Raising Future Adults

In the US, children are typically expected to memorize the times table from 1×1 up to 12x12 before leaving elementary school. I learned them in 4th grade. Reality: There's a small number of answers you need to memorize. Most can be easily and quickly found via tricks. For starters, since it doesn't matter what order you multiply in, about half the chart is a duplicate of the other half of the chart. If you know the answer for 6x8 you also know the answer for 8x6: 48. 1. 1 times anything is the number you multiplied by one. There's nothing you need to memorize.  2. Any whole number multiplied by 2 will result in an even number.   5. All whole numbers multiplied by 5 will end in a 5 or a 0. If it's an odd number, it ends in 5. If it's an even number, it ends in zero. It's typically easier to multiply by 10 then divide by 2. This can work for quite large figures, especially if it's a round number like 1000 or 1500. 1000x5 doesn't really require that. 1×5=5,...

When Tigger was in public school, they taught him some math shortcut and he kept using it wrong because he really did not understand how to do it the long way, so he really did not understand how to apply the shortcut. He would use it inappropriately and tell me "It is a Rule. My teacher said so."  I had to go back and show him the long way and explain WHY the shortcut Usually works but would not work for this specific problem. So, when a concept is initially introduced, the student probably needs to do it the long way a few times in order to understand it. But, AFTER they get the basic concept, I hope my thoughts on factoring are useful to some people: Factoring I handle factoring differently from most people. This is not something I was ever taught. It was something I discovered by observation: It is half as much work (or sometimes way less than half as much work) to stop factoring when the numbers 'meet in the middle'. If I were factoring for 8, once I go...

Division: Cut an actual pie. Square: lay out tiles/blocks/whatever. Cube: build a 3x3x3 cube using cube-shaped items (like blocks or six-sided die). The school treated math in an abstract manner. Whenever my son with dyscalculia got very lost, I made it as concrete, hands on, real world and literal as possible. By literal, I mean I tried to show him that terms like "cubed" or "squared" were literal descriptors of physical phenomenon, not just made up keywords. If you draw up an old-fashioned times table , you can show that multiplication uses the word "times" because you have this number that many times and show why it makes absolutely no difference what order the numbers are listed for multiplication. You can do the same thing with coins or piles of anything (sticks, pebbles, whatever). Five piles of six items or six piles of five items both add up to thirty. I helped my math-challenged son get over his baggage in part by teaching him "Addi...

Not terribly long ago, someone asked "Why is it that when you divide by a fraction, you have to turn it upside down and multiply?" I had a lot of trouble trying to figure out how to explain that and a good explanation unraveled from the dialog, both on the list and what she and I e-mailed each other privately. At one point she exclaimed "So, you mean it really is The Same Thing and not some kind of 'trick'?!" And I said "Yes, it really is the same thing." It never occurred to me that anyone would view a shortcut as a 'trick'. I ultimately showed that you can directly divide by a fraction, it is just very convoluted and difficult to keep it all straight in your head, even for me, and that is why this is something where they teach you the Rule in place of teaching you the long process. Usually, schools teach the long process first and only let you use a shorter version if you have thoroughly mastered the long method first. One example ...

I have on more than one occasion made a fool of myself by recommending the long out-of-publication game Pit Droids . I went so far as to ask around , essentially to no avail.  The story behind Lucas Learning is that George Lucas wasn't a very good student and wanted to create edutainment materials for kids like him. So it turns out he kind of lacks something as an educator too and Pit Droids and Droid Works are out of print, probably because they don't tell you what they are teaching you. The Fandom description of Pit Droids suggests to me this is the one that teaches Set Theory, something I learned in my college level math classes in high school, though the Fandom description seems to say nothing about what it teaches. And both games may teach Set Theory. I didn't play the games, so I don't recall. My math challenged oldest son LOVED these games. I encouraged him to play and counted it as math in his homeschool portfolio because while it doesn't cover the mathemati...

Math Encounters -- Five Balls, Two Hands  -- The Patterns of Juggling The man featured in the video is named Colin Wright and I was internet acquainted with him at one time. I thought we were kind of friends and ended up feeling burned by him, a story told here . He's got a few low quality shorts that he probably made. He didn't make  the above video, so it's kind of like some album I once owned, bought for the one hit wonder on it and that one song was produced by one company and everything else was produced by someone else and the rest of the album was terrible. So you probably don't need to look for more material by him. He's not a very nice guy. He burned me and he makes jokes in the video I don't like, such as he does an audience survey and says "You CAN lie." I never liked that joke.  Anyway, THIS video is from the National Museum of Mathematics who invited him to perform in New York and he doesn't drive and he's an Australian living in E...

From Reddit:  Why do I have to learn math? That's a teacher who loves math wanting help explaining to kids who ask why they need to learn math. I have ZERO advice for them. Technically, no one has to learn math. We can just let society devolve into a worse trash heap than the cesspit we currently have if no one wants to learn math. My understanding is the first math book involved NO numbers at all. It's a geometry book and has drawings of geometric figures and rules about relationships between angles. I'm guessing the kids most likely to ask this question of school teachers are kids who had elementary school teachers who not only couldn't teach it but were actively math phobic. I argued this once on Hacker News and some people backed me up: Women who go to college and have trouble with the math portion of something they want to pursue get told "Oh, it's not a big deal. Just go into early childhood education." Men don't get told that. Men who want to t...

From Reddit :  ASD child says he can't remember anything I teach There's information elsewhere on this site about supplements I used to help my oldest. Autistic kids may have metal poisoning or other health issues. My oldest has a serious medical condition and getting him generally healthier and better fed helped his academic performance enormously.  I mostly OBSERVED my kids to see what they could do. They didn't want to be quizzed. I mostly didn't test them. They hated having to prove they knew it and my oldest has a scathing phrase about public school: "guess the teacher's password." In other words, public school isn't designed to educate children. Children survive it by memorizing what the teacher wants to hear and their competency be damned. It's not relevant to getting passing grades. And he had trouble guessing the teacher's password because he's not neurotypical and struggled to figure out what the heck they wanted him to say. Whe...

I was always a sickly child. In eighth grade, I missed like a week of school or something and so I turned in my project late, well after everyone else. We were supposed to make a scale model of the solar system. I used a beach ball for the sun and various sizes of other balls and marbles for the planets. I was a smart kid and this teacher took GLEE in busting me. She's the same bitch who got after me for explaining the letter-substitution thing to my Hispanic friend who spoke English as a second language. That's the point at which I concluded I'm not necessarily inherently smarter than anyone else. I knew what it was because my high school drop out father did the cryptoquote in the newspaper every single day. This kid had no idea where to start and she bitched at me about "cheating" for telling him it was a letter-substitution puzzle so he had some hope of succeeding. So we are having a fairly private conversation about my very late project and she asks me about s...