1st major study of reform math: epic fail

In the August 2014 issue of Economics of Education Review:

Abstract

We investigate the impact of an ambitious provincial school reform in Canada on students’ mathematical achievements. It is the first paper to exploit a universal school reform of this magnitude to identify the causal effect of a widely supported teaching approach on students’ math scores. Our data set allows us to differentiate impacts according to the number of years of treatment and the timing of treatment. Using the changes-in-changes model, we find that the reform had negative effects on students’ scores at all points on the skills distribution and that the effects were larger the longer the exposure to the reform. [emphasis added]

[snip]

In this paper, we estimate the impact of Quebec’s (the second most populated province in Canada) ambitious and universal school reform implemented in the early 2000’s on children’s mathematical ability throughout primary and secondary school. At the time of the reform, the performance of students in the province of Quebec was comparable to that of students from the top performing countries in international assessments. Nonetheless, the educational system in Quebec was still subject to severe criticism at home due to its alarmingly large high school dropout rate, especially among male students.6 To ensure the success of all students, the province decided to implement an ambitious reform introducing a new program in each and every school across the province which drastically changed the way teaching was delivered to all children in primary and secondary schools. The Quebec education program (MELS, 2001, 2003, 2007) relied on a socio-constructivist teaching approach focused on problem-based and self-directed learning. [emphasis added] This approach mainly moved teaching away from the traditional/academic approaches of memorization, repetitions and activity books, to a much more comprehensive approach focused on learning in a contextual setting in which children are expected to find answers for themselves. [emphasis added]

. . . . More specifically, the teaching approach promoted by the Quebec reform is comparable to the reform-oriented teaching approach in the United States. As of 2006, this approach was widely spread across the United States (although more traditional approaches remained dominant) and it was supported by leading organizations such as the National Council of Teachers of Mathematics, the National Research Council, and the American Association for the Advancement of Science. Yet few studies in economics have addressed the impact of various teaching approaches, let alone the approach promoted by the Quebec reform.

[snip]

[The] approach was designed to enable students to ‘‘find answers to questions arising out of everyday experience, to develop a personal and social value system, and to adopt responsible and increasingly autonomous behaviors’’ (MELS, 2005).

In the classroom, students were expected to be more actively involved in their own learning and take responsibility for it. Critical to this aspect was the need to relate their learning activities to their prior knowledge and transfer their newly acquired knowledge to new situations in their daily lives. ‘‘Instead of passively listening to teachers, students will take in active, hands-on learning. They will spend more time working on projects, doing research and solving problems based on their areas of interest and their concerns. They will more often take part in workshops or team learning to develop a broad range of competencies.’’ (MELS, 1999). This centralized approach in providing the program and training with a school-based execution is in many ways comparable to the current approach taken within the comprehensive school reform (CSR) models at the national level in the United States (Borman et al., 2003). The main differences are that in Quebec, implementation was mandatory in each and every school, funding was not tied to the implementation, and training packages and support are centralized in many ways. These differences are critical: they imply that the reform had to be implemented in all schools, and that the resources and training was not tied to individual school characteristics. Whether private or public, English speaking or French speaking, all schools across the province were mandated to follow the reform according to the implementation schedule. This implies that all children in Quebec were treated according to same timeline, and that parents were not able to self-select their children into or out of the reform, except by moving out of the province which they did not.

The school reform was planned at the highest level by civil servants at the Department of Education (MELS). The MELS imposes the program to be followed in each grade by every school. The 69 School Boards (60 Francophone and 9 Anglophone) responsible for all public schools, their superintendents and the school principals, are the channels and drive belts between the MELS and school teachers and students.

[snip]

Conclusion

We find strong evidence of negative effects of the reform on the development of students’ mathematical abilities. More specifically, using the changes-in-changes estimator, we show that the impact of the reform increases with exposure, and that it impacts negatively students at all points on the skills distribution. . . . Students from the lower end of the distribution do not seem to be in a better position to successfully complete their schooling. Mathematical abilities are strongly related to school attainment and labor market outcomes, and for lower performing students they are at best equivalent post reform, but most likely lower.

