Joined August 2010
Attention
📘 My new Teaching for Attention Playbook is a 70+ page, evidence-informed guide that breaks down the science of attention and provides 6 practical strategies to support teachers. It covers how to: 🎯 Secure Attention: Create the conditions for students to focus 🎯 Direct Attention: Guide students towards important information 🎯 Orchestrate Attention: Manage where attention goes as learning unfolds 👉 Want a free copy? REPOST and comment ATTENTION below, and I’ll DM you the link. ⏰ Available free until Wednesday 30 September at 11:59pm AWST
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Christine Lenghaus retweeted
Euler's formula is not a formula. An MIT professor spent a whole lecture proving it is a definition, not a discovery. This is 18.03, Lecture 6, Arthur Mattuck. Free on MIT OpenCourseWare. The formula is e^(iθ) = cos θ + i sin θ. Most people memorize it and move on. Mattuck refused to. He asked one thing. What gives that the right to be called an exponential at all? An exponential has to obey one law: e^a · e^b = e^(a+b). So he checked it. He multiplied e^(iθ₁) by e^(iθ₂), expanded the sines and cosines, and looked at what fell out. The angle-addition identities. cos(A+B) and sin(A+B), the two formulas you were forced to memorize in school. They were never two formulas. They are one line: e^(iθ) obeying the law of exponents. Then the payoff. An integral that normally needs integration by parts twice and a trick, ∫ e^(-x) cos x dx, drops out in a few lines once you let the numbers go complex. Nothing is easier to integrate than an exponential. Someone once asked him what beauty in math looks like. He pointed at the board. Something long became something short, and lost nothing.
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Christine Lenghaus retweeted
After reading this from @dylanwiliam every time I was writing feedback on student work I did a mental check: "Am I telling them to be more systematic?" Or anything to which they'd respond: "If I knew how to do that I'd have done it in the first place". Really useful check.
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Christine Lenghaus retweeted
You know how the movie version of a book is never as good as the book? Now do the digital version of a lesson. I have the receipts. fawnnguyen.substack.com/p/on…
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Christine Lenghaus retweeted
Paper wrapped around a cylinder and then cut at an angle produces an ellipse as the cross-section shape and a sine curve as the paper is unrolled. What if paper was wrapped around a square rod instead? What cross section shape and paper edge pattern would you see?
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Christine Lenghaus retweeted
Max Roser speaks the truth: “The poorest economies in the world are not achieving economic growth. The consequence is that progress against the very worst poverty is coming to a halt. This is one of the worst problems in the world today, but hardly gets any attention.”
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Christine Lenghaus retweeted
I was listening to the @SuzeOrmanShow and was thrilled to hear Suze and KT discuss my book: Limitless Mind (tinyurl.com/LimitlessMindJB), recommended by a teacher who called in. She said she plans to buy it and read it - I look forward to future conversations!
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Christine Lenghaus retweeted
Would anyone like an uplifting summer read? Math-ish is currently only $1.99, instead of $29.99 on Kindle (amazon) / tinyurl.com/MathishKindle
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Christine Lenghaus retweeted
I'm a big fan of numberless word problems because they force students to think rather than mindlessly compute. Brian Bushart shares lots of free problems for elementary teachers here: numberlesswp.com/
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Christine Lenghaus retweeted
A Norwegian neuroscientist spent 20 years proving that the act of writing by hand changes the human brain in ways typing physically cannot, and almost nobody outside her field has read the paper. Her name is Audrey van der Meer. She runs a brain research lab in Trondheim, and the paper that closed the argument was published in 2024 in a journal called Frontiers in Psychology. The finding is brutal enough that it should have changed every classroom on Earth. The experiment was simple. She recruited 36 university students and put each one in a cap with 256 sensors pressed against their scalp to record brain activity. Words flashed on a screen one at a time. Sometimes the students wrote the word by hand on a touchscreen using a digital pen, and sometimes they typed the same word on a keyboard. Every neural response was recorded for the full five seconds the word stayed on screen. Then her team looked at the part of the data most researchers had ignored for years, which is how different parts of the brain were communicating with each other during the task. When the students wrote by hand, the brain lit up everywhere at once. The regions responsible for memory, sensory integration, and the encoding of new information were all firing together in a coordinated pattern that spread across the entire cortex. The whole network was awake and connected. When the same students typed the same word, that pattern collapsed almost completely. Most of the brain went quiet, and the connections between regions that had been alive seconds earlier were nowhere to be found on the EEG. Same word, same brain, same person, and two completely different neurological events. The reason turned out to be something nobody had really paid attention to before her work. Writing by hand is not one motion but a sequence of thousands of tiny micro-movements coordinated with your eyes in real time, where each letter is a different shape that requires the brain to solve a slightly different spatial problem. Your fingers, wrist, vision, and the parts of your brain that track position in space are all working together to produce one letter, then the next, then the next. Typing