explanation, please

$1,675?

How exactly does a publisher arrive at this figure?

I would like to know.

who decides?

from Steve H :

"It's a numbers game. The argument is how many people actually have it and use it. If it's not a significant portion of the population than you can make the argument that it's a ludicrous goal to set that says we have to get every student there."

Who makes this decision and when do they make it?


"This thread poses the argument that the kids have already figured this out, long before the adults."

What, exactly, do they figure out? Do they come to the conclusion that they are just not good in math; that they don't like math? Is that really the case or is that because of bad teaching and curricula? KTM is all about fixing the problem of K-8 math and making sure that kids don't come to the wrong conclusion. It's about keeping educational doors open. Besides, up to a point, I don't care what my son likes or doesn't like. He has to do the work. I will decide which doors to close, and I will thank the school and other adults for not making that decision for me. I would also hope that they would not make that decision for kids who do not have parents who protect them from do-gooders and societal bean counters.

I agree. I have put three children through the public school system, two with autism. For all three of my kids, educators have made assumptions about what they couldn't do that were flat wrong.

Probably our worst experience of this was the public school in Los Angeles where the teacher thought Jimmy was nonverbal. We had no idea they thought that, and when we found out Ed videotaped me working with Jimmy on his flash cards.

"vacuum cleaner"

"newspaper"

After the teacher saw the video, she said, "I wish you'd told us."

E.D. Hirsch: a brief history

Hirsch writes:

In the 1830s Alexis de Tocqueville wrote admiringly: “In the United States the general thrust of education is directed toward political life; in Europe its main aim is to fit men for private life.”

[snip]

The reasons for this communitarian emphasis were obvious to American leaders in the nineteenth century. Loyalty to the Republic had to be developed, as well as adherence to Enlightenment ideals of liberty and toleration. For without universal indoctrination by the schools in such civic virtues, the United States might dissolve, as had all prior large republics of history, through internal dissension.

The aim of schooling was not just to Americanize the immigrants, but also to Americanize the Americans. This was the inspiring ideal of the common school in the nineteenth century, built upon a combination of thrilling ideals and existential worry. By the end of the century we were educating, relative to other countries, a large percentage of the population, and this forward movement continued well into the twentieth century. In the post–World War II period, the US ranked high internationally according to a number of educational measures. But by 1980, there had occurred a significant decline both in our international position and in comparison with our own past achievements. Two decades ago I was appalled by an international comparison showing that between 1978 and 1988 the science knowledge of American students had dropped from seventh to fourteenth place. In the postwar period we have declined internationally in reading from third place to fifteenth place among the nations participating in the survey.

The root cause of this decline, starting in the 1960s, was a by-then-decades-old complacency on the part of school leaders and in the nation at large. By the early twentieth century worries about the stability of the Republic had subsided, and by the 1930s, under the enduring influence of European Romanticism, educational leaders had begun to convert the community-centered school of the nineteenth century to the child- centered school of the twentieth—a process that was complete by 1950. The chief tenet of the child-centered school was that no bookish curriculum was to be set out in advance. Rather, learning was to arise naturally out of activities, projects, and daily experience. A 1939 critic of the new movement, Isaac Kandel, described it this way:

Children should be allowed to grow in accordance with their needs and interests…. Knowledge is valuable only as it is acquired in a real situation; the teacher must be present to provide the proper environment for experiencing but must not intervene except to guide and advise. There must, in fact, be “nothing-fixed-in-advance” and subjects must not be “set-out-to-be-learned.”

By 1950, with new, watered-down schoolbooks and a new generation of teachers trained in specialized colleges for education, the anti-bookish, child-centered viewpoint had taken over the schools. The consequence was a steep decline in twelfth-grade academic achievement between 1962 and 1980, after which, despite vigorous reform efforts, reading and math scores on the federally sponsored National Assessment of Educational Progress have hardly changed.

