kitchen table math, the sequel: 3/25/07 - 4/1/07

## Saturday, March 31, 2007

### Weird

This blogger login has always been a problem. It would invariably take me to my OLD blogger login, and until yesterday, I would clear the cache, close, then rerun Firefox to get to the NEW blogger login.

Then yesterday because I was inn a fog, when I got the OLD blogger login, I clicked logout--and it took me too the NEW blogger page. So if you're having trouble logging in, try logging out.

### Good Research, Poor Terminology

ScienceDaily: Kids Learn Words Best By Working Out Meaning:
During the inference trial, Brinster showed the youngsters both familiar and strange objects (for instance, a ball and a plumber's "T" connector). After saying a nonsense word ("blicket," for instance), she would ask them to either point to or grab hold of the "matching" item. Since a ball is a "ball," the children might conclude that the unfamiliar object — the "T" — was the "blicket".

In the direct instruction trial, the child was simply shown an unfamiliar item and heard the nonsense word.

A short while later, Brinster would invite the children to play with typical, familiar toys in the Lab's waiting area. During the relaxed play period, she would bring out a "blicket" or a "dax" that the children had seen during the trial, and ask the youngsters a question.

"For instance, I might say, 'I think one of these is called 'blicket,' but I can't remember which one it is. Can you help me? Do you know which one is the 'blicket?'" Brinster said. "This way, I could ascertain how well they learned the word. Once we analyzed all of our data, it was clear that inference worked best."
The article, based on a study by undergraduate researcher Meredith Brinster at the Johns Hopkins University Laboratory for Child Development, compares the effects of learning by "inference" compared to "direct instruction". I question whether the use of the term "direct instruction" is appropriate, considering that the term "direct instruction" is commonly used to refer to a specific pedagogy.

According to Zig Engelmann, who is the father of "Direct Instruction", instruction must be "logically faultless",

Faultless Communication (Faultless Instruction): A sequence of instruction, frequently involving examples and non-examples in a well-crafted order, which logically leads to an accurate communication of the concept and eliminates the possibility of confusion.

For an example of faultless communication, please see http://psych.athabascau.ca/html/387/OpenModules/Engelmann/theory.shtml

Using the term direct instruction to describe simply giving a positive example as opposed to giving a negative example, overly simplifies the term, especially since true direct instruction would also include logical inference as described in the study.

My concern is that the work could be taken out of context to argue against a curriculum that has proven to be successful at raising the achievement of low SES students.

(I emailed the student mentioned in the study, to see if I could get a copy of the paper, and to express my concerns about terminology.)

### Almost there.

Memphis Commercial Appeal - Memphis' Source for News and Information: Education:
'If only the parents did what they were supposed to do, I could teach these children.'

Donna Ford has heard teachers say that countless times, and she's not buying it. Most of the problem, she says, is with the schools, not the homes.

Educators have to stop making excuses for the achievement gaps that plague the nation's schools and roll up their sleeves, the Vanderbilt University professor said Friday at a conference at the University of Memphis.
School districts can institute all the new programs and curricula they want, but it will all be for naught if they don't address the most practical needs of students, said Pat Cooper, superintendent of the McComb, Miss., school system.

"If we don't do our job in the school, then there's not one group in the community that can work," he said. "We can't wait for somebody to wave the magic wand and get rid of all of the poor children."

Using the same curriculum for more than a decade, his school district was able to raise the reading scores for all of its students, who are mostly poor and minority, from the low double digits to the high 90s. (link is mine)
Even when schools do well, the media still doesn't mention which curriculum the school used.

For those who are curious, it was Success for All.

## Friday, March 30, 2007

### great moments in world history

So yesterday we were all driving to Salon Vivace at 9 am to get the boys their haircuts (superintendent's day).

Ed said something about 20% of the public doing something or other, and I asked Christopher, "What fraction of the public is 20%."

"One fifth."

Until the words came out of his mouth I didn't know whether he could answer that question off the top of his head.

So.....ummm......I can't really say I've gotten the hang of formative assessment, can I?

### Diane Ravitch on NCLB

In the future, the federal government should do only what the federal government can competently do. Its historic role has been three-fold: one, to collect and disseminate information about the condition and progress of education in these United States; two, to write checks help schools educate specific groups of students, especially those who are poor and have disabilities; and three, to enforce civil rights laws.

