why not delay math?

[ElizaG]

To me, *formal* means "intentional, regular, deliberate, and methodical."

That's more or less how I understand it, too, at least when it's used in a phrase such as "formal math instruction."

 

There are all sort of ways to build mathematical understanding in ways that are intentional, regular, deliberate, and methodical" that have nothing to do with seat-work. I can't say how much value we got out of shopping in the produce aisles combined ith deliberate and intentional questions. If these real life activities are "methodical" are they formal or not formal?

I think, as parents, we can be deliberate and intentional about (informally) teaching a lot of things. If I tell my preschooler not to lick the grocery cart, and then extend the conversation to talk a bit about germs, I wouldn't call that formal hygiene instruction. It certainly isn't regular or methodical.

 

If children play with C Rods and base-10 "flats" I'd this formal or not formal?

The children's play itself isn't formal, from their perspective. They're just exploring their home environment. But the fact is that they wouldn't be doing this unless:

 

1) someone had designed and manufactured these formal items specifically as a method of teaching about math, and

 

2) someone else had purchased them and put them on the shelf, presumably for the same reason.

 

We really do not need to choose between two bad options. One being forcing developmentally inappropriate work on kids who are not ready for it, and the other of letting them rot. There is a rich alternative of creative engagement, and that is the best path.

There are multiple alternatives to the extremes you describe. One would be "creative engagement" that includes some combination of planned lessons and dedicated math manipulatives (self-teaching through the exploration of a prepared environment, in Montessori terms). Another would be "creative engagement" that does not include these things, but is intentional and deliberate about taking advantage of math-related teaching moments as they come up in the context of real life. There are surely others as well, but even between these two, I don't think we have conclusive evidence as to which one is the better choice for primary and elementary aged children.

 

 

That aside, my main reason for posting is to bring up something that hasn't been talked about yet in the thread:

 

What were the children in the experimental group doing, during those hours when the children in the control group were doing math?

 

Benezet seems to have credited much of their success to the addition of these specific classroom activities, rather than to the absence of math instruction in itself. I think this is very much worth exploring.

 

ETA a few excerpts:

 

"... concentrating on teaching the children to read, to reason, and to recite - my new Three R's. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language."

 

"The children in these rooms were encouraged to do a great deal of oral composition. They reported on books that they had read, on incidents which they had seen, on visits that they had made. They told the stories of movies that they had attended and they made up romances on the spur of the moment."

 

"The formal arithmetic was dropped and emphasis was placed on English expression, on reasoning, and estimating of distances."

Edited April 16, 2012 by Eleanor

[birchbark]

How did I miss this thread? *Sigh* I started a similar thread recently but didn't get nearly as many responses!

 

Which I think is what the study in question is really asking about. The kids in that study who had delayed instruction did not just catch up to the normal group - their problem solving skills were actually better. Why would that be? The questions it raises for me are: whether our systems tend to try and teach some concepts too early and so actually stunt real intuitive number sense and problem solving ability later on - this seems quite possible because when we learn an abstraction befor the concrete thing it represents it is often difficult for the brain to really marry the two up; and possibly more seriously, whether giving children the abstraction or formalized notations can actually, in itself, condition the way in which they take in the concrete experience, and perhaps limit it.

 

I think Bluegoat nailed it. I think the issue is not delaying math, but working on mental/conceptual math in the early years as opposed to working on abstractions on paper from the get-go. There are curricula for this: Ray's, The Verbal Math Lesson, and Making Math Meaningful.

[Catherine]

I'm pretty sure my 10 year old would have been that child. He has struggled mightily with math. I think it is a big leap, unsupported by good evidence, that all children will intuit time-telling, multiplication, and fractions without any instruction. Given how much my child struggled with these topics, at 8 and 9, even WITH instruction, I just don't believe all children intuit these topics. Well, I'm not being clear. At 8, he struggled to learn to tell time, even with considerable instruction. It took us many months and a lot of practice.

 

The problem with any plan to delay instruction until the child is "ready" is that some children, those with learning challenges like dyslexia or limited working memory, will not benefit from this delay, they will just be that much longer in catching up.

[bluemountainmama]

I am also trying to make a decision regarding delaying math. I am very intrigued by Benezet's work, but I plan to use mainly Waldorf. I'm wondering if math is taught in the whole to parts, practical way that Waldorf approaches it if it might be better to go ahead and start slowly. My teaching materials say something like learning math teaches concentration and diligence. Maybe this would be the point of starting something earlier rather than waiting until it is easier later? Or could these habits be aquired another way without the risk of ruining her mental math skills? I haven't "taught" any math yet. My daughter is almost 6 and can multiply, divide, estimate measurement and work with fractions all from practical experience. She would fail a standardized test because she has no idea what those things look like on paper, but orally give her a recipe to triple or ask her how much each ticket is if the whole family based on what bill I gave the teller and how much I got back and watch her go. The question is would math instruction enhance this early learning or squash it? And if I don't do the Waldorf math blocks, what will we do instead? I think the math blocks are there in part to give a break from language arts so I'd want the replacement block to serve that function.

[happybeachbum]

 

http://www.inference.phy.cam.ac.uk/sanjoy/benezet/index.html In the article it's not arithmetic that's postponed, but formal instruction. Just looking at article two shows that arithmetic isn't gone.

[Ellie]

Ellie, I read the article. I saw a man experimenting on school children in ways that I do not agree with. He suggested teaching one to three 'mathy' concepts per year through sixth grade and then finally getting down to business.

 

I noticed the date of the article. The dawn of the progressive era was a horrible time for using children as guinea pigs in schools. My grandmother went to a school where they were first experimenting with whole language learning and informal math, and she never did learn math and English skills very well. Grandpa went to an old-fashioned school and studied Algebra and Latin in 8th grade. He was only one county away from his future bride, but they went to school in two different universes.

