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My spouse and I are currently both pursuing our undergraduate degrees. I'm double majoring in Computer Science & Mathematical Sciences and my spouse is double majoring in Economics & Finance. I have always had a very strong mathematical background prior to college. My spouse however, was not blessed with the same mathematical foundation.

My spouse will often seek my assistance solving algebraic expressions or transforming graphs. I'm happy to help but it troubles both my spouse and I that my spouse did not receive an adequate algebra education high school. There are noticeably troublesome short comings in my spouse's algebraic knowledge. My spouse is also aware of, and frustrated by, these short comings and has expressed a desire to learn what was not properly taught. My spouse did very well (B+) in the introductory college level calculus course, which proves to me that my spouse has a solid ability to learn mathematics when taught by a competent instructor.

While my situation is specific, my question is very general:

What is the best manner to assess a persons mathematical short comings and develop a specialized curriculum to remedy them? Are there any standardized reliable approaches/tests to determine which areas of algebra to focus on?

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I'm sorry for this. I upvoted your question; it's a perfectly reasonable question, but: from K-12 I was educated in the public school system in Philadelphia. My education was so good that I got a full tuition merit-based scholarship to the University of Chicago and went on to do a PhD in mathematics at Harvard University. (I also learned nearly impeccable spelling and grammar...) So maybe the expensive private school / deficient public school dichotomy is not the best explanation for the phenomenon in question. –  Pete L. Clark Feb 17 '13 at 23:55
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Just to take a crack at an actual answer: your spouse might consider hiring a private tutor: a very qualified one, who has graduate-level expertise in the mathematical sciences. Working one on one, a tutor can relatively quickly see what is well understood and what isn't. I would expect to pay at least $50 an hour for this service, possibly more, but for an economics/finance major I think that would be an excellent investment. –  Pete L. Clark Feb 17 '13 at 23:59
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Based on the sound of this post, how am I not surprised "manner" is spelled "manor"...before it was corrected right now...and +1 to @PeteL.Clark... –  gnometorule Feb 18 '13 at 0:47
    
I did not realize people felt the need to so vehemently defend public schooling... I have edited my question to place no implication of failure on this most sacred institution! –  awashburn Feb 18 '13 at 0:57
    
One idea that she can immediately put into use is to record in a personal notebook (or perhaps use index cards) the various algebraic techniques that she comes across (because someone else told her, or something she saw in a book, or something she saw on the internet, etc.) that she didn't originally know about (or know very well). Here's a possible example of such a technique: Using the Factor Theorem to factor polynomials –  Dave L. Renfro Feb 18 '13 at 18:24
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1 Answer

Certainly, there are many approaches to your issue, but with my limited data about your problem I can suggest only meta-solutions.

The very first thing to do is to check with a math curriculum of a good university. The point of this is to know what you are up to. Would it be a part of one subject or maybe your spouse will have to go through everything again. Some helpful things might include example questions for B.Sc. or M.Sc. examination (those are still performed at some universities).

If you know your spouse really need just algebra, then taking some final tests for algebra courses may point at deficiencies in knowledge. There are also books or online teaching services, where you can fill-up what you don't know (and remove the dust from what you have learned ages ago).

However, as the best thing, I recommend you to arrange a meeting (for you and your spouse, possibly more than one) with somebody with broad math knowledge. Meeting in person and talking (i.e. two-way communication) really makes a difference. It does not have to be a university professor, but I think it would be the easiest to search there. It should be somebody you can trust (e.g. recommended by a friend who is a math grad student, etc.), and who would be willing to spend a few hours (hours, not minutes, you should approximately know how much after the first step; depending on the person, some compensation might be in order) to assess your spouse skills. Knowing exactly the problem, he can then suggest some approaches (probably better than most of us here).

Finally, on the brighter side, answering questions here, at Math.SE (including, but not limited to "Algebra & Co." tags) is also something to consider (e.g. maybe as secondary means). It will not only let her test her skills or learn, but will also help our community (and, of course, she can ask whenever she feels lost).

Good luck!

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Thanks for the suggestions, these are some good approaches to consider. –  awashburn Feb 18 '13 at 0:27
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@awashburn Just to make it clear (so I can sleep soundly, it is not my intention to offend you in any way), in "the meeting for you and your spouse" I meant "for you to arrange and for her to go", unless, of course, she is so shy or so nervous that she can't do it alone (but in such situation it is probably better to change the person she would be to meet). –  dtldarek Feb 18 '13 at 0:50
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