Those are the principles that should be the underpinnings of the reauthorized NCLB.

First, the federal government should establish national standards in basic academic subjects (reading, mathematics, science, and history). Second, it should annually administer national examinations in those subjects. Third, it should make the results available to states and school districts.

It should be left to the states to decide which actions to take in response to this information. The states, working with the school districts, should decide which combination of rewards and sanctions will improve student achievement.

We should, in this instance, use the states as laboratories of democracy. Since we do not know which rewards and sanctions will have the most salutary effects, we need to let the states work with educators to try different approaches. When there is a clear pattern, other states and districts will learn from the experiences of others who are successful as well as those that are not.

One of the benefits of this approach is that the states will be relieved of the cost and burden of testing, as the whole cost and burden will shift to the federal government. Another benefit will be that all of the red tape and mandates associated with NCLB will disappear overnight.

Knowing the ways of Washington, I am doubtful that my solution will find a warm reception. Just last month, a bipartisan commission funded by the Gates Foundation and co-chaired by former Governor Roy E. Barnes of Georgia (Dem.) and former Governor Tommy Thompson of Wisconsin (Rep.) proposed a vast expansion in the number and reach of mandates associated with the education law.

But if we truly want good schools and well-educated students, we won't get them by piling on more mandates and regulations. The recipe for good education involves a solid curriculum, effective instruction, adequate resources, willing students, and cultural support and encouragement for education. Washington can pick up some, but not all, of this responsibility.

My first impulse is to agree with this.

My second impulse is to ask what effect this will have on schools like mine.

I'm drawing a blank.

I'm pretty much on board for national standards at this point, however. New York state's standards, which, in history and science, are quite good are the only thing standing between us and the abyss.

Not to put too fine a point on it.

### Spitzer wins one

This is extremely good news. (If you can't access it through ktm, you can through eduwonk.)

I would rather be working on a new charter school for Westchester County than trying to change my district.

### bar models and multimedia learning

Myrtle's post on bar models reminded me of an interesting interview I read with Richard Mayers, who is apparently a major researcher in the area of "multimedia learning."

Multimedia learning is much simpler than I realized: Mayers defines it as "the presentation of material using both words and pictures.”

This is the kind of research that jibes so completely with my felt experience of learning math (learning anything, really) that I'm simply going to assume it's true until someone demonstrates otherwise.

Principles:

...[I]n Multimedia Learning (Cambridge University Press, 2001), I describe some research-based principles for the design of multimedia instructional messages including the following:

• multimedia principle, in which people learn better from words and pictures than from words alone;
• coherence principle, in which people learn better when extraneous material is excluded rather than included; [ed.: RESEARCH PROVES! PAGE SPLATTER IS BAD!]
• contiguity principle, in which people learn better when corresponding words and pictures are presented at the same time or next to each other on the screen;
• modality principle, in which people learn better from animation with spoken text than animation with printed text;
• signaling principle, in which people learn better when the material is organized with clear outlines and headings; and
• personalization principle, in which people learn better from conversational style than formal style. [bullets added for emphasis]

For example, in designing a PowerPoint slide it is important to not present an overwhelming amount of information (i.e., coherence principle) and it is useful to have simple graphics to supplement words (i.e., multimedia principle). Finally, it is important to note that good design principles for inexperienced learners might not be the same as for experienced learners.

[snip]
Bullets don't kill learning, but improper use of bullets kills learning.

uh-oh

Cliff Atkinson interview, Richard Mayer

### Bar Diagrams II

Algebra without algebra:

Fifth grade word problem from Singapore: Jim and Dan have \$24 altogether. If Jim gives \$2 to Dan, he will have three times as much money as Dan. How much money does Jim have?

Observe the mighty bar diagram in action:

The kid thinks, "I can see that \$24 will be divided into four equal groups of \$6. Jim will have 3 groups of 6...that's \$18.

Method #2

Let j be Jim's money and d be Dan's money: j + d = 24; j - 2 = 3*(d + 2) so j = 3(d + 2) + 2 substitute in to the first equation: 3(d+2)+2 + d = 24 simplify: 4d + 8 = 24, solve: d = \$4; j = \$20.

