Studying Young Minds, and How to Teach Them (reviews, IEP, educators)
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A lot of research-based curricula are moving in a direction to encourage number sense in children. I was actually just writing about this in another thread about Chicago Math. What's important to know is that children are developing pre-math skills very early, but they may not be able to execute symbolic equations. For example, the article references young children working on division. What they are really doing is grouping manipulatives. Using one-to-one correspondence, they can make equal groups of equal size from a larger quantity. That does not mean that they could understand that same problem if presented symbolically as 20/5 = _____ . However, grouping is an important skill that will later help them to understand division.
We've actually had the research to inform such instructional decisions for some time. Twice Five Plus the Wings of a Bird, a BBC production from 1986 shows how researchers documented the development of mathematical thinking in children. They essentially found the same patterns as described in the NY Times article. The trouble has been bringing the research into classroom practice. Many adults want rigid adherence to the teaching methodologies that worked for them, even if newer methods are easier to learn, more developmentally appropriate, and more fun for kids.
I read the article last night and thought that most of it was rather obvious. Doesn't everyone already know this? was my thought. But I must disagree with it still. They are playing absolutes still in the article, stating kids will and won't by a certain age. That is the number one issue. Those connections are made individually at different ages and can happen much sooner and at a faster rate with proper instruction. One example was were they were saying it took them three months to get the kids to count to 7. If the school had really wanted to, they could still play the fun games and have all the kids counting to 20 and be able to know what number they are looking at in a week. I've seen IEP children learn it in a week so there goes the theory that they can't learn faster.
One thing that really gets me is the fact that these people who are all coming up with this informtion are all just doing a small bit here and there. None of them seem to have enough logic to bring it all together and look at the big picture. They need to start with the study on 9 month old chimps that was done that proved that baby chimps know more than 9 month old human babies. The report does not say anything more than more studys need to be done to figure out why but that it quite obvious why We have become so advanced that we actually believe that we are so much smarter than any other species we can't stop for a moment and learn from them. Chimp babies are smarter because mother chimps start teaching their baby skills from birth, something we are so much smarter about now that we "know" our babies can't learn anything under a year old and we have all these "experts" putting out all these articles stating that our childrens minds can't do certain things by a certain age. That is the very first mistake. If we are teaching them from bith, and I'm not talking about doing anything more but naming what they see and touch throughout the day, the kids will have a strong foundation to learn from. Instead of saying the word block over and over when our child places one in our hand repeatively, we should be saying, that is an orange cube, that is a red rectangle prism and so on. They benefit from seeing that things are not all the same and from the full sentences being spoken to them.
That is what I mean when I say that eduction is watered down. Schools are set up on all these absolutes, following the trends of modern child psychology, and instead of using big words, we believe they can not understand them so we replace them with small ones, regardless of the fact that most kids can concure the meaning as long as it is used in a sentence and the word is repeated often enough. If a child can learn the word plant, why isn't it possible for them to learn the specific plant name? That one is from my own experience...calling all the weeds inthe yard weeds. Then one day my 2 year old starts pointing out poison plants as well as others in the yard and starts naming them to me, and knew to stay away from poison ivy, which the next year he remembered and pointed out to me not ten inches for my hand. DH had been telling him the names of the plants everytime he asked what one was. The kid knew which ones to stay away from, and which ones were even safe to eat, though DH had also taught him he could not place any in his mouth unless he asked each and everytime. (Once he asked if he could eat a piece of pineapple weed and I said I didn't care. I'd set him in a patch of it next to the car while preparing for a trip. I didn't realize he ate a bunch until we got on the road and the kid had to pee every half hour (its a diuretic) I didn't not realize he was sitting in so much of it and didn't realize he was asking permission to eat not must one.) Now most would say that a 2 year old, regardless of iq should not be learning these things for safety reasons. What if the child were to put one in his mouth he thought was safe? Well the chimp mothers teach their babies and they aren't killing them with nothing more than knowledge. The problem is that human parents usually don't know how to teach their kids such things effectively and their kids learn to not listen. The thing I worry about is that someday we will need to rely on the those natural skills of teaching our children and being so disconnected, our species will only suffer because of it.