The teaching approach dictated by the reform is based on socio-constructivism. According to Pinker (1997), proponents of this method believe that children must construct mathematical knowledge for themselves with the teacher only guiding the discussion on the topics and that repetitions and practice are seen as detrimental to learning. He argues that constructivism is not appropriate for mathematics. For him, ‘‘. . . without the practice that compiles a halting sequence of steps into a mental reflex, a learner will always be building mathematical structures out of the tiniest nuts and bolts’’. Certain skills for mathematics may be very difficult to ‘‘construct’’ at a young age and can possibly be better attained by old-fashioned practice and a more mechanical approach. Pinker suggests that the poor performance of the United States in mathematics could be linked to the teaching approach, which is mainly contextual with no teaching of mathematical concepts. The evidence presented in this paper supports this argument.

The distributional impacts of a universal school reform on mathematical achievements: A natural experiment from Canada by Catherine Haeck, Pierre Lefebvre *, Philip Merrigan

Well, well, well.

Contra Elizabeth Green (again), history does not fold itself meekly into a Bill Gates-approved narrative in which "the traditional approach we take to teaching math — the one that can be mind-numbing, but also comfortingly familiar — does not work."

Using the traditional approach, Quebec schools produced students whose achievement "was comparable to that of students from the top performing countries in international assessments."

Using constructivism, they produced students whose achievement suffered at every grade level, and at every skill level to boot. Good students did worse, bad students did worse, in-between students did worse. Everyone did worse in constructivist math.

Because constructivism doesn't work. 

As to the teachers, whom Green cites as the source of Reform Math failure, the article notes that "Extensive training was provided to support the new program."

Elizabeth Green is funded by Bill Gates

Needless to say, I was horrified by Elizabeth Green's Why Do Americans Stink at Math?, which is the single most breathless endorsement of constructivism I've ever seen in the Times. Actually, it may be the only breathless endorsement of constructivism I've seen in the Times.

I read it this morning, just before a meeting with Ed and his editors at Oxford, and as we were rushing to get ready I joked that Green was probably funded by Bill Gates.

Then tonight it occurred to me that I should check.

Chalkbeat: About Us

The Times has no business publishing an advocacy piece, albeit an advocacy book excerpt, without disclosing the Gates connection.

UPDATE 7/29/2014: Bill Gates is very likely the major funder of Elizabeth Green

not puzzling, and not a paradox, either

Barry spotted this Thursday session (pdf file) at the NCTM's upcoming 2011 Annual Meeting:

The Chinese Paradox: How Traditional China Trumps U.S. Reform Attempts
(General Interest) Session

Using video of urban Chinese math classes and professional development, the speaker will explain the puzzling paradox for how seemingly traditional Chinese educational methods—large, teacher-centered, lecture-based classes; exam-driven curricula; and so on—produce students who excel over their U.S. peers, despite the United States’s recent reform attempts initiated by NCTM.

Thomas Ricks
Louisiana State University, Baton Rouge

The success of large, teacher-centered, lecture-based classes where students learn exam-driven curricula is not a puzzling paradox to me.


seemingly?

I'm wondering about that word seemingly.

seemingly traditional Chinese educational methods

I'm wondering whether Thomas Ricks is going to resolve the paradox by arguing that Chinese educational methods are only seemingly traditional.

I hope not.



Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series)

math wars

comment left on Numbers Wars: School Battles Heat Up Again in the Traditional versus Reform-Math Debate in the March issue of Scientific American:

Sad but true. I was at a fast food drive thru when the computers were down. They had to make change the old fashioned way. But the girl could not figure out how much change to give me. She seemed lost as she tried to calculate the difference between what I gave her and what the food cost. She had to call in the manger, who took way to long to compute the change (eventually she found a hand-held calculator).

Apparently even simple arithmetic is no longer well taught, learned and/or retained. Reliance on machines to "teach math" is only good if one has a machine when it is needed. My daughter had these classes where the calculator was required. The problem was that after smacking the keyboard a few times, she could come up with an obviously nonsensical answer. She would just write it down and move on. I asked her one time how she could multiple two numbers that each were less than one and come up with an answer that was greater than ten. The blank stare said it all (fyi - she failed to enter the decimal points correctly).