With the current emphasis on testing and accountability it might be assumed that the days of child-centeredness are now over. But that assumption would miss an essential point. The schools still lack a definite, pre-set, year-by-year curriculum (though this is changing in math) and yet at the same time schools are being required to make measurable progress on year-by-year tests.

How to Save the Schools
New York Review of Books
May 13, 2010
by E. D. Hirsch Jr.

advertisements for myself

A couple of days ago I caught sight of Ed's copy of The New York Review of Books lying on the kitchen table. (Where else?)

I looked at the cover, didn't see anything that caught my interest. Normally that's the end of it. I never look at the table of contents.

For some reason, though, this time I did. I opened the paper, turned to the contents, and was skimming down the list, asking myself why I was doing this since I wasn't feeling any more interested on this second pass, when suddenly I realized I was reading familiar words: Animals Make Us Human: Creating the Best Life for Animals by Temple Grandin and Catherine Johnson. Which hadn't been mentioned on the cover.

I had no idea!

After I stumbled across the review I called Ed to alert him, then left the house without reading more than a few paragraphs. I hate reading reviews. Ed called later to say that it was a "rave," and I still have not read the thing in its entirety.

But I'm glad it's there.

Joanne Jacobs community college blog

it's new!

Math on a farm

Jane wrote:

I suspect that the data that say the vast majority of people don't use math is inaccurate. I suspect that every small business owner is constantly using basic algebra. We have a family farm and constantly, daily use algebra. My contractor calculated angles, areas, amount of paint, flooring, labor and materials necessary to remodel our house. Our banker uses a calculator, but easily and obviously has the mathematical fluency to have a real time conversation about prices, quantities, exchange rates and whether certain data sources are reliable. The sales people we deal with calibrate machinery to determine how much material we need to use on a field. Of course, I check their calibration calculations as well. Yes, we all use tools, but without the understanding of how the math fits together, the tools would be black boxes and we wouldn't know when a number didn't make sense. And we are constantly figuring out, how much seed to put on a field, if a chemical needs to be applied at a certain flow rate and dilution, how fast does the tractor move. If we can x crop and it costs z to grow and we might sell it for a range of y1 - y2, Which crop should we plant.

My dad was a farmer. He always had a slide rule handy on his desk. I was fascinated by it.

I don't know why he had it, and I can't guess because I've never learned to use a slide rule.

I'd like to.

missing knowledge

Barak Rosenshine on teacher effectiveness research:

I suggest that the teacher effects era, between 1955 and 1980, was an impressive run of cumulative research. During this period, over 100 correlational and experimental studies were conducted using a common design and the different observation instruments shared many common instructional procedures. And it was cumulative: researchers cited and built upon the instructional findings of others.

After several years of immersion in the education world, I am just now finding out about this.

Return of the repressed.

success or failure

Constructivist Instruction: Success or Failure by Sigmund Tobias and Thomas M. Duffy

I discovered the book while Googling Barak Rosenshine.

Until last week, reading the Direct Instruction list, I had never heard of Barak Rosenshine. He is apparently Doug Lemov's predecessor;^* he did what Lemov did, which was to find highly effective teachers and then watch what they were doing.

Later on, he trained teachers in the techniques and compared their students' achievement to that of students in classrooms with conventional teachers. The teachers trained in direct instruction were more effective.


^* Please correct me if I'm wrong - just getting into this. Rosenshine has researched teacher effectiveness and summarized the research; I'm not sure which studies he did.

how to start a charter school

Laura sends this resource: Charter Schools Development Center

off-topic: stand up desks

I keep meaning to get one.

worse than you think

Klein said he believed staff at Public School 38 in Brooklyn answered school surveys honestly, even though the Daily News reported that Principal Yolanda Ramirez berated them for 40 minutes for slamming her in their responses.

"First of all, my own experience is it's pretty hard to pressure anyone in the system," Klein said. "I'm convinced - these are anonymous surveys - I'm convinced people play them overwhelmingly straight. "

Ramirez was caught on tape telling teachers that they shouldn't publicly slam her because, "if I were to begin putting out some of your dirty laundry a lot of you wouldn't be here."

