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Every student knows two unhelpful kinds of help. One is the friend who takes your pen and solves the problem; you nod along and can't do the next one. The other is "just try harder" when you have no idea where to start. Somewhere in between is help that leaves you able to do it alone next time. The psychologist Lev Vygotsky gave that middle ground a name.
What is the zone of proximal development?
In Mind in Society (Harvard University Press, 1978), Vygotsky defined the zone of proximal development as "the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers," as quoted in New Learning's summary.
Put simply, any task falls into one of three zones for you:
What you can do alone. Practising only here feels good and teaches little.
What you can do with help. This is the zone of proximal development.
What you can't do yet, even with help. Help here gets copied, not learned.
Vygotsky wrote that learning "awakens a variety of internal developmental processes that are able to operate only when the child is interacting with people in his environment," and that once these processes are internalized, "they become part of the child's independent developmental achievement." Today's assisted problem becomes tomorrow's solo problem.
Where does the word "scaffolding" come from?
Not from Vygotsky. It comes from a 1976 paper by Wood, Bruner and Ross, "The role of tutoring in problem solving", in the Journal of Child Psychology and Psychiatry. A tutor helped three-, four- and five-year-olds build a pyramid from wooden blocks, as described in an open textbook on children's problem solving.
The authors described six things the tutor did, as summarised by the psychologist Barbara Rogoff:
Recruiting the learner's interest in the task.
Reducing the number of steps by simplifying the task, so the learner can manage parts of it.
Keeping the learner pursuing the goal.
Marking critical features: the differences between what the learner produced and a correct solution.
Controlling frustration and risk.
Demonstrating an idealised version of the act.
Put together with Vygotsky's idea, scaffolding is help fitted to what you can't yet do alone, and withdrawn as you become able to.
Does one-to-one help actually work?
Tutoring is the most direct way to keep a learner in this zone, and the evidence is encouraging, though more modest than legend. Kurt VanLehn's 2011 review in Educational Psychologist found an effect size of 0.79 for human tutoring compared with no tutoring, and 0.76 for intelligent tutoring systems, "nearly as effective as human tutoring." That is well below the "two sigma" figure often quoted, which we examine in our post on Bloom's 2 sigma problem.
A hint ladder for problem practice
You can scaffold yourself, or ask a friend, parent or teacher to do it with you. When you are stuck on a physics problem, climb one rung at a time and stop as soon as you can carry on:
Restate the goal. What exactly is asked? Which quantity is unknown?
Point to the critical feature. Is there friction? Is the frame accelerating? Is charge conserved?
Shrink the task. Draw only the free-body diagram for one block, or write only the conservation equation.
Give a partial step. Write the first equation, then hand the pen back.
Demonstrate. Show a full solution to a similar, not identical, problem.
Re-test without help. Within a day, attempt a fresh problem of the same type alone.
Parents can use rungs 1 and 3 without knowing any physics: they are questions anyone can ask. Our guide on when to help with homework has more.
Where Fermi fits
The hard part of scaffolding is judging, moment to moment, how much help to give. Fermi's AI tutor is designed around that judgement: it notices where you are stuck and decides whether to explain, ask or show, rather than handing over the answer. Once you've made your attempt, the Fermi Problem Library has a step-by-step solver that explains the reasoning.
Next time you're stuck, ask for the smallest hint that lets you keep going.
