I've written a little bit about it here: 1 2 3 4. Links 2 3 and 4 have long excerpts. My copy cost 60 dollars, I see there are some on amazon for under 50. I can't explain! When I see a crummy paperback for 1000 dollars on amazon I sometimes wonder if there is a flawed computer program setting the prices.

I have a first-grader who doesn't read independently, not even fiction. So this is just a speculation not from too much experience. I think reading nonfiction is easier when you already know a little about the subject — maybe easier and easier the more you already know about it. But kids don't know anything about any subjects. If that's right, it suggests that you might have more success going into some depth on one subject over a long time (very slowly at the beginning of that time), than sampling from many subjects.

What is precalculus? If a high school offers calculus, will it also typically offer "precalculus" or is it language that is more often used at colleges?

Do you remember any examples? A year ago I read about the citric acid cycle and I remember that citrate or isocitrate or something like that inhibits an early step of glycolysis. I don't think I could have guessed from your profs prompt...

I'm glad I didn't offend you! You are right to kid, I didn't intend to be casually skeptical of anybody's genius. I think my child is a genius. But I've found that she gets a lot out of material designed for low performers, if I can find the right time to present it to her. I either have a budding theory about this, or I have cognitive dissonance. It pretty abruptly stops using the weird font for the last 25 lessons, maybe two or three lessons of phasing it out. It was pretty seamless for my kid.

I'm another case of "100 easy lessons." It worked like magic on my illiterate 5-year old. With two older kids I wonder if you've heard of it or used it before? I don't think it only works on geniuses, just the opposite actually it was designed for what Engelmann called "low performers."

I'd be very excited to see them.

I'd love to hear more about combinatorics for 6-year-olds. I only know Art-of-problem-solving from their beast academy books. Do the books for older kids have something in common (an "AOPS style"?) with BA? I admire Beast Academy, with growing reservations. editing to add that I could have asked @pgr the same question: Can you tell something about the format?

What kind of math have you been doing with your 4.5 year old? I have a recommendation: the author of "Teach Your Child to Read in 100 Easy Lessons" wrote another book in the 60s called "Give Your Child a Superior Mind." At the end there's a math curriculum for four-year-olds, that I had a great time following with my kid aged 5.5.

Were you following a program or did you improvise reading exercises on your own? My daughter learned to read from the "100 Easy Lessons." I know some people for whom it didn't work, but it amazed me and kind of changed my whole view of education. I've been thinking to myself since then, about whatever topic: if I can find a way to make this really easy for her, then it will be easy for her. She'll learn it and know it. That might be the opposite of what you're describing.

Do you mind giving a little detail? I don't think I have the picture, I wonder what it looks like the 50% of the time you present some math material and they "fail to do it," the 50% of the time you present some reading material and they "fail to do it."

I'd like to hear more. What kind of material are you presenting this way?

Are they "homework" problems that she's doing on her own, that you catch later on when correcting or marking them? One thought is that this list: might be shorter than you think. 10 items long instead of 10 thousand. It might be much harder to teach someone to "be more careful in general" than to "be careful about this issue in particular." You can't empty the ocean one teaspoon at a time but you can empty a teacup that way.

There's a very good one narrated by Lawrence Olivier from 1973, called "The World at War." The whole thing used to be on youtube but I don't see it there now.

I think there is something different about high school geometry.

I have a suggestion for this. It could only help in narrow situations and it requires a lot of paper. But my 6-year-old will go through 10 problems on 5 pages, each with lots of white space on it, faster and more enthusiastically than she will go through 10 problems on 1 page.

Don't press the edit button! I haven't been reading you wishing you'd express yourself better, just wishing you would say more.

Concision is great but you can only get to it by writing too much and then editing it. Start by writing too much.

I hope you don't feel ganged up on. It sounds like many people are interested in learning more about what you're doing. So how should you explain it? I think among all of us here giving you grief — and I don't mean to boast! — I have the best advice for you. Just write down what happens over the course of one session, not a "typical" or an "ideal" session but one that really happened and that you have a fresh memory of. Go into way more detail than feels natural. This might be a sticking point for you: you think we surely understand well enough to fill in the blanks, we'd be bored to tears by the details. I don't think so. A lot of the lessons I post I don't even introduce. I just say "DD5, go work." Occasionally, I'll tell her not to use poker chips and to do it mentally. Occasionally, she'll ask if she should use poker chips. She's slowly getting more and more able to do things mentally at this point "Go work" counts as an introduction, and new information to me. What goes on in the 60 seconds after you say that? What goes on in the 60 seconds after that? I don't have a good guess. "Occasionally X and occasionally Y" is too cloudy of a description, for me. What specifically happened today? I don't think so.

A video would explain a lot but I share your pessimism about bad outcomes from posting videos that involve your kids. Don't do it. I don't think you should make a years-long plan about how to communicate your ideas. Write up a lesson transcript and maybe write some comments on it. You might inspire yourself to write something else, you might inspire someone else, or you might get inspiring feedback. If instead you wind of disheartening yourself and you don't get any good feedback, I hope you wouldn't give up right away but you wouldn't have to continue for years. The kind of transcript I'd like to see at least once: not just one thing that happened in the lesson but how you prepared it, how you introduced it, how your pupil reacted to your introduction, how you reacted to that reaction, on and on till you tell how you closed the lesson. Think of Jane Goodall's field notes.

