness of their own thinking.
Metacognition shows up when students plan, monitor, and evaluate their thinking. The Education Endowment Foundation’s (2024) work on metacognition and self-regulated learning highlights that explicitly teaching these strategies yields large gains in learning, especially for historically disadvantaged groups of students.
The key descriptor here is explicitly. Students don’t automatically become metacognitive just by doing lots of tasks. They need these processes modeled, named, and practiced in context. Language like: “What did you learn from that clue?” “How did it change your thinking?” and “Now adjust your thinking.” becomes powerful. It’s not just a routine; we are fostering lived experiences that teach students to monitor and regulate their own cognition.
A Different Script to Try Tomorrow
If we frame math class as a place where students are supposed to lock in quickly and never revise, we’re teaching a way of thinking that doesn’t match how the world actually works. Normalizing “adjust your thinking” gives students practice with cognitive flexibility, intellectual humility, and the courage to stay engaged in situations that are uncertain.
We don’t need a brand new curriculum. We can start with the questions we ask, the language we use, and the opportunities we create for students to revisit their ideas. When we shift the script from “get the answer” to “work with what you know and be ready to revise,” we change what counts as success. We tell students: your job here is not to be instantly correct; your job is to think, to adjust, and to keep going.
That might be one of the most important invitations we extend to students in math class.
References
Education Endowment Foundation. (2024). Metacognition and self-regulated learning: Guidance report (2nd ed.). Education Endowment Foundation.
Frabasilio, A. M. (2022). Relationships between middle school students’ adaptive reasoning when creating learner-generated drawings and partner talk during inquiry-based mathematical tasks (Publication No. 8506) [Doctoral dissertation, Utah State University]. DigitalCommons@USU.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. National Academy Press.
Nurlita, M., Juandi, D., & Priatna, B. A. (2025). The essence of students' adaptive reasoning ability in mathematics learning: A systematic literature review. The Eurasia Proceedings of Educational and Social Sciences, 47, 95–108.
What Now?
- Download a routine: Slow Reveal Graphs and start embedding them into your instruction
- Read this article next: Shifting the Data Conversation: From Deficits to Assets
- Try this routine as well: Esti-Mysteries
- Bring All Learners Network (ALN) to your school or district for embedded professional development.
All Learners Network is committed to supporting pedagogy so that all students can access quality math instruction. We do this through our online platform, free resources, events, and embedded professional development. Learn more about how we work with schools and districts here.
