Math Tutors & Teachers - Most Common Errors?

Question

I'm a math tutor (and occasionally a substitute teacher). As I'm sure many of you also grumble about from time to time - I keep seeing high school students making elementary errors (elementary school errors) in their mathematics. In particular, I find I need to spend at least 1/2 my time re-viewing concepts that should have been learned years earlier. 
Negative numbers - an almost certainty of a mistake to come.
Manipulating fractions - 'simple' errors - that give bizarre results.
Exponents - for some these are a real bug-a-boo.

I'm trying to put together a 'Top Twenty' or 'Top 50' error-sheet - to give to the parents of my students - and to guide me toward making a 'pre-tutoring' test sheet - to see what simple mistakes they tend to make.

What are the most common, or most irritating mistakes that you see from high school students in pre-algebra, algebra, geometry, and calculus?

fizixx · Accepted Answer

I've seen college students make all kinds of rudimentary mistakes, let alone high school...lol...sad as that is.

They have trouble with everything you mentioned plus the use of parentheses, and even knowing how to break numbers down into factors --- 54 = 9*6 = 3*3*3*2

They have problems reducing numbers and using the distributive property believe it or not. They don't recognize simple forms of various properties, like the difference of two squares, or cubes, how to complete the square, and believe it or not, how to combine like-terms and knowing the difference between terms and factors.

I think most of it is just laziness, but trying to tutor people like that is frustrating because you have to teach them everything up to what they're having trouble with to make any progress. It's no fun for them, and I hated it so much I stopped doing it. Now I only do it for people I know.

Look at the link below. Classic question here especially, but I just saw this question a few minutes ago, and I almost made my typical sarcastic remarks, but I didn't this time. This person thinks the material is 'super-complex' apparently. I think it's mostly laziness, but it is very typical of the mentality or skill-level on here, but I have also seen this in people I have tried to teach and tutor. So, I'd suggest you see if you can find a way to stress that the student actually has to DO the work to gain the understanding. They need to practice.

Good luck

plays_poorly... · Answer

You might also mention an inability to focus on the problem, 

as well as a certain lack of ability...due, I am sure, to lack of

actual practice doing problems...to see a line of attack.

These days, math ability has become like a superpower...but 

I know it can be taught, because we were...and that was long 

before No Child Left Behind or Core Curriculum.

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Math Tutors & Teachers - Most Common Errors?

2 Answers