Where I come from STEM means sport, travel, entertainment and music. Great skills for a holiday, but nothing compared to reading, writing and arithmatic for being able to engage with the modern world.
I want to live where you live.
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It sounds like your son is well ahead of most of his peers in terms of his skills / pursuits. I donât have personal experience with homeschooling apart from seeing how some transition into traditional schooling at our school in later years. I think it safe to say your son would probably be bored with much of a traditional math class. So your homeschooling pace adaptability is shining through here I would guess in ways that traditional classrooms can only struggle to match. So I too hesitate to try to give too much counsel as an outsider to your situation.
The whole rush to get kids to advanced math topics like calculus as early as possible may not (IMO) be serving the best interests of many involved. With the exception of a very top few savants who do plow through everything thrown at them and more, it would seem that too many precocious students feel a competitive urge to rush and end up with gaps among mundane topics --holes that would hopefully have been plugged by traditional class coverage. But precocious students often donât have the patience to wade through all the other stuff that is far behind where they could be. Patience-building interaction with others in that context isnât a bad thing either. There is nothing like teaching / coaching others to help solidify subjects in oneâs own mind. It helps cultivate interpersonal skills too. So it isnât just the materials/people who can challenge him from out in front that are important (though that is certainly valuable!) This is just to say that any context you can give him where he tutors others behind him will serve him well too!
And that kind of brings us full circle back to the OP topic, thanks!
Well, I didnât rate a shout out, but thatâs okay. 
By way of background, I am certified to teach both secondary math and English, and I also had a son who was precocious in math. @Mervin_Bitikofer was right about gifted kids often being bored by the pace of traditional classes. This is one area where the flexibility of home schooling could work to your benefit. Mervin also pointed out the negative, which can be a huge problem for home schoolers who donât follow a good math curriculum. Namely, if the childâs interests end up dictating what the parent teaches, the child is very likely to wind up with gaps in his/her knowledge.
The main thing is to encourage the childâs curiosity. Itâs your job to worry about the mundane things like curriculum. Let the boy explore what he wants to explore. Encourage him in his pursuits. Your goal is to foster a love of learning. If you can do that, you already have done more than the majority of us âprofessionalâ teachers out there.
On the personal front, my son was also precocious in math. He was in a STEM program at his high school in 9th and 10th grade, and he went to a STEM charter school at a local college for his junior and senior years, receiving dual credits. He ended up graduating from SMU (a top-20 business school) with a degree in finance at the age of 19. But ⌠there was a downside that I didnât anticipate as his father. At that age, he was competing with young men of 22-23 in job interviews, and there is a great difference between the social maturity of a 19 year old and that of a 23 year old. He eventually found a job, of course, but not at a top firm, and not in his chosen field. Sometimes, jumping too far ahead of your contemporaries isnât the best thing.
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I thought you swore off the forum to focus on your real work 
(I just tagged people who had already chimed in on the thread.)
Yes, I have heard similar stories from several people.
Focus? What is this focus whereof you speak? haha
Coming off a Christmas road trip and checking in with old friends before getting back on the horse again. Doing my best not to get bucked âŚ
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[quote=âChristy, post:19, topic:37561â]
My husband will be really happy about the importance you see in Excel. I sometimes think he loves Excel more than me.[/quote]
Excel rocks. IT and IS departments hate supporting applications developed using Excel but when you need something fast and portable, itâs the way to go. It is a pity that Microsoft is trying to move it to the web but hasnât managed to port a useful macro language with it. Visual Basic for Applications is an old dog but theyâve not been able to replace it.
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If your child is gifted, I would resist cookiecutter answers like this. It really depends on the kid. For me, I did worse when they kept me at the same level. I was just bored out of my mind. I did better as they let me go further, and I was rewarded for it. It really depends on the kid. If he has mastered the easy things, it can suck the joy out of learning to force him to repeat things over and over.
Speaking of soft skill,s do what you can to encourage him to NOT get arrogant, especially because might outperform your daughter. Remind them both that different people are good at different things.
