The funny part of partial products is that I have seen some of their examples where one adds the partial sums using the traditional adding approach with carrying.

Oh, that is rich!

Unbelievable.

-- CatherineJohnson - 11 Jun 2005

As for a conflict between the two math programs, the difference is not too great yet at the end of third grade, Everyday Math has fallen behind, but the supplementation (mastery practice) helps.

I'm very interested to hear this.

This has been an ongoing concern for me: will what I'm doing here at home 'conflict with' what is being done at school.

By 'conflict' I don't mean will the material conflict, but, rather, will my son's starter-knowledge of the material get jumbled up inside his head.

One complaint I'm hearing from parents in constructivist curricula, which I believe, is that the kids are asked to do problems so many different ways that they are bewildered.

OTOH, I was also curious to see, with Christopher, whether the fact that he was being taught two completely separate curriculum, in two completely separate settings, by two completely different teachers, might be an advantage.

It seemed possible to me that this rather odd set-up might work against PatternTraining.

Of course there's no way to tease all these factors out, but Christopher has done very well this year, and survived a pretty huge jump, in the middle of the year, from 'Phase 3' to 'Phase 4.' (Not just survived; he's done well.)

So I'm feeling that teaching this separate curriculum has not confused him, and has helped . . .

-- CatherineJohnson - 11 Jun 2005

Thank you SO much for taking the time to post all of this. I'm going to pull it up front on Monday.

Readership of all blogs is down on weekends, and I want people to see this.

I'm very interested to hear your take on private school.

This had been my strong suspicion, just from conversations with parents who have kids in private schools.

I'm surprised to learn, though, that your teachers have been through ed school.

What is the percentage of private school teachers with ed degrees; do we know?

Around here you do see, in private schools, teachers who've never set foot inside an ed program.

-- CatherineJohnson - 11 Jun 2005

"I agree that they have to get used to variables and equations as soon as possible. Next question: how soon is that?"

I don't know. I think that teachers can introduce variables with the balance beam or balance scale model of the equation very early to solve very simple one variable problems. I've done it (unscientifically) with a number of kids and they don't have any problems. I prefer to use traditional variable names (x,y,z, etc.) than using question marks. However, in the earlier grades, it should all be about mastering the basics; add subtract, multiply, divide, fractions, percents, ratios, and so forth - without calculators.

"I'd love to hear more about your experiences with Singapore Math versus Everyday Math: how have you done both at the same time, how did you make that decision, how did you choose Singapore, do the two ever conflict or does Singapore help with E-Math--I'd love to hear more!"

He gets Everyday Math in his private school - supplemented, they say, which is another issue. Most schools seem to supplement the bad math curricula rather than admit their mistake and go to a program like Singapore Math. I think that it's easier to supplement a NCTM-type math program (badly) that to replace it with something that would be hard to get past the NCTM-influenced faculty. You can't get away from it in private schools. Most of the teachers are trained in ed schools and have been indoctrinated.

He is in a private school because our public schools still use MathLand(!) in a full-inclusion, child-centered, spiraling (circling in some cases) setting. They don't care about the above average kids because they have no influence on getting the "high performing" rating on the trivial state tests. That is why 25 percent of the kids in our town go to other schools and that is why our IEP percentage is at about 22 percent. Sometimes my wife and I can't believe that we are spending lots of money to get Everyday Math (I don't know of any school in our area that uses Singapore or Saxon Math) - and that we have to supplement! If we put him back into public school, then we would have to make up so much more.

As for a conflict between the two math programs, the difference is not too great yet at the end of third grade, Everyday Math has fallen behind, but the supplementation (mastery practice) helps. The difference will be more of a problem in later grades. However, my son knows how to do carrying and borrowing and I expect him to understand anything that Everyday Math throws at him. He doesn't see any conflict in the two programs. He does hear his father grumbling (sometimes loudly) about EM, but so far, no conflict.

