I'm a nanny and tutor to two boys who have been diagnosed on the spectrum. They're also both untested for giftedness, but I suspect both (the older is soon to be 11 and the younger is 6) are at least MG. This post is going to focus on SK11, since SK6 isn't having some of the behavioral problems at school (he's pretty laidback and doesn't really care if the work is "too easy.")

SK11 is currently in fourth grade at the local elementary school and his class (? I don't know what homework the other children receive) is apparently only working on math (basic multiplication of 2-digit numbers; long division; the very occasional word problem, but over the last 4 months or so he's only had 2 that I've seen) and literacy skills (spelling word likes "correct," "guide," etc., some bare-minimum vocabulary work in the form of looking up a few words in the dictionary and writing the definitions about once a month, and occasionally writing 3-sentence essays). His handwriting is awful, mostly because he hasn't built up his hand strength, and we (his parents and I) noted dyslexia/dysgraphia-like symptoms (for example he would spell guide out loud, G-U-I-etc., to me perfectly and then write "gduie") while he was working on school spelling words. Yesterday we worked on an 11-word list including "anaphylaxis" (included because he has life threatening allergies, as do most of his family members), "clarification," "pontificate," "alliteration," "exaggeration," "peninsula," "premonition," etc. He didn't misspell any of them when copying the words from the list, which is unusual, and then had no issue typing them into the computer afterwards to look up definitions on Merriam-Webster's website. He even volunteered sentences including some of the words he previously didn't know (e.g. "I need to clarify my thoughts") and, with little prompting, drew a picture of a peninsula, labeled it, and noted Florida is a peninsula.

He also had no trouble solving the (pretty lengthy and wordy) word problem I came up with for him-- a rates problem about my pet dog, as he's very fond of her and it would be motivating, and her fantastic food intake. This required him to read the problem over a few times searching for the necessary information, figure out a bit of unit conversion (hours to minutes-- nothing too wild but he hasn't done it before that I know of), and extrapolate implied information from what was given in the problem.

This was all accomplished in about an hour and a half, with 0 whining, and he managed not to get distracted despite SK6 running in circles around us playing with the dog and screeching. He was obviously exhausted by the end ('use this word in a sentence' and writing are very tiring for him-- some of his issues include poor working memory and difficulty using, for lack of a better term, his 'imagination' when called upon to do things like come up with unique sentence structure and content), but waited until I asked him if he'd like to write a story using the vocab words or be done to very politely say he'd prefer to stop working for the day.

This is like night and day compared to the usual experience. Most days he'd come home from school, have 4-5 drill problems for math ("Solve: 56x132. Use the square division method," etc.) and a list of around 6-7 words to copy down once or twice. That often takes us an hour, during which time he whines, repeatedly notes that he's hungry, has to use the bathroom, he's tired, "owww! my arm," etc. He'll pick up anything and everything off of the table to fidget with and turn in his hands; if asked if he's thinking about the problem, he'll blankly reply "What problem were we on?" so he's not using it as a thinking device. I know novelty may be part of this, but even tired he was pretty hyped about the prospect of doing science on Monday.

I don't know what to think, to be honest. Obviously he needs more practice on everything-- and a LOT more handwriting practice-- but he's way more engaged with harder and more top-down work. SK6 is going to be joining us on Monday to pick a science project for the next 2wks-1mth and we're going to work on learning proper scientific method, but I'm a little panicked about what's going to be developmentally appropriate. I was a PG child (graduated at 14yo) and note some of the same behaviors re: work which is much too easy in SK11 as I exhibited, but I'm leery of treating him too much according to my past experiences, since I was not on the spectrum.

TL;DR Teacher to two boys, 11 and 6. SK11 is getting work which is not developmentally appropriate at school, so parents are having me take over for the most part. Behavior change is astonishing from school work to harder word problems and spelling/vocab. How hard do I push him? What kind of science topics are developmentally appropriate? Should I also start doing at least a weekly history/geography lesson of some sort?