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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]Yes, you should complement. Have your child enroll in RSM or AoPS either concurrently or shortly before. That's what we did. School instruction is insufficient in multiple ways. First, students aren't doing any problem solving in school (all they do is textbook worksheets and SOL prep); second, they don't do any mathematical writing in school; third, the school curriculum is abridged for an advanced student [b](e.g., no complex numbers in Algebra 1, no linear programming[/b]). Fourth, school math is much less fun.

In short, if your child is gifted and interested in math then you cannot rely on the school curriculum.[/quote]

Is this a joke?  Why would there be complex numbers in Algebra I?  You sound nutty.[/quote]
When covering math at a level appropriate for mathematically gifted students you introduce complex numbers before the quadratic formula. For instance, AoPS's [url=https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/toc.pdf]textbook does so in Chapter 12[/url]. [/quote]

Complex numbers have never been part of Algebra I.  If you want to pay money to have someone teach your DC ahead, fine, but it's not &quot;abridged&quot; or &quot;appropriate&quot;.  
[/quote]On the other hand elementary algebra textbooks for college are better structured and start with numbers (including complex) and arithmetic, then move to equations and then systems.[/quote]
Can you name one such book?[/quote]

Stewart, College Algebra
Openstax, College Algebra

All college algebra books, I’m not aware of a single one that doesn’t use complex numbers in the treatment of quadratics.

The division between algebra, geometry and pre calculus is also quite arbitrary, with many areas of overlap. Of course arithmetic, equations and systems belong in algebra, shapes, angles, lines belong to geometry, and vectors and matrices traditionally taught in precalculus. But functions are thought in both algebra and precalculus, analytical geometry are taught in algebra, geometry and precalculus, etc. trigonometry is another one that can be taught alone, or almost any high school math class.

I found it somewhat amusing when posters decree that complex number are taught in Algebra 2. What exactly is Algebra 2? Then why are they taught again in precalculus. There’s an apt analogy that math is a spiral, it’s up to the individual how fast one goes around and the breath and depth of the material studied.[/quote]
Those are college algebra books, not elementary algebra books. Those are two different math classes.[/quote]

It’s the same content, my kids school is using Stewart as textbook for Algebra 1 and 2, although they skip a lot of sections.[/quote]
No it's not.
https://www.knewton.com/wp-content/uploads/2020/04/alta-Elementary-Algebra-v2-TOC.pdf
https://openstax.org/details/books/elementary-algebra-2e

Notice the lack of imaginary numbers.[/quote]

It is the same content, some books introduce concepts earlier, some omit them etc. an honors class will go more in depth, introduce more topics etc. as you correctly point some books include complex numbers some don’t. Both Elementary Algebra and College Algebra books from openstax are one semester introductory courses that have some differences.

Essentially the student should choose based on interest and capability, if you can handle go for the more difficult version. If not the lighter version is good too.[/quote]
It's clearly not the same content, as elementary algebra does not include complex numbers even though you (or the person whose point you're arguing) claimed otherwise.
&quot;On the other hand elementary algebra textbooks for college are better structured and start with numbers (including complex) and arithmetic, then move to equations and then systems&quot; -&gt; unproven and now demonstrably false.[/quote]

Lol, I’d be curious to know what your math background is. Based on your deep paragraph analysis in guessing you majored in English (or worse!).

For college, all algebra is actually remedial and is called either simply Algebra, or Elementary Algebra to differentiate from Linear Algebra, which is a typical sophomore year math course. Some community colleges break Algebra in two semesters and call it Elementary and Intermediate, but that’s because they see more students with large deficiencies that need to be plugged before credit courses starting with precalculus. There’s no credit for any Algebra class. Basically if it has numbers, equations and systems, it is (Elementary) Algebra.

Seriously, you’re out of your depth here nit picking on semantics.

If we’re talking on supplementation for a more advanced student, it matters little to me how some random book is organized. I’ll simply go for the most complete and exhaustive treatment the student can handle. For quadratics that will include complex numbers. For linear graph it will include all the forms: standard, slope intercept, two points, point slope, parametric. I’m sure some of the books you listed omit one or more, and some will include all. As I said I’ll choose the curriculum that goes in more detail.

You’re free to pick whatever you like for your child.[/quote]

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