> Why is it that questions from students about different bits of math > cause so much agitation among teachers? > > I wonder how often English teachers get "why should we study > Shakespeare?" I don't know about the often, but I suspect their > answer is that people without passing knowledge of old Will are > ignorant. > > As for trig, those without passing knowledge of trig are just as > uninformed as those who wouldn't know Macbeth from > Macdonalds. Personally, I'd put calculus on the list for everybody > too, and you can't really make much sense of calculus unless you > are comfortable with trig.
> * George Yanos *
The problem with George's take on this issue and his analogy with English teachers and Shakespeare is that no one has the final say on where the line gets drawn (nothing personal, George). As someone who has taught both English at the university level and mathematics (mostly at the less awe-inspiring level of a New York City community college), I'm chary of arguing to students that any given bit of information on their learning plate of the day is essential for distinguishing themselves from the ranks of the ignorant. On that basis, what bit of knowledge ISN'T essential? And getting E.D. Hirsch to put it in one of his books makes the morsel of knowledge not one whit more important. Shakespeare, no doubt, is such a giant that total ignorance of his work impoverishes one in an attempt to grapple with aspects of the writing of many authors. Yet I'd guess that I've read much more Shakespeare than most Americans and yet there's much of his work I've not yet read. So am I Shakespeare-knowledgable or Shakespeare-ignorant? SHould I include a list of which plays and poems I've read at least once?
More to the point, any kid who is going to read Shakespeare (even a single play), is unlikely to do so just because her teacher states or implies that failing to do so is an indication of being unlearned. And the same goes for any particular bit of mathematics. How much trig is enough? Will a student who firmly believes he'll never attend college (or won't take more than the barest minimum of college math) really buy "You need to know this for calculus"? I'm skeptical, to say the least.
I've had some success with remedial math students by taking certain topics in a given course and finding some connection to things in their lives that are already important to them. After doing that several times, along with other things that reduce the intimidation factor and help build trust between teacher and students, I've found them more willing to struggle with some other piece of mathematics simply because I ask them to look at it. I prefer, of course, that students get excited about the math on its own merits, because they find it intellectually engaging, and for a host of additional reasons. But it doesn't always happen that way. ANd for some students, I'm not able to find a connection or perspective that works for them. Having tried sincerely to do so, I feel like I've done my job.
Of course, a completely different slant on the original question in this thread might be to require that students who wish to be relieved of responsibility for knowing something have to make a convincing argument as to why they should be so relieved. They must demonstrate sufficient 'research' to show that they actually know what it is that they "want out of" and have well-considered reasons for being allowed to skip over it. Perhaps the process of having to think about what's contained in the particular area of knowledge will help them see its value. Or maybe they'll convince the teacher that they should indeed be able to opt out. But that would be scary, wouldn't it? Maybe we're better off just telling them that we know best. That argument from parents and teachers always won the day when I was in K-12, so I'm sure it's just as impressive today. -----------------------------------------------------------------
Michael Paul Goldenberg University of Michigan 310 E. Cross St. 4002 School of Education Ypsilanti, MI 48198 Ann Arbor, MI 48109-1259 (313) 482-9585 (313) 763-9683 email: firstname.lastname@example.org