I found A Mathematician's Lament again, and realizing I had never finished reading the essay, I did. Plenty of LOL moments reading it.
The first big LOL moment was the part about the difference quotient on page 15. I definitely do that in my Honors Algebra 2, and the students hate it. I don't think it's necessarily a bad thing, but maybe I could present it in a different light so that it's not just "another boring math problem to solve because you'll eventually see it in calculus."
Then, there was the description of trig as "masturbatory definitional runaround." My first thought was that's an interesting word choice. Why would that comparison be made to trig? I then looked up the definition of the word, which also means excessively self-absorbed or self-indulgent. I guess that makes sense considering a person would be quite self absorbed when he's, well, never mind.... I just would love to teach that word to someone and have them use it in an English paper.
Simplicio exemplifies all of the same concerns I have. Do we put students at a disadvantage if they don't have basic arithmetic and algebra skills? And are we just creating an excuse for students instead of pushing them to actually learn how to do it? I get that calculators and computers can do a lot of this stuff now, but isn't an understanding of how the processes behind them work important?
Then, again starts the butting heads of educational philosophies on Twitter.
This Paul Bruno article and this one from AJC showed up in my feed on Friday and Saturday, promoting research that teacher-directed instruction is more effective than student-centered instruction, especially for students with math difficulty.
My response: No shit Sherlock! If most standardized tests and traditional classroom tests test a narrow set of skills, then of course explicitly teaching the students how to do what's on the test is going to result in higher scores.
The question becomes: what do you sacrifice for higher scores? Are we trying to train monkeys, or are we trying to teach students to love learning, think, and grow. Do we want students to learn math or learn to pass math tests? Do we want bored students playing (or more often not playing or playing poorly) the school game or do we want students conjecturing, discussing, arguing, productively struggling, and truly engaging in meaningful learning? Furthermore, I think we need to ask do these students really have "math difficulty," or are they just not good at taking tests?
I get a lot of complaints in my classes for "not going over" or "not reviewing" things enough because I do more student-centered activities. When I would try to do games or activities in the past (which I reduced significantly over the past few years in lieu of tasks), I would often be asked "Can't we just do a worksheet?" When summative assessments comprise the entire grade for my students, can I really blame them? My scores are sometimes lower than I would want, but the "aha" moments that happen in class are so powerful.
I really feel shitty when I make my students cry and when they feel bad over a test. Even though I've emphasized how mistakes help us grow and that I don't think anyone is or ever should think of themselves at stupid, I think the number at the top of the paper speaks much more loudly than I can. If I could find ways to affirm the things that they are good it and push them to keep learning, improving, and expending true effort, things would be a lot better.
Yes, I want my students to feel successful. But I want them to be able to more than pass a test that I've prepared them for. How many students go into a shell as soon as they see something that "we haven't learned" or "we didn't go over?" when they probably could do it. That's what I want my students to able to do: to actually APPLY and TRANSFER their knowledge. And I'm not sure you can do that if class is just example, example, worksheet, repeat, and then "study guide" with "problems just like the ones on the test." Sounds more like training monkeys to me.
So what are the options? Different assessments? I can do it more with my Algebra 2 Honors course since I'm the only one that teaches that, but in order to make more headway, I would need to convince more people, especially ones I teach common courses with. Plus, it's the regular students that would need it the most. My assessments would need to reflect growth and continuous improvement rather than a narrow set of skills.
And then the final question: if I change the way I assess and if I change my definition of what being good at math looks like, am I making it better for students, or am I just cheating?