Yes, I think doing things in order doesn't matter on a blog. Even less than it mattered in the Iliad or in Pulp fiction.

To me, it sounds like you could get writers block right away.

I don't think so: "how things started" and "what things look like now" are separate reading problems (and more importantly: separate writing problems for you). We won't have trouble visualizing anything that you describe vividly. We don't have to know right away why you're describing it, why you did it the way you're describing and not some other way, or how you got to the point that you were able to do what you described.

I'm very interested in a transcript. I think you should take a break from writing the theory of what you're doing. Write ten thousand words about the practice — "case studies" or just lab notes. If you could go into very fine detail about one of your tutoring sessions, every day for two weeks (impossible — but even longer would be better), I think some people would be interested and afterwards you would have a lot of material to crib from and link to, for synthesizing a more theoretical explanation. In media res is no problem: you don't have to remember how it all started and try to catch us up. Just tell what happened yesterday, but go into twice as much detail as you think is overkill.

I took NaN's advice about poker chips for place value in March, and I've been really pleased with them. I wrote a little bit of detail about my first experience using them (with my 6-year-old daughter), not quite publicly, and I looked it up again a few days ago because I'm about to introduce them to a relative. I'll paste it below. I've been using some handmade "poker chips," each of them is a square inch that I cut out of red or orange or blue construction paper. March: I gave her a light load of worksheets this morning, and told her that when she finished we would play a game with little paper squares I had made. These red squares are 1, and these orange squares are 10. "Then the blue squares must be 100!" Yes. These won't be her only "model" for three-place numbers, she already has experience with pirate numbers (from BA), plastic cubic centimeters that stick together, the number line, the numerals themselves. But I had reviewed some questions over the last week like "451 is the same as 3 hundreds, __ tens and 1 one" and they weren't effortless. One way the cardstock squares are worse than plastic poker chips: when you give someone a stack of 8 or 9 of them it takes a little bit of dexterity to separate and count them. Anyway I set it up like this. She has a blank sheet of paper and pencil, and I slide some orange and red squares to her. "I want you to write down the value of these squares that I gave you, as a two-digit number." She didn't need any explanation, she counted the two orange squares as "ten, twenty", looked at the six red squares, and wrote 26. "Now here are some more. Don't mix them together yet. How many did I give you in this group?" and she wrote 29. When I asked her to add them together, she did it in her head by saying "forty fifteen." That's a joke that she likes that I don't always discourage. "That's kind of a good answer as a joke, but you have to remember that 15 isn't a digit. What do you really mean by 'forty fifteen'?" She knows to answer 40 + 15. "Good, you can remember 40+15 for a minute. Before we talk more about it I want you to write "problem 1" on your paper, and then write 26+29 since that's the problem you're doing." I let her guess a little about the letters in 'problem' before spelling it for her. Then she wrote 26 + 29 = ▢. I hadn't asked her to write the equals sign or the box, and didn't mind that she did. "OK what was 26+29 again?" 40 + 15, which is 55. "Good. Now, you still have 4 orange squares on your side of the table, and 15 red squares on your side of the table. Is there a way we can make that look more like 55, without changing the value?" This stumped her, she couldn't guess what I wanted her to say. "Here's a rule for the game. A red square is 1 and an orange square is 10, so whenever you like you can trade me a 10 red squares for 1 orange square. Let's try that now." She counted out ten of her red squares, slid them to me and I handed her one orange square. "Now, how many tens do you have? How many ones do you have?" She shouted back, I think excited because she had put together what we were doing, "Fifty-five!" Next problem. "OK, write problem 2 on your paper. No, don't hand those back to me, this time you're going to start with those 55. How many do you have there, five oranges and five reds? Can you write that as a two-digit number." She wrote "PROBLeM 2," underlined it, and wrote 55 underneath. "Here are some more for you." I gave her 1 blue square and 1 orange square. She knew I had given her 110, I had her write down 55+110, and she knew that was 165. I didn't make her prove it to me by counting her squares. "OK, now write Problem 3. You can keep those 165. Now I want you to tell me: what's 165 minus seven. Can you use your paper squares to find out?" She fussed with her squares for a little bit and then asked me "can I have two more reds?" I told her no, I don't want to change the value of the number you're starting with. "But you can give me one orange square and I'll give you back ten red squares. That won't change the value and it will help you." After the trade she was reluctant to give up the seven red squares she was taking away to the "bank." I told her it was fine, she could keep them on her side of the table, she just had to get them out of the way of the squares she ended up with. "When you subtract you take seven away from the number you start out with, so take those away, put them over there, and don't count them when you tell me what you end up with." She didn't count at first, she was pretty sure she had 148. I asked her why, she said "because 10 minus 2 is 8." Well, that's true and it's a good observation for your problem but let's look at how many orange squares you have, remember you started out with six and you only traded one of them to me, I think you have five. "I'll write 158." I thought that was the right place to stop for the day.