throws all of that away. Every key on a keyboard requires the exact same finger motion regardless of which letter you are pressing, which means the brain has almost nothing to integrate and almost no problem to solve. Van der Meer said it plainly in her interviews. Pressing the same key with the same finger over and over does not stimulate the brain in any meaningful way, and she pointed out something that should scare every parent who handed their kid an iPad. Children who learn to read and write on tablets often cannot tell letters like b and d apart, because they have never physically felt with their bodies what it takes to actually produce those letters on a page. A decade before her, two researchers at Princeton ran the same fight using a completely different method and ended up at the same answer. Pam Mueller and Daniel Oppenheimer tested 327 students across three experiments, where half took notes on laptops with the internet disabled and half took notes by hand, before testing everyone on what they actually understood from the lectures they had watched. The handwriting group won by a wide margin on every question that required real understanding rather than surface recall. The reason was hiding in the transcripts of what the two groups had actually written down. The laptop students typed almost word for word, capturing more total content but processing almost none of it as they went, while the handwriting students physically could not write fast enough to transcribe a lecture in real time, which forced them to listen carefully, decide what actually mattered, and put it in their own words on the page. That single act of choosing what to keep was the learning itself, and the keyboard had quietly skipped the choosing and skipped the learning along with it. Two studies. Two countries. Same answer. Handwriting makes the brain work. Typing lets it coast. Every note you have ever typed instead of written went into your brain through a thinner pipe. Every meeting, every book highlight, every idea you captured on your phone instead of on paper was processed at half depth. You did not forget those things because your memory is bad. You forgot them because typing never woke the part of the brain that would have made them stick. The fix is the thing your grandmother already knew. Pick up a pen. Write the thing down. The slower road is the faster one.
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Christine Lenghaus retweeted
A fluency drill gives you one thing: a score. Connected fluency practice gives you fluency and vocabulary and comprehension and background knowledge — all moving at the same time, inside the same ten minutes. @TimRasinski1 @SoRclassroom @0Beanie05923291 @smorrisey @janhasbrouck
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Christine Lenghaus retweeted
A Stanford neuroscientist published a paper a few years ago that quietly answered one of the oldest questions in human history, and almost nobody outside his field has heard of it. The question is why we dream. Not what dreams mean. Why they exist at all. Why your brain spends a third of its sleep hallucinating images instead of just resting like every other organ in your body. His name is David Eagleman. He runs a lab at Stanford. The paper is called "The Defensive Activation Theory", and the moment you read it the explanation collapses every other theory you have ever been taught about dreams. Freud said dreams were repressed desires. He was guessing. He had no brain scans. He had no electrodes. He had a couch and a notebook and a century of credibility that nobody has been able to fully scrub off the subject since. Modern neuroscience replaced him with the memory "consolidation theory". The idea that dreams are your brain sorting through the day, filing things away, deciding what to keep. That story is partially true. Sleep does consolidate memory. But it does not explain the single strangest thing about dreams, which is that they are almost entirely visual. You do not dream in pure sound. You do not dream in taste. You do not dream in smell. You dream in pictures. Vivid, detailed, often impossible pictures that activate the back of your brain so hard a scientist scanning you would think your eyes were wide open. Eagleman started from one fact almost nobody outside neuroscience knows. The brain is territorial. Every region holds its turf through constant electrical activity. The moment a region goes quiet, its neighbors start invading. They take the silent territory and reassign it to themselves. This is called "cortical takeover", and it is not slow. It is not a long process measured in years. In experiments where adults are blindfolded, the visual cortex starts processing touch and sound within an hour. One hour of darkness, and the territory is already being annexed. In congenitally blind people, the visual cortex is fully repurposed. It runs language. It runs hearing. It runs touch. The hardware never went unused. It was just reassigned to whoever showed up first. Now sit with the implication of that for a second. Every night, when you close your eyes and fall asleep, the sun has set. The planet has rotated. The visual cortex, which takes up roughly a third of your entire cortex, is suddenly receiving zero input. For eight hours. Every single night. For your entire life. And evolution has shaped your brain inside a planet that has been spinning into darkness for billions of years. If cortical takeover happens in an hour, the visual cortex should have been lost a long time ago. Stolen by hearing. Stolen by touch. Reassigned by morning. Humans should have evolved into a species whose vision works fine during the day and then degrades every time the sun goes down because the territory keeps getting renegotiated overnight. But that did not happen. Vision works the moment you open your eyes. Which means something is defending the territory while you sleep. Eagleman's claim is that dreams are that defense. Every 90 minutes through the night, a precise burst of activity fires from the brainstem into the visual cortex. Pontine-geniculate-occipital