How we teachSee how it really works
We teach the way curious minds learn.
Every Layerfall journey follows one loop: How? How does that work? How does that part work? What if? Where else? Each step rests on learning research, and every fact on this page names its study.
Why we start with questions
Curiosity is how people learn. School rarely feeds it.
Small children ask constantly. In class, the questions almost stop, and the pleasure of learning fades with them.
In class, a student asks about one question every six to nine hours. With a one-to-one tutor, about 26 an hour.
Graesser & Person, 1994In observed fifth-grade classrooms, curiosity showed itself less than once in two hours.
Engel, 2011In Gallup's 2016 poll of students whose schools opted in (not a representative sample), 74% of fifth graders were engaged at school, against about a third of students in grades 10 to 12.
Calderon & Yu, Gallup, 2017The pleasure of learning for its own sake fell from age 9 to 17, most of all in maths.
Gottfried, Fleming & Gottfried, 2001
Children as young as two can tell a real answer from a brush-off. After a non-answer they were more likely to ask again; after a real explanation, more likely to ask a follow-up.
Frazier, Gelman & Wellman, 2009Curiosity and effort together mattered as much as intelligence for how well students did.
von Stumm, Hell & Chamorro-Premuzic, 2011Curiosity in kindergarten is linked to better reading and maths, and the link is two to three times stronger for children from low-income families.
Shah et al., 2018
Step 1 · How?
Start with a mystery, not a topic.
A topic tells you what you are about to learn. A mystery makes you need to know.
Curiosity is the feeling of a gap in what you know, and it needs a little knowledge to start.
Loewenstein, 1994Curiosity peaks when you half-know the answer: not when you know nothing, and not when you are sure.
Kang et al., 2009People remembered 71% of answers they were curious about, against 54% of the rest. A day later: 46% against 28%.
Gruber, Gelman & Ranganath, 2014A question before the lesson helps you learn what it asks about, and barely anything else. So every opening question aims at the principle underneath.
St. Hilaire, Chan & Ahn, 2024
Every journey opens with a How question about something you already know from the outside, phrased so the answer is not obvious, and aimed straight at the principle underneath.
You know less than you think. Everyone does.
1How well do you understand how a zipper works?
2Now explain it, step by step, out loud. What does the slider do to the teeth? What locks them together?
Tried it? See how people did
In a Yale study, people first rated their understanding of devices like this 3.9 out of 7 on average. After trying to explain one, 2.5. Explaining shows you the gap, and the gap is where curiosity starts.
How a zipper works: the slider's Y-shaped channel squeezes the two rows of teeth together at an angle, so the bump on each tooth slips into the hollow of the tooth opposite and locks. Pulled the other way, the wedge inside the slider pries them apart.
People rated how well they understand everyday devices such as a zipper. After trying to explain one step by step, their rating fell from 3.9 to 2.5 out of 7.
Rozenblit & Keil, 2002Asked to draw a bicycle's pedals, chain and frame, 44% of adults made a serious mistake, most often a chain looped round both wheels.
Lawson, 2006
Careful: seeing a mechanism is not the same as understanding it. That is why the loop asks you to predict and to compare, not only to watch.
Step 2 · How does that work?
One layer at a time.
Complex things are built in layers, so they are easiest to understand in layers: one idea, one picture, then the question that opens the next.
- Outside sound
- Microphone
- Digital signal
- Processor
- Opposite waveform
- Speaker
- Interference
- Quieter sound
Complex systems are built in layers. In Herbert Simon's parable, a watchmaker who builds from stable parts finishes about 4,000 times faster than one who must start over after every interruption.
Simon, 1962A mind holds about four new things at once. More than that, and something falls out.
Cowan, 2001Words with pictures teach far better than words alone, especially when the words arrive with the picture they describe.
Mayer, 2021Animation helps a little overall, and most when it shows the change you are trying to understand.
Höffler & Leutner, 2007After seeing 10,000 pictures for five seconds each, people still recognized most of them.
Standing, 1973
Each layer teaches one idea, starts from the step before, explains a hard word before using it, and ends with the question that opens the next: How does THAT part work? Every layer is a picture first, and it moves when something in it changes.
Step 3 · How does that part work?
You choose the depth.
What helps a beginner can hold back an expert. So every layer is true at three depths, and you pick the one you need.
How do noise-cancelling headphones work?
Your headphones play a second sound: the noise, turned upside down. The two cancel.
