state test

I've been forgetting to mention that it looks like our marathon test-prep operation paid off.

Christopher missed only 2 of 30 multiple choice questions (the tests are scored at school).

I don't know how he did on the 8 short answer questions, but I imagine he did well.

I'm sold on the test prep books the school ordered from Triumph Learning. They're terrific.

Each concept/skill/procedure in the state standards is explained clearly in a brief, succinct lesson followed by a problem set consisting of multiple choice, short answer, and extended response questions.

At the end of each section ("algebra," "geometry," "probability") there's a "Progress Check" with problems from all of the lessons.

The books also include several practice state tests.

This is exactly what I've been needing, because the book is targeted to the state standards; it has exactly the material actually being taught in C.'s class, and nothing more. I'm not having to scrounge through zillions of on- and off-line workbooks trying to come up with problems that match the course content.

Better yet, a parent can read the lesson, work the problems, and be in a very good position to "help with homework."

We're going to be using the 8th grade book to help prepare Christopher for his classroom tests for the rest of the year.

I should see whether Triumph has a similar book for Regents Math A. If so, I'm going to order it.


California test prep

Triumph writes books for the CA standards, which are the best in the country. I just looked at a pdf file sample from the algebra 1 book (link may not work - you may have to navigate from homepage). It's terrific.

Here's the ad copy:

This Coach book is the ideal supplement to classroom instruction for students who struggle with difficult algebra concepts. Every math skill students are expected to know is covered by concise lessons, specifically written to reach students at all levels of ability. All lessons are correlated to California Standards so that instruction can be focused on those areas where students need the most help.

The California Standards-Based Coach, Mathematics-Algebra I can be flexibly used in a variety of ways throughout the year. It is ideal as a classroom supplement, for intense review toward the end of the year, for independent study with advanced students, in intervention programs, or in summer school programs for struggling students.

Notice the fact that these books are suitable for students at all levels.

That's direct instruction. Direct instruction pedagogy is (almost) never geared toward one student population. Typically everyone can use the same lessons. The difference amongst students lies in the speed at which they master the material.

This approach -- same curriculum for everyone, "grouping" by placement in the curriculum -- stands in direct opposition to the approach taken by my district.

Here we separate the men from the mice by creating difficult ("challenging" is the term of art) courses only 25% to 30% of the student body can handle.

That's what we pay the big bucks for!


state test coming right up (2006)
throwing money at the problem
more stuff only teachers can buy
help desk 1
state test coming right up (2007)
help desk 2
my life and welcome to it
inflammatory
canadianteacher.com
progress report
despair
28 out of 30

all the answers are belong to us
email to the math chair
second request
teacher's manual
it would be unusual

fantastic site - homeschooling & afterschooling

Myrtle linked to this site.

It's incredible.

Here are his choices in math textbooks.

Solutions to problems in Gelfand's Algebra text here.

geometry test grade 6 translations

For some reason I can't get this link (pdf file) on the sidebard.

test prep hell

So tomorrow Christopher has a big test on translations.

Last night Ed and I taught ourselves point symmetry; we also had Christopher do the practice lessons on reflection, translation, etc. in the NY State test prep book for 8th grade.

Naturally he refused to do the actual problems in the test prep book the way they were written, insisting that these weren't the problems Ms. K had taught, etc. So we'll be duking it out on that front tonight.

He did do most of the problems correctly, I think. I'll have to go through the pages and figure out what he can and can't do.

The problem last night was multi-tasking.

It's impossible to teach yourself point symmetry and monitor your child's progress in his test prep workbook and fight with him about doing the problem the way the book says to do it as opposed to doing the problem the way he thinks his teacher taught him to do it in class.

Christopher has ZERO idea, and I mean ZERO, of what point symmetry actually is. Ms. K. taught him a "formula," and he is rigidly insisting on sticking to it. He can't explain the "formula" to me; he can't even demonstrate it. I finally discovered (discovered! constructivist help with homework!) what it was after doing a few rotations on graph paper.

He doesn't get the bit about rotating the graph paper 90 degrees to see what the coordinates of a figure rotated 90 degrees would be.

