Steve H & Becky C on "independent study"

from May 18, 2006, reacting to a sample tiered instruction assignment:

Where is the "instruction"? There is none, because Tiered Instruction is in their Independent Study section. I looked through everything they had there and all I ever found (in any section) was a reference to "mini-lessons" given by the teacher. They really have to stop using the word teacher or instructor because that is not what they are doing. Differentiated Instruction with no instruction. How about Differentiated Learning. Or, "You're on Your Own Learning".

This write-up looks more like a grading rubric. Perhaps they grade based on what they expect from a child. I've seen this before in job reviews. If you always exceed expectations, then you can't get much of a raise because you are just doing what you normally do. Are they going to give a "meeting expectations" to an "Above Grade Level" child and an "exceeding expectations" to a "Below Grade Level" child, even though the former student did more and better work? Of course, if you read the information at the site, the assessment is fuzzy and all individual. Once a Below Grade Level child; always a Below Grade Level child.

Even if one really thought that tiered (differentiated expectations) is a good thing to do, the explanation and examples on this web site are just so incredibly horrible.

Just look at this assignment. In eighth grade - "create a flag for Nunavut" is an Above Grade Level task. "Write an essay about what you would do if you were Prime Minister." Do about what? Citizenship? What in particular? "Trace your family heritage and present it." Just in Canada? How far back? Why? I've had assignments like this - poorly thought out and whipped together by lazy teachers.

Not only is it a wrong approach to education, it is done very badly.

here is Becky C:

Not a single one of these activities will be graded for quality. Did the Slow kid write well about his most memorable trip in Canada? Did the Medium kid do a good job representing the life of a PM? Did the Fast kid find the right amount of important details about the creation of Nunavat?

This is about teachers sending their teaching work home for parents to do.

As you might guess, we have had quite a few writing assignments sent home to our family this year from the public school. I have been working really hard to teach my boys to write. I have been feeling bitter about this.

Differentiated Instruction does not happen in real life. It is about as scarce as Direct Instruction.

and:

...if even one gullible parent of a 4th grader directly instructs her child how to write a summary paragraph by holding the child accountable for the quality of their paragraph, which is to say that the paragraph contains the right amount of important details... why, that's one more child who magically shows up in 6th grade already knowing how to write, and one less child that will need direct instruction in writing in 6th grade. Magical!

I've just HAD IT with writing assignments that are ASSIGNED to the student but are not GRADED constructively by the teacher as a means of instruction.

HAD IT HAD IT HAD IT

A mom in town here, who is actively concerned about the writing instruction, told me this week she would like to see her child get back just one paper without the sole feedback being the word "Terrific!" written on top.

Apparently she's decided to throw caution to the winds and skip the part about being careful what you wish for ...

no common sense-y

comment left by Paula V:

This is the first year my third grader has had an attitude about a teacher. However, I keep hearing how third grade is a transition year. Perhaps this attitude is part of the territory.

My third grader was cautious up until this year. His classroom is full of boys and only a handful of girls. It seems the boys are ruling the roost, and it is driving the teacher nuts.

His teacher is young and sweet, but I fear she isn't very effective in illicting compliance among her boy students. Taking away recess points in a room full of boys isn't working.

My sister, a former middle school teacher, said that was not a good strategy. Single out the misbehaving kids and take away their points. I told her that would never happen...it might embarrass someone. She said that was absolutely ridiculous.

[snip]

No, my son's teacher does not single the misbehaving students out. Yes, she keeps the whole group inside.

When I questioned her on the taking away of recess points, she said children must understand how to work within a group. They need to know how to make wise decisions as a group.

Fuzzy thinking, fuzzy ethics, and a violation of the Geneva Convention to boot!

magic white people

Over at ktm - 1 we got to talking about magic white people at some point (scroll down), magic white people being middle and upper-middle class white parents who somehow manage to imbue their children with advanced K-5 knowledge and skills over the dinner table.

Judging by Monday's op-ed, white folks are getting more magical by the minute:

Schools serving mostly wealthy and white students have a distinct advantage when it comes to testing. Their students are far more likely to be raised in an environment that gives them the necessary tools to succeed on tests. They grow up with the intellectual abundance their wealth provides: books, educational videos and Baby Einstein games, to name a few. Having these resources may not make children smarter, but it does educate them in many of the skills -- such as letter sounds and addition facts -- that are covered on standardized tests. Knowing their students are likely to succeed on tests gives these schools freedom to teach higher-level thinking skills.

Who knew a child could learn phonics and phonemic awareness from Baby Einstein games?

If parents would just do their job and expose their kids to books, educational videos, and Baby Einstein games, dyslexia would go away tomorrow!

Of course, if we got rid of the tests we wouldn't have to worry about letter sounds at all.

We could go straight to higher-level thinking.

policy analysts bite back

here

and

here

Responding to Classroom Caste System

Missing from all of these analyses, as usual, is the hapless parent.

You know, the parent, the person actually teaching the basic skills all these white kids supposedly possess in spades before they set foot inside a public school. (gosh. I wonder why we have all those "reading specialists" floating around our K-3 school? Aren't parents supposed to be handling phonics? How could an upper middle class white kid possibly have trouble learning to read?)

The idea that there could possibly be a critical thinking gap when white kids are spending their earliest years in school not learning "basic skills," but checking out "the role of quilts on the Underground Railroad," is plain wrong.

Of course, if NCLB has created a situation in which disadvantaged black and Hispanic children are being taught basic skills and advantaged white children are being taught quilts and dances "based on retellings of Cinderella," we should be seeing the last of the achievement gap pretty soon here.

connect the dots

• by nearly all accounts, constructivism taught in schools of education to the exclusion of all other pedagogies
  

• baby boom teachers retiring

• teaching staffs consisting almost entirely of young, childless females who know one thing and that one thing is constructivism
  

• in some communities, parents who are appreciably more affluent and/or better educated than parents in previous generations - i.e., parents who have some hope of remediating the deficiencies of the school either through their own reteaching of content or by availing themselves of the tutoring that can be provided by district teachers for a handsome fee
  

The result, perceptible only to parents who have children currently enrolled in the public schools, it seems, is a role reversal Tex calls "the new normal."

• newsletters sent home in the backpack telling parents they are responsible for teaching the math facts, and assigning them a deadline by which this feat is to be accomplished

• first-grade spelling lists drawn up for parents along with instructions that the words are to be mastered by the end of the school year
  

• pages and pages of text and PowerPoint slides posted at the DOE telling parents how to "help with homework"

• "We have far greater, bigger things to think about."

• "If students need distributed practice, parents can find worksheets online."
  

• official, university-sponsored involve parents in schoolwork programs with names like "TIPS" (Teachers Involving Parents in Schoolwork)
  

• "contracts" and "acknowledgement of letter" forms for parents to sign re: involvement in child's grades and/or homework
  

• humorous personal narratives about middle school assignments no middle schooler can actually do

• routine references to teachers "requiring" parents to help with homework

• etc.
  

I feel as if I'm living in a parallel universe.

Our pundits, wonks, and columnists reside in a land where wealthy white schools are good to excellent; poor black and Hispanic schools are wretched.

Apparently, in the world of policy analysis, people get what they pay for.

George Bernard Shaw

My father-in-law, a classics professor, and I share a little joke that all educators are socialists, which isn't true, it's a little joke, but a study of socialism has given me a great deal of insight into the hopes and dreams of the nice people who believe in whole language and other constructivist teaching practices. They really mean well. They really mean for us all to enjoy heaven on earth.

