kitchen table math, the sequel: 11/18/07 - 11/25/07

Saturday, November 24, 2007

Christmas books


Looking at this list, I don't necessarily see joy and euphoria breaking out Christmas morn' when folks open up their dog-eared Amazon Marketplace copies of War of the Worlds and Deluxe Transitive Vampire.

I will have to do better.

* question: Do I have the nerve to wrap this up and give it to C. for Christmas?

Some Horses

Lynn G put me onto Thomas McGuane's book Some Horses.

A wonderful book. Perfect! Whether you know anything about horses or not.

coming right up:

books I'm getting people for Christmas

3 categories:

  • books they'll like
  • books they won't like but ought to
  • books they might or might not like, but I'll read them if they don't

It's a family tradition.

Wednesday, November 21, 2007

being horizontal

John Perry has a fancy web site!

I am not left-handed, but I have another less well-known situational handicap. I am a horizontal organizer in a world set up for vertical organizers.

The main mark of a vertical organizer is the ability to make use of filing cabinets. These people use filing cabinets to store materials in that they intend to use just an hour or a day or a week later. When they need that stuff again, they reach into the filing cabinet, pull out the folder and resume working on it.

It probably seems pretty silly to the vertical organized reader for me to be going on and on about how filing cabinets are used, but I think the horizontal organizers may never have actually realized how the other half lives and may find this account completely incredible, so let me go on for a minute.

Yesterday I was working on a letter to the Palo Alto Medical Clinic explaining why my bill is screwed up and I don't owe them as much money as they think I do. It's pretty complicated stuff, and I didn't finish by the time I had to leave. A vertical organizer would have scooped this stuff up, and put it in a file to retrieve later. Had I done this, there would be a bare spot on my desk. These bare spots are the mark of vertical organizers. They are a dead give away.

Now of course that is not what I did at all. I left the letter on the desk, with the materials spread out. Actually, it is not exactly on the desk, because some other ongoing projects were already be spread there; the letter and supporting documents are on top of half-graded papers, half-written lectures, half-read brochures and the like.

The fact is, I am a horizontal organizer. I like all the things I am working on spread out on a surface in front of me, where they can beckon me to continue working on them. When I put something in a file, I never see it again. The problem isn't that I can't find it (although that has happened), but that I don't look. I am constitutionally incapable of opening a filing cabinet and fishing out a half-finished project to resume working on it. I do use filing cabinets. They are for a) storing finished things that one plans never to look at again and b) putting things that one would feel bad about throwing away but has no intention of reading.

A Plea for the Horizontally Organized
Be sure to check out the designer credit in the lower left hand corner.

I am a horizontal type, too, the only difference between me and John Perry being: I am not organized. I'm just horizontal. My stuff is, I mean.

lion love


Be sure to watch to the end.

You aren't going to be able to do that dry-eyed.

Tuesday, November 20, 2007

NEA weighs in on Who Wants to be an Engineer?

The NEA has always been quite helpful in providing parents with guidance on how to teach their children what isn't being taught in school, so I was delighted to see that they are offering online brochures on a number of topics.

Parent guides on a number of topics, including helping your child with math are available here.

I was particularly impressed with the guide on what children need to know to become engineers.

Here are some excerpts:

"What do kids do in a technology class?
They think about and solve problems like:
• Cleaning a polluted lake or river
• Creating an invention to solve a household problem
• Designing and building a habitat for a unique
Second-graders might design and make a home for
their favorite bug. They would draw a plan (complete
with measurements) and use boxes and other
materials to build the home. They would have to think
creatively about how to keep the bug in the house,
how to provide water and food, and how to make
sure the home was the right size for their pet."

Silly me; I thought for sure they would need to learn something about bugs in their science classes. But, after all, we’re talking about future engineers here. Mere facts are of no use in the modern day classroom.

"Fifth-graders might design and make their own paper
airplanes. They would test them to see which ones
flew the furthest or the highest and then revise the
design to see if they could make a better paper
airplane. They would use mathematics, learn aviation
science, and practice reading and writing skills
throughout the design process."

Just curious; what type of mathematics would they be using other than measuring the distances? Also, any clue about how “aviation science” would be used? I don’t think I have to ask about reading and writing skills used throughout this activity. Writing: How I Feel About Today’s Assignment. Reading: Various essays about paper airplanes in a rascist world.

"Eleventh-graders might investigate the idea of
growing plants in a hydroponic system (without soil).
They would design, build, and test the system. They
would study the effect of this type of growing on the
environment and figure out whether this system was
more cost effective than growing plants in soil. They
would become engineers!"

