Students are solving single variable equations with one and two steps.

This is where I can wedge into the process all kinds of reinforcement of the stuff we only pretend you are confident with: operations with variables and integers.

I can say for w/2 = 10 that w is a number so big that when you divide it by 2, the answer is 10. I can make sure you do more than grind out the procedure to get the answer.

When it says -4 + 4y = 16, and you’re not sure whether to add or subtract, when I say “yes, you could subtract the negative four but that would be the same as adding,” and I can see that it connects.

I’m sure some students figuring things out on their own are doing just fine and making a lot of those connections. Most of those are students who actually expect math to make sense.

Rather many students in college learning this honestly don’t think math makes sense, so “figuring out” means getting through that problem set with whatever garbage nonsense it takes. It means making up “rules” to survive that may have nothing to do with mathematical sense (because in your life math hasn’t made sense anyway).

It means asking me for help and informing me ‘confidently’ that -(y/4) is positive because the teacher said it was the same whether the negative was on the top or the bottom, and a negative divided by a negative was a positive. When I suggest that actually, it can be on the top or the bottom, but that it’s not on both, you inform me righteously that well, that’s NOT what you learned in class; my explanation of where the negative can be placed doesn’t quite penetrate. (You end up leaving in tears about the fourth time you insist on telling me why the math can’t work and I insist on asking you questions about what you do know. You go out to the main tutoring lab and I hope you got those last 8 problem sets done…)

Showing students who aren’t confident in connections how to make them makes a big difference… but it takes time and practice.

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howardat58

September 10, 2015

My (very strong) feelings on this algebra stuff is that frequently students rarely see that an equation in symbols is actually a statement in words, and that putting it back into words brings back the meaning. Some simple rules matter, for reordering stuff, and then the word form is clearer.

I take your -4 + 4y = 16

Reorder to 4y – 4 = 16 and it can be read as “four times some number is 4 less than 16”, and “four times that number must be 12, then” follows.

xiousgeonz

September 11, 2015

This is my primary approach, too, though it is not always the path to success with my more dyslexic folks and I simply struggle absolutely the most with the Serious Whiners. I could hear “talking down” in my tone with the one student, asking her if she might want to have me explain how what she had told me the teacher said really meant — because negative and positive were not the same. (And mainly… I need to know when to take my three minute lap when I’ve heard all the negativity I can handle.)

xiousgeonz

September 11, 2015

(and then there’s the student today who tells me the things she has to do to learn as if she will do whatever she has to do to learn, but if I make a suggestion, she simply states, “oh, I wont’ do that.” It’s not that she is refusing; it’s that she thinks that she cannot control what she does.)