My husband has a set of Encyclopedia Britannica volumes published in 1946. It dares call itself "A New Survey of Universal Knowledge." In Volume 20, Sarsparilla to Sorcery, I have looked up Socialism and Socrates and Sophistry, for instance. After Socialism, but before Socrates and Sophistry, there is an entry entitled "Socialism: Principles and Outlook."

Now, the Socialism article itself appears complete at first reading. It gives the origins and history of Socialism; Owenism, Marxism, national movements and the Russian Revolution are each treated in turn. The entry is written by a gentleman named G. D. H. Cole.

But "Socialism: Principles and Outlook" is written by George Bernard Shaw. In the spirit of inquiry, independent research, and consulting original sources, I thought you guys might like the following observation Shaw makes with regards to schooling:

Democracy, or votes for everybody, does not produce constructive solutions of social problems; nor does compulsory schooling help much. Unbounded hopes were based on each successive extension of the electoral franchise, culminating in the enfranchisement of women. These hopes have been disappointed, because the voters, male and female, being politically untrained and uneducated,have (a) no grasp of constructive measures, (b) loathe taxation as such, (c) dislike being governed at all, and (d) dread and resent any extension of official interference as an encroachment on their personal liberty. Compulsory schooling, far from enlightening them, inculcates the sacredness of private property, and stigmatizes a distributive state as criminal and disastrous, thereby continually renewing the old prejudices against Socialism,and making impossible a national education dogmatically inculcating as first principles the iniquity of private property, the paramount social importance of equality of income, and the criminality of idleness.

He continues,

Capitalism has never produced the necessary enlightenment among the masses nor admitted to a controlling share in public affairs the order of intellect and character outside which Socialism, or indeed politics, as distinguished from mere party electioneering, is incomprehensible. Not until the two main tenets of Socialism -- abolition of private property (which must not be confused with personal property), and equality of income -- have taken hold of the people as religious dogmas, as to which no controversy is regarded as sane, will a stable Socialist state be possible....

The private individual, with the odds overwhelmingly against him as a social climber, dreams even in the deepest poverty of some bequest or freak of fortune by which he may become a capitalist, and dreads that the little he has may be snatched from him by that terrible and unintelligible thing, State policy. Thus the private person's vote is the vote of Ananias and Sapphira; and democracy becomes a more effective bar to Socialism than the pliant and bewildered conservatism of the plutocracy.

Hmm. I'd better go find out who Ananias and Sapphira are.

I think Scarsdale is a "pliant and bewildered conservatism of the plutocracy."

So, I'm siding with Vlorbik today. Rather than schools being used as tools for training capitalists or socialists, let's agree to abolish the schools.

comments needed

I've just left a loooong response on The Gadfly.

If anyone else cares to chime in, that would be great.

Vlorbik's find: abolish high school?

This is a terrific article, I think:

"Let's Abolish High School"

The first compulsory education law in the United States wasn’t enacted until 1852. This Massachusetts law required that all young people between the ages of 8 and 14 attend school three months a year—unless, that is, they could demonstrate that they already knew the material; in other words, this law was competency-based. It took 15 years before any other states followed Massachusetts’ lead and 66 years before all states did. Along the way, some powerful segments of society staunchly opposed the mandatory education trend. In 1892, for example, the Democratic Party stated as part of its national platform, “We are opposed to state interference with parental rights and rights of conscience in the education of children.”

Restrictions on work by young people also took hold very gradually. In fact, the earliest “child labor” laws in the United States actually required young people to work. It wasn’t until the late 1800s that laws restricting the work opportunities of young people began to take hold. Those laws, too, were fiercely opposed, and in fact the first federal laws restricting youth labor—enacted in 1916, 1918, and 1933—were all swiftly struck down by the U.S. Supreme Court. After all, young people had worked side by side with adults throughout history, and they still helped support their families and their communities in countries around the world; the idea that there should be limits on youth labor, or that young people shouldn’t be allowed to do any work, seemed outrageous to many people.

Eventually, multiple forces—the desire to “Americanize” the tens of millions of immigrants streaming into the United States to get jobs in the land of opportunity, the effort to rescue millions of young laborers from horrendous working conditions in the factories and mines, the extreme determination of America’s growing labor unions to protect adult jobs, and, most especially, the extremely high unemployment rate (27 percent or so) during the Great Depression—created the systems we have today: laws severely restricting or prohibiting youth labor, and school systems modeled after the new factories, established to teach “industrial discipline” to young people and to homogenize their knowledge and thinking.

Unfortunately, the dramatic changes set in motion by the turmoil of America’s industrial revolution also obliterated from modern consciousness the true abilities of young people, leaving adults with the faulty belief that teenagers were inherently irresponsible and incompetent. What’s more, the rate at which restrictions were placed on young people began to accelerate after the 1930s, and increased dramatically after the social turmoil of the 1960s. Surveys I’ve conducted suggest that teenagers today are subject to 10 times as many restrictions as are mainstream adults, to twice as many restrictions as are active-duty U.S. Marines, and even to twice as many restrictions as are incarcerated felons.

[snip]

Anthropologists have identified more than 100 contemporary societies in which teenage turmoil is completely absent; most of these societies don’t even have terms for adolescence. Even more compelling, long-term anthropological studies initiated at Harvard in the 1980s show that teenage turmoil begins to appear in societies within a few years after those societies adopt Western schooling practices and are exposed to Western media. Finally, a wealth of data shows that when young people are given meaningful responsibility and meaningful contact with adults, they quickly rise to the challenge, and their “inner adult” emerges.

A careful look at these issues yields startling conclusions: The social-emotional turmoil experienced by many young people in the United States is entirely a creation of modern culture. We produce such turmoil by infantilizing our young and isolating them from adults. Modern schooling and restrictions on youth labor are remnants of the Industrial Revolution that are no longer appropriate for today’s world; the exploitative factories are long gone, and we have the ability now to provide mass education on an individual basis.

If this is what differentiated instruction meant, I'd be for it.

abolish college, too?

And here's Walter Russell Mead:

Paying for college education is one of the biggest financial worries facing middle class and working families. Fancy liberal arts schools that let your kids live in essentially unsupervised coed dorms while majoring in such helpful subjects as deconstructionist literary theory and Why America Sucks now cost north of $40,000 per year, and even less-prestigious schools that teach more useful subjects can cost as much per year as a round-the-world cruise. Some kids come out burdened with insane levels of debt; others are frozen out of the market.

The liberal answer is that the government should pick up the ever-escalating cost of supporting Ward Churchill and his fellow astronauts of theory in the lifestyle to which they aspire. But maybe there's an alternative.

There is no reason the government should try to prevent American families who value the traditional college experience from paying hundreds of thousands of dollars, but perhaps it could offer an alternative: a federally recognized national baccalaureate (or 'national bac') degree that students could earn by demonstrating competence and knowledge.

With input from employers [ed.: and, one hopes, from actual disciplinary specialists], the Department of Education could develop standards in fields like English, the sciences, information technology, mathematics, and so on. Students would get certificates when they passed an exam in a given subject. These certificates could be used, like the Advanced Placement tests of the College Board, to reduce the number of courses students would need to graduate from a traditional college. And colleges that accepted federal funds could be required to award credits for them.

But the certificates would be good for something else as well. With enough certificates in the right subjects, students could get a national bac without going to college. Government agencies would accept the bac as the equivalent of a conventional bachelor's degree; graduate schools and any organization receiving federal funds would also be required to accept it.