Want to terrify a teen-ager? Ask them to multiply 12 times 12. Is the answer immediate or not? Forget adding simple fractions. And we expect these kids to learn algebra and higher mathematics?

Are kids today less proficient even in arithmetic than in the past? Surely we can tell if these newer teaching methods are getting better results or not. As for me, I think my daughter did better in arithmetic in elementary school. After middle and high school, she seems to have "lost" the ability to easily do the arithmetic she learned earlier in life. I blame the calculator.

Twenty years of reform math.

That's a long time.

no one can teach

In reality, no one can teach mathematics. Effective teachers are those who can stimulate students to learn mathematics. Educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding (MSEB and National Research Council 1989, 58).

Constructivist Learning and Teaching

Time to put the public back in public schools.


CT Coalition for World Class Math
NJ Coalition for World Class Math
PA coalition for World Class Math
United States Coalition for World Class Math
Parents' Group Wants to Shape Math Standards
Common Core Standards: Who Made the List?

the number sense, redux

Unbeknownst to the NCTM, it seems, people have been looking into the question of what the number sense is or is not:

This led to Dehaene’s first encounter with what he came to characterize as “the number sense.” Dehaene’s work centered on an apparently simple question: How do we know whether numbers are bigger or smaller than one another? If you are asked to choose which of a pair of Arabic numerals—4 and 7, say—stands for the bigger number, you respond “seven” in a split second, and one might think that any two digits could be compared in the same very brief period of time. Yet in Dehaene’s experiments, while subjects answered quickly and accurately when the digits were far apart, like 2 and 9, they slowed down when the digits were closer together, like 5 and 6. Performance also got worse as the digits grew larger: 2 and 3 were much easier to compare than 7 and 8. When Dehaene tested some of the best mathematics students at the École Normale, the students were amazed to find themselves slowing down and making errors when asked whether 8 or 9 was the larger number.

Dehaene conjectured that, when we see numerals or hear number words, our brains automatically map them onto a number line that grows increasingly fuzzy above 3 or 4. He found that no amount of training can change this. “It is a basic structural property of how our brains represent number, not just a lack of facility,” he told me.

[snip]

These three modes of thinking about number, Dehaene believes, correspond to distinct areas of the brain. The number sense is lodged in the parietal lobe, the part of the brain that relates to space and location; numerals are dealt with by the visual areas; and number words are processed by the language areas.

Nowhere in all this elaborate brain circuitry, alas, is there the equivalent of the chip found in a five-dollar calculator. This deficiency can make learning that terrible quartet—“Ambition, Distraction, Uglification, and Derision,” as Lewis Carroll burlesqued them—a chore. It’s not so bad at first. Our number sense endows us with a crude feel for addition, so that, even before schooling, children can find simple recipes for adding numbers. If asked to compute 2 + 4, for example, a child might start with the first number and then count upward by the second number: “two, three is one, four is two, five is three, six is four, six.” But multiplication is another matter. It is an “unnatural practice,” Dehaene is fond of saying, and the reason is that our brains are wired the wrong way. Neither intuition nor counting is of much use, and multiplication facts must be stored in the brain verbally, as strings of words. The list of arithmetical facts to be memorized may be short, but it is fiendishly tricky: the same numbers occur over and over, in different orders, with partial overlaps and irrelevant rhymes. (Bilinguals, it has been found, revert to the language they used in school when doing multiplication.) The human memory, unlike that of a computer, has evolved to be associative, which makes it ill-suited to arithmetic, where bits of knowledge must be kept from interfering with one another: if you’re trying to retrieve the result of multiplying 7 x 6, the reflex activation of 7 + 6 and 7 x 5 can be disastrous. So multiplication is a double terror: not only is it remote from our intuitive sense of number; it has to be internalized in a form that clashes with the evolved organization of our memory. The result is that when adults multiply single-digit numbers they make mistakes ten to fifteen per cent of the time. For the hardest problems, like 7 x 8, the error rate can exceed twenty-five per cent.
The Numbers Guy
by Jim Holt
The New Yorker

in a nutshell:

• number sense--right now! is bunk. number sense--5 or 10 years from now! might be more like it, depending on what kind of numbers we're talking about. For instance, number sense for exponents--not in this lifetime! would capture a normal human being's ability to grasp intuitively the nature of exponential growth. [Is an exponent a "kind" of number? Probably not.]
  