They both have their charms.

multimedia learning (Catherine)

### this afternoon's brilliant idea

I'm going to have to get this book.

I think.

flap copy:
White papers are at the forefront of an educational marketing revolution. Powerful enough to lure readers and able to persuade with unyielding strength, the well-written white paper is a super weapon in the marketing professional's arsenal.

Wearing many hats, the white paper can talk business or converse technically, and it can inform or influence. Best of all—it is highly sought-after. The white paper's underlying strength rests on this premise: If you give readers something of value, they will give you their loyalty, and ultimately their business. This book aims to equip anyone with the tools necessary to immediately begin writing white papers that attract readers and keep them engaged.

Ed has a friend from Princeton who quit journalism several years ago (bureau chief at AP) and has been making a bloody fortune writing White Papers and books ever since.

### punished by rewards

In light of the desire of educators to rethink our schools, this bit that Catherine posted from Cheri Yecke caught my eye,

I became alarmed as I read article after article in which middle school activists expressed their arrogant assumption that America’s public schools were their personal vehicles for social engineering. I came to see how radical middle school activists were driving many of the policies and practices that have been so damaging to the public education system in America at all grade levels, and how such policies and practices were responsible for damaging the trust between many parents and the public schools.

One person’s damage is another person’s progress. Reading the Bowles and Gintis paper cross-linked by Vlorbik, I learned that schools "prepare [children] for adult work rules... by what we call the correspondence principle, namely, by structuring social interactions and individual rewards to replicate the environment of the workplace." Bowles and Gintis are quite optimistic that schools can bring about social change by socializing children to not "function well, and without complaint, in the hierarchical structure of the modern corporation."

First, schools influence which cultural models children are exposed to. Second, schools immerse children in a structure of rewards and sanctions.

Concerning the first, we note that a huge body of evidence attests to the fact that a society’s values are passed from generation to generation through a process of transmission which may be vertical (from parents) or oblique (from others in the prior generation) and involves a psychological internalization of values. The school system is an unusual form of oblique transmission whereby a particular group of people that is often quite unrepresentative of the population of parents (teachers) occupy privileged positions as behavioral models for children (Marx 1963/1852):125).

Children initially acquire cultural traits by vertical transmission from their parents (assume the parents have identical traits). They are subsequently paired with a cultural model (a teacher, that is) who may have the same or a different array of cultural traits.

Confining attention to a single trait, suppose the teacher has the same trait as the parents. Then the youth is assumed to retain the trait. But if the parents and the teacher have different traits, the youth considers which one to adopt, surveying the experiences of those he knows (his classmates) for guidance in making the switch. Among the experiences the youth may find salient are the rewards and punishments associated with the particular structure of schooling. The reward structure … includes the close association… between the personality and behavioral traits associated with getting good grades in school and the traits associated with garnering high supervisor rankings at work.

In this view, culture thus evolves by some individuals (those paired with an unlike model) shifting from what they take to be lower-payoff to higher-payoff cultural forms…. In this model, it is possible for a school system or any other system of socialization to promote the spread of a cultural trait that would otherwise not proliferate, suggesting that schools do more than simply reproduce the reward structure of the rest of the society. Schooling thus may promote prosocial traits even if these are not individually advantageous.

I highly doubt that "prosocial traits" like the willingness to conform quietly to group norms in school group work, leading to group-think as well as free-riding and table-pounding, are not seen as "individually advantageous” by the individual children who exhibit these traits.

[S]chooling can also promote traits which are advantageous to one group (the group determining the structure of schooling) even if they are not generally advantageous.

In the following paragraph, I set Bowles and Gintis’ variables “A” and “B” to specific extreme values. You can choose your own values according to your own tastes for social change, or not.

Schooling can affect the direction of cultural evolution in two ways. First, if most teachers are [socialists] then the children of [socialist] parents will rarely switch, while [capitalist] children will virtually all have the occasion (a mismatch) to consider a switch. Second, if the reward structure of the school favors those with [socialist] traits (even if the [capitalists] might do better in adult life) then a significant number of [capitalist] children will become [socialists]....

