Gifted Issues Discussion homepage Forums Age or Ability Specific Forums Elementary School how hard would you try to avoid Everyday Math?

Do they accelerate kids who get a high score on the pretest? My DS10's 2nd grade school gave him a math pretest that covered concepts for the year. He got 100%. They were very impressed...and they made him go through the entire 2nd grade math curriculum anyway.

Val

Yes, they will accelerate if the overall math knowledge is high. My daughter is not very mathy so for her it will be a nice way to fill in the holes and move forward as she is ready. She's ahead in certain math areas but not others.

My other dd, (dd7) is accelerated in a program that uses Math Expressions by H. Mifflin. The spiraling is there as well. That's the reason her teacher thinks she'll continue to be ok even though she is still a bit behind (since they will revisit the topics.)

hmmmm... lots of food for thought. We have plenty of time to figure this out - this would not be for this fall. (I'm secretly hoping that they suddenly change the math curriculum in the next year or two - I can dream )

I have pretty detailed curricula outlines from the private school for each grade level in all subjects, so I want to take a close look at those, for math and for everything else. I want to make sure my kids have actually covered all the topics they're supposed to. That's one aspect of montessori that I don't like - I'm often afraid there will be holes (perhaps wrongly).

I haven't asked them about placement tests yet - great question! Also, great point about bringing over current test results. The montessori school is pretty liberal about MAP testing starting in second or third grade, and at least one of the teachers may do it by special request. DD just did her third set of MAP tests this year over the last couple of days, which is funny because I had been thinking of asking the teacher to do that before the end of the year.

Also, I signed the older kids up for a few weeks of summer camp at this school. Ds actually requested a math class instead of a physical outdoor activity. It's grouped by age. I called the person in charge of the camp, and he said I can talk to the teacher about where he's at with math. Supposedly, the camp teachers are the regular teachers, so I'm hoping I'll at least get a little peek at what school would be like, at least for that one ds. DD will be taking creative writing, but most of the rest of the stuff will be non-academic.

Thanks for your thoughts! If anyone else has anything to share on this EM issue, please do not hesitate to do so

While looking into something else tonight, I came across the following:


From http://everydaymath.uchicago.edu/about/research/distributed_practice.pdf

I quite possibly missed something here, because I can't figure out how they made the leap that "spacing" review and practice (is this the common meaning of "spiraling"?) must be at the expense of mastering the skill the first time around (except that they're hoping that not requiring mastery will avoid anxiety about math in the student?) Why can't there be both? Something about the quote makes me feel slightly ill.

Both what? Mastery the first time and later review and practice? But if a course is designed in the expectation that (most, or all) children will master a new concept the first time it is introduced, there would be no benefit in revisiting it later. I suppose you could say that it's useful to do a very brief review of something just to check it's still there, but if a topic really has been mastered, then by definition it'll still be there and you wouldn't want to spend more than a few minutes on checking that. I take this quote to mean that EM is designed so that most children will not master a concept the first time round, but just take a large bite of it, and get the rest the next time round. I know this is unpopular with people here because their children get these concepts the first time round and that's what they see as they "right" way to do things, but bear with me a moment...

... thinking about it, what we might call pulsed learning is indeed how my DS6 learns mathematical concepts that are really at the level that's appropriate for him. (I've seen this recently with various things from proof and logic, e.g. the idea of decidability and the Halting Problem, proof trees, Goedel's theorems.) He reads about it a bit, talks about it enthusiastically, wants to try things out relating to it, has obviously some some correct ideas and some misconceptions. At this stage, he is not always up for discussing the misconceptions; if I try to correct one, he may pay attention for a moment and then fade out. I've learned not to push it, but just to say "that's not quite right, we'll talk about it some time". Then it stews for a while; he may carry on talking about the topic at the same level, or he may stop talking about it altogether. A while later - weeks, months - he'll pick up the book or start talking about the topic again, and off he goes again, enthusiasm intact, to do the next chunk.

Now, this kind of learning provokes anxiety in me, but I have come to think that that's probably a fact about me and my miseducation - like most of you, I always expected to get things completely first time at school, and never met anything challenging enough that I couldn't at that stage. However, what it is very like is doing research, and indeed, I think, solving any genuinely challenging problem, grasping any really stretching concept. Isn't it the school situation of first-time mastery that's unusual, really?