Subject exams calibrated to a national standard would give employers something they do not now have: assurance that a student has achieved a certain level of knowledge and skill. It is the easiest thing in the world today to find English majors with BA degrees from accredited colleges who cannot write a standard business letter. If national bac holders could in fact perform this and other specific tasks that employers want their new hires to perform, it is likely that increasing numbers of employers would demand the bac in addition to a college degree. Students who attended traditional colleges would increasingly need to pass these exams to obtain the full benefits of their degree.

For students from modest or low-income homes, as well as for part-time students trying to earn degrees while they work full time jobs or raise families, the standards would offer a cheaper, more efficient way to focus their education. Students could take prep courses that focused on the skills they actually needed to do the jobs they sought. Parents could teach their kids at home. Schools and institutes could offer focused programs. Public records could show how well students performed on the exams, offering students and parents far more accountability and information than they now get.

Such programs would be both cheaper and more flexible than conventional college degree programs. The contemporary American college is solidly grounded in the tradition of the medieval guilds. These guilds deliberately limited competition to keep fees high. In the best of cases, guild regulation also protected consumers by imposing quality and fairness standards on guild members. Few observers of American education today would argue with straight faces that the quality of undergraduate education is a major concern of contemporary guilds like the American Association of University Professors. Colleges today provide no real accounting to students, parents, or anybody else about the quality of the education they provide. No other market forces consumers to make choices on so little information.

One consequence of this poorly functioning market is to grossly exaggerate the value of "prestige" degrees. Especially these days, a lot of kids work very hard in Ivy League colleges, but others still major in booze and other diversions. Meanwhile, there are plenty of kids studying at, say, Regular State University, where they work very hard at demanding courses under tough professors. A national bac exam would allow these kids to compete on a level playing field against the Harvard and Yale grads; employers could look at the scores and see for themselves which kids knew more.

Less unearned privilege for Harvard, more opportunity for Regular State....
As a Yalie myself and a part-time college professor to boot, I find these ideas a bit unsettling. But to voters worried about paying for education, resenting the advantages that prestige diplomas confer on a handful of mostly privileged young people from well-to-do families, and conflicted about the lack of practical focus, educational coherence, and moral guidance found at so many colleges today, an alternative route to a college degree might seem like a helpful idea.

And, by the way, to hardworking immigrants slogging through night school, to working single mothers trying to improve their lives and their kids' prospects, and to many other Americans who don't have the time or money for frills but urgently need a serious college degree, these reforms would open the door to a better life.

By setting open standards for the national bac, and by allowing anybody to offer the service of preparing students to take the exams, Congress could break the guilds' monopoly on education. A century ago higher education was still a luxury, and it scarcely mattered that it was offered only by arcane guilds in a system that took shape in the Middle Ages. But today many people of very modest means need a BA-equivalent degree to succeed in the workplace.

The power of the guilds in the goods-producing industries had to be broken before the factory system could provide the cheaper goods of the industrial revolution. The service and information revolutions require the breakup of the knowledge guilds: The professoriat is a good place to start.

experimenting with students' lives

The proposed changes to Scarsdale High's curricula (pdf file) are, admittedly, an experiment:

Second, for at least the first five years after SATP is initiated, the school will solicit feedback from college and university admissions officers during and following each admissions cycle, with the aim of determining how the program has affected student access to the colleges and/or Scarsdale students’ attractiveness as candidates.

Third, the school will conduct cohort studies of students for at least the first five years after the SATP is initiated, in order to understand the program’s impact on their success in college and on their college experience more generally.

I served on the board of the National Alliance for Autism Research for seven years. The IRB process is stringent, intricate, and time-consuming. I don't know whether it's correct to say that this is as true of research involving animal subjects as it is for human subjects, but I do know that animal research is also closely scrutinized by IRB boards. As I recall, we rejected at least one project due to animal welfare issues. (I could be remembering this incorrectly; it's possible we sent it back for revision. My memory, however, is that we decided not to fund.)

question:
How much time and energy has the administration of Scarsdale devoted to meeting IRB requirements?

answer:
None.

Schools are not required to obtain permission from parents or undergo IRB review in order to conduct research using their students as human subjects.

A ktm commenter left this link a couple of weeks ago:

Committee on the Use of Human Research Subjects: Exemptions

Research that is

• conducted in established or commonly accepted educational settings, and
• involves normal educational practices.

Generally applies to the study of teaching methods, strategies, and curricula in the process of education. If individuals may be identified directly or indirectly, file for Expedited Review.

FERPA and PPRA also regulate research in school settings and limit information that may be gathered from schools and minors without subject or parental consent.

FERPA

Protection of Pupil Rights Amendment

These 19 curricular projects have essentially been experiments.

animal moms and kids

These photos are wonderful.

(from Drudge)

3 strikes against pure discovery

pdf file posted here

stickiness

I mentioned this book a few weeks back, and am finally getting a link posted:

Made to Stick: Why Some Ideas Survive and Others Die

It's terrific.

the website

Made to Stick in TIME Magazine

Made to Stick in U.S. News


U.S. News

It seems to happen every day. A meeting is called to outline a new strategy or sales plan. Down go the lights and up goes the PowerPoint. Strange phrases appear—"unlocking shareholder value," "technology-focused innovation," "maximizing utility." (What does that mean?) Lists of numbers come and go. Bullet point by bullet point, the company's goals float across the screen.

I think we can all agree that concepts like "technology-focused innovation" are not made to stick.

Of course, I would have said the same thing about activating prior knowledge and constructing your own knowledge.

So don't listen to me.

thinking, not teaching, in Scarsdale

Tex reminded me of this line from the Trailblazers implementation story:

Teachers are continuing to shift their emphasis from teaching material to focusing on children's thinking and learning.

constructivist coup in Scarsdale

Proposal for Advanced Topics Implementation

Ed is reading it now: "This is an unbelievably radical document."

It's also, for my money, one of the most fatuous.

Here's Jay Mathews.

The middle school model comes to Scarsdale High.

more later

Doug on rebuttable presumptions and other things

Second, anyone who would use the phrase, "we have been inserviced on", in a discussion of the teaching of language must be considered presumptively untrustworthy. There is a more-widely understood synonym of "inserviced on" that one might expect a teacher to know and use: "taught".

Willfully and egregiously bureaucratic phrasing of this sort raises a rebuttable presumption of a willfully and egregiously bureaucratic mind. I contend that presumption has not been rebutted in this case.

Damn straight.

school boards behaving badly

A picture is worth a thousand words.

It's all here.

The silencing of parents and taxpayers.

The righteous rejection of accountability (a school superintendent who cannot be criticized "in public").

The standing rule that parents can speak for themselves only,^* followed by the dismissal of parent concerns as merely "personal."

And, finally, the core belief that school personnel possess a natural right to do what they want to do.

No matter what.


that said .....

That said, I'll add that I've seen nothing as bad as this in Irvington. Not even close.

Of course, I also haven't seen anyone with the ba*** to ask whether the Board is planning on rehiring the superintendent right in the middle of a board meeting.

Whoa.

I wonder what the school board will make of this parent?

If they're smart, they'll realize she is trouble-with-a-capital T.

She's not the only one.

Back to Irvingtonland, I gather there are quite a few parents in town who want to see the district move to something more akin to a business model.

Good idea! (I think.) In the business model -- not that I know anything about the business model -- I believe folks have the expression, "Make it go away."

That's what this school board needs to do with this superintendent -- and with this parent.

