Monday, November 27, 2006

I'm more afraid of the midterm than they are...


Tomorrow is the fall midterm for my Algebra 2 Honors class. It covers everything from the start of the year: the real number system and its properties, solving equations with rational coefficients, everything about functions and graphical analysis, systems of linear and non-linear inequalities, and 3x3 systems of equations. That's quite a large chunk of material for anyone, let alone students who were below grade level less than 2 years ago.

DCP students are notorious for being able to do well in the short term, but completely falling apart in the long term (>3 weeks or so). Traditionaly, the majority of a class will get a C or an F (no Ds at DCP!) on a midterm or final, even if they had been doing well all along. We haven't figured out yet how to help them do better on large cumulative exams. Sometimes it feels like their brains are a cup that can hold a fixed amount of liquid - as soon as you pour more in, the rest splashes out to make room. For this reason, final exams are only 10% of the class grade in all freshmen classes, and it goes up by 5% a year. We need our seniors to be prepared to take college classes where the final is 25 - 30% (or even more) of the grade, and to understand how significant that is.

I don't know if their retention problems mean that they did not really understand the material in the first place, or if it means that they still don't really understand how to study (or how you need to study differently for this kind of exam), or if there is something else going on. I was helping a student review today, who admittedly has been struggling to do well, but usually has a pretty good sense of what's going on. He got confused on a problem, so I posed a simpler problem (or so I thought...) to try and help him understand. I wrote on the board: if f(x) = x + 2, what is f(3)? He looked at me like he had no idea what I was talking about. Honestly, I am amazed by this. I have no way to explain why he couldn't answer that question. I do have one observation: when students are struggling with one difficult concept, they seem to be unable to access previously learned concepts at the same time, even if they could use that concept well in a different context. Maybe it's like being able to toss and catch different objects individually with no problem, but dropping them all when trying to juggle.

It makes sense to me that students would forget complex formulas or methods over time - this happens to me too. But, if they learned them properly, a little bit of review should bring them right back. However, when students don't recall foundational concepts (I had a calculus student once ask me, while studying for the final, what a derivative was), I don't know how to help them, except to implore them to see me for as much extra help as possible.

So, we'll see tomorrow how it goes. I'm predicting a bloodbath, but I hope they'll defy the trends. If anyone has ideas about how to better prepare students for cumulative tests, please share them in the comments section.

Update:
Here are the scores:

10| 2
9| 7
8| 0 1 5 8 8
7| 1 2 2 2 4 4
6| 2 5 7 8
5| 2 4 5
4| 9
3|
2|
1|

Well, as predicted, the scores were much lower than a typical unit test. At least the majority of the class still passed, and my top student is still getting over 100%! She's an algebra machine.

2 comments:

Anonymous said...

When something like this happens to me (not remembering basic definitions just before a test, etc.) it is often the case that I learned the material properly when it was taught but didn't practice working with it enough for it to sink in. Certainly review brings it back, but it might take almost as long for me to get it straight the second time as it did the first time. The more time I spend upfront doing exercises and so forth, the better I remember the concepts in the long term.

I'm also very familiar with the "juggling" issue. The only remedy I know of is to stop for a little while until the mind clears, and then start slowly with the easier problem and work up gradually to the original question.

On the other hand I don't know what to say about your student who didn't remember what a derivative was. Where was s/he all year?

Dan Greene said...

I agree with what you are saying - I guess my question mainly focuses on the idea of what it means to learn something. If you can learn it today and do a bunch of application problems on your own perfectly, but then can't do it tomorrow, did you really learn it? I'm not sure. Then again, not all things learned will end up in your enduring long-term memory. I don't know enough about how the memory works to say any more on this issue. I'd like to look into it more, read some of the research into memory, and see how it applies to curriculum and assessment.