Finally, one thing that really helped me was reading about the stories of scientists and mathematicians. Just a few books that had a big impact on me:
https://www.amazon.com/Mits-Wits-Logic-Lillian-Lieber/dp/0393063275
https://www.amazon.com/Advice-Young-Investigator-MIT-Press/dp/0262681501
https://www.amazon.com/Einsteins-Dreams-Alan-Lightman/dp/140007780X
https://www.amazon.com/Zero-Biography-Dangerous-Charles-Seife/dp/0140296476
There were also a few books i read at a high school level on Einsteinâs Relativity that were really formative. Canât find then, but this could be interesting:
Initially math can be attractive because their is a definitive answer. In the long run, it becomes most attractive when we understand the extent of the open questions and the creativity it demands of us. As someone else mentioned, math/science really requires us to become accustomed to failure, and to learn how to persist through it. Hearing about the stories of failure that other have had, and their slow progress to knowledge is really helpful. Also, these books are easy enough to follow that you will certainly be able to read along and talk with him about it.
I agree with taht [quote=âJay313, post:25, topic:37561â]
@Mervin_Bitikofer was right about gifted kids often being bored by the pace of traditional classes.
[/quote]
That is a very important point. In particular, its not just the âadvancedâ maths that are important. Geometry is surprisingly important as the first time that kids are expected to do proofs. That is critically important training. Certainly do not skip things because he does find them as interesting.
Regarding calculus, I would not necessarily put him calculus class immediately. But letting him read the stories of how it was developed might have a really positive effect. At last sometimes. Building anticipation on what he will be learning soon.
Excel is nice. But show him python tool. Python rocks more. =)
This website is great:
Hope thatâs helpful. Do not worry to much about âscrewingâ it up either. Ultimately, he will have to learn in college the key things for real. At this stage you are just laying that well-rounded foundation.
Iâm just chuckling over the ratings this turn of words would get from the politically correct overlords. I think I can hear klaxons going off somewhere! You give great advice, Dr. Swamidass --and sometimes very enjoyable typos. You might want to edit the above and get the intended ânotâ where you want it!
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All due respect to the professors in the building, but they know next to nothing about pedagogy. The articles are essentially correct. Again, let your boy explore whatever he wants to explore on his free time. Find ways to connect his interests to what you are currently studying, but donât let his interests dictate your curriculum. This is especially important in math, where skills and understanding must be built layer upon layer. Resist the urge to skip ahead. Youâre more likely to do harm than good.
Khan Academy is a good resource, though youâre probably already aware of it. Here is a nice search engine for lesson plans that might be of use. One of the best sites is Illuminations, by the National Council of Teachers of Mathematics. Plenty of ideas there.
Good luck!
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That is kind of the beauty of the Art of Problem Solving textbooks. There are no easy things. No drill. Just introduce a concept and then apply the concept in increasingly creative and complex ways the kid hasnât seen before. They are written for independent study for kids who do math competitions, not for use in schools. (But they have added a market with homeschoolers) But the philosophy is that gifted kids shouldnât breeze through an easy algebra program and then breeze through an easy geometry program. They should be exposed to the hardest things algebra has to offer and really be forced to wrestle with the topic before moving on to the next thing. Itâs a good fit.
I assume you mean not get arrogant? Yes, this is a challenge. We have thought about not keeping them together, but in the end I think itâs best for both of them. Itâs good for my son to have to explain how he got answers to my daughter (He is terrible at the âshow your workâ component, but getting better. Weâve moved beyond âThe answer is 4 because itâs obvious and nothing else makes sense.â) Itâs good that she sometimes gets things right that he gets wrong. And itâs good for her to have the competition, even though it is frustrating for her sometimes. She is very good at math for her age, just not a prodigy.
Thanks for the book recommendations! Flatland is like my husbandâs all-time favorite book from when he was a kid. Iâll check out the other ones. My son loved the biography of Nathaniel Bowditch we read together. (He advanced the science of navigation and was completely self-taught.)