waves. PGO for short. They are anatomically aimed. They are not general arousal. They are a targeted volley of signal launched directly at the back of the brain where vision lives. The cortex lights up as if it is receiving real images, and you experience that artificial activation as a dream. The bizarre narrative your conscious mind invents around it later is just your brain trying to make sense of the noise. The dream is not the point. The dream is the side effect. The point is keeping the territory occupied. The evidence for this is the part that should haunt you. Newborns spend roughly 50% of their sleep in REM. Adults spend twenty. Old adults spend fifteen. The amount of dreaming you do tracks almost perfectly with how plastic your brain is. Newborns have the most plastic brains on earth. Their visual cortex is in the highest danger of being overrun by neighboring senses while it develops. So evolution gave them an enormous defense budget. As you age, your brain becomes less plastic, the takeover risk drops, and the defense system scales down accordingly. Eagleman and his co-author ran the same correlation across twenty-five primate species. The more plastic a species' brain, the higher the proportion of REM sleep. The relationship held across the entire primate family tree. Plasticity and dreaming move together. They are two halves of the same evolutionary equation. A species that ranks higher on flexibility and learning also dreams more. A species that is born ready to walk and survive dreams less. Plasticity is the asset. Dreaming is the insurance premium. And the prediction the theory makes is the one that quietly closes the case. Of all your senses, only one is disadvantaged by darkness. You can still hear in the dark. You can still feel in the dark. You can still smelll and taste in the dark. The only sense that depends on light is vision. Which is exactly the sense your dreams are made of. The defense system is targeted at the only territory that is actually vulnerable while you sleep. Memory consolidation is real. Emotional processing is real. Your brain does do those things at night. But Eagleman's argument is that those functions piggyback on a much older system whose original job was simpler and more brutal. Keep the lights on inside the visual cortex while the planet is dark, or lose it. For thousands of years, people have asked what dreams mean. Prophets wrote about them. Poets wrote about them. Freud built a discipline on them. None of them had access to the actual answer, which is that dreams may not mean anything in the symbolic sense at all. They may be the visible flicker of a defense system running in the background, the way a screen saver protects a monitor by keeping the pixels moving even when nobody is looking. The strangest thing about the theory is how cleanly it explains why dreams feel so real. Your visual cortex cannot tell the difference between a PGO wave and an actual photon. It is the same hardware lighting up the same way. The cortex does its job. It builds an image. Your conscious mind, half-awake, wraps a story around it and calls it a dream. You are not seeing your subconscious tonight. You are watching your brain defend a piece of itself from being stolen. Every animal that has ever closed its eyes on this planet has done the same thing.
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Christine Lenghaus retweeted
A Hungarian psychologist raised three daughters to prove that any child could become a chess grandmaster through early specialization. He succeeded. Two of them became grandmasters. One became the greatest female chess player who ever lived. Then a sports scientist looked at the data and found something nobody wanted to hear. His name is David Epstein. The book is called "Range." The Polgar experiment is one of the most famous case studies in the history of deliberate practice. Laszlo Polgar wrote a book before his daughters were even born arguing that geniuses are made, not born. He homeschooled all three girls in chess from age four. By their teens, Susan, Sofia, and Judit were dominating tournaments against grown men. Judit became the youngest grandmaster in history at the time, breaking Bobby Fischer's record. The story became the gospel of early specialization. Pick a domain young, drill it hard, and you can manufacture excellence. Epstein opens his book by telling that story honestly and then quietly demolishing the conclusion most people drew from it. Chess works that way. Most things do not. Here is the distinction that took him four years of research to articulate, and that almost nobody who quotes the 10,000 hour rule has ever read. There are two kinds of environments in which humans develop expertise. Psychologists call them kind and wicked. A kind environment has clear rules, immediate feedback, and patterns that repeat reliably. Chess is the cleanest example. Every game ends with a winner and a loser. Every move is recorded. The board never changes shape. The pieces never invent new ways to move. A child who plays ten thousand games will see most of the patterns that exist in the game, and pattern recognition is exactly what chess mastery is built on. A wicked environment is the opposite. Feedback is delayed or misleading. Rules shift. The patterns that worked yesterday may be exactly the wrong patterns to apply tomorrow. Most of the real world looks like this. Medicine is wicked. Investing is wicked. Building a company is wicked. Scientific research is wicked. Almost every job that involves a complex changing system with humans in it is wicked. The Polgar sisters trained in the kindest environment any human can train in. Their success was real and the method was correct. The mistake was generalizing the method to fields where the underlying structure of the environment is completely different. Epstein's research is what made the implication impossible to ignore. He looked at the careers of elite athletes outside of chess and golf and found that the pattern was almost the inverse of what people assumed. The athletes who reached the very top of their sports were