tag:blogger.com,1999:blog-2750355884816556227.post7426735423488608991..comments2023-04-15T06:16:25.962-05:00Comments on Long tails of \int_e^r est: And I Ask Myself, How Do I Work This?CalcDavehttp://www.blogger.com/profile/14039458440867020542noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2750355884816556227.post-83679673770038813312010-10-12T03:02:50.711-05:002010-10-12T03:02:50.711-05:00One of the main changes I'm doing this year is...One of the main changes I'm doing this year is purposefully aiming my teaching at the next-to-highest quarter of every class. I read some research somewhere (don't ask me to dig it up) which said teachers usually aim at the next-to-lowest quarter of students, and I worry that this approach not only dumbs down math into this horrid boring collection of meaningless procedures - it also communicates low expectations which make students set low standards for themselves and therefore work less. <br /><br />So I haven't found raising expectations to be a problem. What IS a problem, however, is finding the time and competence needed to create rich problems suitable for all or at least most students in class. I teach psychology as well as math, and so in statistics it's easy to get student interest with a "do men or women have higher IQ?" problem which opens into standard deviation, correlation (husband and wife?) and pretty much whatever else you'd like. How do I do that in calculus? <br />If I had a background in natural science, it wouldn't be difficult - I suppose - but can/should we expect mathematics teachers to be well-versed in a variety of fields outside mathematics?<br />Meyer's WCYDWT stuff is very good, but am I mistaken or is it mostly aimed at "lower" math such as linear equations and systems of equations? It also works by creating a quite superficial curiosity (who REALLY cares how fast it takes to run down an up-escalator?). In contrast to Cornally's approach using fascinating problems from physics (http://101studiostreet.com/wordpress/?p=1271 for example) Dan's stuff is entertaining and open but little else. In both cases however, you need the kind of time and skill on your hands that few teachers possess. <br /><br />My solution so far is to focus on rich mathematical problems - with less emphasis on real-world context. This is working out OK except some students simply don't care about math that way. I don't know how to reach them.<br /><br />So ultimately I'm saying that it's not just low expectations - it's also lack of teacher time and skill - which are the big obstacles to how teaching math in a creative and rich way. And that's a hard nut to crack.Julia Tsyganhttps://www.blogger.com/profile/04354702485097004759noreply@blogger.comtag:blogger.com,1999:blog-2750355884816556227.post-41881279493114930782010-10-12T01:31:04.266-05:002010-10-12T01:31:04.266-05:00Glad to know my Mazur tweet made sense--and resona...Glad to know my Mazur tweet made sense--and resonated with you. And your point about teachers not remembering how to grow plants is an emperor-has-no-clothes moment. If I don't know how to solve a problem, I'm probably afraid of what will happen if I turn my students loose on it. It's much less risky to have them memorize and follow recipes.Derekhttps://www.blogger.com/profile/08592511479434162146noreply@blogger.com