kitchen table math, the sequel: calling all math brains

## Thursday, September 6, 2007

### calling all math brains

Any suggestions you may have about afterschooling geometry would be more than welcome.

More than welcome, because.....Irvington has purchased and is now implementing a new geometry text!

From Glencoe!

That's Glencoe as in Page-Splatter Glencoe. Glencoe Geometry, New York Edition ISBN: 0-07-873320-0.

yippee

So....moving right along.....we see, linked to a real-world problem on geometric properties of class ring design....a box!

Many companies that sell school rings also offer schools and individuals the option to design their own ring.

Excellent!

And, on page 90, a Key Concept:

Five essential parts of a good proof:

State the theorem or conjecture to be proven

List the given information.

If possible, draw a diagram to illustrate the given information.

State what is to be proved.

Develop a system of deductive reasoning.

One year from now, this will be my life.

That's one year from now assuming I manage to figure out some way to teach enough pre-algebra so my kid can maintain a B average in his "accelerated" math class this year.

speaking of which

I've already left this anecdote in a Comment, but this one belongs front and center. Here it is:

I was talking to a math-brain friend here in town.

Probably some of you recall that until a couple of years ago, for reasons now lost in mists of time, Irvington had 4 math tracks.

Phase 1 was the slowest; Phase 4 was the fastest. Kids were placed in a Phase at the beginning of 3rd grade in 3rd grade; that is to say, at the end of 2nd grade kids went into the track in which they would be expected to remain for the rest of their school career. Which meant that at the age of 8 my own child, placed in Phase 3, had been placed out of calculus in senior year without the school seeing fit to mention this fact to his parents.

Naturally I had always assumed that Phase 1 was SPED. I mean....I knew what was going on in Phase 3; it wasn't advanced work. I knew what the kids were doing in Phase 4, which was the same thing the kids in Phase 3 were doing along with some Math Olympiad problems the parents solved over the weekends. Then there was Phase 2, a whole other level also more or less doing the same material only slower..... which didn't seem to leave much room for a Phase 1 for regular-ed kids. A normal class divides into thirds: fast, medium, slow. Statistically speaking, the fourth track had to be outliers, which meant it had to be kids with real learning disabilities.

Talking to my friend, I said something about the teacher who taught the SPED kids in Phase 1.

She said, "Phase 1 isn't special ed."

"Yes, it is," I said. "It's Phase 1." I may not know much about statistics, but I have absorbed the concept of a normal distribution.

"No," she said. "Phase 1 is just kids who aren't any good at math. Or math isn't their thing." Then she told me one of the Phase 1 kids at the high school had just scored a 94 on Regents (algebra 1 & geometry)

Talk about it's always worse than you think.

We've got an entire lowest-possible-level class for kids with no discernible learning disabilities, no classification, no nothing --- an entire class of kids who, apparently, are simply assumed to be "no good at math" or "math isn't their thing."

"How the hell did that happen?" I said.

She didn't know.

................................

This really is worse than I thought.

I've always thought the Irvington bell curve needs to be picked up in toto and simply moved down the field.

The fast kids take geometry in 8th grade; the "big middle" takes algebra; etc.

Turns out we don't even have a bell curve.

Is there a name for a distribution that has a huge bump at the bottom? I'm sure there is.

Anonymous said...

Maybe Harold Jacobs' math textbooks.
http://www.pahomeschoolers.com/jacobs.html

http://www.amazon.com/Geometry-Understanding-Harold-R-Jacobs/dp/0716743612/ref=pd_bbs_2/002-6825010-0056045?ie=UTF8&s=books&qid=1189128314&sr=8-2

Anonymous said...

Or Aleks.com

Anonymous said...

I'd call that distribution "dysfuctional teaching", but it's probably just me

- Andy Lange

Catherine Johnson said...

lol

yeah, me, too

I have Jacobs, Moise & Downs, and thanks to the "Book Fairy" I have a copy of Jurgenson, too

SteveH said...

Your link to Page-Splatter Glencoe talked about their Pre-Algebra book. My son is using the latest edition: 2008. There is page-splatter, but not a ton of gratuitous graphics, AND, it's a whole lot better than Everyday Math! Everything is relative.

It's one self-contained textbook, it follows a careful progression of topics, there are many examples right before the homework exercises, and there are links backwards from the exercises to appropriate examples.

It seems a little bit slow in introducing new topics, so I hope that the teacher moves right along. Like many curricula, there is a good chance that the teacher will not get to important material at the end of the book. This is the first year they are using the book (after using CMP), so we'll see how it goes.

Seventh grade math seems to be nowhere; it's not arithmetic and it's not really algebra. Perhaps it's a good chance for schools to get everyone up=to-speed for the attack on algebra. My impression is that if math in K-6 is taught well, then kids could go directly into algebra. Even with pre-algebra in seventh grade, so few students are properly prepared for algebra. Something is very wrong. Math is not THAT hard and there is plenty of time. They can't blame this on kids, parents, or society.

Anonymous said...

re: steveh's comment about middle school math -- yes, I have no idea what all that time is spent on, and this is one of the things that concerns me about figuring out the education plans for my kids.

Anecdote, with a huge grain of salt: I was accelerated several years in math in the elementary grades such that they gave me the 6th grade book in 4th and let me take pre-algebra with the 7th graders in 5th, and they let me skip the 8th grade pre-algebra class altogether so clearly that wasn't necessary to algebra (IIRC no other kids in my class jumped over that class, even after they took the 7th grade pre-algebra class in 7th grade, though I think a kid or two in the class behind me did.) Now, if you were to ask me what was in that 6th and 7th grade book that I did, I don't think I could tell you, though I suspect decimals and percents were probably involved. These were also my first hardcover math texts, which was a big deal to me since we mostly used consumables for non-reading subjects in elementary school (since our families paid for our texts).

I remember having done a small specifically fractions book for at least some of the year in 3rd grade. And in 2nd grade I had a cool paperback black & white text that had a running space/aliens comic book in it and most of the story problems were themed. :-) (That would have been 1981-2, and I believe the content was multi-digit arithmetic.)

-m

SteveH said...

So, the question is what's the big deal about algebra in 8th grade? Why do so many educators think it's normal that so few take algebra in 8th grade. Perhaps they just can't believe that their assumptions and curricula are so screwed up.

Our 4-8 grade principal (who is much more flexible about ability grouping) said that there is still a lot of resistance by lower school teachers against setting expectations in math (or any subject). Grades K-4 are all about socialization and getting along. The low grade teachers pace everything based on the slowest learners. Some students will survive this and excel, many others won't. When you get to fifth or sixth grade without knowing your times table, it's hard to recover.

There is time to recover, however, but it's much more difficult to do. They think that math is a "filter" because of drill and kill. Actually, math is a filter if you don't drill and kill.

Catherine Johnson said...

There is page-splatter, but not a ton of gratuitous graphics, AND, it's a whole lot better than Everyday Math! Everything is relative.

definitely

every once in awhile I REFLECT on my motives for getting into all this (not too often!)....

cognitive science tells us introspection is mostly bosh; we have no idea what our motives are

that said, every once in awhile it strikes me that one of my goals has been a preemptive strike against fuzzy math in the middle or high school

we now have a brand new set of expensive Glencoe algebra books & expensive Glencoe geometry books

we're not going to be buying Core Plus

I can live with that

Catherine Johnson said...

otoh, I can't live with \$100 calculators

nor can I live with the fact that we're spending a fortune in property taxes not to even CONSIDER Saxon, Foerster, Dolciani, Moise & Downs, or Jurgenson

if we're going to spend this kind of money on our schools, we need a voice

we don't have one