 

But the second section of the article shows that there was actually lots of arithmetic instruction going on.

 

ITA that experimentation can lead to non-education and woefully illiterate children. The U.S. is still feeling the affects of the failed sight-reading and whole-language debacle. But this article really outlines a pretty comprehensive foundation in basic arithmetic for elementary-aged children. And I was impressed with the English skills the children achieved while taking a slower pace at math.

[Lang Syne Boardie]

 

But the second section of the article shows that there was actually lots of arithmetic instruction going on.

 

ITA that experimentation can lead to non-education and woefully illiterate children. The U.S. is still feeling the affects of the failed sight-reading and whole-language debacle. But this article really outlines a pretty comprehensive foundation in basic arithmetic for elementary-aged children. And I was impressed with the English skills the children achieved while taking a slower pace at math.

 

Hey, now, you quoted something I said a year ago. LOL I'll have to find out what we're talking about and why I said what I did, and see if I still think that....I'll reply in the spring of 2014.

 

 

 

 

 

 

Just kidding. I think I do remember this, and if I failed to fully read the article and get the details I'm afraid I'm notorious for that. It's a really bad habit. I know you and I generally agree on philosophy for both Math and English, so if you tell me there's more to it than I gathered in my initial impression I'm willing to believe you.

[happybeachbum]

It's a very interesting article and I kind of wonder if we try to shove to much math on children before they are ready. 

[SweetMissMagnolia]

don't remember the "program" or whatever but I have read about delaying formal studies until the child is a little older--how do I feel about it? I guess it depends on the situation and the child.....I don't know-I'll have to stew on it a bit and come back and respond...I don't see a problem with it-I mean it makes sense....

[go_go_gadget]

I mean, seen a kid whose math instruction was delayed and who then later caught up and became really good at it?

I am not saying it is impossible, I just have never observed it. The kids whom I have personally seen whose homeschooling parents delay math education never caught up and ended up behind and struggling. Algebra 1 at age 17 is not a disaster, but not what I consider a particular success in math education if the child has no developmental issues.

So this whole "delay a few years and then the kid will breeze through because he is ready" may work in theory - just not with the kids I've seen. I'll be happy to hear examples to the contrary.

 

My math education wasn't delayed in elementary school, but in all of middle school I learned essentially nothing (not unusual, I think), and because I left high school to go a CC at 15, I wasn't forced to go further with math, and didn't. I took elementary algebra at 20, in a self-paced, self-taught class (an instructor was available for questions and to administer tests as needed), so there was a six year gap between math classes for me, and a ten year gap between math classes I learned anything in (50% of my life). Learning on my own was what led me to the math love, and in June I'm getting my undergraduate degree in pure math. I apply to graduate schools this fall. I'm never going to be a big player, but I'm ''good enough'' at it to be able to achieve my goals. I don't know if these circumstances are the kind you're interested in, though.

 

However, I don't believe in delaying unnecessarily. If a child balks even at a gentle, play-based introduction to math then clearly the child isn't ready. But for any child that doesn't balk, I can see no benefit in delaying. It may well be true that absent any special abilities a child taught addition at five and a child taught at 10 will be equal in addition skill as adults, but the child who begins at five and makes continual progress will obviously have the option of going farther in their math education than a child who makes continual progress after starting at age ten. I think the same thing about the Waldorf ideas about teaching children to read: sure, they'll probably end up being equal skill-wise, but the child who reads fluently at six will have the option to have read three years' worth of books more than the child who reads at nine, assuming all other factors are equal. There isn't enough time in life to read all the wonderful books, but I'd rather my kids have those three years to make a slightly larger dent. Forcing them would be counter-productive, of course, but I don't advocate forcing, either.

 

Likewise, I will never catch up to my fellow students who began their higher math education at 17 or 18 instead of 27 (the age I was when I took calculus). They're not necessarily smarter than I am, but assuming that we progress at the same pace, they have those ten years that I never will.

 

For my own kids, I like things like RS and Miquon, and BA a bit later. 

[MistyMountain]

I do not believe in delaying math. I personally need a curriculum or something to work with. It is great that people talk about math a lot and incorporate it into life really informally without a curriculum and that works for them. I would rather have something to work with. I do want something that takes the kids ages in mind but I don't like to plan things out or come up with things on my own and I don't naturally talk about math all the time. All the curriculums I know start out using manipulatives and explaining the concepts for a great while so the kids understand the operations before they expect them to just know the facts. If I could go back I would have actually started incorporating math into daily life even earlier with my kids. We know that the more a parent talks to their children and the more books we read to them or they read that the higher they score in verbal ability. Taking some time to work on math with kids however that is done either formally or informally will not cause harm but I think doing the opposite can for some kids. Some kids need a lot of practice ad exposure to master math. Singapore has some of the highest math scores in the world. They don't delay math.

[mama27]

I mean, seen a kid whose math instruction was delayed and who then later caught up and became really good at it?

I am not saying it is impossible, I just have never observed it. The kids whom I have personally seen whose homeschooling parents delay math education never caught up and ended up behind and struggling. Algebra 1 at age 17 is not a disaster, but not what I consider a particular success in math education if the child has no developmental issues.

So this whole "delay a few years and then the kid will breeze through because he is ready" may work in theory - just not with the kids I've seen. I'll be happy to hear examples to the contrary.

 

My 14 yo didn't do any formal math till she was 8 or 9, maybe later. So far she doesn't struggle with ANY math concepts. The 2 I have graduated did. And they started Saxon in ps. till 3rd and 1st grade.