Depending on the specific assumptions of the model and the specific value of parameters, there can either be two stable “homogeneous” cultural equilibria involving very high frequencies of either the advantaged or disadvantaged trait, or a single stable “heterogeneous” equilibrium involving a moderate frequency of both cultural forms.

These propositions show the importance of such oblique cultural institutions as schools, which are necessary to stabilize cultural forms, such as the legitimacy of being subservient in the workplace, that benefit one group, in this case employers, at the expense of another, the employees.

Let the destabilization begin.

My take on the cooperative, socialistic ideals promulgated in the public schools is that they don’t stop administrators and teachers and parents and children from being competitive. Humans want to compete. Neither school reformers nor teacher unions eliminate competition; they drive it underground and it pops up again in weird new ways that are less transparent and less fair to everyone. At least Bowles and Gintis are refreshingly honest about teachers using rewards to punish capitalists.

### into the Green Zone

KIPP is looking for smart, savvy, energetic people to help it carry out its newly-assumed obligation to stabilize and reconstruct Iraq, and to spread its "work hard, be nice" message to traditionally underserved religious minorities and militias. For more information, see here. Email rÃ©sumÃ©s to KIPPFertileCrescent@dod.mil

### oldies but goodies

You guys are too much.

from Myrtle:

The first contact my school has had with me via email was a few days ago. It was a "kindergarten round-up" and the remainder of the email spelled out the legal ramification for providing false documents and then an explanation of how they would call the police and you WOULD be investigated if you didn't provide a birth certificate within a month of enrolling since this might be evidence that you had kidnapped the child. (They didn't use kidnapped but some other phrase)

Lovely. Just gave me the warm and fuzzies. It's like having a boyfriend spell out on a first date exactly how he will beat you up if you cheat on him, "just FYI!"

vintage Doug:

I think it would be only fair if you were to respond to this importunate demand for documentation with a list of circumstances which would cause you to swear out a child-abuse complaint against the kindergarten teacher and the school administration.

Just so everyone's on the same page, don't you know.

Doug checked:

I think in Texas schools are legally exempt from any sort of CPS investigation. A friend of mine's chld suffered a bad concussion and the school never called an ambulance. The ER doctor called CPS, the child spent time in ICU. CPS said they couldn't investigate it because it was a public school. It was the school's responsibility to do their own investigation.

And there is a cap on how much they can be sued for civilly.( I think in Texas the ISDs have their own police force) and at one point it was proposed to legally fine parents who don't show up to conferences.

This happened in my suburban district. And I can't explain why I don't feel like voting yes on their bond proposals. Maybe it's their stellar public relations outreach and customer satisfaction guaranteed or your property taxes refunded.

Yeah, we're all on the same page.

PS I'm betting they bully their teachers the same way they bully the parents.

Susan S:

Hey, he got a "C". Isn't that average?

Reading this I had one of my not-infrequent moments of empathy for our public school educators and their active dislike of parents.

We really are a pain in the tochus.

But that's what makes us great!

(And, ummm, we'd probably be less obnoxious if we didn't get stuff like this in the mail.)

### more fun with middle school!

This letter arrived in the mail yesterday.

We've never met this teacher.

We've never spoken with this teacher.

We've never received an email from this teacher.

We've never received a telephone call from this teacher.

Nice to make her acquaintance now, though!

today's form letter from the school!

## Thursday, March 29, 2007

### The War Against Excellence

from the preface of Cheri Pierson Yecke's book:

My dual passions for advocating for academic excellence and examining the motivations behind the contemporary middle school concept drove me to write this book. As a mother of two daughters who were academically gifted and as a middle school teacher, I experienced firsthand the frustrations of trying to meet the intellectual needs of high ability and highly motivated children within the prescriptive confines of the radical middle school plan.

My husband referred to my advocacy for our children as an example of the “she-bear” instinct--”if you mess with my cubs, you had better look out.” While both of our daughters generally had very positive experiences in their schools, during their middle school years I had to fight one battle after another as I sought to ensure that their educational needs were met.