Of course, if he forgets the formula on the test, or mixes it up -- which he did last night -- he has no way of figuring it out. Nor does he have any means of checking whether he's remembered it correctly.

Ed says not to try to teach him the graph rotation. He's got the procedure memorized, "he'll be taught this a zillion times again," etc.

Good grief.

The fact is, C. won't be taught point symmetry a zillion times again. He'll be taught it again once, one year from now, at which point he will have forgotten everything he "knows" about it.

Meanwhile I'm trying to figure out how many different variations on point rotation I need to cram into his head tonight. I'm positive he needs to be able to rotate a figure around the origin; I have no idea whether he needs to be able to rotate a figure around any old point at all -- or whether he needs to be able to construct one figure that has point symmetry "within itself," the way a face card has point symmetry within itself.

I told C. this morning, on his way out the door, to ask Ms. K. what kinds of point symmetry they're supposed to know.

He said, "When we ask her if something's going to be on the test, she says Maybe."


question: Why am I paying $20K/year property taxes for this?


I'm sure the test will be one big, huge problem requiring him to construct a figure, reflect it, slide-and-glide it, then rotate it around some random point in some random quadrant.

I better get cracking.

Myrtle on teaching math with proofs

I had a six hour conversation today with my husband on proofs vs. calculations. How can I be so sure that this proof approach is the right thing to do? While I personally think it's entertaining, how do I know that the kid will do okay on the SAT or won't be counting on his fingers later on?

ooooo....

This sounds fun:

I've exhausted my interest in the topic of Fuzzy Math and I'm now interested in Junk Geometry.

Drat These Greeks

Birkhoff's Geometry, Singapore NEM (doesn't cover quadratic equation until 9th grade), Frank Allen's axiomatic algebra instruction, Apostol Calculus, and more.

Go read.

Moise and Downs TOC

Myrtle's find:

Table of Contents


also:

• SMSG Geometry at ktm-1
  

• Amazon review of Moise and Downs (at ktm-1)
  

• An A-maze-ing Approach to Math by Barry Garelick

Huns and more Huns!

from commenter Tyrian Purple:

I've seen an episode or two of that Barbarian series (I keep missing it). One of the historians on it, Peter Heather, has a book I'm reading, "The Fall of the Roman Empire."

Don't feel bad about not knowing who the Huns are, because apparently, their precise origins are unknown. Many people speculate they came from China (or near China) originally. Hungary's name comes from Hun, and that's not a coincidence; they settled there among other places. The other part of Hungary's name is from the Magyars. Heather says that even the Romans weren't sure where the Huns came from exactly, just that they guessed the Huns came from beyond the Black Sea. The Huns confused the matter by taking on Germanic names, so tracing them is even more difficult. Apparently the Huns are important because they drove the Goths toward the Roman Empire, although this was not a part of a grand master plan, it just happened that way.

The Huns were nomads, and the Romans thought they were vicious. Heather says they didn't have a single leader, just a series of "ranked kings" who could act on their own, so some Huns acted as allies on behalf of some Goths, against other Huns.

The Huns were horse-bound archers. They used these innovative kick-butt bows. If you've seen pictures of Cupid's bow, that's the kind of bow the Scythians--the Ukraine--had, which was powerful. The Huns lengthened the same kind of bow, but shortened the bottom part of it. Modifying the bow let them shoot farther and hit harder, which allowed them to use their favorite battle tactic: hit and run. When they offed enough of the enemy with their arrows, they closed in on horseback, with their swords.

Hope that helps.

It does help!

Thank you!

And may I say....

Wow.

Huns.

I must be entering my spring hypomanic phase, to be thinking good thoughts about Huns.



eSchool News on Singapore Math
more huns
Huns and more Huns!

DIY electronics kit

I have no idea whether this thing works or not, but it looks cool.

Full-sized photo here.

point symmetry

So tonight we've learned point symmetry.

• point symmetry at teachersnetwork.org

• point symmetry at Math Forum

• an intuitive notion of point symmetry at Regents Prep

• point symmetry at math is fun
  

• working with point symmetry
  

• point symmetry at Harcourt Brace (pinwheel -- very good)

Thank God my Sudden Math Learning Curve has speeded up.


