Re: Integrated, Connected Math

[Victor Steinbok <Victor.Steinbok@VERIZON.NET>]

>  > >>> arthurhu@ATTBI.COM 09/12/02 09:48AM >>>

Welcome back, Arthur. I hope you don't expect any "old-timer"
rhetoric discount--you'll get hit just like the rest of us. ;-)

>  > Integrated Math? THAT's your problem right there. They've combined a
> >  slew of math across disciplines up to graduate level linear algebra
> >  and statistics across 3 grade levels instead of the old stair step
> >  method of algebra 1, algebra2, geometry, etc. Algebra 1 covers maybe
> >  25% of the content of an integrated math course. Integrated is probably
> >  fine
> >  for kids who can suck down math through a firehose, but it's gotta be
>  > a kick in the pants for anybody else.

Well, I beg to differ here. Integration is more likely to appeal, if
done right, to those who are not overly advanced in math. It does
however require FAR MORE mathematically advanced teachers, which many
schools lack (Art's point below). Moreover, integrated courses are a
disaster with lazy teachers who think they know everything they need
(I've encountered a few who've been teaching EXACTLY the same way for
20-30 years and absolutely refuse to change)--they are the ones who
sabotage the reform process in math.

>  > Now my 5th grader is getting homework from Connected Mathematics and
> >  I'm getting a feel for why parents are up in arms about it across the
>  > country.

For those who have not met Arthur Hu on-line before--it is trivial to
get him up in arms over just about anything, so I am not surprised by
this rhetoric. Compare this to Saddam's "Mother of all battles".

>  > He's spending 3 hours generating some stupid chart of every possible

It is only "stupid" to those who already know what direction the
exercise is going in. I've felt the same way about a number of tools
(software and otherwise), which I found to be trivial. As it turned
out, they were not so trivial to first-time learners. What Arthur
thinks is "stupid" his own kid may find quite entertaining on
occasion (unless he's already been brainwashed).

>  > move in a "factor game", and then extending from 30 to 49, and
> >  answering questions about what would be the worst and best move. It

To be honest, I have no idea what, specifically, you mean here,
Arthur. If you want to discuss the mathematics off-list, feel free.

>  > takes a 70 page booklet to cover what my old 1973 book covers in 7
>  > pages about factors and primes.

Yes, of course, and if you ask around you will find that those who
went through schools with you (or even before you) and who are NOT
software engineers--or other engineers or natural scientists and
mathematicians--will readily admit to not having been very good in
math or hating math or other some such recollection. In any case, few
adults over 25 have much positive to say about math and fewer still
remember any of it beyond balancing the checkbook. In this light, it
seems, those 7 pages were grossly insufficient except for those like
Arthur and me (I used to browse through my math books in June and
never open them the following year).

>  > I'm going to try negotiating to let me
>  > assign my own kid my own homework so he doesn't have to waste his time
> >  with this garbage where you spend too much time and thinking learning
> >  too little math. I assume the parents are too lame to keep me from being
> >  the only parent in the district who's got enough sense to realize
> >  something
>  > is terribly wrong with this stuff.

"This garbage" actually has had a lot of thought put into
it--something you, apparently, are not willing to do.

>  > Try this one out:
>  >
>  > Draw and label 3 circles as shown below. The numbers 12, 15, and 16
>  > have been placed in appropriate circles. Use your factor list to
>  > figure out what each label means. Then write each whole number from 2
> >  to 30 in the correct circle.
> >
> >  12: abundant
> >  15: deficient
> >  6: perfect
> >
> >  b. Do the labels seem appropriate? Why or why not?  c. In which circle
> >  whould 36 belong d. In which circle would 55 belong?
>  >
> >  I peeked in the back of the back - turns out there's a glossary that
> >  says a perfect number is one that is equal to the sum of the factors.
> >  How a 5th grader is supposed to figure that out from the 3 circles is
>  > beyond me.