So I think it's very likely that a spiralling approach has something going for it. Trouble is, the idea that a course designer can lay down in advance what an appropriate amount of material to present so that everyone will be challenged enough that they don't get it all, and noone will be so overwhelmed that they give up, seems implausible. Certainly I can't predict that even just for my DS - we just provide the material and see what he takes.

Yes, I mean both mastery and review. Or perhaps a more precise way to say it would be understanding and practice. I think practice is important even where there has been understanding - with some kids, even though they understood the first time, they may not remember it well until they've used it again and again in different contexts. But that's not the same as not understanding it and then being asked to use it in different contexts in the hope that the light bulb will suddenly turn on. What if the light bulb never goes on - a whole lot of learning built on whatever the misunderstood concept was is also going to fail.

I have two problems with the EM approach as set forth in that quote. The first one is about anxiety about math. I can't think of a better way to create more anxiety than to constantly introduce concepts that the students are not likely to understand, or aren't expected to understand. Self confidence is generated by actually completing challenging tasks, not by being allowed to slide by without learning what has been presented.

My second issue with it is more fundamental. A couple of my kids are definitely big-picture-before-the-details kids. Without a context, there are no memory hooks on which to hang information presented. From one angle, EM's approach may sound like it make sense, that they'd learn the info better the next time around when it's presented in a(nother) context. However, kids like mine are less likely to remember anything from the prior experience with the information precisely *because* they didn't understand it (except perhaps they'll recall the uneasy feeling that goes along with not understanding), so the time spent on the information previously may well have been wasted at best, and couterproductive at worst, as it builds a lack of self-confidence with the topic.

I can see the importance of providing a big picture first - I think that can be very helpful for some kids. But I do not think that's what EM does with its spiraling or that that has anything to do with the way EM is set up (just from various things I've read, years may go by before a big picture is evident in EM, if ever). In my opinion, purposely and continually introducing things that the students are not expected to master provides a convenient excuse for a teaching method/explanation/instruction, etc. that just didn't work. If the child didn't understand the first time, then the topic would be better approached differently during the next lesson or during extra help sessions, not six months later in the middle of a new topic. (that's me, the expert on teaching LOL.) So much in math depends on understanding what one has previously learned - I wonder what happens in the meantime before the topic comes back around again.

I think the EM approach is likely to be even more problematic for an average or struggling student than one who understands math easily.

It might be that I really don't know EM well, but this is my take on that quote I found last night. To me, the way you described your ds's learning of new and challenging topics is not analogous to a curriculum applied in the classroom to a broad range of students for a subject in which it is often critical to build on a sound foundation before moving to a new topic. I guess that is the gist of what bothers me - I don't see how a student can learn a new topic if the new topic requires knowledge that they failed to learn during the previous topic. I'm not sure if I'm making any sense...time for more coffee

I haven't yet had the coffee and here I am already editing. I can envision a situation in which the student doesn't understand the bits until it's presented in the larger context (the big-picture-first kid) but that still leaves the first go-round as a waste, at least for that person. For that person, the "backwards from traditional linear curriculum" is not the same thing as spiral learning.

You are making sense, and I don't want to sound like an apologist for Everyday Math, which I don't know nearly well enough to take that role. I do want to write a bit about this point:
Yes and no. Let me witter, but please bear in mind that I'm making a case that I think interesting, not necessarily one I am totally convinced is correct - I'm in the process of thinking about this.

It's really deeply embedded in how we teach maths that we expect children not to move on until they understand. But I really am very far from convinced that that's the best way to teach maths. (I should confess - you may be relieved to hear :-) - that I have no involvement in teaching children other than my own, although I teach adults for a living.) It's certainly not the only way to learn maths - e.g. if one goes to a research conference on maths, with highly technical talks being presented from 9 till 6, absolutely nobody in the audience will understand everything, and yet in order to be getting anything from the conference they have to be getting some understanding even though a full understanding depends on something they've missed. I remember a very hard transition from the school model of not feeling allowed to move on with the tiniest thing unclear in my mind, to a mode of learning like that.

