...let me count the ways.Below,
Lisa Donlan, parent activist from District 1 on the Lower East Side, leaps into the fray of the discussion raging on the math wars over at the NYC Ed News listserve, where some trashing of constructivist education has been going on.
Philosophically, I am a constructivist, but recognize it requires small classes and some assistance that goes beyond one teacher. And lots of time for kids to explore and learn by trial and error. But in times of test prep mania, there is almost no chance. Interesting that the initial Klein choices were Diana Lam and then Carmen Farina, major constructavist operators. (When Carmen went from big C district 15 Supe to taking over Region 8 there were just a few cultural clashes with my district (14) which had a very old hat teaching philosophy - like from the 5th century.) But they were dogmatic and considered any resistance or questionning their dogma heresy.
So, how did I teach long division? Any way that worked. I remember how I learned it by rote but never had a clue as to what was going on. If you asked me what 356 into 15,000 was, I had I could only get the answer by the long tedious method.
And I got a 98 on the geometry regent and was the only one at Jefferson, which had some pretty heavy hitters, to get a 100 on the advanced algebra regent. So I was no slouch. But it goes to show you the fallacies of standardized tests. Yes, we had test prep and I pored through old regents to study, but never really understood basic arithmetic.
But in my 6 week wonder course in the summer of '67 that turned me into an instant teacher, one instructor did Base 2. And then Base 5. And Base 8. That was an aha moment. I began to see the relationships. Thus, I can tell you in 3 seconds that the answer would lie south of 50 and north of 40. And a few seconds later be able to say it was south of 45. And have multiple ways of making that guess. That gives me an instant advantage before I even start the long division and in fact may not have to do it altogether.
Over the next few years, I really learned math by teaching it. One of my other AHA moments was when I was teaching division of fractions where you reverse the denominator and actually saw an explanation in the math book as to why that worked. I ate this stuff up.
I tried to communicate these nimble ways of looking at numbers to my kids, using charts and number lines. Paperless tests. Did I neglect the times tables? Not at all, as they are the key to so much. But if they couldn't remember them I at least wanted them to have the tools to be able to figure them out. And I taught them the 9 times table trick of reversing 0-9 vertically. Just in case.
So, now it it time for Lisa Donlan to take over with this wonderful piece based on her experiences as a parent:I really am loathe to join in on the Math Wars, but after biting my tongue for dozens of posts, I feel I need to share my experience with the constructivist model as used to teach my own two children and their school mates.
The approach yielded a rich and fruitful learning experience for both of my kids, who have gone on to perform well on tests and in traditional math classes in HS and college.
Today both kids like math, have an ease with computation and a deep understanding of the underlying mathematical concepts they are learning and using.
It may be significant that besides working extensively with staff in this area, their schools also put a lot of energy into training and explaining the approach to parents. As result many of us became informed partners, who could actually help with homework and support the pedagogy.
I can say that the numerous workshops and hands-on math activities parents participated in turned our initial tendency to push back on this new (to us) way of seeing mathematics and see it instead through our children's eyes. The tendency to distrust or critique a different way of seeing number - of adding or dividing, for example, could very well could have worked to undermine the teacher's authority and perhaps negatively affect our children's learning. I could only imagine it might be hard for a child to feel open to a methodology his or her parents are (even unconsciously) undermining at home.
Did my kids spend a lot of time "mucking around" with numbers and manipulatives , drawing and grouping, skip counting and breaking down, even creating emotional relationships with numbers? Did they routinely spend 10 minutes to do what I could do in 2?
Yes. Oh, yes.
Did they eventually learn the traditional methods and algorithms, math facts and times tables, formulae and equations, and learn to perform short cuts for times tests?
Also yes.
For instance they were eventually able to learn how to do the long division I had been taught as a child, and they also learned the very different method their father had been taught in France. Over time, they amassed a multitude of tools to choose from to figure out life's math problems.
When I hear the frustration and critiques of many parents over constructivist math, I sometimes feel the way I do at the soccer field watching kids play.
Very often the kids will dribble too much and lose possession of the ball, make mistakes in tactics, technique and strategy as they learn and experiment, take risks and solve problems.
The adults I see often watch these players with the critical eye of pro game fans, expecting 8 year olds to juke like Ronaldo, or 12 year olds to play like little Drogbas.
It hard not to act like an arm chair coach, or an arm chair math teacher, when we watch our little ones try out new skills.
We would never take a block out of a four year olds hand and show her the right way to build a tower.
We allow her to experiment and learn from the successes and failures of play and mucking around.
Just as there is no right way to make a mask or draw a face, I think there are many ways to learn about and interact with the world, and that includes math.
Like anything else, when a methodology is taught well and deeply and consistently it can work quite well, including child centered developmentally focused pedagogy.
This is only my own personal and anecdotal experience, but I think it highlights just how unlike a business is the business of education.
I am not an educator by training, but there does not seem to be one way, a one-size-fits-all, right or wrong, efficient way to teach all kinds of young minds.
Lisa Donlan
Deborah Meier threw in these comments, where she endorses the concepts of the New Math which is what I was really talking about above:How would you have them "measure" results?
As in the reading wars, we argue about (I think) all the wrong issues. Neither bad math teaching nor bad teaching of reding is what's wrong with American education--although the way we get stuck aguing about these may well be the problem.
Until we solve the depth vs breadth question in math, and stop our obsession with everyone taking advanced algebra/calculus we're stuck with bad math programs. Best of all I liked the "new math" of the 60s an 70s--which were abandoned too soon - largely because of parental complaints like yours! No subject on earth raisesd more hackles--by mathemticians and/or parents.
I like TERC's effort, if not their solution. But then I truly think that the only important thing to teach is a "love" of looking for patterns in numbers , and other patterns as well. We could teach the useful--practical--stuff in 4th grade if we hadn't messed it up by rote learning before that--and you probably think the opposite!! And we can actually both point to experts and evidence. But what we dare not argue about is "purpose".
It's always bound to create a stir! But I'm sorry to see Class Matters get into either of these wars.
Deb