As a middle school teacher, I became increasinly frustrated with administrative policies that were implemented by fiat with the solemn declaration that “this is good for kids because everyone is doing it.” Trendy new policies, such as the widespread elimination of ability grouping, the dumbing-down of the curriculum, and a wholesale embrace of cooperative learning and peer tutoring, were not good for all kids—and I didn’t care who else was “doing it.”

As a mom and as a teacher, I knew intuitively that these practices did not serve the best interests of all children, and I wondered where they were coming from.

As our district’s Teacher of the Year and as a concerned parent, I had a voice to express my views, but it did not carry the weight of those who were looked to as experts. I found that concerned parents and dedicated educators were often made to feel ignorant and insignificant when they attempted to argue against the latest trends and fads. Self-proclaimed experts, cloaking themselves in pseudo-wisdom, often looked with disdain upon anyone who dared to question either their beliefs or the translation of their beliefs into practice.

I left the classroom and went back to earn my doctorate so that I could become more knowledgeable and perhaps obtain the same level of mainstream credibility as these so-called “experts.” During those years, I became alarmed as I read article after article in which middle school activists expressed their arrogant assumption that America’s public schools were their personal vehicles for social engineering. I came to see how radical middle school activists were driving many of the policies and practices that have been so damaging to the public education system in America at all grade levels, and how such policies and practices were responsible for damaging the trust between many parents and the public schools.

The battle to determine the focus of the middle school—either as a vehicle for social engineering or one that supports rigorous levels of academic achievement—crystallized in a war of words between advocates for the middle school concept and advocates for gifted learners.

### Teaching Textbooks

My sister just switched from Saxon to Teaching Textbooks.

More later --

### here we go again

I have no problem with discussion questions. Our students' projects culminate in a report and presentation, after they have downloaded around 15,000 rows of data, run 26 different analyses (which must be done in a specific order, since some analyses provide the input or variables for other analyses), and decided on recommendations based on those analyses. They must include a section in the report critiquing their analyses and discussing the strengths and weaknesses, which lets us see how well the UNDERSTAND what they are doing and WHY, and not just whether they can do it or not.

But discussion questions come in the whole quality spectrum, and some are just plain idiotic. Consider this one:

In a couple of paragraphs, explain how you would estimate the square root of 170.

The square root of 169 is 13, so the square root of 170 is slightly larger than 13. I guess. A couple of paragraphs? Of what? What is she looking for, and what is the purpose of this question?

This one is a little better, but not much:

The base of a right triangle is 3 meters long, and the height is 4 meters. In a couple of paragraphs, explain how you know the third side is 5 meters long.

At least with this one we know what she's after. But why give them the answer, and why use the classic 3-4-5? If she really wants to know if they understand how to apply the Pythagorean Theorem, why not just give them a triangle problem? What does this tell her about what they know the triangle problem wouldn't?

Is this woman just out of ed school, or what?

## Wednesday, March 28, 2007

### blogs I'd like to link to

For some reason I can't get either of these two blogs posted on the sidebar:

Teaching in the 408

The Common School

So now they're here.

I'll keep trying.

### weapons of math destruction

Lynn G sent this from Weapons of Math Destruction.

### vlorbik.com (cross)posts something KTM-ish

Here's a (PDF) paper called "Schooling in Capitalist America Revisited" (2001). Economists Samuel Bowles and Herbert Gintis understand that schools aren't failing, as so many claim: they're doing exactly what they're designed to do (keeping kids ignorant). While I'm at it: the great John Taylor Gatto hasn't updated his page in years. Go buy his book anyway.

### in case you were wanting to hear something funny about cancer

I for one was not, but this really is pretty funny.

(from kausfiles via Drudge)

Well, maybe not funny. It's funny at first, and after awhile you think......oy.

## Tuesday, March 27, 2007

### nice work if you can get it

So I was talking to a friend today whose kid is having trouble in a class. Most of the kids are having trouble.

Extra help doesn't help.

She talked to the department chair who recommended one of the other teachers, a novice, as a tutor.

Fee?

\$100/hour

My friend protested, so the teacher said she'd work 1 1/2 hours.

One hundred dollars/90 minutes for a teacher who has been teaching only a couple of years.

One hundred bucks for a teacher currently teaching a class in which a number of the students "are struggling and don't belong." direct quote, middle school principal

In Irvington, if a student is struggling, he doesn't belong.

