People eventually figured out that such instruction just wasn't going to work. Here we are, 40 years later, and we're going to do it again:
In 1961, New Math “was supposed to transform mathematics education by emphasizing concepts and theories rather than traditional computation,” as this article shows.I believe Mr. Bonagura, a fellow teacher, to be correct.
Flash forward 50 years, and Common Core is today making the same promises:
The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.New Math, Sequential Math, Math A/B, and the National Council of Teachers of Mathematics Standards also “promised to transform (America’s children) into young Einsteins and Aristotles,” writes Bonagura. It didn’t work out that way...
With so much focus on teaching students the “why” of math, teachers will have little time to teach the “how,” Bonagura predicts.
Mathematical concepts require a high aptitude for abstract thinking — a skill not possessed by young children and never attained by many. What will happen to students who already struggle with math when they not only are forced to explain what they do not understand, but are presented new material in abstract conceptual formats?“Instead of developing college- and career-ready students, we will have another generation of students who cannot even make change from a $5 bill.”
Additionally, I agree with this statement from the linked post:
Despite claims that Common Core doesn’t tell teachers how to teach, the new standards come with a flawed pedagogy, Bonagura charges. “Common Core buries students in concepts at the expense of content.”Repeat after me: would you like fries with that?
I can't speak to every math student, but what I can tell you is ... I began to understand math, to be able to do it, to advance, and to eventually teach it when I had a teacher who was patient enough to make sure we knew why things worked ... algorithms and memorization have their place (times tables and long division, for example ...) But there is plenty of time in class to develop full understanding of why things work, to show the logic, and to rebuild on the previous day's lesson ... unless, like so many math teachers, you use the class time to let students do 'home'work ... I always felt uncomfortable doing that ... My thought was always ... "Shouldn't I be teaching now?" Memorization and practice is obviously preferable to some ...but, not me. I fight this with my daughter every time I help her with her math homework ... "Daddy, can't you just tell me how to do this problem?" Yes, I could... but what good would that do, save finding the solution to that problem?
ReplyDeleteAnd ... i realize i didn't actually address the practicality part ... yes, everyone should be able to make change ... that's predominately an elementary level skill that should be taught along with all the basic functions. And, it isn't a 'why', it's a 'can you'... I was referring to the more conceptual mathematics of Algebra and beyond ... which are dependent on having memorized basic mathematical operations ...
ReplyDeleteI also remember messing with Venn diagrams and expressing numbers using different bases. I still remember one story problem that left me amused.
ReplyDeleteIt seems to me the current "fad" is probability.
Yes, please.
ReplyDeleteOnce you to teach the "HOW", the "WHY" becomes more understandable.
ReplyDeleteJMHO of course
...Mark
KauaiMark ... i think once you know the 'how' , you don't need to know the 'why'. I think deriving theorems is really important ... Because even if you can grasp the 'how' first-- and lots of kids can't-- the 'why' reinforces it and builds understanding, even if the student could have just applied a formula and been done with it ... Not to say that that means lots of group based discovery learning, though, occasionally it works.
ReplyDeleteFor those kids capable of, and motivated to do,the REAL college-prep math track, conceptual understanding is important. I'd be happy if all kids of low-average ability or more had a solid grasp of the traditional k-8 arithmetic, without calculators; addition, subtraction, multiplication, division, fractions, decimals, percentages and a basic understanding of mean/median/mode, standard deviation. That's far more than many current HS grads can do
ReplyDeleteAnd sales tax and making change
ReplyDeleteK-8 teachers have been much better about calculators, recently ... but it drives me nuts when I'm helping her with her pre calc homework (so, as a sophomore, she's clearly above average), and she whips out her calculator to multiply a single digit number by a two digit ... and I can do it in my head faster than she can get it on her calculator. I try to make that point ... but I've taken to just not helping her until she surrenders the calculator to me. She gets to use it, when I deem it necessary. I must say, though ... textbook producers have not made a great case for themselves by making so many numbers unreasonably cumbersome, when the skill you're trying to teach is, let's say algebra 2 level, and you're using numbers like 2 3/5 and 6.54. At that level, you should be teaching the Alg 2 concept, not arithmetic. I think the reason why they are doing that? Is the arithmetic is not being taught well when it should be.
ReplyDeleteAs a New Math survivor, I can tell you that I can do basic functions almost as quickly as my students can do on computers. What I cannot do is fathom why my shorter different series of solutions are wrong even when they get the right answer. This is why I hated math after fifth grade and why I never excelled in anything but Geometry, which made sense because it relied on logic.
ReplyDeleteI recently attended a conference where I had the opportunity to chat with a couple of people who have definitely drank the kool-aid of CCSS. One was a (former?) NCTM director. I asked him point blank how CCSS was an improvement over the previous situation (NCLB), considering that they would still be giving students assessments which have no direct impact on their grade. His reply, in effect, was that the silver lining of CCSS was the pedagogy, meaning that CCSS institutionalizes the NCTM-favored approach (group work, discovery learning). However he agreed it was not optimal to assess without offering credit toward a course grade. A similar response was made by Sol Garfunkel (a nationally-known author of mathematics texts), who said he was once a contributor to CCSS in the early stages. He was asked during a Q&A session what he thought of CCSS, to which he replied that he was dissatisfied with what it had become, and the only part that he liked was the pedagogy (group work, discovery learning).
ReplyDeleteIn hindsight, it seems the mathematical progressives used CCSS much the same way that the democrats here in CA used redistricting: as a vehicle to help them achieve other, larger goals.