Gee, Arthur. If you are so mathematically literate, how come you had
to peek in the glossary to find what a perfect number is? Was it
because the definition would not have been found on those 7 pages?
This is ridiculous. The kids are actually learning real mathematics
here albeit in a bit spoon-fed fashion. For most schools thirty years
ago--here and in Europe--this would have been an "enrichment
exercise". Now we have parents complain when their "average" kids do
it. Yup, no progress here...

>  > This would be one of maybe 10 problems per night assigned as homework.

I would be opposed to the quantity of homework, if it only contained
a few questions that made students think. This one is borderline on
this scale--students do have to come up with their own classification
and justify it. The real question is where does the teacher take the
discussion from there, which is why you don't want too much homework
(too many threads to follow).

Arthur, lighten up. There is nothing wrong with what your son is doing.

> Art Burke wrote:
>
> >  Aother part of the problem is that many elementary school teachers
> > lack adequate preparation in mathemtatics.
>  > Art
> >

At 12:22 PM -0500 9/12/02, Kate Nolan wrote:
> Now I must weigh in on both Connected Math and Integrated Math.
> These are some of the best mathematics  programs I have encountered.
> Both of my daughters used them and both are highly successful in
> college (Sarah studies Political Science at UW-Madison, Hannah
> studies Geophysics and Environmental Studies at BC).

One thing that contemporary parents often refuse to accept is that
their kids might be "average" or below, God forbid. So I am always
skeptical when a high school graduate or a parent tells the world
that the math book was at fault that somehow the content did not make
it into the student's brain. There was one Andover, MI, graduate who
whined all the way to Congress that CorePlus pilot she was subjected
to had left her mathematically illiterate. My response would have
been--you should have paid more attention in class.

I can vouch, however, that a particular program CAN be a contributing
factor to someone's success, and, in case of your daughters, it may
or may not have been the case. I suppose, it's kind of like
professional sports--players get the credit for success, coaches get
blamed for failures, even when there is no evidence that either one
is true.

> Rather than falsely separating out areas of mathematics, these
> approaches teach students how to use tools from a variety of
> disciplines to solve problems.  Their dad, a mechanical engineer, is
> thrilled with this approach, and wishes more of the new engineers
> and techs he trains were able to use an integrated approach.

Uhm... The areas of mathematics are not separated "falsely", not even
"artificially". The real problem is that US curriculum puts up false
walls BETWEEN the areas, which are traditionally quite closely
entwined. "Integration" does not refer to simply presenting material
en masse, without any content differentiation. It simply means that
parts are related within the whole.

> I once (1991-1996) conducted several years of research into
> mathematics around the world.  Only 2 countries used the "separate
> the math into algebra, geometry, trig, calculus, data/stats"
> approach--the US and the former USSR (which abandoned the practice
> in the post-Soviet era).

Being somewhat rather directly familiar with math education in the
former USSR, I can unequivocally state that their model of math
education was nowhere nearly as differentiated as the US model. Only
two strands were separated--Algebra and Geometry--by grade 6 (now 7
out of 11). Even though the subjects were split up, they were still
INTEGRATED. Not only that, the presentation of topics and content was
closely coordinated with the chemistry and physics courses ALL TAUGHT
CONCURRENTLY through last year of secondary school (along with
biology, but that's another matter). For example, the coordinate
system in Algebra appeared at the same time as vectors were being
discussed in Geometry and just before forces were being talked about
in physics. So, when students learned about forces, momentum, etc.,
they could use the vector notation, and when dealing with vectors,
they could place them in a coordinate system. That's integration,
even though the courses were split by subject matter. No such
integration can be found within even individual schools in the US,
let alone any kind of national curriculum integration--everyone wants
his own piece of the pie.

> The integrated approach is used in France, Netherlands, throughout
> Scandinavia, Hungary, the Czech Republic, Germany, Japan,
> Singapore...you name it.

You will find that the approach in Hungary, Czech Republic and many
other European countries closely parallels the old Soviet model.
Germany and France had always had their own and Scandinavians may
also follow the German model. So the issue is not just integration,
but the KIND of integration.

       VS-)

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