Orientation and awareness will beat speed. In a world where intelligent tools can draft ten plausible answers in seconds, the scarce resource isn’t calculation—it’s judgment: framing the question, naming assumptions, comparing rival models, and deciding with intentional care. In my work—and at MathTrack Institute —we treat mathematics as the creative power it is, and math class as the storytelling studio where young people evolve their senses and practice disciplined attention. In this room, students don’t just “do problems”; they learn to see what’s salient, name what’s at stake, and choose the next wise move under uncertainty.
Large language models (LLMs) are pattern engines. Trained on vast corpora, they learn statistical regularities in language and generate the next likely token, step by step. With guardrails and tools, that prediction game can look like planning, coding, or argument—but fluency is not the same as truth or judgment. Without verification or retrieval, an elegant paragraph can still miss the world, especially at the edges where data is thin and novelty is scarce. Because these systems optimize toward explicit objectives, they take the shape of those aims: tune for speed and you get brisk but brittle; tune for smoothness and you risk confidence without calibration. And the “memory” is curated—what a model appears to know in a moment depends on what we include, omit, and foreground. All of this is why the human component of education is non-negotiable: if orientation and disciplined attention are the scarcest resources, then learners must practice framing questions, naming assumptions, comparing rival models, and deciding with care. We can build that capacity at scale—and treat AI as a powerful voice inside the loop, not a substitute for human judgment.
What does this look like in a classroom or professional setting? Treat AI as a role inside the human sensemaking loop—sense → model → move → update—not a replacement for it. In practice, intelligent tools can act as a rival modeler by proposing competing models under different assumptions; a skeptical reviewer by naming failure modes and the evidence that would falsify a claim; an instrumentalist by producing a quick table or simulation we can check; and a narrator by drafting an initial memo that humans revise for accuracy and ethics. The rules of engagement keep judgment human: make assumptions explicit, require sources or uncertainty statements, verify claims with local data or domain expertise, and reserve final decisions—and accountability—for people. Used this way, AI strengthens the conversation without substituting for the community that gives it purpose. This is learned work: a craft of attention that develops through practice, tuning both our use of AI as a capable voice within the community and our own senses to read our surroundings with increasing sophistication.
To evolve sensemaking, we must evolve the senses—the very human tools that focus our attention. In classrooms and professional settings alike, we treat judgment as embodied and shared. Begin with sight: curate the field of view so that the problem highlights what matters—units, bounds, and representations that foreground structure and can be shared across a team. Keep hearing tuned to separate signal from fluency; don’t accept the first smooth answer from a person or a model—hold rival models against evidence. As literature has reminded us, we should caution what keeps our attention and be disciplined rather than dazzled:
“Believe nothing you hear, and only one half that you see.” — Edgar Allan Poe, The System of Doctor Tarr and Professor Fether (1845)
Use touch to probe assumptions: surface them, move and try, and revise as new data (including failures) arrive. Maintain balance by stating uncertainty—ranges, confidence, and sensitivity—and prefer a next best move over false finality. Track proprioception by staying oriented inside the human sensemaking loop—sense → model → move → update—and be able to explain why you shifted stance when you did. Attend to interoception by checking purpose and ethics: who is affected, what good you seek, what harms you’ll avoid. And respect taste/smell for their role in human orientation; as Proust observed, a reminder that emotions and memory shape what we notice and how we decide:
“The smell and taste of things remain poised a long time… bearing…the immense edifice of memory.” — Marcel Proust, Swann’s Way (1913)
Finally, give the work a voice. Close each cycle of sensemaking and decision with the ability to name and communicate the choice, the evidence, the risks, and the potential next activity. These are mathematical habits of mind and body—intellectual ways of being that keep attention disciplined and judgment human, even as we leverage AI as a capable voice within the community rather than a substitute for it.
In practice, this means re-centering the grammar of responsible modeling across classrooms and workplaces alike. Intellectual ways of being are modeled by near peers, just beyond peers, or master craftsmen and mentors. In class, students need to see human models for making units explicit, setting bounds, naming invariants, checking feasibility, and estimating error—because those moves determine whether a model deserves our trust. In professional work environments, including apprenticeship settings, teams do the same: they must have a culture of intellectual engagement and learning, where activity and work are followed by reflection on evidence of viability as it emerges. Instead of teaching or managing toward a single sanctioned path, we normalize comparative modeling: students (and teams) develop two or three viable models, compare fit and limits, and increase their sensitivity to see which assumptions actually move the needle. Assessment of learning shifts accordingly. Learners can be assessed for what we chose, why, the uncertainties, and the recommendations for viable activity. Judgment (not just answers) becomes visible and improvable. Which is a more convincing argument?
Society will greatly benefit from increasing students’ ability to compute math problems on an assessment, or society will greatly benefit from increasing students’ ability to make sound judgments?
Finally, we embody the intellectual way of being through sensemaking and orientation by modeling, prompt curation, and source auditing, utilizing mathematical judgment rather than relying on “tech tips.” This involves specifying what goes into a prompt and why, tracing claims to data, requiring uncertainty statements, and logging changes to assumptions. In schools, this builds habits of attention. In organizations, it becomes culture: a living apprenticeship where disciplined modeling and transparent decisions are how the work gets done.
In Part 1 I argued that mathematics evolves the senses, and now with this Part 2 I’ve attempted to show explicitly how we can situate AI as a capable voice inside a human loop to enhance and scale out ability to evolve those senses. The argued value is simple: orientation beats speed because judgment is shared work. In Part 3: From New Tools to New Culture, I’ll translate these ideas into team-ready activities and routines. This will aim to provide visibility on how schools and workplaces can integrate them into schedules, meetings, and apprenticeship pathways, making them a standard approach to how work gets done.
Call to Action: If this resonates with you, please pass it on to a colleague. If you are a member, please share your thoughts in the National Council of Teachers of Mathematics - NCTM thread, and let’s trade artifacts so we can refine them together. Help us grow a community where mathematics is practiced as a shared human endeavor, guided by attention, orientation, and judgment.