I really do oft reflect happily about our Math courses being taught for understanding, and speculate that I’d find another job if they weren’t.
Summer courses… ugh. Tech math so they’re allowed to use calculators for everything, including algebra problems like z/2 – 2/3 = -1/3z + 1/6 . No, there’s no context where you’d ever use this. No, there’s no meaning attached to any part of this. We just have to practice entering the numbers into the fraction-capable TI-30X . It’s not working particularly well because the symbols have no meaning, so knowing which numbers to do what with is all “what’s the rule?” not “does that make sense?” So when the student added the 1/3z to both sides, student then added 2/3 to *that* number, not the 1/6. Hey, the rule is they have to be “like terms.” I am watching learning rules not work as well as understanding… and helping the student survive the requirement instead of learning math 😦 It’s small consolation that this is a man with a great work ethic and yes, he’ll learn what he needs to learn in context, reasonably quickly…
Resource Room Dot Net Blog 
howardat58
June 26, 2017
I am confused with the term 1/3z
It looks as though it means “one third of z”, in which case it should be written (1/3)z
Maybe the printer cannot cope with fractions
Separately, if this is an equation then multiplying every term by 6 keeps z intact and makes things a lot easier.
3z – 4 = -2z + 1
They can still screw it up!!!!!!!!!!
xiousgeonz
June 26, 2017
Oh, that was me being imprecise. On the computer it’s 1/3 as a fraction and then z in the middle.
The big problem is they’re not teaching things like “clearing the fractions.” They’re teaching “plug it in to the calculator, these are the rules, except for here when you need to know different rules.” If you hit 3 (fraction key) 1 (fraction key) 3 that enters as 3 r 1 r 3 which you *might* recognize really means three and a third. Then you can punch divided by 2 (fraction key)) 3 (fraction key) 4 and it will give you the answer as 1 r 7 r 33 which you write on your paper or type into the computer as 1 and 7/33.
If this were what I did for other classes… I’d bail. Anybody could do it.
Happily, *most* of my day was helping people in contexts where we were learning math, not how to punch a calculator…
howardat58
June 27, 2017
Like !!!
Algebra doesn’t have fractions ! Of course American algebra is different.