Yes, it’s axiomatic that when students design, build and test hydroponic systems, they grow up to become engineers. No one really knows why, but there is a flurry of “action research” taking place in our classrooms to find out.

Wait. There’s more!

"When those juniors in high school study
hydroponics, they think creatively about ending
hunger and about how to grow food in places where
the soil is not ready for planting."

RIGHT. Of course, how to get the water to deserts is part of another class. Creative thinking is the order of the day here.

What content should I expect my child
to be learning?
What students should know and be able to do
is identified in standards developed by the
National Science Foundation (NSF) and NASA–
Standards for Technological Literacy: Content for the
Study of Technology. Standards for K–12 were formally
reviewed by the National Academy of Engineering,
the National Research Council, and the technology
teaching community.
The standards address content for K–12. Content is
integrated into thematic units at the elementary
levels, while course titles at the middle and high
school levels may include:
• Exploring Technology
• Innovation and Engineering Design, Technological
• Engineering Design Fundamentals
• Inventions/Innovations
The standards also address medical, agricultural and
related bio-technologies, energy and power,
information and communication, transportation,
manufacturing, and construction topics."

Yep. No need for math, biology, chemistry or physics. Just get them up to speed on technology and engineering design. It’s gonna be a beautiful world!

Monday, November 19, 2007

help desk: how to teach the factoring of trinomials?

I'm having trouble reteaching trinomial factoring to C.

He's now "got it," but I don't think he's "got" the fact that we are "unmultiplying" -- or that we're using the distributive property when we do these two steps:


I've found over the past couple of years that sheer repetition "naturalizes" a procedure in my mind, which feels like comprehension. But when I returned to the procedure for factoring a trinomial in which the coefficient of the squared term was greater than 1, I had forgotten how to do it -- and I couldn't figure out how to do it.

In other words, I didn't understand what I was doing well enough to reconstruct the procedure myself.

Here's the part that keeps stumping me.


factors 3 & 4 add to 7


I'm going to sound dumb, but I am having trouble grasping why the factors of 12 work as the addends of 7.

I guess I have two questions:
  • what is the best way to show that the final step above is a use of the distributive property?
  • factors and addends - HELP!
I should add that this year's class continues to go pretty well. I'm doing no preteaching at all, I don't always have to reteach, and the reteaching I do have to do happens because of the pace of the course, not because concepts haven't been explained and demonstrated well in class.

"Reteaching" this year tends to mean "reminding" and "reviewing."

again with the answer keys

This weekend C's teacher sent home 4 pages of review problems to practice before taking today's test.


On Saturday I realized he hadn't sent the answer key. [update 11-25-07: Teacher says he got the worksheets at a workshop - oy - and the workshop didn't supply the answer sheets. My tax dollars at work.] So I spent my weekend staring at a guillotine deadline (official publishing industry terminology) for my book and factoring trinomials on my son's review sheet so he can figure out whether he's actually doing the problems correctly.

Needless to say he was doing many of them incorrectly on Saturday. Some of his mistakes were "careless errors"; some were missing a step-type errors.

Both errors require marking and redoing, or at least analysis of what went wrong.

Speaking of which, C. is beginning to want to analyze his sequence of steps instead of simply starting over again. I think that's good, right? Often he'll say, "I see what I did wrong." Of course, he can't do this if he doesn't know he got the answer wrong.

Marking careless errors is particularly important in the case of trinomial factoring, I think, because along with learning how to factor a trinomial you need to learn how to check your answer mentally if possible. (Which I'm pretty sure C. has not learned...)

In the case of trinomials, students could check their answers by multiplying the factors they've ended up with, but I don't think they've been told to do that; they definitely haven't been given homework requiring them to do it. I managed not to figure this out until late last night, sad to say.


We need the answer key.

I will never understand this place.

on beyond help with homework

Meanwhile, the course is now beyond most parents' ability to "help with homework." Ed took engineering calculus at Princeton and has no memory of how to factor trinomials. Plus I find the textbook, Glencoe Algebra, to be mystifying in most instances. It's not like Saxon or Foerster or Dolciani, textbooks a parent can use to teach or reteach himself the lessons his child has been taught at school.

If I find it mystifying it's a cinch other parents will, too. Not to mention the students themselves.

(Btw, my experience thus far has been that Foerster is incredible when it comes to a parent having to rapidly "teach" herself a concept she's never before seen in her life so she can (re)teach it to her child in time for the test.)

So.....what is the thinking here?

By the time most students reach 5th grade math, their parents are no longer able to "help with homework." (The math teacher/tutor I know told me: "I get the call in 5th grade.")

How are the kids supposed to learn algebra?

Can you FOIL the answers?