Heâs done some of the Python tutorials at Code Academy. But I think he and his friend are into JavaScript at the moment because they have some big plan they are working on. I canât keep up with the computer stuff.
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Excel still has the best user interface for a lot of work. Itâs not the best graphing program but for its versatility, itâs pretty awesome. Iâve seen some attempts to integrate Python programming with Excel but itâs a bit of a hodge-podge. Iâd second the recommendation on Python as a language to learn. Iâm trying to encourage the use of Jupyter (Python-integrated, formerly iPython?) notebooks for scientists at work. It works fine with R as well. Right now weâve got way too many tools in various languages. A scientist will develop a useful application but too few will understand all the ins and outs of the particular programming environment to support or modify the work. As expected, this drives IT/IS crazy because they ultimately end up supporting junk we cobble together.
Ultimately, weâll need computers with sufficient AI to create programs from basic specifications and save us from our own cruft.
Could be, but that eventuality is decades in the future.
The most likely outcome IMHO will be a decreasing emphasis on code hacking accompanied by an explosion of higher order use of code generation and analytical tools. Just as over the past 40 years the decline of punch card operations was accompanied by an explosion of code hacking.
Chris
I thought that about self-driving cars.
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You know, I do not know of anyone working in AI that believes that. That is what I have PhD in. I am not concerned at all about being replaced by a computer. The languages and abstractions will change. In my career, they have several times already. However it will always require competent people to make use of the languages.
With all due respect, science professors at the highest levels are required to excel at a specific type of pedagogy.
We are pretty bad (usually) at teaching mediocre to poor students. We excel, however, at teaching the high end of the curve. That is, essentially, what our success depends on. Iâve never met a successful scientists that did not excel at teaching. We teach (apprentice) brilliant and informed students to become truly exceptional, and use that training to answer important and significant questions that serve the common good.
This is pretty much worthless for dealing with the complexity of a classroom, which includes the full range of aptitudes. So in that sense, do not come to use for advice. However, it is very closely relevant to dealing with gifted children. That is something we do have some understanding of.
The âshow your workâ piece is really important. Give him some perspevctive. Math at the most interesting levels is not about established answers. To make progress you always have to show your work, to convince people you are right when they do not see it clearly. Showing your work is just as important as getting the right answer.
Having him tutor other kids is a great way to reinforce that too. Itâs not just about getting the ârightâ answer. We also have to be able to demonstrate its the right answer. (Once again, we are getting into soft skills).
@Christy, I think your son is lucky to have you. Kids like him can do really well in homeschool, if they get the right support and direction.
Have you heard of AlphaZero? Googleâs new AI chess engine taught itself to play in four hours and destroyed Stockfish, the reigning âworld championâ of chess engines, in a 100-game match by a score of 28 wins, 72 draws, and 0 losses. Fascinating stuff. (Sorry weâre off topic, mods.)
https://www.chess.com/news/view/google-s-alphazero-destroys-stockfish-in-100-game-match
https://www.chess.com/article/view/how-does-alphazero-play-chess
An overemphasis on Science-Technology-Engineering-Math that relegates the arts to the back burner has been addressed by the STEM-to-STEAM initiative of the Rhode Island School of Design. A stands for âArts,â so STEM + A = STEAM. Read about this at StemToSteam. It might be fun to check your public schools to see what they are doing about it. (Or maybe they never got to STEM in the first place. We should finance our schools!)
At the end of the day, though, STEM is still extremely important, especially if we want to remain competitive in an increasingly technological world.
BioLogos used to have a âSenior Fellow of Arts and Humanitiesâ named Mark Sprinkle, whose work can still be found on this site. I donât recall an enthusiastic response to his work, even though he tried to keep things âaccessible.â
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Even Sesame Street is getting into the Stem + Arts action for their 43rd season. This might be a valuable resource for homeschoolers of the very young. Read about the new curriculum on the Sesame Street Web site.