Chancellor Joel Klein says teachers answer survey questions honestly because they are anonymous
by Erin Einhorn and Rachel Monahan
April 16th 2010

Leveling The Playing Field

I wonder if teaching math should be made to look more like recess. Now that spring has sprung and the grass has dried out, my kids are doing lots of football and baseball after lunch. I've always been fascinated at the range of behaviors you can observe when a ball comes out .

Some boys never engage in these things. Others will only get involved if the ball hits them. Still others only engage when a group of similarly skilled boys coalesce. These kids aren't great at it but they have a good time with each other and almost never engage with the experts. The experts are at the top of this food chain. They exhibit skills that are simply amazing, given their young age (12-14)

The experts are usually (>80%) engaged and the others of course trickle down to no participation at all. There's a natural filter at work. The best are amazing, exhibiting a fluidity and naturalness that you can just tell is extracting the absolute best out of them. The worst (sorry) throw like girls. Actually I have a few girls who throw really well but they've never developed the requisite full motion skills to catch well. Might have to do with breaking a nail, sigh.

What's key is that everybody can throw and catch but there is an elite that clearly will go on to become accomplished athletes in football or baseball (or both). These kids will eventually get formal training in the underlying theory of what is making them excel naturally. For now they just excel and presumably they got that way from huge amounts of play (practice) that they chose (value proposition) because they were good (wired for it) at it.

You could easily conjure up a scenario where if bureaucrats were to see this (fortunately they mostly stay inside) they would be appalled at the disparities on display. They would retire to their offices and write a standard to ensure that no child is left behind in playing catch. Then they would set up classroom training to guarantee that every student has access to the new standardized curriculum. They would introduce nerf balls so that nobody gets hurt or breaks a nail. Then they could train us teachers to introduce mixed ability groups so that the experts are forced to play with the geeks. They would want to ensure that all sports were covered so they would schedule a new game every week in an elaborate multiyear spiral.

Before long every kid in school would hate recess as much as math. The playing field would be leveled and we would get the miserable equal outcomes that we are getting in the academic disciplines. Pretty far fetched, eh?

Well what if you thought of academics more like sports. In math maybe you work with calculators from day one and you make sure that every kid can do the kinds of things we all do with calculators, mastering every day mathematical application. As this process evolves you would see who has the passion and talent to go deeper. Along the way, kids who can't cut it get to drop out of the pursuit of theory and depth but they do so with a repertoire that ensures they can at least use the gadgets in their lives effectively. You could continue this natural filter throughout the K-12 years. Wouldn't every kid get what they need?

Right now we have a tendency to turn off kids at every step in the process by delivering theory first. Eventually the experts get what they need but only after suffering through 12 years of torture playing catch with people who can't catch. Many of the non-experts get turned off before they get the basics of application and leave school unable even to use a calculator properly. Wouldn't it be exciting to demonstrate some neat result and have kids jaws drop and quiz you on why that works? Wouldn't that lead to more interest than theory first?

Isn't it true that history and science are taught this way now? Two subjects that my middle school students love! Hmmmmmm.

Arguments against Corrective Math

Just came across three articles arguing against using DI's Corrective Math as remediation for students in Philadelphia's low-performing "Empowerment Schools."  The venue is The Notebook, an online journal that describes itself as an "independent voice for parents, educators, students, and friends of the Philadelphia Public Schools." The author is a lecturer at the University of Pennsylvania Graduate School of Education, and a consultant for two of these Empowerment Schools.  

Using familiar arguments and buzzwords, she argues that the solution instead is better implementation of the existing ("rigorous," "research-based") Everyday Math and Math in Context curricula.

