Does a Good Teacher Pass On Answers or a Way of Seeing Problems?

How a Person Builds a World · Season Two: “Others, Dialogue, and Shared Knowledge” · Article Four

A student has just followed a problem demonstrated by the teacher. He remembers the formula and can reproduce the steps on the board to obtain the right answer. The next problem changes only the wording and one condition. Now he does not know where to begin.

In the first problem, he acquired an answer. In front of the second, he discovers that he may not yet have acquired the problem.

“A good teacher does not give answers but teaches students how to think” is an attractive saying. It points broadly in the right direction while creating a false choice. Without sufficient facts, concepts, examples and accurate feedback, students cannot generate methods from nothing. If a teacher supplies only answers and procedures, however, students may mistake knowledge for a path that works only on the original question.

What a good teacher passes on is neither an isolated answer nor a content-free set of universal thinking skills. It is the structure by which, within a domain, answers are constrained by questions, evidence, concepts and methods of testing.

Answers, procedures and ways of seeing are different kinds of learning

When a teacher solves a problem, a student can learn at least three layers.

The first is the result: the answer to this problem, the year an event occurred, the definition of a term. Results provide necessary coordinates for shared inquiry. A person who lacks basic factual knowledge will not enter a complex domain through “critical thinking” alone.

The second is the procedure: how to formulate the equation, compare historical sources, identify a premise or test a program. Procedures allow a learner to handle similar tasks, but can also be applied mechanically.

The third is a way of seeing: what to notice first in a new problem, which surface differences are irrelevant, what evidence could change the conclusion and when the current method no longer applies. This layer is hardest to state directly and closest to the understanding that transfers.

Experts have often automated many judgements. When they see a problem, the decisive condition appears “naturally” salient. When they read a historical source, they rapidly register the position of the author and the date of composition. None of this is natural to a novice. If a teacher shows only the final clean solution, the choices, eliminations and checks that produced it remain concealed.

One central idea in cognitive apprenticeship is to make these otherwise invisible cognitive processes visible. A teacher not only demonstrates a performance, but explains why they pause here, reject another path, test an assumption and gradually withdraw support. Teaching moves from displaying a finished product to displaying how judgement works.

Why a learner's mistaken structure needs to appear

A clear direct explanation is often effective. Sometimes it is too effective in a particular way. While following the explanation, the learner experiences each step as sensible and mistakes “I can recognise this path” for “I could independently find this path”.

Research on self-explanation illustrates why understanding needs to be generated. Michelene Chi and colleagues examined how students learned from worked examples in physics. Stronger learners produced more explanations, connected operations to principles and monitored gaps in their understanding more accurately. They acquired knowledge that depended less on the original examples. The classic study of self-explanation in learning from worked examples should not be reduced to “talking more makes learning better”. It shows the importance of actively constructing relations between steps and principles.

Research on productive failure explores a different instructional sequence. Learners first meet a new problem and generate incomplete or mistaken solutions; the teacher then organises comparison and formal instruction. In particular mathematics and science tasks, this problem-solving-before-instruction design has improved conceptual understanding and transfer. Manu Kapur's account of learning from productive failure makes clear that the approach does not consist of abandoning students to struggle. Exploration must be followed by consolidation and knowledge assembly. Analyses of when productive failure fails also show that fidelity of design and appropriateness of task matter.

The important point is not to romanticise failure. It is to let the learner's own representation of the problem become visible. A wrong answer can show the teacher which variable was ignored, which concepts were conflated, or whether a procedure was memorised without its conditions of application. Instruction then works on an existing but revisable structure rather than delivering content to an imaginary empty mind.

A good teacher transmits the correctability of judgement

“Method” is often misunderstood as a stable sequence of steps. In real knowledge, an important capacity is knowing when the established method should no longer be used.

Historical sources require provenance, but cannot simply be ranked as “objective” or “subjective”. Statistical models need evaluation, but high predictive accuracy cannot by itself settle whether a policy is fair. A literary text permits close reading, which is not a reason to ignore historical context. Domain knowledge cannot be replaced by one generic technique because different objects admit different forms of evidence, explanation and counterexample.

A good teacher gradually passes on several kinds of judgement: how to distinguish understanding from familiarity; how to look for evidence capable of separating two plausible explanations; how to say “I don't know” without ceasing to inquire; and how to preserve an intelligible path of revision when a conclusion changes.

This is more specific than the slogan of “independent thinking”. Independence does not require rejecting the teacher. It means that, after initially borrowing the teacher's selections and demonstrations, a student can continue to ask comparable questions in a new setting and can respond to counterevidence without requiring the teacher's authority as permission to change.

Teaching therefore communicates a relationship to correction, not only correctness. Watching a teacher handle a verbal mistake, obsolete source or genuinely difficult question teaches students whether epistemic authority permits revision. A teacher who performs certainty at all times may deliver many correct answers while teaching that ignorance is shameful and changing one's mind is failure.

AI can answer a question without knowing when it should not answer immediately

Generative AI has made answers available with almost no delay. Students can request an explanation of a formula, a chapter summary, an essay structure or even a sequence of Socratic questions. This availability creates real possibilities for individual practice and immediate feedback. It also makes the sequence of instruction more consequential.

If a student receives a complete solution before forming a representation of the problem, AI performs the very thinking that most needed to become visible. The assignment may be completed faster, while the teacher loses diagnostic evidence contained in the error and the learner loses an opportunity to compare a personal attempt with a better one.

The opposite rule—that AI must never provide the answer—is equally weak. Novices need accurate examples. Struggle without timely consolidation can preserve confusion. A better tutoring interaction changes roles with the stage of learning. It first asks the learner to state an existing understanding or attempt; offers limited hints; makes alternative solutions comparable; provides explicit explanation at the right time; and finally tests transfer with a changed problem.

This cannot be solved entirely by a clever prompt. An AI usually lacks a student's long learning history and may provide plausible but mistaken feedback. A teacher must still determine curricular purpose, choose a task that produces useful difficulty, diagnose misconceptions and decide when exploration should give way to explanation. AI can expand the available teaching moves. It does not automatically possess pedagogical judgement.

An answer should become evidence for a method

A good teacher certainly passes on answers. Education that refuses explicit answers forces every student to rediscover knowledge that could have been shared. The decisive issue is not whether an answer is given, but how it enters learning.

An answer presented only for memorisation closes a question. An answer situated among reasons, boundaries and comparisons can become evidence from which the learner later recognises a new problem. The teacher is not preserving mystery. The teacher makes visible why this conclusion holds here, how it differs from adjacent errors, and which altered condition would require another judgement.

A good teacher therefore passes on neither answer nor method alone. More accurately, the teacher places an answer within a reconstructable path of judgement so that the student can eventually carry the path away.

The deepest result of education is not a student who copies the teacher's world. A teacher lends the student ways of attending, conceptual distinctions and habits of checking. The learner alters these through new material, failure and life beyond the classroom, gradually forming an understanding for which they can take responsibility. Many of the original answers may then be forgotten. What remains is an ability to begin in front of an unfamiliar problem—and to recognise when it is necessary to stop and ask the question again.

Primary sources and further reading

• How People Learn: Brain, Mind, Experience, and School — National Academies
• Self-Explanations: How Students Study and Use Examples in Learning to Solve Problems
• Learning from Productive Failure
• When Productive Failure Fails

Continue reading: Explore the How a Person Builds a World series.