[ ummmm..... I'm not saying the parent should "go away." I'm saying the problem this parent represents should go away. ]

The superintendent needs to move on to another district; the board needs to move on to other business. They need to dump TERC, Connected Math, and whatever constructivist text they're using in the high school (I assume this parent was exercised about something to do with TERC, though I don't know) and be done with it.

Make it go away.

School boards and administrators need to develop street smarts.

Yes, on paper it says that boards and administrators wield absolute power.

But in reality no one wields absolute power, not even the most brutal totalitarian dictators (something we'd all know if our schools taught history instead of social studies).

Administrators and school boards need to start horse trading like the rest of the world.


update

Actually, there are probably plenty of savvy administrators who know how to horse trade, and who do horse trade.

Or, perhaps more likely, there are probably plenty of savvy administrators with the political good sense to pick and choose their battles.

Probably school boards, too.

That's not what we see in this video.

________________


^* hit refresh a couple of times if page doesn't appear

Ken De Rosa in debate on whole language at Edspresso

Ken De Rosa who is familiar to readers of KTM II and his own D-Ed Reckoning can be read in action now here as he takes on Nancy Creech, a whole language teacher from Oxford Michigan. For those looking for a fight on the order of Rocky Balboa vs Apollo Creed, this would not be the place in my opinion. Ken's arguments and command of facts makes it look more like Bill Clinton vs Lyndon Larouche. I'll let you figure out who's who.

Common Algebra II Test

Nine States announced that they will give a common test for algebra II starting next year. Achieve.org is helping design the test.

Arkansas, Kentucky, Indiana, Maryland, Massachusetts, New Jersey, Ohio, Pennsylvania, and Rhode Island will share standards and the tests, and are expected to release scores on the test to colleges.

Apparently, this is being driven by the recent research that showed students that pass algebra II are more likely to succeed in college. U.S. News carried this article today.

This seems like a great idea. Now I need to lobby my State Dept of Ed to join in. If the colleges find it useful, I hope it puts pressure on many more states to join the group.

new math blog!

Math Concepts Explained

This is serendipity. Christopher began a unit on functions today!

update

For some reason I'm having a terrible time posting sidebar links to other Blogger blogs.

I'll keep trying...

If anyone has any suggestions, let me know.

down the rabbit hole

from The College Puzzle

The National Assessment of Educational Progress (NAEP) released the grade 12 results recently. The results in Reading demonstrate a decline between 1992 and 2005. The results do not bode well for aspirations of higher academic readiness, college preparedness and college success.

[snip]

The results found that the reading skills of 12th graders tested in 2005 were significantly worse than those of students in 1992, the first time a comparable test was given, and essentially flat since students took the exam in 2002. The share of students lacking even basic high school reading skills -- meaning they could not, for example, extract data about train fares at different times of the day from a brochure -- rose to 27 from 20 percent in 1992. The share of those proficient in reading dropped to 35 from 40 percent in 1992.

Yet, high school graduates in 2005 had studied more than their counterparts in 1990, averaging 360 more hours of classroom instruction during their high school years, the transcript study showed. Their grade point average was a third of a letter grade higher than in 1990, and more students were taking foreign language and other courses aimed at preparing them for college.

[snip]

The bottom line is that high school students are taking harder courses and earning better grades yet reading at significantly lower levels than their peers did 13 years ago.

This decline comes on top of the twenty-year decline in SAT scores that took place between 1963 and 1980.


in a nutshell

• Average SAT verbal scores fell from a high of 478 on the verbal portion in 1963-1964 to a low of 424 in 1980, where they have essentially remained for 27 years.
  

• In 1995 the College Board recentered SAT scores, adding approximately 70 points to verbal scores. (SAT individual score equivalents here)

• The new NAEP 12th grade scores "demonstrate a decline between 1992 and 2005."

• Percent of students lacking basic high school reading skills rose from 20 percent in 1992 to 27 percent today.

• A high school student who lacks basic high school reading skill cannot "extract data about train fares at different times of the day from a brochure."
  

• The share of those proficient in reading dropped to 35 from 40 percent in 1992.

• smoking more and enjoying it less: "high school graduates in 2005 had studied more than their counterparts in 1990, averaging 360 more hours of classroom instruction during their high school years."

• grade inflation: GPA for 2005 12th graders "was a third of a letter grade higher than in 1990, and more students were taking foreign language and other courses aimed at preparing them for college."

• smoking more and enjoying it less, part 2: "number of students who took 4 years of English is up from 40% in 1990 to 68%"

more:

This is alarming because many states, including California, have been making significant gains at elementary grades, and it doesn't show up here in 12th grade.

My sister-in-law, who is a superb elementary school teacher, told me on this trip that in her district the K-5 teachers "have it together."

She sees a problem with teachers and teaching in the upper grades, which, given her description of her high school child's experience, sounds right to me.

The bottom line is that high school students are taking harder courses and earning better grades yet reading at significantly lower levels than their peers did 13 years ago.

I'm thinking....SAT & ACT scores haven't declined significantly during these 13 years, have they?

ACT research page

ACT Research

speechless

Googling the phrase "homework gap" this morning, I came across this piece of advice to teachers about how to assign homework:

Be careful about parent involvement. Consider the time and skill resources of parents when requiring their involvement. [emphasis added]

Apparently, we have now reached the point at which teachers can require that parents teach their kids, but parents cannot require that teachers teach their kids.

predatory reading

from Bowdoin:

Reading scholarly material requires a new set of skills. You simply cannot read scholarly material as if it were pleasure reading and expect to comprehend it satisfactorily. Yet neither do you have the time to read every sentence over and over again. Instead, you must become what one author calls a "predatory" reader. That is, you must learn to quickly determine the important parts of the scholarly material you read. The most important thing to understand about a piece of scholarly writing is its argument. Arguments have three components: the problem, the solution, and the evidence. Understanding the structure of an essay is key to understanding these things. Here are some hints on how to determine structure when reading scholarly material...

how to ask good questions

This page seems pretty good:

1. Good questions require thought and research. It is easy to pose a question like "should the atomic bomb have been dropped on Japan?" Such a question is simply an opinion question: it requires no research or special understanding into the problem. One way to begin framing better questions is to steadily add facts into the stew. These complicate your argument, basing it on solid historical premises (which of course you would need to prove in an essay). Think in terms of "givens." For example:

• Given that the Japanese military establishment had vowed to fight to the bitter end, should the United States have dropped the bomb on Japan?
• Given that the United States' government was becoming increasingly concerned with post-war struggles with the Soviet Union, should the United States have dropped the bomb on Japan?
• Given that many in the United States expressed what may be called racist views of the Japanese, and in fact interned Japanese Americans in concentration camps during the war, should the United States have dropped the bomb on Japan?
• Given that the United States had already embarked on an extensive and deadly campaign of carpet-bombing Japanese cities (like Tokyo), should the United States have dropped the bomb on Japan?

2. Explore premises and make them explicit. The questions above are not quite explicit enough. For example, so what if many in the United States were racist towards the Japanese? What does that have to do with the legitimacy of dropping the atomic bombing?

[snip]

3. Keep going. Even these questions can be further broken down:

Did racism lead the U.S. to drop the bomb on Japan when it would not have done so on Germany? How exactly did American views of the Japanese and Germans differ? How could such popular cultural views have influenced a foreign and military policy thought to be rational?

[snip]

As you can begin to see, once you start thinking about it, one simple question can lead to a huge chain of questions. Remember, it is always better to keep asking questions you think you cannot answer than to stop asking questions because you think you cannot answer them. But this can only happen when you know enough about your subject to know how to push your questioning, and this depends on reading and understanding the assigned material.

helpful pedagogy or hellish event?