If you have a moment, please comment on these articles (most of the existing comments support the author's views):

http://www.thenotebook.org/blog/102440/correcting-corrective-math-problem

http://www.thenotebook.org/blog/102440/correcting-corrective-math-problem-ii http://www.thenotebook.org/blog/102455/correcting-corrective-math-problem-iii

(I haven't yet commented myself because, as a Philadelphia parent and educator, I wanted to pitch a response article first).

Eat, Poop, and Play

I caught one of my kids, who hasn't done a lick of work all year, diligently working through a math problem the other day. Astounded, I walked over to compliment him on his efforts. He admonished me not to expect this type of exertion all the time as it "was not his life". I was surprised at his candid offering and inquired as to what exactly he thought his life was. His response?

"Eat, Poop, and Play! That's my life!"

This, even more candid assertion, set me back on my heels a bit and I was curious to know how he had come to this frame of mind so I asked him what he thought his parents life consisted of. His response?

"Parents? My parents work for me!"

At first, this exchange simply tickled me in the same way that any number of open, uninhibited kid conversations do, but this one was different. It's been rattling around in my head for a week now and I can't shake it. It's one of those throw off comments that has more truth than humor in it, I suspect.

It's made me ponder the entire relationship of middle school kids to school and more specifically the role of education from their perspective. In this modern world, how many people really need math anymore? You can get a job at McDonald's and have the register do all the math you'll ever need for work. You can get a phone that has a sophisticated calculator in it. You can get computer programs to perform all manner of things that we used to accomplish only through painstaking pencil and paper scribbles.

So I'll pose a simple thought experiment to you all. How many people actually need a math education in the modern world that goes beyond knowing the number system and the names of simple geometric shapes? What careers would people be limited to if their mathematical knowledge was this limited? What careers would they be truly excluded from pursuing?


Have my kids figured out what they need from their perspective and is our push to have them all learn algebra simply a throwback to a time when it was more important in a world bereft of gadgets? Are my (disadvantaged) kids making a perfectly rational decision when they don't apply themselves to math?

How much education do you really need for a life of: eat, poop, and play?

zero

At least somebody around here is smarter than a 5th grader:

Their answer to question 29, "Any number to the power of zero is equal to what value?" is incorrect. Zero to the power of zero is indeterminate, not 1.

Neils Henrik Abel

Why is this true?

Will Burrow on Teach Like a Champion

There's been a discussion of Teach Like a Champion on the DI list, and the consensus seems to be that Lemov's taxonomy is very close to DI.

Will Burrow gave me permission to post this reaction:

I have read about half of it. for $16 it is the buy of the century. Anyone who teaches a child must read the book and keep it close at hand forever. The book has solid suggestions for delivering any type of material--and yes it validates DI.

Another Will Burrow link.

political season

Hey everyone -- the school board election is coming up and I'm going to be campaigning more and posting less for a few weeks.

Board candidates

pop quiz, part 4

Elementary

I didn't do very well.

Alternative Learning Theories to Constructivism

Nothing is going to dislodge constructivism from its pedestal until a competing theory understands what's so appealing about constructivism.

Constructivism is a coherent way to understand ourselves and how we learn. Our intuitive experience of mastery is that we gain it through a highly inefficient process. Whether it's learning that letting go of something makes it fall, or that not all animals have teeth, our primary way of learning about the world is not from books or even from a master, but from our ambling around. first, by bumping into ideas/new concepts, where we don't even know what we don't know. Then, as we dimly start to figure out what the elements are to this new notion, we explore. Maybe we vary the conditions a bit. Maybe we play with things in our hands, build a model. If we finally get somewhere on this without giving up, we start to build hypotheses that can be tested and hopefully test them. If we hit upon a relatively correct one, we go with it, applying it to everything around (until we hit a problem again, and then we start over...)

Watching children learn to walk or to speak reinforces this notion of constructivism: kids just learn these things, quite inefficiently, but no teaching (outside of very rarefied conditions) would have helped. Kids do it at their own pace, with great variation, yet they nearly all arrive at the same place.

Constructivism is at its core, natural.

