One of my Facebook friends asked me to comment on this recent New York Times article.
I decided not to comment in the mass of comments on the original page simply because I don't want to get into arguments or discussions with numerous random people...I already have enough of those on my other pages. So, if you want to read my comments/thoughts on math, they are below:
1) Students are encouraged to use calculators entirely too soon. There is nothing wrong with memorizing basic arithmetic facts. Doing so facilitates the understanding of algebraic (and other) principles later. If you know your facts cold, then you will understand other concepts better later. Those who do not have clearly documented reasons why they can't memorize their basic facts, should. Laziness or "My Mom said I don't have to" is NOT a reason.
2) Being able to perform and remember certain computational tasks by hand (ie. long division) helps to reinforce the "why and how" of the process--but the reasons behind the process must be clearly taught and demonstrated. That helps to reinforce the process and the concepts. Simply teaching these procedures as "arbitrary" magic to be memorized doesn't do anything. The problem is that some teaching the process do not understand it, so they teach it like magic.
3) Teachers are not always prepared adequately to teach concepts in new ways. Much of the "new math" is not so much "new," but rather an attempt to more clearly model mathematical concepts from real world examples. The difficulty is that when you did not "learn" math this way yourself, it makes it a challenge to teach it in a new way...especially if there aren't really good people doing the training on this sort of thing. (Many presenters at national conferences are NOT good presenters or teachers, in my opinion and are only presenting at national conferences to get another line on their vita for tenure at a university where they will never really interact with people who are learning math at the elementary level). Modeling concepts, if done reasonably correctly, helps to reinforce concepts and the "why" behind things. My Dad never taught me my basic facts from flash cards, but I can remember as a 5 year old being asked if I have 5 hogs and I buy 2 more how many is that? Obviously higher concepts need more sophisticated real world models, but hogs I could visualize---symbols on flash cards don't always make sense to kids.
4) Parents get frustrated when their child brings home something they can't understand. Parents who are actively involved need to be made a part of the process...and if teachers know that parents may not understand something the kid brings home for homework, they need to help the parent. One third grade teacher I know (who shall remain anonymous) would copy the "instructions" or "explanation" on the back of homework sheets so that parents who helped their kids could see the instructions on the back. Of course, some parents are clueless. My 8th grade math teacher told me she had a parent (who was a farmer) demand to know why his son was being taught decimals. She asked him if he ever looked at those slips he got from the elevator when he hauled in grain. She should have asked him if he knew what corn having 20% moisture really meant.
5) The "new" math and learning any math really well requires the student to be an active participant in the process. Too many students just want to sit and watch something to learn how to do math. If watching someone "do math" was sufficient to learn it, we wouldn't have the problems we do. Students also don't like it when they are frustrated or don't understand something--they don't like to be confused. Well in order to learn something sometimes you have to be confused before you can really understand it.
6) Standardized tests, multiple choice or other wise, are a crock of (@#* that only subsidizes testing companies, gives state bureaucracies too much power, and allows some administrators who probably haven't taught in 20 years to hold the test over everyone's heads.
7) I'll stop now....but I do have a few more thoughts but I feel like I am rambling...so I'll stop.