I've been cruising writing across the curriculum websites. (scroll down)

a history professor explains how he grades papers

fact, argument, etc.

writing in the disciplines at Cornell

The WAC Journal (all articles online)

WAC bibliographies

writing across the curriculum at George Mason

sample college English papers

Bowdoin: writing history papers (terrific)

"vacation" over

Ed spent 2 hours helping with homework last night.

Easter Sunday. Two hours.

He had to spend two hours helping with homework because once again C's ELA assignment was over his head.

He was to do a "quote analysis," but he doesn't have the necessary skills to do a quote analysis on his own.

For one thing, he has no idea how to select an appropriate quotation to analyze. This is a highly sophisticated skill [see below].

Nor does he understand what his reader does and does not know; he doesn't know what he should explain and what he can assume. He doesn't know that he should be thinking about these things, either.

He simply has no idea how to write expository prose -- and, of course, he's spent practically no time reading expository prose. He spent 5 years in K-5 writing personal narratives (an approach to writing instruction that now appears to be installed as permanent practice K-5 here in Irvingtonland). And that's about it.

So his idea of analyzing a quotation from The Curious Incident of the Dog in the Nighttime was to inform the reader that the boy in the story reminds him of Andrew.

Then, after that, he wanted to talk about the (autistic) character's feelings.

Of course, that will probably turn out to be what he was supposed to do, and Ed will have racked up another B- in middle school. He's probably got it coming. Christopher opened his analysis with a sentence that went something like, "The quotation tells about the character," and Ed made him get rid of it. C protested, saying he's supposed to start his paragraph with an introductory sentence; Ed said C.'s introductory sentence wasn't a very good introductory sentence.

I can see where that's headed.

Ed is sooooo annoyed.

This is a person who has spent his entire career teaching and refining his teaching. In particular he has spent years of his life figuring out what a good assignment is and is not.

A good assignment, according to Ed, is first and foremost an assignment a student can actually do.

Of course, you don't have to be a college professor to figure that one out.

A good assignment, he says -- and you do need to be on top of your game to figure this one out -- does not simply send a student off into the night to "write a paper." Or, in C's case, to perform a "quote analysis."

Undergraduate students, even very bright, accomplished students, aren't academically ready to choose their own topics; nor are they adept at shaping a topic once they've chosen it.

Just to put in my own two cents: finding and shaping a book topic is HELL. I've been a professional writer for years, and it still takes me months to home in on a topic. Finding and shaping a topic is never going to be easy for me.

So why would you send 12 year olds off to find their own quotes to analyze?

Ed says the teacher needs to have all the kids read the same book -- or choose one from a small selection of books. Then she needs to select the quotes herself. Here, too, she could offer choice; she could choose a handful of telling lines from the handful of novels she's provided. If the object is to give kids choice so as to allow them to activate prior knowledge and whatnot, she can do this by providing limited choice.

Ed always gives his students suggested topics. He is a professor European history at NYU; his students are smart and reasonably-to-very-well prepared to do college work. Also, none of them is 12.

Nevertheless, Ed does not expect them to choose their own topics.

Last year, after listening to me talking about formative assessment, he decided to give his students explicit instruction in writing history papers.

He told his students how long their papers should be and how many subtopics would be too many. He wrote model introductory paragraphs; he looked over the students' introductory paragraphs if they wanted him to and told them how to revise.

In one semester his students went from grades of C and B- to grades of B+ to A.

None of this professional expertise is of the slightest interest to our district. Ed is a parent, and the views of parents are foolish, old-fashioned, and plain wrong by definition. I believe I mentioned that one of our administrators recently said to him, after Ed pointed out that he had been a "disciplinary specialist" for 25 years, "Did you ever think that might be your problem?"

logic alert: Well, suppose that is his problem. So what? Everyone else around here has the same problem. Everyone wants his kids to go to college; Ed is a college professor. What Ed has to say about what college professors are looking for in a college paper ought to, at a minimum, arouse some curiosity.

You'd think.


Twiki fiasco

Some of you probably remember that I wrote up a detailed post about all this last year; then Twiki lost it. So I'm going to interview Ed soon and rewrite it.

I have to get to this, because it's obvious the middle school is fixing to implement a writing workshop model next year. I'm going to campaign for a "prep school model" or maybe a "writing in the disciplines" model, in lieu of or in addition to the writing workshop model so dear to our administrators' hearts.

(Naturally we'll be expected to cough up more money to fund the model; there's a second teaching-learning facilitator on the budget. We hired our first last year; the super said an evaluation would be performed of the first one, but that seems not to have happened. Instead we are receiving glowing backpack letters about our fourth and fifth-graders workshopping their writing under the watchful eye of teaching-learning facilitator number one.)

Memoirs, ahoy!

do poor people need better character?

source:
Quantity Over Quality
by Darius Lackdawalla


So....74% of parents who failed to graduate high school themselves report helping their kids with homework.

Compared to 96% of parents who attended graduate or professional school.
source:
Parent and Family Involvement in Education: 2002-2003 (pdf file)

I'm going to recommend again that New York Times columnists and New York Times Magazine feature writers stop obsessing over poor people's character and start obsessing over why parents are serving as their kids' reteachers, especially given the fact that we've experienced a very large drop in average class size over the past 40 years.


update: it's official

A couple of years ago I looked up "homework" on the DOE website and found a short article describing the qualities of a good homework assignment.

The qualities of a good homework assignment, as I recall, pretty much boiled down to statements like this one:

The purpose of homework is to provide additional practice on previously introduced skills or to enrich classroom experiences.

That was then.

What do I get today if I search ed.gov for "homework"?

Hundreds of links on how parents can help with homework & What Teachers Can Tell Parents about Homework.


help with homework

Edie Pistolesi on Van Gogh

Three points:

1. Contemporary pedagogy in art education begins with the idea that art
comes from the art that came before us and from culture. It has been
long acknowledged that we all learn by copying. We, meaning all of
us-kids, grown-ups, Van Gogh, Picasso, other artists-everybody. Art
teachers are supposed to teach by teaching specific skills & concepts to
empower kids to express the ideas of art. Using the work of artists to
show how artists used color, texture, line, etc. to express ideas IS the
way to teach art. Anybody who still thinks that "art comes from within"
is suffering from what might be called the "20th century hang-over." You
have the right idea and stay true to it! Fear of contaminating kids by
teaching them something is so 1950s.

2. When Commodore Perry opened the door of Japan to the world in 1858,
artists went wild! The book "Japonisme: The japanese Influence on
Western Art Since 1858" (S. Wichmann,2001) shows how many, many artists,
including Van Gogh, copied japanese images. And they didn't just copy
in a loose or general way. Van Gogh created carefully constructed grids
in his efforts to understand the structure and composition of the
Japanese art.

3. Some quick thoughts: Get past VG's personal problems with the ear
story right away. Talk about him as a serious artist who learned how to
draw from copying from books and other art, just like the other artists
of his time. If you are going to show the painting of the sunflowers, I
would also include a bouquet of real sunflowers for kids to see and
examine closely. Looking at the real ones and VG's painting, examine
VG's yellows. Those yellows are not straight from the bottle, but have
lots of color blended into them. And look at the textures caused by
VG's brush strokes. The kids can learn a lot by copying these things,
"in the manner of VanGogh."

Also, VanGogh said that art was like algebra: there are certain
foundational skills that are necessary to know, and must be learned.