Ed school theories can articulate constructivism using a variety of words, but in the end, all of them posit a cycle, often with 4 stages.

One version is:
awareness --> exploration --> inquiry --> utilization -->awareness

Another is:
engagement -->exploration -->explanation --> elaboration -->engagement


These theories are coherent. But being a coherent theory doesn't make it right, and even if it is, it doesn't make it *the best way to help children* reach mastery. One reason it is viewed as best is because it is natural to our experience: why fight nature? The history of humans gaining knowledge of the world is clearly constructivist from fire and the wheel to geometry to public sanitation. Another reason is the theory can be taught in a lecture, from a textbook, and then by observation. It's easy to express. It fits our intuitive experience, at least in part. And what other theories compete with it?

Constructivism will never leave ed school until some other theory replaces it.

Lemov's taxonomy might work as a competing theory, if it were a theory. But it's more a proto theory of the interaction of student-teacher learning, and could still all be fit into the constructivist learning theory. Here's one example from Lemov's book:
"

There's a consistent progression to the lessons of the champion teachers who informed this book. It's best described as "I/We/You." This name refers to a lesson in which responsibility for knowing and being able to do is gradually released from teacher to student. It means beginning with "I" by delivering key information or modeling the process you want your students to learn as directly as possible, then walking your students through examples or applications. In the "We" step, you first ask for help from students at key moments and then gradually allow them to complete examples with less and less assistance on more and more of the task. Finally, in the "You" step, you provide students the opportunity to practice doing the work on their own, giving them multiple opportunities to practice

Many people might say that the above is explicit instruction/direct instruction. His "model directly as possible, walk them through examples" is to the well informed a vastly different model than constructivism.

But to the not-fully-versed-in-ed-school, it may not seem different at all. A constructivist would say it fits his model, too: first you introduce a carefully tailored environment for the awareness phase. The tailoring delivers key information. A student and teacher go through the exploration phase by walking through examples or applications, using them as focal points and areas for jumping off. Then, in the inquiry phase, you ask for help from students at key moments, gradually allowing them to complete a problem with less and less assistance, as you turn the inquiry from teacher-inquiry to student inquiry. And then the utilization phase is the practice opportunity phase, where you allow them to practice and reinforce as they interact with the world.

Cog Sci ala Willingham doesn't compete either, mostly because it's not coherent, and the individual elements can be shoehorned into constructivism. He calls for understanding the need for distributed practice, but certainly proponents of the cycle can argue that each time around the loop, you're getting another round of practice, each at a deeper level. He calls for recognizing the difference between how children learn and how adults do, but I think this supports the constructivists more: children, especially young children, have even more bumping-into-things to do. Constructivism supports giving kids more free range to do this bumping. Many would intuitively see that and think only adults can learn from books. He calls for getting the reward system tuned just-so, but that can fit if you build the environment correctly, and if the teacher does nothing but reward.

Engelmann and Carnine's work won't, because they created a theory of instruction, not learning. It doesn't concentrate on explaining how *we* get to mastery; it says how we teach *them* to get to mastery: isolate the necessary concept with enough positive and negative examples to disambiguate all possible misconceptions from this core concept. It is a method for *efficiency*, and rests on the notion that in order to help the low performing student to catch up, you will need efficiency. But in isn't focused on learning. Engelmann and Carnine argue the *number of examples* needed for a low performing child is exponentially more than for a high performer--they aren't at core arguing the low performer learns differently.

They violate constructivism because it isn't *natural* to push for efficiency. It doesn't speak to how we go around making sense of our own world. And in our post-baby boomer world, we're all about ourselves and how we experience the world.

Are there competing theories to this? I'll address one in the coming days.

Teacher Training No Boon for Student Math Scores

Sigh. The more it changes, the more it stays the same.


Published Online: April 16, 2010
Teacher Training No Boon for Student Math Scores
By Debra Viadero

First-year findings from a federal study of 77 middle schools suggest that even intensive, state-of-the-art efforts to boost teachers’ skills on the job may not lead to significant gains in student achievement right away.