Moise and Downs

We were sitting at the dining room table flipping through our dozens of math books, looking for point symmetry.

Ed found a point symmetry lesson at the very end of the Moise and Downs geometry text.

C. is in 7th grade; Moise and Downs was a sophomore text when Ed was in high school.


sink or swim

This is Darwinian gatekeeping, pure and simple. An expensive sorting machine.

C. can learn this stuff.

He can learn it easily.

But not in this class, not with this curriculum & this pedagogy.

He'll get through because we'll reteach the course at home. Down the line the school will take credit for his high SAT math scores; in the meantime we'll be identified as helicoptering lunatics and Huns.


I guess I can live with that. (may have to hit refresh before page comes up)


wit and wisdom
eSchool News on Singapore Math
more huns

more huns

I like Huns.

Of course, since my own K-12 education is only slightly superior to what you'd see in a person raised by wolves, I don't actually know what a Hun is.

So I probably shouldn't be popping off about Huns and how much I like them.


eSchool News on Singapore Math
more huns
Huns and more Huns!

curriculum map

Beyond TERC has a discussion of curriculum maps.

One of the list members found this Second Grade Concept Map.

Looks interesting. I'd love to have something like this from my school.

special ed by the numbers

I subscribe to the Institute of Education Sciences News Flash. It's pretty useful:

An e-mail-based alert service designed to inform you about all new content posted to the IES website including news from its four Centers and programs within Centers such as the Regional Educational Laboratory Program.

This came today:

This Issue Brief reports the timing of entry into special education and the number of grades in which students receive special education across the primary grades. About 12 percent of students receive special education in at least one of the grades: kindergarten, first, and third grade, including 16 percent of boys, 8 percent of girls, 18 percent of poor children, and 10 percent of nonpoor children. One in three students who receive special education in early grades, first receive special education in kindergarten. Half of those who begin special education in kindergarten are no longer receiving special education by third grade. In addition to students’ gender and poverty status, results are presented separately for other student and school characteristics, including race/ethnicity and school control, urbanicity, region, and poverty concentration. Data for this brief come from the Early Childhood Longitudinal Studies, Kindergarten Class of 1998-99 (ECLS-K).

To download, view and print the publication as a PDF file, please visit:
Timing and Duration of Student Participation in Special Education in the Primary Grades

in a nutshell

• 12 percent of students receive special education in kindergarten, 1st, or 3rd grades
• 8 percent of girls
  
• 16 percent of boys
  
• 18 percent of poor children
• 10 percent of all children
• 1/2 of children receiving special ed in kindergarten are no longer receiving it in 3rd grade

These figures don't surprise me.

Special ed is the only part of our public schools in which children have legal rights, and in which direct instruction prevails.

You can't count on schools providing evidence-based instruction in special ed. That's an ongoing battle everywhere.

But the school assumes it has some responsibility to teach the material on the IEP and to assess whether the material has been mastered.


update

from a Commenter:

Many school districts do not use direct instruction for special ed students. They take constructivist curricula like Everyday Math and modify it a little for the special ed students.

The special ed teachers try to make it more explicit and direct than it would otherwise be, but it's still, at heart, a discovery based program.

It's one of the drawbacks to full inclusion. If the general ed kids are doing constructivist math, the special ed kids are doing it also. If the general ed kids are doing "balanced literacy," then so are the special ed kids, even if they desperately need phonics.

As for IEPs, the schools usually set very modest goals for themselves. When they have to ensure that a child has to actually master something, they are very, very careful. For example, in an IEP, they'll take an area where the kid has 50% mastery and make the IEP goal 80% mastery.

Kids who receive special ed in kindergarten are probably those who have more specific, discrete problems. I don't think the schools are so successful with the older kids who are labeled with learning disabilities.

Actually, this is an interesting question. Who are the kindergarten kids in SPED, the ones who are no longer classified in 3rd grade?

I've known quite a few of these kids, but I'm not sure I can make a generalization.

I think it's correct to say that they had mild language delays.

But I'm not sure.

eSchool news on Singapore Math

Looking to Singapore for success

The paragraphs on Singapore are fine, though naturally the theme is conceptual understanding "combined with" procedural knowledge. According to the folks at eSchool, the Singapore books are the first in world history to attempt such a feat.