One might respond that this mode of learning is only applicable to adult researchers, but my response to that would be to point at how children learn language. We don't introduce a child to their native language systematically, one word or grammatical concept at a time, refusing to go on until we're sure the child has understood up to this point. Even with foreign languages, we understand that immersion is the most efficient way to learn, even though if you analyse the things that people have to understand in order to become fluent in a language, it looks just as dependency-structured as maths does. When you learn a language by immersion you make lots of mistakes, all the time; you fail to understand basic grammatical constructs, you form false hypotheses about what words mean and how grammar rules work. Gradually by greater exposure you sort it out.

Of course, you have to have lots of exposure to native speakers to make this work: you can't put 30 children with one adult who's scared of speaking German and expect them all to end up learning German! Maybe this is the real reason why we can't transfer this to maths. I completely agree that there's a big gap between what works for one child at home and what works for a class following a curriculum. In fact I'm quite happy to stipulate that EM is (in most hands) horrible.

I do think, though, that when we're paying attention to our own children on an individual basis it's important not to insist on them mastering topics in sequence. I think this is intimately related to the importance of learning by solving lots of problems. If they skip ahead to something that interests them more, fine: let them do problems to do that relate to what they're interested in. If an earlier skill really is essential, then they'll find they have to brush up those skills in order to solve the problem they're interested in, and really needing to understand something for one's own purposes is surely better motivation than just being told that this is what's next.

For me this is all part of letting maths be a real subject, that can really do things and be intrinsically enjoyable in its own right, as opposed to for the extrinsic reward of a row of ticks.

I agree with you on this quite a bit, except to the extent that we're talking about a math curriculum in a classroom, which is the scenario of EM (I'm not familiar with anyone using EM as a homeschool curriculum). Perhaps we ought to compare EM to Saxon, which I don't really know either, but I believe Saxon spirals with tons and tons of review, and might not have this issue that EM has over not expecting understanding. In a classroom setting, there's no reaching forward and then backward via intrinsic motivation. It's external, and it's not individualized. In contrast, I can envision a situation where a student could struggle with a topic, move on to see where it fits in the bigger picture, and then return to it with new zeal to master it, along with far more understanding that comes from context (just such a thing happened with one of my kids) - the mastery did occur, even though it may have been out of the usual sequence (which tells me that perhaps the sequence ought to have been reversed for his learning style). I don't get the feeling that that would be the case in an EM classroom at all.

I'm afraid that EM's allowing kids - especially non-gifted ones - to not understand essentially allows them to not learn things that are ultimately fundamental to their ability to do math. Here's some food for thought that I came across, though I'm not sure I can explain at this late hour why I feel as though it's relevant:

(from ftp://math.stanford.edu/pub/papers/milgram/milgram-msri.pdf)

thanks for allowing me to think out loud - off to bed...

I largely agree with you too :-)

I will not write much but I have to put in my 2 cents because my child has been truly affected by this program along with the older "guinea pigs" who are now in 8th grade. My son is in 4th grade and has had the worst year in math that I have ever seen. He is a math guy and I have never seen him be so bored and struggle at the same time with EM concepts. Last year he was lucky enough to have a teacher to give him accelerated homework to make up for the boredom in the classroom. However, this year his math teacher says he is spacey, lazy, sulky and makes many mistakes - thus "he must not know how to do the work in the first place so why should I give him harder work". Along with the idea of learning a concept, moving on and then coming back to the previous concept to tie it all together they must explain EVERYTHING in written language and if this is not done they are penalized on tests. He has been doing horribly on tests and it is creating problems between he and I and also his teacher and I. Another concept of this program is that children who are at higher levels will be able to serve as role models to the other students and will help bring those other students up. This is explained under the companies explanation of Connected Math (which is used in middle school to help connect children who used EM to the transition into high school). And there have been many negative stories because the philosophy of EM does not match up with high school math. At this moment our middle school in NJ is on the watch list for math after taking the NJASKs(our state test) and many feel it is because of the connected math. My son has always been so bright in math and numbers have come so easily to him and it is just fading away into this slow process which kills me. I am actually going to be sending him to a private school for 3 weeks this summer which teaches a traditional math class and will assess him and teach to his level. The woman who runs it also had a daughter who went through EM and said she would never have her do it again. When my son gets assessed I will not be surprised to see that he has fallen behind the other bright children who have been learning traditional math. I am not saying it is all bad but especially if you have a child who just gets it and has a wonderful natural ability it may not be where you want to be. But this is completely my opinion. I'm just waiting for this year to be over so we can start anew and maybe advocate for something different . Good luck with your endeavor.

Jules