The "Middle School Mathematics Professional Development Impact Study," which was released April 6, is the second major experimental study by the U.S. Department of Education’s Institute of Education Sciences to find that a high-quality professional-development program failed to translate into any dramatic improvements in student learning. A two-year study of efforts to improve teachers’ instructional skills in early reading reached a similar conclusion in 2008.

“What accounts for this somewhat consistent pattern of results? We don’t really know,” said Michael S. Garet, a vice president at the American Institutes for Research. His Washington-based organization conducted both studies with the MDRC research group of New York City. “I think what we’re learning,” Mr. Garet added, “is that it’s challenging to make a big enough difference in teacher knowledge and instructional practice to have an impact on student learning.”

The results are already providing some intellectual ammunition for finding better ways to select and retain effective teachers—and shedding those who are ineffective—as the best way to improve instructional quality in schools.

The new study shows that “you can’t change teacher effectiveness very well with the tools that we have, and that you can’t change ineffective teachers into effective ones,” said Eric A. Hanushek, a senior fellow at the Hoover Institution, based at Stanford University. He is also the president of the IES advisory board, which heard a presentation on the new study’s findings last week.

But other scholars said it is too soon to issue a verdict on the effectiveness of professional development.

“We know teacher change takes time,” said Hilda Borko, an education professor who is also at Stanford. “The general belief is that it takes a while for teachers to take ownership of change and really incorporate change into their instruction.”

.....

Findings in Detail

By the end of the school year, the researchers found, teachers who participated knew slightly more about rational numbers, overall, than their control-group counterparts, but the effect was not statistically significant. Those slight improvements were most notable on a test of pedagogical content knowledge, where teachers stood a 55 percent chance of getting a question right, compared with a 50 percent chance for their counterparts in the control group. (In comparison, the trainers’ chance of answering a question correctly on that test was nearly 93 percent.)

On the plus side, the training did lead to changes in teaching practice. Compared with the control group, the teachers in the experimental group were more likely to try to draw out students’ thinking by asking students whether they agreed with a classmate’s response, or inviting them to share their mathematical strategies.

The changes in practice were not dramatic enough, however, to translate into student-learning gains on the computer-adaptive tests that students took in the spring. The students, most of whom came from schools where more than half of students qualified for federally subsidized school meals, continued to score, on average, at the 19th percentile on the tests, which were developed for the experiment by the Northwest Evaluation Association of Lake Oswego, Ore.

Mr. Garet said the researchers are now analyzing the results from a second year of similarly intensive teacher training in the same schools, which they hope to publish this year.

If those results show learning gains from the training, they might suggest the need for even more sustained professional development.

“You might need to have pretty intensive professional development all the time, every year, and then slowly get schools into a culture such that the expectation is that you always keep working on your knowledge,” said Sybilla Beckmann, a math professor at the University of Georgia in Athens and an adviser to the study.

The Case With Reading

The results from the 2008 reading study were based on two years of data, but just one year of professional development. That study also differed from the latest one in that it provided in-class coaching, randomly, to only about half the group in an effort to see whether that approach yielded any added benefits for teachers or their students. But that did not turn out to be the case.

The reading study also found that, while the skills of the 2nd graders in the study did not improve, there were some measurable gains in teachers’ knowledge.

For the middle school math study, Mr. Garet said, the researchers tested various possible explanations for why the training had failed to affect student achievement. They ruled out the hypothesis, for instance, that the tests were too hard or too easy for the teachers or their students.

“As you move away from the study itself,” Mr. Garet added, “one hypothesis worth testing would be to see what would happen if the professional development aligned with what teachers were evaluated on.”

Ms. Borko, who is leading her own study of teacher professional development, said it also would have been instructive if the federal studies had measured the quality of the instruction that teachers were getting.

Teacher Training No Boon for Student Math Scores