#MTBOS — a twitter followee notes how confusing algebraic expressions are. Yes, this is something that created cognitive dissonance for me, until I connected that oh, explicitly teaching what symbols means applies to math as well as reading. Why should f(x) = mean “the function of x” when, applying the *rules* we teach, it could mean “f times x.”

I intuitively inferred that f(x) had its own meaning because it was so common and in the multiplication contexts, generally two variables being multiplied would be written fx. I didn’t even realize I’d made the generalization.

(I don’t know if this is the same kind of thing happening with Canvas. I don’t think so. I don’t think the contexts are that different. I just think that once you’ve been told a weirdness — like “Oh, they ask if you haev a Canvas account but if you don’t have *that kind* of Canvas account, and you’d better peek up at the address to see what it is, you have to make a new one” that … you forget, because once you have that account you never have to deal with that again.)

Another “logical if I think about it” confusion is the struggle to know when a dash is a negative and when it’s subtraction. Today’s ALEKS had negative integer distribution problems, looking like -3(x^2 + 91 – 3W) … and then (2r^3 – 81 + m)(-7).

I encourage students to rewrite the mess with the integer first so they can do the little arrows to all the terms and keep things familiar… so the student said, “I can move it to the front, and I don’t need the parentheses, right? Why?”

So student it seems had seen enough problems to know that’s how they looked. I ‘splained that w/0 the parentheses to wrap things up, it would be a subtraction problem but at the beginning of a problem, there was nothing to subtract from, so it meant negative.

I know students often subtract instead of multiply in that situation…

… oh, and the college prez was here for a “drop in and chat with students” thing, and chatted up a soon-to-graduate person, who said that the “walking” thing would not happen here. Why? Among other things, finances. PRez says it’s free. Stu says “not the robe.” “Well, what if the robe was free?”

Now, perhaps the prez is going to make all the robes free. However, we discussed after he left the nuances of normalized corruption and people in power bestowing favors…

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howardat58

December 2, 2016

There are several things here:

0: The minus sign and the dash are one and the same.

1: In algebra the plus sign indicates that the contents are added, and the minus sign indicates that the contents are subtracted, from whatever has been previously calculated.

The plus sign is IGNORED at the beginning of an expression, or a variable.

So a+b is really +a+b, and a-b is +a-b, and -a+b is complete.

The “contents” is an expression, either a simple variable or something surrounded with brackets (parentheses), or zero.

2: The term f(x) means “the function f of x” – subtle difference, but very important.

3: u, v, w, x, y, and z are usually variables, or variable values.

a, b, c, d are constant values, and f is included if it does not denote a function.

4: Meaning is crucial.

5: So what is the difference between -3 and 0-3 ? Good question.

xiousgeonz

December 2, 2016

Love your perspective!

That subtle difference … the function f of x … yes, that’s *exactly* the difference in processing. They want “a function of x” or … of means times… sometthing times x. No, it’s exactly one layer more complicated.

and … we do not generally, actually *teach* about constants and variables and the letters we choose for each. People like me just absorb it. For my guys — they’re all letters!

That whole “well, there’s an implied zero minus that because it’s subtracted from whatever you had unless you don’t have anythign in which case it’s zero” .. is fundamentally unfair 🙂

The difference between -3 and zero minus three? Oh, you mean subtract. -3 – (0 -3) … or shoudl the parentheses be there? 🙂 It’s all for naught. Or zero. or something or nothing like that…