Then, inevitably, we get to TERC.

Eric McDowell, who oversees Bellevue's math curriculum, says parents misunderstand Investigations. McDowell says schools supplement the program with more traditional drilling in the basics, and students end up flourishing. "It's not an either-or situation," he says.

In the Alpine School District in Utah, parent Oak Norton, an accountant, has gathered petitions from 1,000 families to protest the use of Investigations. His complaints began more than two years ago, when he discovered at a parent conference that his oldest child, then in third grade, wasn't being taught the multiplication tables.

Barry Graff, a top Alpine administrator, says the system has added more traditional computation exercises and plans to give each school a choice between Investigations or a more conventional approach. Graff, who says Alpine test scores tend to be at or above state averages, expects critics to keep up the attacks.

"Other than the war in Iraq, I don't think there's anything more controversial to bring up than math," he says. "The debate will drive us eventually to be in the right place."

Right.

It's just like Iraq.

Parents don't understand and we're a pack of crazed, warmongering Huns.

Actually, crazed warmongering Huns is probably fine.

Who wants to tangle with Huns?

Not me.



Here are some more Huns.

Just in case I haven't made my point.





eSchool News on Singapore Math
more huns
Huns and more Huns!

think outside the box

I was reading our Sunday paper and I happened to look at the "Parade" insert. They had an article called "Do you have a better idea?" Creativity. What caught my eye was a section called "How to think outside the box". The first item was called:

"Open your eyes and 'plagiarize.'"

"Inspired by the Tom Lehrer song, the idea is to look around you and see how things are done in other countries and contexts. What smart solutions already exist, and how can they be adapted for your problem?"


Amazing. More knowledge and skills improve creativity!

The problem with ideas is that they are a dime a dozen. I have many of them a day. Some of them are probably extremely good. Some of them are probably extremely bad. The problem is that I can't always tell the two apart. Besides, I'm busy right now.

Creativity is not a problem. Lack of knowledge and skills is the problem - and time and opportunity and motivation and the ability to work really, really hard on something that isn't always going to be fun. Drive, ambition, taking risks, knowledge, and skills get the job done, not creativity. Creativity is a vague and cheap commodity. Schools should focus on knowledge, skills, high expectations, and hard work. Creativity will take care of itself.

Everyone is creative and has ideas. The problem is whether you have anything else to back it up.

Planet Earth

My mom says this show is going to be great.

true confessions

re: wall-mounted grocery bag holders

We use a milk jug for the same thing.
- rightwingprof


I've got a cloth one that hangs on a door knob. I love it. My husband thinks I have a bag problem.

I'm a bag hoarder. But I don't want to re-use them in case I don't have enough. So, I just collect them. Just in case.

There's probably a special medication out there for something like this.
- Susan S


I store mine in empty kleenex boxes. That way I can hoard both plastic and paper.
- anonymous


I use a 2L bottle with a hole cut in the side (flame the edges of the hole so they aren't scratchy). With two young boys around, I go through lots of plastic bags, and we haven't even hit "play in the fountains" season yet.

As for dog bags, we decided the odds of holes in re-used bags was too high, and instead buy them online 1000 at a time: http://www.leisuremore.com With two large dogs, this is so worth it!

And don't knock the sensor trash can. Our dog figured out how to open the lid on our step-can, so we decided to try the sensor can. He's skittish, so when the lid opens he runs away. We're hoping that he won't desensitize and figure out it's really a self-serve buffet. Our back-up plan is to block the sensor and use the open/close buttons.
- Stephanie Ozenne


My problem is: I have a solution that isn't working.

I store my newspaper bags in a King Arthur Flour small flour bucket, which I keep outside, in the front of the house.

The bags never make it out to the bucket, because.....it's too far away, I guess. And it's cold out, etc.

I need to move it indoors.

Clearly.

math isn't English

My sense of the Johnson - Bouchard study is that it weighs in directly on the side of parents who intuitively perceive that math isn't English.