For example, EM is bound and determined to do things differently than the traditional algorithms. Not better; differently. They like to do everything left-to-right, rather than the traditional right-to-left. You can see this in the partial sums and partial products algorithms. Perhaps they don't want to overload the kids brains with carrying and borrowing. Actually, I think they call borrowing "trade first and then subtract". Perhaps they think that a left-to-right approach can be better applied to making estimations. This is not a bad idea, perhaps, but learning the traditional methods didn't stop me from learning how to estimate using left-to-right techniques - in my head, of course. The funny part of partial products is that I have seen some of their examples where one adds the partial sums using the traditional adding approach with carrying. Can you imagine using the partial sums approach on all of the partial products?

If you want to learn more about the justification of EM, see the following paper by Andrew Isaacs.

Algorithms and Everyday Mathematics

http://everydaymath.uchicago.edu/educators/references.shtml

It is very poorly justified and they don't deal with issues about how much content they cover and how much mastery they expect. (Let alone the common practice of supplementation.) I have had a few exchanges with Andrew Isaacs on other forums about these issues and he sticks right with the party line.

-- KtmGuest - 11 Jun 2005

I'd love to hear more about your experiences with Singapore Math versus Everyday Math: how have you done both at the same time, how did you make that decision, how did you choose Singapore, do the two ever conflict or does Singapore help with E-Math--I'd love to hear more!

-- CatherineJohnson - 10 Jun 2005

Oh, and I'd like to know what exactly the Singapore authors believe they're developing or gaining with bar models.

Oh, and I'd like to know what exactly the Singapore authors believe they're developing with bar models.

As I say, I can tell that my brain is 'different' after having done 300+ bar models, and I think it's different 'in a good way.'

I'll have to finally write up my bar-model induced revelation about the nature of subtraction . . .

-- CatherineJohnson - 10 Jun 2005

• whether bar modeling does develop 'spatial ability' (I have to put 'spatial ability' in quotes because I have no idea what it is, or whether I'm using the correct language)

I would love to know

• whether bar modeling does develop 'spatial ability' (I have to put 'spatial ability' in quotes because I have no idea what it is, or whether I'm using the correct language

• whether graphs also develop 'spatial ability' and, if so, whether they do it just as well

• why Singapore specifically decided on bar modeling, and whether the bar models are crucial to their success

-- CatherineJohnson - 10 Jun 2005

Another sort of problem that doesn't lend itself to bar modeling is this one, that Catherine pointed out to me:

A parking lot has motorcycles and cars. There are a total of 23 vehicles in the parking lot, and 86 wheels. How many of the vehicles are motorcycles?

Catherine commented to me that 'this problem defies bar modeling'. The reason is that the quantities one is given to deal with are incomparable; the first equation is in units of vehicles, and the second is in units of wheels.

It might be possible to tie yourself in knots, in order to do the problem with a bar model. But by the time a kid is ready to do this problem, he's ready to use equations.

-- CarolynJohnston - 10 Jun 2005

KtmGuest^?,

good point! You could probably turn yourself inside out and do that problem with bar models, but why would you?

I agree that they have to get used to variables and equations as soon as possible. Next question: how soon is that?

-- KtmGuest - 10 Jun 2005

You have to watch out for techniques that may work well for some situations or for "nice" numbers, but make life difficult in other cases.

For your bar modeling problem, what if the weight of A and B combined is 100, the weight of B and C is 80, and the weight of A and C is 120. How would this be done with bar modeling? It is a very simple problem if it is done with equations.

Please don't get me wrong, I love Singapore Math and use it with my son who just finished 3rd grade. He get Everyday Math at school and I see first hand the difference. I just think that it is important to get him used to variables and equations as soon as possible. As for any spatial/3D development with bar modeling, I don't know. I would rather focus on the different classes of equations and having my son be able to graph and visualize their shapes. Then again, he just finished 3rd grade and I am more worried about having him master the basics.

-- KtmGuest - 10 Jun 2005

BarModelingVsGraphing

Go check out interesting comments on bar modeling versus graphing by a Ktm Guest here. (Scroll down to the Comments section.)

I'd love to hear what others think.

My curiosity about the history of the Singapore curriculum is now so intense I realize I'm going to have to see if someone there will do an interview . . .

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