overwhelmingly people who had played multiple sports as children, specialized late, and often switched disciplines well into their teens. Roger Federer played squash, badminton, basketball, handball, tennis, table tennis, and soccer before tennis became his focus. The kids who specialized in tennis at age six and trained year-round for a decade mostly burned out, got injured, or topped out at lower levels of the sport. The same pattern showed up everywhere he looked outside of kind environments. Inventors with the most patents had worked in multiple unrelated fields before their breakthrough work. Comic book creators with the longest careers had drawn for the most different genres before settling. Scientists who won Nobel Prizes were dramatically more likely than their peers to be serious amateur musicians, painters, sculptors, or writers. The skill that mattered in wicked environments was not depth in one pattern. It was the ability to recognize when a pattern from one domain applied unexpectedly in another. That kind of thinking cannot be built by drilling a single subject. It can only be built by accumulating mental models from many subjects and learning to move between them. The deeper finding is the one that should change how you think about your own career. Specialists in wicked environments often get worse with experience, not better. Epstein cites studies of doctors, financial analysts, intelligence officers, and forecasters showing that years of experience in a narrow domain frequently produce more confident judgments without producing more accurate ones. The expert builds elaborate mental models that feel comprehensive and turn out to be increasingly disconnected from the actual structure of the problem. They stop noticing what does not fit their framework. They mistake fluency for understanding. Generalists do better in wicked domains for a reason that sounds almost mystical until you understand the mechanism. They have less invested in any single mental model, so they abandon broken models faster. They are used to being a beginner, so they are not threatened by the discomfort of not knowing. They have seen enough different domains that they can usually find an analogy from one field that unlocks a problem in another. The technical name for this is analogical thinking, and the research on it is one of the most underrated bodies of work in cognitive science. The single most useful sentence in the entire book is the one Epstein puts almost as a throwaway. Match quality matters more than head start. A person who tries six different fields in their twenties and finds the one that genuinely fits them will outperform a person who picked one field at fourteen and stuck to it on willpower alone. The lost years were not lost. They were the search process that produced the match. Every field they walked away from taught them something they later imported into the field they finally chose. The reason this is so hard to accept is cultural, not empirical. We tell children to pick a path early. We reward the prodigy who knew at six. We treat the late bloomer as someone who failed to launch on time, when the data suggests they were running an entirely different and often more effective optimization process underneath. The Polgar sisters were not wrong. The conclusion the world drew from them was. If your environment is genuinely kind, specialize early and drill hard. If it is wicked, and almost every interesting human problem is, then the people who win are the ones who refused to specialize until they had seen enough to know what was actually worth specializing in. You are not behind. You were running the right experiment all along.
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The third video in my series about understanding #mathshacks and #mathstricks is now out. This one features a lovely trick for approximating square roots of whole numbers that has beautiful connections to straight line graphs, calculus and even the Newton-Raphson method. Watch the full video here: youtu.be/IlMeZFe-m0M
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Christine Lenghaus retweeted
If you teach anyone at all, and you don't know about @helenrey's CogSci book summaries, you are missing out. It's a wonderful resource summarizing the most important books on cognitive science: bit.ly/3Q7dEnG
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Christine Lenghaus retweeted
One of the big discussion points from our How Do We Learn? book study was active learning—learning by thinking. Students need to actively think about the learning object, seek meaning, and connect it to their prior knowledge to make learning meaningful. This has major implications for how we design learning activities: ✅Clearly define learning objectives ✅Ensure students spend more time thinking about the learning object than not ✅Avoid unnecessary details or context ✅Prioritize tasks that require thinking and meaning-making—explaining, summarizing, analyzing, comparing I also shared how Project Zero’s Visible Thinking Routines have long been one of my favorite ways to promote learning by thinking in this way. Here’s a reference document I created a few years ago that categorizes the routines based on the type of thinking you want to emphasize 👇 docs.google.com/document/d/1…
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Christine Lenghaus retweeted
Have you ever tried the amazing Painted Cube Task? This is me teaching my Stanford Undergraduates and a newsletter about it. Do share #youpaintcubes mailchi.mp/youcubed/newslett…
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Focus isn’t forced. It’s trained. Small daily drills - tracing dots, steady lines, simple patterns - build stronger hand-eye-brain coordination. Patience today becomes confidence tomorrow. 🧠✨
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Christine Lenghaus retweeted
If you want to help students develop conceptual understanding of points on a coordinate plane, then this lesson called Pomegraphit from can't be beet: classroom.amplify.com/activi…
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