Best of luck,
Edie Pistolesi
Professor of Art
Department of Art; Art Education area
CSU Northridge

help with homework

I've just found an amazing statistic:

In kindergarten through grade 12, 95 percent of children had parents who reported they assisted with homework (table 4).

source:
Parent and Family Involvement in Education: 2002-03 (pdf file)
NCES

Table 4 reveals that only 16% of students in grades 11 and 12 have parents who report giving no help with homework at all.

Even more incredible, parents who did not themselves graduate from high school report spending more time helping with homework than parents who have attended graduate or professional school. (Don't know whether the difference is significant.)


parents helping w/homework 1-5 days a week, by education level

Less than high school: 74%
High school grad or equivalent: 73%
Vocational/technical education
after high school or some college: 71%
College graduate: 68%
Graduate or professional school: 67%


Ed went to school in Levittown, PA. He had no help with homework, and yet somehow managed to acquire an education good enough to prepare him for Princeton.

Steve H has said many times that he received an education good enough to major in science and math in college (first physics, as I recall, then computer science?)

No help with homework in Steve's case, either.

The bad gets normal.


reality show

Ed says he'd love to see a student body swap.

Send all the Yonkers kids to Scarsdale; send all the Scarsdale kids to Yonkers.

Keep the teachers, principals, and superintendents in place.

What happens to the scores?


meet the parents

copying sunflowers

I have been reading up on Vincent Van Gogh to prepare to give a short Art Literacy lesson at my children's school. I will read from a script, but I do a better job if I have read more than the script, beforehand.

The constructivist ethos of our Art Literacy program is to give children as much freedom as possible in achieving the production goal that follows each lesson. In this case, the goal for each child will be to paint a sunflower and show its texture by using specially thickened paint and a palette knife. Vincent used a lot of paint on his canvases.

In art, as in learning to read words or to add numbers, constructivists do not want children copying someone else’s good idea, whether it's how to paint a sunflower or how to sound out a word or how to add two numbers by counting-on. The child who copies is the child of a lesser god. He has fallen short of the goal of constructing original aesthetic or literary or mathematical meanings.

So I will read the Van Gogh lesson script and assign the painting, but I'm not supposed to finish what I've started by leading the children step by step through one method of creating one copy of one of Vincent's sunflowers. I show them one sunflower, and then let them learn the rest by doing it themselves as best they can. Once. Because they won't get a second chance because there isn't time.

They must copy one of Vincent's sunflowers, but I can't teach them how to use the tools they are given to achieve an aesthetic meaning that would be mine and not their own. I would be putting words in their mouths, so to speak, if I led them.

I was amused to read letters that Vincent wrote to his brother Theo and find that Vincent was often quite skeptical of his fellow artists and their methods. Among other observations, here is one excerpt from a letter he wrote from St. Remy on the subject of copying another artist’s work:

It is a kind of study that I need, for I want to learn. Although copying may be the old system, that makes absolutely no difference to me. [I have copied the Pieta and] I am going to copy the Good Samaritan by Delacroix too. What I am seeking in it and why it seems good to me to copy them I will tell you - they are always asking we painters to compose ourselves and be nothing but composers. So be it - but it isn't like that in music - and if some person plays Beethoven, he adds his personal interpretation - in music and more especially in singing - the interpretation of a composer is something, and it is not a hard and fast rule that only the composer should play his own composition. Very good - and I, mostly because I am ill at present, I am trying to do something to console myself for my own pleasure. I put the black and white [Pieta] by Delacroix… in front of me as a subject - and then I improvise colour on it, not, you understand, altogether by myself, but searching for memories of their pictures - but the memory, the vague consonance of colours which are at least right in feeling - that is my own interpretation.

Many people do not copy, many others do - I started on it accidentally, and I find that it teaches me, and above all it sometimes consoles me.

I am sorry he was not consoled more, sooner.

During the Art Literacy lesson we are to tackle the subject of Vincent’s mental illness right out of the box because even the littlest kids already know that he cut off his ear, and we need to manage their interpretation of the event.

We can also say that Theo sent Vincent money to keep him alive and painting, and we can say everybody is sad that Vincent never knew how famous his paintings would become.

But we don't tell the children that he made copies. Or that he took art lessons in Paris and he read books on technique that Theo bought for him. We don’t explain that Vincent made preparatory sketches and studies before he painted. We skip right over his many careful revisions, as he frequently returned to favorite subjects in favorite colors like sunflowers. We don't tell the children that, in his correspondence with Theo (who was working for an art dealer in Paris) the two of them were always desperately trying to figure out how to sell more of Vincent's paintings.

Number Sentences

On the SAT 9 math test for the spring of fourth grade (or the fall of fifth), you’ll find items talking about “number sentences,” a remnant of New Math that has been resurrected in the New New Math. Go visit the mathematics department of a good university and ask a senior mathematician if “math is a language,” with “sentences” and the like. Chances are fair that someone will start screaming at you, or even might just beat you up.

Your State Test Was Not Divinely Inspired

Doomed By Careless Math Errors

My 5th grader brought home her recent pre and post-tests on fractions. I can't fault the schools, teachers, or the typically lousy EM curriculum on this one. The topic is appropriate -- fractions in 5th grade requiring her to find the common denominator, add or subtract or multiply, and putting fractions in order, least to greatest. She's had plenty of classroom instruction and practice (she's also had a lot of afterschooling on this as Singapore Math's 5A and 5B spend a lot of time mastering fractions). The tests themselves were not particularly challenging.

So what's the problem? On a test she could easily have gotten 100% she got a 78. Why? Careless errors. She added when she was supposed to subtract, she failed to read the question properly, one she skipped entirely -- just missed the question. The one she skipped she got right on the pre-test. The ones she got wrong on the post-test she got right on the pre-test and vice versa.

So what next? Pedagogically, instructionally, what is the best way of getting kids to take their time and be careful? Is this just one of those 5th grade things? I'm tempted to ask the teacher for a copy of the test and have her retake it. Is there anything gained by having a consequence/punishment for carelessness?

Attention to detail seems critical in math. Am I overreacting? Anyone have success with this particular aspect of teaching?

Math Study Guides - SparkNotes

Math Study Guides - SparkNotes

Another math site.

This one covers prealgebra through Calculus BC II. It covers all the formulas, has sample problems and has online tests for each class.

I am more certain than ever that my 3rd grader could probably complete Algebra by the end of 5th grade. He knows 50% of the stuff covered in the prealgebra test already.

against Saxon

Linda Seebach's column on Ron Aharoni, with a swipe at Saxon Math (not from Linda, but from mathematician Alexander Givental).

I will say that I've thought for awhile that if I were starting a homeschool program, I'd probably choose Primary Mathematics for grades K-6, then switch to Saxon.

Don't know exactly why I think that & can't justify it logically.

But that's where I seem to have ended up.

I would write more, but I have to pack and catch a plane for Evanston. However, you can find several posts about Aharoni's terrific work over at the old ktm (link to "Posts Search" on the sidebar); Linda's column tells you where to purchase Aharoni's book.

Aharoni's wonderful article in American Educator is here,

Back in a week!


(I'm taking Saxon Algebra 2 with me....)

Effective Programs in Elementary Mathematics: A Best-Evidence Synthesis

I stumbled upon this recent metastudy on elementary math programs by Bob Slavin.

Here is the summary.

Here's the whole thing (DOC). (Link fixed)

There are lots of good observations in it,

• How few math curricula perform well in research studies,
• How many bogus post hoc studies are out there,
• How Bob Slavin shouldn't be doing an objective study involving his own programs, and
• I caught a mistake involving the CMC study I recently blogged. It was randomized, not post hoc.
  