Interestingly, it is the image rotation abilities that have repeatedly shown the most robust sex differences among cognitive abilities (favoring males, Voyer, Voyer, & Bryden, 1995).

[snip]

It has been known for some time that performance on spatial tasks, particularly those involving image rotation, predicts success in fields such as airplane piloting, engineering, physical sciences, and fine arts better than does general intelligence, and especially verbal ability (Gottfredson, 2002; Humphreys & Lubinski, 1996; Shea, Lubinski, & Benbow, 2001; Sheppard, 1978).

Academic prose.....pretty impenetrable.

Instead of cutting and pasting any more of this, I'll post the short version of what I take to be Johnson's and Bouchard's points. (Take this with a grain of salt; I would need to interview them to feel confident that I've got this straight.)

• a general intelligence factor - g - exists which "contributes to all mental abilities"
  

• "residual" factors also exist: once a general intelligence factor is extracted from any collection of ability tests, the correlations among the residuals fall into two main groups ["verbal" and "perceptual" in Vernon's classic model].
  

• Johnson and Bouchard find 3 "residuals," not 2: verbal, perceptual, and image rotation
  

• these 3 map directly onto the classic distinction between the left and right brains, with verbal skills being left-brain and spatial skills being right-brain, "though it is clear that all tasks of any complexity involve contributions from both hemispheres (Gray & Thompson, 2004)."
  

• you can be high in verbal intelligence and not so high in spatial abilities, and vice versa
  

This study appears to support parents' felt sense that it's wrong to force a mathematically-inclined child (note the use of the term "inclined") to "demonstrate understanding" by putting math into words.

Math and English aren't the same subjects, and the abilities that underly achievement in the two subjects differ.


it's not just the gifted

Another terrific aspect of Johnson's and Bouchard's article is that it appears to support a perception I've had for quite awhile now:

It has been known for some time that performance on spatial tasks, particularly those involving image rotation, predicts success in fields such as airplane piloting, engineering, physical sciences, and fine arts better than does general intelligence, and especially verbal ability (Gottfredson, 2002; Humphreys & Lubinski, 1996; Shea, Lubinski, & Benbow, 2001; Sheppard, 1978). There is also evidence (Humphreys, Lubinski, & Yao, 1993) that failure to include assessment of such abilities in the standard batteries used for college and graduate school admissions is resulting in loss to those fields of potentially highly talented individuals. Perhaps of even greater concern, however, is the possibility that effects of this type may not be limited to the gifted and talented. Elementary school curricula tend to be used to educate those of all ability levels and they are generally much more highly focused on verbal than on image rotation abilities. This may be resulting in alienation from school of individuals unlikely to attend college as well as reducing the achievement of those who may. The social costs associated with early school leaving are well documented (e.g., Henry, Caspi, Moffitt, Harrington, & Silva, 1999).

This is something I see in schools.

I've worked with at least one child, a boy, who is mathematically inclined, but who has problems with learning and is classified SPED. (Very high-end SPED, the sort of kid who is still classified only because his mom correctly continues to fight for and win the designation.)

My frustration with the situation has always been that while everyone is working well with this boy, who is having a far better middle school experience than a lot of the non-SPED kids, no one appears to perceive that he has a particular talent for and interest in math, and thus ought to be pushed and supported in that subject specifically.

Instead there's a global assumption that he needs help.

Which is true as far as it goes.

But oughtn't the "help" offered be different in math than it is in language-based subjects?

Shouldn't the school be trying to move him ahead in his strongest subject?

Part of the reason this doesn't happen, I think, is that this boy isn't mathematically gifted. (At least, I don't think he is.)

He is mathematically inclined.

Mathematical giftedness leaps out at people; it's hard to miss.

But mathematical inclination, especially in a child who finds his other subjects challenging, is more subtle.


bonus passage

Specifically, we would expect that general intelligence will prove to be influenced by several to many genes responding to environmental stimuli to control biochemical processes acting throughout the brain. At the same time, we would expect that there will be several to many genes that influence brain functions that affect primarily verbal abilities and others that influence brain functions that affect primarily spatial and perceptual abilities. Some of these genes may even enhance abilities in one area at the expense of abilities in another, contributing to the lower correlation between verbal and perceptual abilities than between fluid and crystallized abilities in our models. Such environmentally mediated genetic processes may also help to explain differences in strategies used to approach cognitive tasks, individual differences in stimuli that attract attention, and sex differences in performance on various kinds of tasks. Evidence in support of these kinds of predictions is beginning to emerge.

