Math worksheets based on self-explanatory visual examples are a godsend for students with language difficulties - and easier for everyone else to understand too. #YouTeachYou #AmpleExamples #SelfExplanatoryMath #ELLMath

Math problems that students can’t do become behavior problems. #YouTeachYou #SelfExplanatoryMath #MathWorksheets #AmpleExamples

“Modifying” math worksheets by reducing the number of problems a student must complete can mean crucial content gets missed. Better to have everyone work through a structured sequence of self-explanatory, example-rich worksheets at their own pace. That way no one gets rushed or slowed down, and everyone has the chance to master every single aspect of the material. #YouTeachYou #AmpleExamples #SelfCheckingMath #Reproducible #MathWorksheets

The other night my wife and I met our son for dinner and to discuss plans for the You Teach You math method going forward. As we sat down at the table, our son - who's a full partner in our effort to bring basic math to the masses - launched into a story he couldn't wait to tell us. Turns out several days ago, our first-grade granddaughter was playing in his office at home, and he noticed that she had been silent for a while. He didn't think much of it, being occupied with work on his laptop in the next room, but after a while he started to wonder what she could possibly be doing in a room with no “kid stuff” in it. Several moments later he found out when she emerged with a copy of You Teach You: Book One and a pencil in her hands. She had taken it off of the pile of sample books he keeps in his office, leafed through the first few pages, gotten curious, and taken it upon herself to complete the first nine activities at his desk, studying the self-explanatory examples and working through the related practice problems on her own; she had emerged to ask if he could check her work. She hadn't noticed the answer keys on the back of each page, and when he pointed them out to her, she snatched the book back from him to do the job herself. She snuggled in next to him on the couch, and for the next several minutes they worked side by side, him typing on his laptop, her going through the problems she had completed, asking him a question every so often, but mostly just whispering “Yesss,” “Yesss,” “Yesss” to herself over and over again. He choked up a little as he told us this story. We choked up a little as we heard it. The image of the two of them working together independently still chokes me up a little. Of all the claims I've made here on TwitterX over the past two years, the one that's been met with the most derision (expectedly) has been the idea that even young children can teach themselves math with the right materials and assistance. But why shouldn't they be able to? Math can be expressed visually; kids love studying pictures (think of all the “spot the difference” challenges on restaurant placements that keep even the youngest kids occupied). Math offers chances to try things yourself; kids are forever saying “Let me try!” Math offers positive, meaningful reinforcement; kids crave positive, meaningful reinforcement. Above all, mastering math makes a person feel smart, and kids love, love, love feeling smart. Still, I know what some of you are thinking. What if a very young child isn't ready for something like You Teach You? Then they're not ready. That's the beauty of self-paced instruction. (And yet another problem with the “one-size-fits-all” assembly line approach to math instruction that pervades our schools.) When they are ready, on the other hand, self-explanatory, self-checking methods like You Teach You, can motivate them to, like my granddaughter, pick it up on their own. Literally! #YouTeachYou #AmpleExamples #SelfCheckingMath

I have an adult GED student who's among the hardest workers I've ever seen. Every day he comes to class early, takes the first example-based worksheet off the pile, studies the examples, completes the related practice problems with precision, and then asks to see the key - all before most of the other students have even shown up. He always fixes his mistakes too, even if he has to completely rework a complex problem - or several problems - to do so. He asks excellent questions as well, and takes unfinished work home to finish it on his own time. He has all the habits of mind, in other words, to be an outstanding math student, so I was curious as to how he ended up in the GED program. “Did you always work this hard in math class?” I asked him one day. “I tried to,” he said a little uneasily, “but I was slow.” He wasn't just talking about speed. Every time I hear a story like his, a part of me gets a little angrier. How many students have to face life without math because they're slow and careful? Because they're detail-oriented? Because they're trying to master the material and not just “get it done”? These are math virtues for Pete’s sake, and yet the fast-moving assembly line system that is public math education tends to punish students for them! It’s. So. Wrong. But don’t get me wrong. I’m not casting blame (except on the system itself, which existed long before any of us were born). My point is that we can do far better. We now know the cognitive science behind pre-worked examples, the importance of guided and independent practice and discovery, and the non-negotiable nature of instantly accessible feedback - and can incorporate these fundamental “see it, do it, check it” aspects of learning into self-paced instructional sequences, as I've done with the You Teach You book and worksheet series. In other words, we can now give each and every student all the time they need to learn math. I’m not worried at all about the student in this story. He’s now well on his way to passing the GED, and with his strong work ethic and exemplary habits is destined for a very bright future indeed. But what of the countless other math students who are slow and careful and are being marginalized by the system because they're slow and careful? Now they can have all the time they need. #YouTeachYou #SelfExplanatoryMath #AmpleExamples #InstantFeedback #InexpensiveMathSolutions

Good things happen when every math worksheet problem is accompanied by instantly accessible feedback: Misconceptions get cut off at the source. Misconceptions prevent mastery in math, and they multiply when feedback is missing or late. Instant, accurate feedback kills misconceptions before they have a chance to take root and spread. The details get mastered in detail. The details are everything in math; instant detailed feedback is the only way to ensure that every single detail gets mastered, not merely “covered.” Pointlessness disappears. Nothing says “pointless” like classwork without feedback - and nothing says “misbehavior” like pointless classwork. Math anxiety decreases. The fear of being wrong is neutralized when mistakes are seen as a natural part of the learning process, and are revealed to students individually and discretely (on an answer key they can view for themselves, for example). Fear of being wrong only increases when mistakes are pointed out to students in front of their peers. Neatness increases. Nothing improves neatness like having to pay for sloppiness. Students love getting things right and feeling smart; a system of instantly accessible feedback rewards them for neatness with correct answers, and “punishes” them for sloppiness with errors. Neatness inevitably wins. Problem-solving skills sharpen. Increased feedback enables students to discover that alternate problem-solving methods can get them to the same result, that some methods can be more efficient or reliable than others, and that understanding and thoughtfully adapting to situations - not mindlessly following steps - is the real key to mastering math. Flexible problem-solving skills follow. Curiosity is cultivated. Higher-level “What would happen if” questions naturally occur when students have multiple chances to witness causes and effects for themselves. A sense of discovery inevitably kicks in, shifting the focus from extrinsic to intrinsic motivation, and from passive to active learning. “How am I doing?” lies at the heart of learning math (or learning anything). Without continuous feedback, students are flying blind. With it, they can teach themselves to soar. #YouTeachYou #AmpleExamples #InstantFeedback #Reproducible #MathWorksheets #InexpensiveMathSolutions #EquityInEducation

The things others teach us tend to evaporate. The things we teach ourselves tend to endure. #YouTeachYou #SelfExplanatoryMath #AmpleExamples #InstantFeedback #NoTech #Reproducible #AffordableMathSolutions