A lot of research-based curricula are moving in a direction to encourage number sense in children. I was actually just writing about this in another thread about Chicago Math. What's important to know is that children are developing pre-math skills very early, but they may not be able to execute symbolic equations. For example, the article references young children working on division. What they are really doing is grouping manipulatives. Using one-to-one correspondence, they can make equal groups of equal size from a larger quantity. That does not mean that they could understand that same problem if presented symbolically as 20/5 = _____ . However, grouping is an important skill that will later help them to understand division.
We've actually had the research to inform such instructional decisions for some time. Twice Five Plus the Wings of a Bird, a BBC production from 1986 shows how researchers documented the development of mathematical thinking in children. They essentially found the same patterns as described in the NY Times article. The trouble has been bringing the research into classroom practice. Many adults want rigid adherence to the teaching methodologies that worked for them, even if newer methods are easier to learn, more developmentally appropriate, and more fun for kids.
You did a great job in that other thread explaining Everyday Math, which another poster called fuzzy math. It took me a while to see what a great number sense my students were developing with ED Math.
You did a great job in that other thread explaining Everyday Math, which another poster called fuzzy math. It took me a while to see what a great number sense my students were developing with ED Math.
Have you looked at what happens when these kids hit high school math? EDM was designed for kids who won't go on to algebra and that becomes a self fulfilling prophecy. Some methods are springboards to higher learning, while others just a means to get an answer now. It is the former that we need to be teaching our kids.
Only one district in my area, successfully, uses EDM. They have a two inch binder of enrichement for each year and spend two years in middle school on a bridge program between EDM and a standard high school math track. They put a lot of work into making it work. They took what worked and fixed what didn't then put in a bridge to get kids on the right track for high school. Unfortunately, that's not how most districts do this and it's not until their kids start failing algebra that they realize something is very, very wrong.
It's been a long time since I researched this. We spent 3 years fighting the school board on this one. They, finally, admitted it was a mistake this past year. Now they're backpeddling trying to get the kids who are in middle school now ready for a standard math track. Fortunately, we pulled our girls from the school when it became apparent they weren't going to dump it soon enough. My girls came up through Singapore math and are a couple of years ahead of their peers. I feel for their friends though. This is painful to watch.
You should know that mathematicians and engineers across the country stand in opposition of this program because it does not prepare kids for higher level math. Parents like it though so it's a tough fight. It's not until they see their kids struggling with algebra that they realize the mistake.
Here's a detailed assessment of EDM. The first link reviews 2nd grad and the second 5th grade. I see their grades have come up to a C and a C- respectively. It was a D program when our schools adopted it 5 years ago. This is our first year getting out of it.
At what ages can and should we learn what material?
Well, it turns out that much of what we were taught over the last few decades (or thought we were taught, I grant) was in error. Or even wrong!!
An interesting article presenting an even more thought-provoking topic.
Just had the time to read the NY Times article. Interesting, in that it's all the best teaching practices that many of us early elementary educators have utilized for years.
I would like to add that in my experience, one of the most valuable programs to augment math instruction in early childhood is Calendar Math which gives young ones a good number & place value sense with hanging blocks, bundling sticks, assorted permeations with coins, & the various equations that equal a certain number. In fact, Calendar Math can be so involved or so simplistic any given day.
I was shocked when my son was three or four years old and could easily look at a pile of cookies and tell us how many each of us in our family should get. I thought he was a total mathematician... turned out he just liked cookies and did not want to get gypped.
We use Miquon Math, which has been around since the '60s. It's very hands-on, and I'm thrilled that my third grader can do large mental math sums and equations in his head. Not thrilled that he can be a walking calculator, but relieved that he seems to really understand age-appropriate math. He's already learning things like x(y+z)=(xy)+(xz). I know that Miquon was written for public school classes... I wonder if any schools still use it now. Excellent, throrough program, IMO... I believe that he will be well prepared for Singapore Math fourth grade next year.
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