Microphones on each ear cup pick up the noise. A chip works out the opposite wave, and the speaker plays it in time to meet the noise at your ear. It works best on steady, low sounds, like an engine's hum.
The anti-noise is the noise shifted by half a cycle (180°). Where the two pressure waves overlap they add, by superposition, and largely cancel. Cancelling is strongest at low frequencies, where a wave is long compared with the delay through the microphone, chip and speaker.
What helps a beginner can hold back an expert. The right depth depends on what you already know.
Kalyuga et al., 2003“Any subject can be taught effectively in some intellectually honest form to any child at any stage of development.”
Bruner, 1960Students who knew baseball understood and remembered a baseball story better, whatever their reading level.
Recht & Leslie, 1988
Surface gives the big idea in plain words. Deeper shows what is happening inside, every sentence resting on a checked fact. Technical gives the real physics, maths and engineering, with the sources.
Step 4 · What if?
Guess first. Then look.
Watching a demonstration teaches surprisingly little. Committing to a guess first creates the surprise that makes the answer stick.
What if?
What if the anti-noise for a steady hum arrives half a wave late?
Made your guess? Show me
Louder. Half a wave late, the flipped wave lines up crest with crest, so the two add up instead of cancelling. That is why the chip has to be fast.
Students who only watched a physics demonstration explained it no better than students who never saw it (24% against 22%). Students who predicted the outcome first reached 30%.
Crouch et al., 2004A prediction sets up the surprise, and the stronger the surprise at a wrong guess, the more people learned. Even eleven-month-old babies learn most from what surprises them.
Brod, Hasselhorn & Bunge, 2018Stahl & Feigenson, 2015Naming a common mistake and then showing why it is wrong teaches better than a plain explanation.
Schroeder & Kucera, 2022
What-if questions ask for your guess before the answer, answer only from checked facts, and name the common wrong answer. A quick prediction, never a long struggle on your own.
Step 5 · Where else?
Learn it once. Spot it everywhere.
People rarely notice that two systems share a principle, until someone asks them to compare.
Only 20% of people used a story they had just read to solve a new problem with the same answer. Given a hint to use the story, 92% solved it.
Gick & Holyoak, 1980Comparing two cases side by side more than doubled how often people used the idea they shared: 48% against 19%.
Gentner, Loewenstein & Thompson, 2003Experts sort problems by the principle underneath. Beginners sort them by what they look like.
Chi, Feltovich & Glaser, 1981
Every journey ends by showing the same principle in an unrelated system, and asks you to compare the two. Interference in your headphones turns up again in Wi-Fi, in radio telescopes and in light.
And again
Meet it again. Keep it for good.
An idea you meet once fades. An idea that keeps coming back, mixed in with others, stays.
Meeting an idea again later beats meeting it many times at once: 47% against 37% remembered, across 271 comparisons.
Cepeda et al., 2006A week later, students who had practised recalling a text remembered 61% of it. Students who reread it: 40%.
Roediger & Karpicke, 2006In 54 maths classes, practice that mixed different kinds of problems beat practice in blocks on a delayed test: 61% against 38%.
Rohrer et al., 2020
Concepts come back across questions, mixed with others and spaced out over time, and challenges ask you to recall, not to reread.
Guided, never alone
Curiosity picks the route. We guide every step.
- A spark
- Held attention
- Your own interest
- A passion
Discovery with no help teaches less than being shown. Discovery with guidance teaches more.
Alfieri et al., 2011Having a real choice raises motivation and effort.
Patall, Cooper & Robinson, 2008Interest grows in phases: a spark, then held attention, then an interest of your own, then a passion.
Hidi & Renninger, 2006
You choose the question, the branch and the depth; inside it, every step is explained. A film sparks the interest, a journey holds it, and paths turn it into a subject of your own.
Truth is the product
Simple. Never false.
Simplifying never means making things up. Every explanation keeps three things apart.
What really happens
The physical or software mechanism that actually occurs, from checked sources.
A useful simplification
Said plainly and labelled as one. An analogy says where it stops being true.
A picture of the invisible
Drawn to make an unseen process understandable, and never mistaken for the thing itself.
Everyone arrives with ideas about how the world works, and good teaching starts from them.
National Research Council, 2000
Every fact, checked
Don't trust us. Check it.
Every number on this page comes from one of these studies.
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doi.org/10.17763/haer.81.4.h054131316473115Calderon, V. J., & Yu, D. (2017). Student enthusiasm falls as high school graduation nears. Gallup.
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