The structure of human intelligence: It is verbal, perceptual, and image rotation (VPR), not fluid and crystallized (pdf file)

good schools raise IQ, bad schools lower IQ, part 1
good schools raise IQ, bad schools lower IQ, part 2
good schools raise IQ, bad schools lower IQ, part 3
Seth Roberts on IQ
fuzzy math makes you smarter
IQ quiz
school raises IQ
intelligence is verbal, perceptual, and image rotation
math isn't English

help desk - statistics

I desperately need a course in statistics.

My question concerns this passage from a terrific article: The structure of human intelligence: It is verbal perceptual and image rotation (VPR), not fluid and crystallized by Wendy Johnson & Thomas J. Bouchard Jr.^* (pdf file)

Interestingly, though the correlations between the verbal and perceptual and perceptual and image rotation factors were high (0.80 and 0.85), the correlation between the verbal and image rotation factors was much lower, 0.41.

This study sets out to determine the "relative statistical performance of three major psychoetric models of huam intelligence," those being:

• Cattell-Horn fluid-crystallized model
• Vernon's verbal-perceptual model
• Carroll's three-strata model

The fluid-crystallized model, which has been dominant for some time now, didn't work.

Good.

I'm glad.

I'm glad because according to the fluid-crystallized model people get dumber as they age and their "fluid" intelligence gets less fluid. Or something.

This is why we're always hearing that for us old folk "experience and wisdom" have to make up for "ability to solve novel problems" or what-have-you.

Turns out that "experience and wisdom" and the "ability to solve novel problems" are the same thing.

Or so I gather. (If anyone who actually researches intelligence stumbles across this entry, I yearn to be fact-checked on this. Please. Chime in.)

At any rate: Bouchard's new study is good news for geezers because the fluid-crystallized model did not work out.

Nor did the "three-strata model." (Don't know what the three-strata model is; not going to find out any time soon.)

What did work is the verbal-perceptual model, which is pretty much the common-sense understanding of human intelligence most of us non-experts have always believed in.

I still don't really understand the distinction between verbal intelligence and perceptual intelligence. Generally speaking, however, it breaks down this way:

• "verbal: verbal fluency and divergent thinking [ed.: what is divergent thinking?] as well as verbal scholastic knowledge and numerical abilities"
  

• "perceptual speed, and psychomotor and physical abilities such as proprioception in addition to spatial and mechanical abilities"
  

Clear as mud!

What's interesting about Johnson's and Bouchard's study is that they discovered that one needs to add a third category, which is the ability to mentally rotate, manipulate, and twist two-and three-dimensional objects.

As we all know, this is a guy thing:

Interestingly, it is the image rotation abilities that have repeatedly shown the most robust sex differences among cognitive abilities (favoring males, Voyer, Voyer, & Bryden, 1995).

I'll get back to that.

In another post.

Here's my question.

I'm not understanding how verbal intelligence can correlate highly with perceptual intelligence, and perceptual intelligence can correlate highly with image rotation intelligence, but image rotation intelligence does not correlate highly with verbal intelligence.

How does that work?

Am I reading the passage incorrectly?

Is this an expression of a sex difference?

Or what?

Thanks in advance!



^* Bouchard directs the Minnesota Twin Study.

good schools raise IQ, bad schools lower IQ, part 1
good schools raise IQ, bad schools lower IQ, part 2
good schools raise IQ, bad schools lower IQ, part 3
Seth Roberts on IQ
fuzzy math makes you smarter
IQ quiz
school raises IQ
intelligence is verbal, perceptual, and image rotation
math isn't English

smirk

Passive voice is loved by me

- Barry Garelick

.

is there a technological solution?

If I had one of these things in my house would I stop having plastic newspaper bags lying all over the place waiting for me to take the dogs on a walk?

Hard to say.



I'm pretty sure I don't need a self-opening waste bin.