• the fact that I spent 30 years of my life believing that 7x6=43 is perfectly normal and nothing to be ashamed of.
  

• all math looks alike
  

Which reminds me: I never wrote part 2 of my post on cumulative practice.

Number Sense—Right Now!

Number Sense—Right Now!
NCTM News Bulletin, March 2008

"Is 4 × 12 closer to 40 or 50? How many paper clips can you hold in your hand? If the restaurant bill is $119.23, how much should you leave for a tip? How long will it take to make the 50-mile drive to Washington? If a 10-year-old is 5 feet tall, how tall will the child be at age 20?"

OK. I've generally ignored it when people talk about "number sense", but here it is from the president of NCTM. He says: "Number sense is important and needed—right now." What is it, exactly? Is it estimation? No, it seems to be more than that. Does Mr. Fennell define it? No. He just gives the examples above. Let's look at each one.

"Is 4 × 12 closer to 40 or 50"

Do it exactly in your head. It's part of the times table.

"How many paper clips can you hold in your hand?"

How accurately do you have to make this estimate to show number sense? He doesn't say, but I don't think he is talking about plus or minus 25% accuracy. I don't think I could guess that closely.

"If the restaurant bill is $119.23, how much should you leave for a tip?"

Does he think that those who have mastered the traditional method of multiplication are stuck doing this calculation right-to-left on paper? This is a straight estimation problem, and my traditionally-taught wife takes pride in calculating these things down to the penny in her head.

Is number sense more or less than estimation? It seems to be both more and less. Number sense means more than just estimation, but it doesn't require you to provide accurate estimations.

"How long will it take to make the 50-mile drive to Washington?"

About an hour? What are the assumptions? Is number sense equal to estimation with common sense added in? Apparently the common sense level is not very high. How about the number sense to determine how long it will take to drive 400 miles on the highway, accounting for stops for gas, eating, and traffic? What if I gave you the exact times for stops and the lower speed in the traffic? Mastery of the basics leads to number sense, not the other way around.

He seems to be making the case that there is no linkage between mastery of the basics and number sense. But then he really isn't talking about mastery of estimation. Schools could hand out "Arithmetricks" and practice, practice, practice. No, he seems to be talking about some sort educational number sense osmosis. Low expectations.

"If a 10-year-old is 5 feet tall, how tall will the child be at age 20?"

He goes on to say:

"Students who have a good sense of number are able to provide a reasonable response to the examples above, including the driving example. And they know that there is no proportion-driven response for the final example."

Sure there is. If a 10 year old child is 5 feet tall, then proportion tells you that there is some other effect going on when they get to 20. If you were talking about some unusual species of tree, then proportion or number sense is not going to help. You need content knowledge, and we all know what schools think of content. I think I'll coin a new term: Content Sense. That's what we need-right now! Just like with fractions on the real number line, kids need to be able to place major historic events on a timeline.

After all of this, I still don't know what he means by number sense or what performance level is required. Whatever it is, it seems pretty low. Mr Fennell can't define it, but he wants it fixed "right now".

There is another example:

"A sense of number emerges that is built on the foundations discussed above, which
yield responses such as, “I knew 3/4 was more than 3/5 because the pieces were bigger in fourths.” This is what all math teachers want. Such “aha!” classroom moments remind us about the importance of understanding."

"the pieces were bigger in fourths"?

So number sense is something other than math; something other than mathematically knowing why 3/4 is greater than 3/5. And "understanding", according to him, is something other than mathematical understanding. What if the student said that 3/4 = .75 and 3/5 = .6? Is that number sense? Does that show understanding or is that just rote knowledge?

Math is all about tools and methods that you can rely on to give you correct results in spite of the fact that what you might be doing defies common sense. That's the power of math. As I've said before, let the math provide you with the understanding. If you're worried about estimation, teach it directly. Number sense, whatever it is, will take care of itself.

Equity in Mathematics Education (January 2008)

It's amazing what you find on the NCTM site.