I figured I'd release the KTM brain trust on it to pick it apart.

in case your child needs to select a poem from a book or anthology

The Harp and Laurel Wreath: Poetry and Dictation for the Classical Curriculum
by Laura M. Berquist
wonderful!

A Family of Poems: My Favorite Poetry for Children
by Caroline Kennedy

The Best-Loved Poems of Jacqueline Kennedy Onassis
by Caroline Kennedy


All 3 seem to be good (not that I've spent a lot of time reading them).

Laura Berquist's book is wonderful. Ed deliberately had Christopher choose The Charge of the Light Brigade in order to make a point about the importance of classical education.

He's really had it.


silver lining

The good news is: I now know that the name Alfred, Lord Tennyson includes a comma.


help desk
in case your child needs to select a poem from a book or anthology

"learning"

This is hilarious.

non-school factors, math, and reading

More confirmation that advantaged kids get their reading comprehension at home & their math at school. (I'm adding bullets.)

I had been particularly influenced by Wesley Becker's famous Harvard Educational Review article (1977) noting that the impact of early DISTAR success with decoding was muted for reading comprehension in later elementary grades by vocabulary limitations. Becker argued that this was a matter of experience rather than general intelligence by observing that while his DISTAR students' reading comprehension fell relative to more advantaged students by grade 4, their mathematics performance remained high.

• He suggested that the difference was that all the knowledge that is needed for math achievement is taught in school, whereas the vocabulary growth needed for successful reading comprehension is essentially left to the home.
  

• Disadvantaged homes provide little support for vocabulary growth, as recently documented by Hart and Risley (1995).
  

• I was further influenced by the finding of my doctoral student, Maria Cantalini (1987), that school instruction in kindergarten and grade 1 apparently had no impact on vocabulary development as assessed by the Peabody vocabulary test. Morrison, Williams, and Massetti (1998) have since replicated this finding.
  

• This finding is particularly significant in view of Cunningham and Stanovich's (1997) recently reported finding that vocabulary as assessed in grade 1 predicts more than 30 percent of grade 11 reading comprehension, much more than reading mechanics as assessed in grade 1 do.

source:
Teaching Vocabulary:
Early, Direct, Sequential
by Andrew Biemiller


Our schools here teach vocabulary K-8 (don't know about high school).

As with so many other subjects, vocabulary isn't taught systematically; the kids study word lists from whatever they're reading in class.

I imagine vocabulary instruction here would be more effective if they did some form of systematic instruction, too, but I don't know.

We're still struggling through Vocabulary Workshop, which I continue to believe is a dandy series. (Struggling, meaning struggling to find time to do it.)

I'm curious about the Greek and Latin roots approach, too.


non-school factors and math
non-school factors, math, and reading

The school that isn't

Local News No assignments. No tests. No grades. It's "no problem" for Bothell school. Seattle Times Newspaper:

I wasn't going to blog it. I wasn't really, but it's to easy.

Clearwater is one of about 30 schools that follow the philosophy of the Sudbury Valley School in Massachusetts. Such schools are sometimes called "free" and "democratic" schools, where students are responsible for their own learning and have a significant role in governing the school. They also have many parallels with "unschooling," a movement embraced by some homeschooling families who don't follow a set curriculum.
...
When asked what they like best about their school, Clearwater students say the freedom to do what they want, when they want. Even if that means they might not learn everything students at other schools do.

"I won't say I'm amazingly good at advanced calculus," said Josh Pidcock, 19, who's been at Clearwater since he was 12. "I'm not the most studied reader either. I'm OK with that. I figure I can learn that in a college atmosphere much better.(because college is the place to learn how to read)
...
Two of the graduates are now attending community college, and one is enrolled at Earlham College in Indiana. Two others are working. One student left without graduating, Sarantos said, and is in a job-training program.

Three more are set to graduate this year. So far, Campbell has been accepted at The Evergreen State College in Olympia. Before he applied, he organized a math class at school to prepare for the SAT and studied on his own.

But Clearwater doesn't measure success by college acceptances. (Thank God for that.)

help desk

Ed just spent 3 hours helping Christopher with his ELA assignment.

We are on "vacation."

The assignment is huge.

Select a poem (any poem) from a book or anthology; identify three elements of good poetry; interpret the poem in a "well-developed response"; cite sources according to MLA; type the poem and the assignment (school doesn't teach typing, so I guess that's my job); OPTIONAL: research poet, find out about poet, etc.

This is starting at the top.

So....recent assignments have been way over C's head, but the few books he's been required to read are below grade level.

aargh


Anyway, here's the question.

I am not an English major.

I have no idea how to analyze a poem.

I have no idea, even, how to read a work of 19th century literature intelligently.

I know nothing!

So I need books. Books with shortcuts. Books that will give me a superficial but useable map-of-the-world where poetry analysis is concerned.

I thank you in advance.


being your child's frontal lobes

We've just today managed to figure out that C., although terrifically responsible when it comes to homework he can do, is avoidant when it comes to homework he can't do.

Avoidant means:

• didn't select a poem to analyze from the books at school & copy it down (good thing I spent hours researching and purchasing poetry anthologies last school year!)
  

• avoids the assignment altogether; and fails to mention assignment to parents

I guess we can say he's not proactive when it comes to seeking extra help.


Ed awaits his B-.

.

Effective Mathematics Instruction The Importance of Curriculum

I found a nice little study comparing a fourth grade Direct Instruction math program with a well regarded fourth grade constructivist program. The results were surprising, to say the least. (Cross posted at D-Ed Reckoning.)

The study Effective Mathematics Instruction The Importance of Curriculum (2000), Crawford and Snider, Education & Treatment of Children compared the Direct Instruction 3rd grade math curriculum Connecting Math Concepts (CMC, level D) to the constructivist fourth grade math curriculum Invitation to Mathematics (SF) published by Scott Foresman.

Invitation to Mathematics (SF)

SF has a spiral design (but of course). and relies on discovery learning and problem solving strategies to "teach" concepts. The SF text included chapters on addition and subtraction facts, numbers and place value, addition and subtraction, measurement, multiplication facts, multiplication, geometry, division facts, division, decimals, fractions, and graphing. Each chapter in the SF text interspersed a few activities on using problem solving strategies. Teacher B taught the 4th grade control class. He was an experienced 4th grade math teacher and had taught using the SF text for 11 years.

Teacher B's math period was divided into three 15-minute parts. First, students checked their homework as B gave the answers. Then students told B their scores, which he recorded. Second, B lectured or demonstrated a concept, and some students volunteered to answer questions from time-to-time. The teacher presentation was extemporaneous and included explanations, demonstrations, and references to text objectives. Third, students were assigned textbook problems and given time for independent work.

The SF group completed 10 out of 12 chapters during the experiment.

Connecting Math Concepts (CMC)

CMC is a typical Direct Instruction program having a stranded design in which multiple skills/concepts are taught in each lesson, each skill/concepts is taught for about 5-10 minutes each lesson and are revisited day after day until the skill/concept has been mastered. Explicit instruction is used to teach each skill/concept. CMC included strands on multiplication and division facts, calculator skills, whole number operations, mental arithmetic, column multiplication, column subtraction, division, equations and relationships , place value, fractions, ratios and proportions, number families, word problems, geometry, functions, and probability. Teacher A had 14 years of experience teaching math. She had no previous experience with CMC or any other Direct Instruction programs. She received 4 hours of training at a workshop in August and about three hours of additional training from the experimenters.

