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August 28th, 2017, 09:39 PM   #1
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seeking advice for tutoring a student in algebra

Hi, I'm very good at math but not very experienced as a math tutor. I'm going to be helping a friend's son this week. Apparently he is in a Pre-calculus class and they did a "review test" last Friday covering mostly Algebra II stuff (maybe even some Algebra I) .. basic simplification, factoring, etc. of polynomials and the like. Most of the class did poorly. I saw his answers, and they show a lack of fundamentals even in algebra. I'm not surprised, the schools tend to pass along the students before they are really equipped to take harder classes. But in any case his parents are hoping I can prepare him for retaking the test this Friday -- i.e. typical last-minute preparation kind of thing.

I would like to get some advice on the question of how to quickly review algebra and pick some low-hanging fruit to drill. What do you guys do when a student is lacking in fundamentals but the parents want help for a test in a couple days? Any useful "cheat sheets" on the internet? Any skills that are particularly important for me to review with him?

Mike
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August 29th, 2017, 12:03 AM   #2
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I should clarify that I am not trying to teach or strengthen *all* of algebra II in one week -- of course that's impossible -- I'm asking about low-hanging fruit, i.e. easy and simple yet important concepts that will improve his grade. After that, if he and his mother like me, I might get to spend more time with him and really do the work.

Mike
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August 29th, 2017, 03:32 AM   #3
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Surely pre-calculus also includes (or presumes) basic knowledge about geometry, trigonometry, graphs (including the concept of a function, and the nature of the graphs of various useful functions), the use of graphs to represent inequalities, etc.

An important rule is that if you perform any valid operation that may change the value of one side of an equation, you must perform the same operation on the other side of the equation. If any working needs to be written down, it should be written neatly enough to allow it to be checked easily.

Now the various operations can be revised. That might sound too basic, but it's often found that those who haven't done that make quite obvious mistakes, such as assuming that $\sqrt{x + y} = \sqrt{x} + \sqrt{y}$. This leads on to such things as gathering like terms, isolating a variable, etc. One can then introduce particular uses of basic algebra, such as summation of arithmetic and geometric series, problems involving calculation of interest, etc.

To prepare someone for a particular test in just a few days, you need to find questions from previous test papers or example papers, preferably with worked solutions, and get the student to work through them while you observe and make notes of what you need to explain, but try to leave the explaining until a bit later. If you can't get those, find a textbook rather than videos on youtube, as the videos would take too long to watch. Most of the questions are designed to (a) test knowledge of specific things, and (b) be reasonably easy. Except for multiple choice questions, there are likely to be marks for use of appropriate methods, applying those methods correctly, and obtaining the right answers. This means that misunderstanding the question or choosing an inappropriate method may lead to a lot of time being spent on work that earns no marks at all. All the practice needed may be rather boring, but that's probably unavoidable. When reading through a worked example, the student needs to understand why the working is done as well as how. Try to point out what knowledge and skills are being tested in such questions.

Try to broaden the student's knowledge occasionally. You could point out, for example, that whilst x² - 3x + 2 = 0 is (obviously) a quadratic equation, x - 3√x + 2 = 0 can also be treated as a quadratic equation (but in √x rather than in x).
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August 29th, 2017, 07:13 PM   #4
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Thanks!

So let me make sure I understand.

I see that you are pointing out that the student will get partial credit for choosing the right method, and additional credit for working it correctly and obtaining the right answer. So the most essential thing for me is to make sure the student chooses the proper method.

A piece of "low-hanging fruit" is to make sure they understand that anything done on one side of the equation must be matched on the other side.

Another basic instruction is "write neatly enough to check your work."

Point out common mistakes. I could also add the mistakes of

$ (a+b)^n = a^n + b^ n $, $ (a-b)^n = a^n-b^n$

And I know some students think $ \frac{x-1}{x} = -1 $ (because you "cancel" the $x$'s).
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August 30th, 2017, 03:39 PM   #5
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skipper made excellent points. Since you have the review sheet with his answers I would suggest going over that with him too. Work out every problem he got wrong , showing each step , pause after every line you write down , ask him "Is there a question about what I did so far?"

Praise him for every problem he got right , "You did a good job on this one"

If you have time , make up similar questions to the ones he got wrong just change the numbers , let him look at your working while he's trying to solve the similar problems you give him. Observe his working and gently guide him if he goes off track.

If he can do well on the review sheet he should do well on the actual test. The review sheet is the best 'cheat sheet'

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August 30th, 2017, 09:26 PM   #6
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I think I should have concentrated more on the really easy tasks. After all, making mistakes on Algebra 1 questions suggests being weak on basic arithmetic as well.
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