My son is in 5th grade (US) and since he is doing remote learning, we have been doing a lot of topics in pre-algebra just using worksheets. I'd like to start him on a formal middle school curriculum, preferably one that has rigorous fundamentals, similar to the Spivak calculus book I used way back when.

  • $\begingroup$ Off the top of my head, I'd recommend looking through some of the 1960s School Mathematics Study Group (SMSG) books). Even more, I'd recommend getting an older (before 1980 or so) edition of Modern algebra. Structure and Method. Book 1 by Mary P Dolciani et al. $\endgroup$ – Dave L Renfro Dec 2 '20 at 15:18
  • $\begingroup$ I just noticed your son is 5th grade and apparently is beginning middle school math. I saw the title, glanced a few seconds at your last sentence, then went googling for the links to what I thought would be appropriate for someone (apparently not your son, on second reading) who had already been through much of middle school math and was looking for something to self-study at the next level. However, what I gave could still be of use. $\endgroup$ – Dave L Renfro Dec 2 '20 at 15:25
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    $\begingroup$ I've seen artofproblemsolving.com recommended for advanced students in his situation. It is recommended for grades 5+. $\endgroup$ – Opal E Dec 2 '20 at 23:03
  • $\begingroup$ There is no formal middle school curriculum in the U.S. unless you mean Common Core goalposts and textbooks that supposedly align with these goalposts. $\endgroup$ – Rusty Core Dec 3 '20 at 7:18
  • $\begingroup$ I am not sure about rigour, but you can take a look at the Khan Academy courses ( khanacademy.org ) or the online version of the Big Idea Math books ( bim.easyaccessmaterials.com ). As far as I can see these are free resources and cover the common core standards in a systematic way. $\endgroup$ – Ferenc Beleznay Dec 3 '20 at 9:33

I recommend starting him with Beast Academy (maybe even go down to their level 4 or below). Beast Academy is very fun; the rigor may not be obvious, but they are building thinking skills. When he's done with BA, then go to Art of Problem Solving.

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    $\begingroup$ Thanks, i looked at BA (which is part of AOPS) and at AOPS and they're great! $\endgroup$ – rbp Dec 4 '20 at 19:38

You could consider the series distributed in the United States by singaporemath.com:

  • Primary Mathematics for grades 5 and 6
  • New Elementary Mathematics for grades 7 and 8.

You can also find later volumes of New Elementary Mathematics for grades 9 and 10 for sale on the internet. Primary Mathematics has three versions adapted for the U.S., while New Elementary Mathematics is not adapted (hence uses metric measures only).

Secondly, for grades 5 to 10, you could consider the recent Australian series ICE-EM Mathematics, now in its third edition, whose authors include a number of PhD mathematicians. It is published by the Cambridge University Press and comes recommended by Fields medalist Terence Tao.

Unlike the Art of Problem Solving series mentioned in the comments, the Singaporean and Australian series are intended for a wider range of abilities (although New Elementary Mathematics is probably for the top 20 to 30% in Singapore schools, which would equate to a smaller percentage in the U.S.)

An alternative to these would be various mid-twentieth century British textbooks aimed at higher achievers, starting from about grade 7 level. One would have to tolerate the fact that they are obviously so old-fashioned, but the level of competence developed in algebra, trigonometry and particularly geometry (in students of a mathematical bent) is without comparison to more recent textbooks.

  • $\begingroup$ Both of these look great $\endgroup$ – rbp Dec 4 '20 at 19:46
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    $\begingroup$ "the level of competence developed in algebra, trigonometry and particularly geometry is without comparison to more recent textbooks" — this is a nice way of saying that modern math schoolbooks are mostly garbage. $\endgroup$ – Rusty Core Dec 5 '20 at 20:50

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