Teacher A used the scripted presentation in the CMC teacher presentation book for her 45 minute class. She frequently asked questions to which the whole class responded, but she did not use a signal to elicit unison responding. If she got a weak response she would ask the question again to part of the class (e.g., to one row or to all the girls) or ask individuals to raise their hands if they knew the answer. There were high levels of teacher-pupil interaction, but not every student was academically engaged. Generally, one lesson was covered per day and the first 10 minutes were set aside to correct the previous day's homework. Then a structured, teacher-guided presentation followed, during which the students responded orally or by writing answers to the teacher's questions. Student answers received immediate feedback and errors were corrected immediately. If there was time, students began their homework during the remaining minutes.

The CMC group completed 90 out of 120 lessons during the experiment.

The Experiment

Despite the differences in content and organization, both programs covered math concepts generally considered to be important in 4th grade--addition and subtraction of multi-digit numbers, multiplication and division facts and procedures, fractions, and problem solving with whole numbers.

Students were randomly assigned to each 4th grade classroom. The classes were heterogeneous and included the full range of abilities including learning disabled and gifted students. There were no significant pretest differences between students in the two curriculum groups on the computation, concepts and problem solving subtests of the NAT nor on the total test scores. Nor did any significant pretest differences show up on any of the curriculum-based measures.

The Results

Students did not use calculators on any of the tests.

The CMC Curriculum Test

For the CMC measure the experimenters designed a test that consisted of 55 production items for which students computed answers to problems, including both computational and word problems. The CMC test was comprehensive as well as cumulative; problems were examples of the entire range of problems found in the last quarter of the CMC program. Problems were chosen from the last quarter of the program because the various preskills taught in the early part of the program are integrated in problem types seen in the last quarter of the program.

The results here were not surprising, although the magnitude of the difference between the two groups may be.

The SF class averaged 15 out 55 (27%) correct answers on the posttest up from 7 out of 15 correct on the pre-test. The CMC class averaged 41 (75%) correct on the posttest up from 6 out of 15 correct on the pretest. I calculated the effect size to be 3.25 standard deviations which is enormous, though biased in favor of the CMC students.


The SF Curriculum Test

The SF test was published by Scott, Foresman to go along with the Invitation to Mathematics text and was the complete Cumulative Test for Chapters 1-12. It was intended to be comprehensive as well as cumulative. The SF test consisted of 22 multiple-choice items (four choices) which assessed the range of concepts presented in the 4th grade SF textbook.

The SF class averaged 16 out 22 (72%) correct answers on the posttest up from 4 out of 22 correct on the pre-test. However, surprisingly the CMC class averaged 19 (86%) correct on the posttest up from 3 out of 15 correct on the pretest. I calculated the effect size to be 0.75 standard deviations which is large, even though the test was biased in favor of the SF students.

You read that right, the CMC students out performed to SF students on the SF posttest.

The NAT exam and math facts test

The CMC group also scored significantly higher on rapid recall of multiplication facts. Of 72 items, the mean correctly answered in 3 minutes for the CMC group was 66 compared to 48 for the SF group for the multiplication facts posttest. I calculated the effect size to be 1.5 sd.

Posttest comparisons on the computation subtest of the NAT indicated a significant difference in favor of the CMC group. Effect size = 0.86. On the other hand, neither the scores for the concepts and problem-solving portion of the NAT nor the total NAT showed any significant group differences. The total NAT scores put the CMC group at the 51st percentile and the SF group at the 46th percentile, but this difference was not statistically significant.

Discussion

The CMC implementation was less than optimal, yet it still achieved significantly better performance gains compared to the constructivist curriculum. The experimenters noted:

We believe this implementation of CMC was less than optimal because (a) students began the program in fourth grade rather than in first grade and (b) students could not be placed in homogeneous instructional groups. A unique feature of the CMC program is that it's designed around integrated strands rather than in a spiraling fashion. Each concept is introduced, developed, extended, and systematically reviewed beginning in Level A and culminating in Level F (6th grade). This design sequence means that students who enter the program at the later levels may lack the necessary preskills developed in previous levels of CMC. This study with fourth graders indicated that even when students enter Level D, without the benefit of instruction at previous levels, they could reach higher levels of achievement in certain domains. However, more students could have reached mastery if instruction were begun in the primary grades.

Another drawback in this implementation had to do with heterogeneous ability levels of the groups. Heterogeneity was an issue for both curricula. However, the emphasis on mastery in CMC created a special challenge for teachers using CMC. To monitor progress CMC tests are given every ten lessons and mastery criteria for each skill tested are provided. Because of the integrated nature of the strands, students who do not master an early skill will have trouble later on. Unlike traditional basals, concepts do not "go away," forcing teachers to continue to reteach until all students master the skills. This emphasis on mastery created a challenge for teachers that was exacerbated in this case by the fact that students had not gone through the previous three levels of CMC.

Why didn't the CMC gains show up on the NAT problem solving subtest and total math measure? The experimenters opine:

Our guess is that a more optimal implementation of CMC would have increased achievement in the CMC group, which may have shown up on the NAT. In general, the tighter focus of curriculum-based measures such as those used in this study makes them more sensitive to the effects of instruction than any published, norm-referenced test. Standardized tests have limited usefulness for program evaluation when the sample is small, as it was in this study (Carver, 1974; Marston, Fuchs, & Deno, 1985). Nevertheless, we included the NAT as a dependent measure because it is curriculum-neutral. The differences all favored the CMC program.

That no significant differences occurred either between teachers or across years on the NAT should be interpreted in the light of several other factors. One, the results do not indicate that the SF curriculum outperformed CMC, only that the NAT did not detect a difference between the groups, despite the differences found in the curriculum-based measures. Two, performance on published norm-referenced tests such as the NAT are more highly correlated to reading comprehension scores than with computation scores (Carver, 1974; Tindal & Marston, 1990). Three, the NAT concepts and problem solving items were not well-aligned with either curriculum. The types of problems on the NAT were complex, unique, non-algorithmic problems for which neither program could provide instruction. Performance on such problems has less to do with instruction than with raw ability. Four, significant differences on the calculation subtest of the NAT favored the CMC program during year 1 (see Snider and Crawford, 1996 for a detailed discussion of those results). Because less instructional time is devoted to computation skills after 4th grade, the strong calculation skills displayed by the CMC group would seem to be a worthy outcome. Five, although the NAT showed no differences in problem solving skills between curriculum groups or between program years, another source of data suggests otherwise. During year 1, on the eight word problems on the curriculum-based test, the CMC group outscored the SF group with an overall mean of 56% correct compared to 32%. An analysis of variance found this difference to be significant...

And, here's the kicker. The high-performing kids liked the highly-structured Direct Instruction program better than the loosey goosey constructivist curriculum:

Both teachers reported anecdotally that the high-performing students seemed to respond most positively to the CMC curricula. One of Teacher A's highest performing students, when asked about the program, wrote, "I wish we'd have math books like this every year.... it's easier to learn in this book because they have that part of a page that explains and that's easier than just having to pick up on whatever."

It may be somewhat counter-intuitive that an explicit, structured program would be well received by more able students. We often assume that more capable students benefit most from a less structured approach that gives them the freedom to discover and explore, whereas more didactic approaches ought to be reserved for low-performing students. It could be that high-performing students do well and respond well to highly-structured approaches when they are sufficiently challenging. These reports are interesting enough to bear further investigation after collection of objective data.