When you see a gentleman bee round a lady bee buzzin'

[austin_dern]

We had the second exams for the term this week. I wanted to have them last Friday, which would have been just at the two-thirds point of the term, but apparently there was some kind of religious holiday or something that many students found distracting. I can be reasonable. The exam scores worked out to be almost identical this exam as the last one, in both classes, although fewer people were taking the tests. I had thought these exams simpler, and with I assume the weaker students having withdrawn I'd expected averages to be higher. So that's a little disheartening. Or I was just writing harder than I figured.

However, there was some moderately alarming news in the Introduction to Algebra class. This is algebra for college students, so, yes, I'm not fully convinced that anyone here has seen an equation before. But I had worked at describing the procedures starting from addition and subtraction of fractions, and going onward, to the point that we were solving such word problems as ``the circumference of a circle is (this), what is its area?''.

One problem is that a lot of students apparently had no idea what the little center dot meant. This is the vertically centered dot used to represent multiplication where one wants to emphasize that it is multiplication, without using the x symbol that gets confused for the variable x. Quite a few didn't know what to make of it and they seem to have treated it as a subtraction sign.

Worse from my perspective is that they seem not to have gotten the order-of-operations idea. I know we covered this; I went over it in class, and I'm careful to explain the order whenever I do a problem on the board, and I do a lot of problems on the board. This isn't even anything that requires careful thought; it's a fixed procedure whose rules you just have to follow, and if you follow them, you will get the correct answers. But when I have an appreciable fraction of the class turn something like

8 - 5*(2*x + 1)

into

3*6 - 3*x + 1

it's enough to bring despair.

Trivia: Apollo 13 Astronaut Fred Haise had flown for NASA since 1959. Source: A Man On The Moon, Andrew Chaikin.

Currently Reading: Pirates of New Jersey: Plunder and High Adventure On The Garden State Coastline, Mark P Donnelly, Daniel Diehl.

Comments

[http://users.livejournal.com/_fluffy/]

how

how do they get there from there

im just uh

[austin-dern.livejournal.com]

Well, that's a synthesis, but glitches like that happen.

My reconstruction the reasoning for this one would go like this:

1. The 3* follows spotting the 8 - 5* and mistakenly reducing that to (8 - 5)*, or 3*.

2. The 3*6 follows from seeing the (presumed) 3*(2*x + 1), starting the distribution by making 3*2 into 6, and then writing down the distributed 3 times the interior 6.

3. The 3*6 - 3*x would then go from breaking up the 2*x as if it were 2 - x. The distributed 3 times the -x would indeed be -3*x.

4. The +1 comes from the last part of the parenthesis, which is after all a +1. The 3 has already been multiplied in so there's not any 3 left to multiply into.

I can understand making any of these glitches, although making several of them in one problem is amazing, and these are after all people in college. Of course, they wouldn't be taking this course if they were comfortable with the reasoning that needs to be done to avoid them all.

[moxie_man]

Having spent 30 months teaching an intro to weather lab course that "required" knowledge of basic algebra in my grad school days, NOTHING surprises me anymore when it comes to students who lack a clue. And this was back in the days when one line scientific calculators cost over $50 and the graphic plotting ones were first coming out if you could spare $200+ for one.

I'm sure you've read my rant before about the students who didn't know their own names for a pop quiz. Bunnyhugger has even seen the quizzes in question if I recall. I think I scanned them once. Three quizzes that came in with the same name, but different handwriting. No, seriously.

[austin-dern.livejournal.com]

I do remember the famous own-name pop quiz. I haven't had a students-not-paying-attention incident quite of that magnitude; failing to recognize things on a test is at least understandable.

I need to find ways to get the ideas practiced into them.

[porsupah.livejournal.com]

I'm.. amazed. That wouldn't even have let them pass GCE O-level, let alone A-level, generally a prerequisite for University. Nobody thought to test their result with some modest value of x, even?

I don't think I'd be looking forward to teaching them about integrals and differentiation..

[austin-dern.livejournal.com]

Well, this isn't university either. This is community college, and especially, the kind of class people take because they didn't learn this stuff before, or they took mathematics classes so long ago they can't be expected to remember them. It's a course meant to cover deficiencies needed so people can reach freshman levels of mathematics.

However, yes, integrals and differentiation are a long, long way off.

(Some of the students did check their results, although if they made the same mistakes consistently with a value rather than the variable x, they'd get results that seemed to check out.)

[bunny-hugger.livejournal.com]

I don't think they should be giving people high school diplomas if they can't do basic algebra, but I'm a notorious crank on academic matters.

[austin-dern.livejournal.com]

I'm not sure they should. However, I don't know that any of these students had high school diplomas (there are GED programs on campus), and I also don't know how long any of them have gone without using algebra. Like any skill, if untended, it'll tend to decay, although it seems like it should need a lot of neglect to decay this badly.

[bunny-hugger.livejournal.com]

Well, I thought you might say that but I'd say the same thing about the GED. If you accept that a high school education should include mathematical skill through basic algebra, and if you accept that the GED should prove one has the equivalent of a high school education...

Indeed, I looked up the official site and have found that the GED's mathematics component includes the following:

"Number operations and number sense; measurement and geometry; data analysis, probability, and statistics; algebra, functions, and patterns."

http://www.acenet.edu/Content/NavigationMenu/ged/etp/math_test_descriptio.htm

[austin-dern.livejournal.com]

Right, but if the program is to get people their GEDs, then, they have to get the background in whatever they missed out on earlier. I don't know with certainty that any of these students are going for GEDs, although, if they have got a high school or equivalent diploma then they're in really desperate shape.

[bunny-hugger.livejournal.com]

Oh, I see; I somehow misunderstood you to be saying that these students had GEDs instead of high school diplomas. Well, if it's true that these are folks who are studying to take the GED, then my complaints have to be rescinded.

[austin-dern.livejournal.com]

Ah, all right. I probably could've been clearer about what the program was for to start with.