I know I've touched on this before, but I just can't let it go. I was reading a book entitled Math Wars by Carmen Latterell. This title is just another in a long list of books trying to figure out why American students are lagging behind the rest of the developed world in math? At the end of the book there is a study quoted that deals with the mathematics knowledge of American elementary math teachers and the knowledge of those from China. I feel that a summary of the results would be enlightening to many.
The researcher asked the two groups of teachers the same math questions. For subtraction questions 100% of American and Chinese math teachers could perform the problems, but only 17% of the American teachers could explain why subtraction worked, whereas 86% of Chinese teachers could. For multiplication questions, again both groups could solve the problems, but only 39% of American teachers could correctly identify why an incorrect algorithm (e.g., a formula for finding the "nth" term of a series) they were shown was indeed wrong, as opposed to 92% of Chinese teachers. With fractions, only 43% of American teachers could perform a computation involving fractions, while once again 100% of Chinese teachers could. Not one single American teacher could then create a word problem to represent the computation, while 100% of the Chinese teachers could. Apparently there were even more tests done, but Latterell decided not to include this data since the results were even more dismal for American teachers.
The interesting part of all this is not that the American teachers could not achieve at the same level, but rather that the American math teachers in the test had taken three times as many math courses in University as the Chinese teachers. The problem? Low standards. In grade five, my math teacher had us memorize up to and including our "10 times tables." He would not allow us to continue on in the unit until we could demonstrate to him that we knew every product off by heart. As a result I can still perform basic multiplication in my head. In contrast, my Language Arts (English to some of you) classes had us do a book report on Mice At Center Ice... twice (once in grade four and again in grade seven), and build "concrete poems." Is it then a coincidence that I did not know what a pronoun or preposition was until I was 22 when I bothered to search the definitions out on my own? How am I supposed to not end my sentences in prepositions if I don't know what a preposition is in the first place? How did I get Bs and As in English for 12 straight years yet not know that I was wanting in the most basic understanding of English grammar? How am I supposed to now teach my own students what was never taught to me?
I do not mean to attack American teachers. My preposition problem was the direct result of the ineffectiveness of the Alberta school system; a school system that is supposed to be one of the best in the world. My blame is directed squarely on the notion that to "keep kids in school" by passing them through and handing them degrees for just showing up is a good idea. As I was explaining to a friend the other day: students usually achieve up to but no higher than their expectations for themselves. I expect great things from myself, and so I will work hard to make my reality match my expectations even when I initially am achieving well below standard. However, a person who only feels he or she is a 50% student will only work hard enough to get a 50%. Teachers can dumb the curriculum down until we are handing out As for twelve-year-olds who can tie their shoes, but it won't matter. The weak students will only tie their shoes correctly 50% of the time. But, raise all the standards and the students will work harder to achieve the 50% they feel they deserve, and in the process will end up knowing more.
I'm not advocating that we make teachers responsible for teaching more information, we've done that already and our graduates are as dumb as ever. I'm advocating for more stringent standards on the information already being taught. Streamline the curriculum and cut out the concrete poetry and other garbage like learning to tell time on a 24 hour clock. Then, demand more perfection on the remaining concepts.
For example, in high school math in Alberta, the students are required at the beginning of grade ten to buy $100+ calculators that have the ability to graph functions. Then, in their final year of high school math, these same students are told that by using the "log" button present on a $9 Wal-Mart special calculator they could have solved any complex problem (ex. 2^x = 83.5, solve for 'x') that they were using their graphing calculators for. What a joke!
I'll end this now before I go ranting all night. My final point is that a great majority of teachers' educational woes could be solved if all teachers would demand more perfection from their students. 70% is not good enough. Little Sally and all of her classmates coast along through the elementary grades thinking they're doing alright at math because they aren't "failing." The teacher seems fine with this because Sally isn't as bad as Little Jimmy, who for some reason seems incapable of grasping even the simplest concepts. So, Little Sally sails on through elementary school and then is punched in the face with algebra, trigonometry and statistics in high school. She fails miserably and wonders what happened? "I used to be good at math" she says to herself. No you didn't Sally, you were actually pretty bad, but your teacher couldn't bother to tell you that you lacked the basic skills necessary to succeed at more advanced math since you were achieving more than 50% on his arbitrary grading scale. Don't let Sally get punched in the face anymore. Demand perfection.