Core principle.

I'm STEAMED.

I've spent at least 5 hours today studying transformations, creating worksheets, working with Christopher, etc.

It's 9:30 pm and I still need to create a set of worksheets for him to use during study hall.

All of this is happening because I'm too stubborn to shell out \$100/hour to get some other teacher in the math department to do Ms. K's job.

mark my words

I will never hire an Irvington teacher as a tutor.

Ever.

### Class-size Reduction and America's Misplaced Priorities

The Common School: A Question of Scale: Class-size Reduction and America's Misplaced Priorities

Via Eduwonk... new blogger "Dewey", who is reputed to be a minor education wonk, makes the case that class size reduction would have a tiny effect on educational outcomes.
But the really mind-blowing results come when you start comparing a class-size reduction to giving students a teacher with a reasonably good (though not unlikely) combination of teacher credentials (estimated by adding the relevant values in the table above). Clotfelter and Ladd do their own estimates of this sort and come up with a combined effect size of 15% - 20% SD for math (and 8%-12% for reading) of a well- credentialed teacher.

The first time I read this portion of the study I said to myself, "Yeah class size is less important,” but that finding is not particularly novel to anyone who follows this sort of research. But when I decided to actually compare how much less important class size is my jaw dropped. The effect size of teacher credentials is 8 to 10 times that of a major class size reduction in math and 6 to 8 times as big in reading!!!
He figures it would take approximately 150% billion dollars in increased salary costs (if the improvement for reducing students is linear that is), for a net benefit of 1.6% to 4% SD in math instruction. He then goes on to propose several novel ideas about how that money could be better spent for a much more significant educational outcome.

My only observation:

Isn't it possible that reducing class size would actually have a negative effect, instead of a small positive one?

We already have difficulty attracting teachers into teaching, especially in math and science. Doubling the number of teachers would have to entail reducing standards and quality.

Wouldn't the net effect of the lower average teacher quality more than cancel out the small benefits of reduced class size?

Go read the full post and if your statistically savvy, analyze his data and conclusions.

Pretty damn good for his 2nd post though.

(Cross posted at Parentalcation)

### non-school factors and math

from the new blog The Common School, written by an anonymous cog in the D.C ed organization scene:

In general the impact that school-based factors have on reading tests scores is significantly lower than the impact that such factors have on math scores and conversely the impact of non-school factors such as parental education levels is much bigger for reading than for math. Given that parents typically interact with their children more through language than through math, it makes intuitive sense that the parental (and peer etc.) impact on language skills would be larger than their impact on math skills.
A Question of Scale

I've been assuming this was true for some time now, but it's nice to see it confirmed by an anonymous cog.

This phenomenon is clearly true for us.

The ITBS has C. reading at a 12.6 level, which is in the 95th percentile.

At school he's reading books at a 5.1 to 6.5 level.

He's acquiring his reading comprehension at home.

His math is at the 88th percentile, and that's with huge amounts of teaching and reteaching at home. Without our help I assume C. would be much lower. He'd probably have the same kind of Verbal-Math gap our friend D's son ended up with. His SAT-V score was 780 or 790; his math, after massive tutoring, was in the low 600s (iirc).

That's an enormous gap, and it's directly attributable to the constructivist pedagogy of the schools he attended. (Think what that score would have been without the tutor.)

Back to Christopher. The ITBS says he's great on fractions -- and, again, ditto. We've spent lots of time directly teaching fractions at home.

On scales measuring skills we haven't worked on (punctuation, "words with affixes," decimals, etc.) he scores lower.

Looking at C's ITBS report, what I see is very high scores in the areas of "home influence," not so great scores in the areas being handled by the school.

Slide and glide.

### 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.

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!

help desk 1

### fantastic site - homeschooling & afterschooling

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.

Myrtle's find:

also:

### 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

### DIY electronics kit

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

Full-sized photo here.

## Monday, March 26, 2007

### point symmetry

So tonight we've learned point symmetry.

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)

### 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

### 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:

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.

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:

"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.

## Sunday, March 25, 2007

### 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).

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.

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.

### 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:

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

Good.

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?

* Bouchard directs the Minnesota Twin Study.

### 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.