"Equity in Mathematics Education (January 2008)"



NCTM Position

"Excellence in mathematics education rests on equity—high expectations, respect, understanding, and strong support for all students. Policies, practices, attitudes, and beliefs related to mathematics teaching and learning must be assessed continually to ensure that all students have equal access to the resources with the greatest potential to promote learning. A culture of equity maximizes the learning potential of all students."

[This sounds vaguely nice enough, but they don't leave it at that.]

"A culture of equity depends on the joint efforts of all participants in the community of students, educators, families, and policymakers:"

"All members of the community respect one another and value each member’s contribution.

[Except for the contributions of parents and mathematicians and anyone else they disagree with. We're not allowed to contribute. All we get are open houses and the opportunity to be "informed". Even the national math panel only gets to define "a first step". NCTM gets the rest.]

"The school community acknowledges and embraces all experiences, beliefs, and ways of knowing mathematics."

["Ways of knowing mathematics"? Did the national math panel define this? Did they define various ways to know algebra? They did the opposite. They defined what algebra is.]

"All necessary resources for optimal learning and personal growth of students and teachers are allocated."

[This is the more money escape clause.]

"High expectations, culturally relevant practices, attitudes that are free of bias, and unprejudiced beliefs expand and maximize the potential for learning."

[As long as they are in charge of defining what all of this means.]

All students have access to and engage in challenging, rigorous, and meaningful mathematical experiences."

["Meaningful mathematical experiences"? How about having access to rigorous curricula, quality teaching, and no excuses? How about making sure that kids actually learn math, not experience it?]

"Such practices empower all students to build a relationship with mathematics that is positive and grounded in their own cultural roots and history."

[OK, I reject the zero because it wasn't grounded in my own cultural roots and history. I want Roman Numeral Math.]

"Different solutions, interpretations, and approaches that are mathematically sound must be celebrated and integrated into class deliberations about problems."

["Must be?" As long as they are not the traditional algorithms.]

What Algebra? When?

I came across this message from Mr. Fennell when I went to the NCTM site to see if I could find any information about the math panel. I only found their press release about the panel report, but there was a big emphasis about data on the home page: "Focus on Data/Probability". Keep that in mind when youy read this message.


"President's Messages: Francis (Skip) Fennell"

"What Algebra? When?"

NCTM News Bulletin, January/February 2008"

"Currently, about 40 percent of eighth-grade students in this country are enrolled in first-year algebra or an even higher-level math course (for example, geometry or second-year algebra)."

[Really? What kind of algebra? Surely not the math panel type.]

"As Chambers (1994) notes, algebra for all is the right goal—we just need to make sure that we’re all targeting the right algebra in our teaching. This algebra would focus on topics like expressions, linear and quadratic equations, functions, polynomials, and other major topics of algebra. (Note that these ideas will be discussed in the National Math Advisory Panel’s report on algebra topics.)"

[OK, what is the percentage now, and how many of these kids get help outside of school. How difficult is that kind of research?]

"At a time when maintaining our nation’s competitive edge means encouraging more students to consider math- or science-related majors and careers, should we address the challenge by moving more students into higher levels of mathematics earlier? Well, I am not so sure."

[If students aren't ready, then it can't be the fault of the school or curriculum? It's also not a matter of when you get to algebra, but how well you are prepared for algebra. Many kids can't even handle algebra when they get to college! So, the problem is that many kids can't get to algebra at ANY time, but he sees the problem as a "when" problem. The rule is (apparently) that if you want to deflect criticism, redefine the problem.]

"Yes, we have more students taking higher-level courses in mathematics, and yes, the path to a good job often begins with algebra. But is mandating algebra for all seventh- or eighth-grade students a good idea? Teachers of algebra frequently tell me that far too many of their students are not ready for algebra, regardless of how it is defined (first- or second-year algebra, integrated mathematics curriculum, etc.)."

[Well, if they are not ready for algebra, then figure out why. Will they magically be prepared by ninth or tenth grade? No, our high school has to have lots of remediation to fix K-8 school problems. This is not a "when" problem. "When" allows them to avoid fixing problems.]

".. most teachers indicate that their students don’t know as much about fractions as they would like. By fractions, I mean fractions, decimals, percents, and a variety of experiences with ratio and proportion."

[Duh? And this is NOT a curriculum and/or a teaching problem?]

"Of course, we must not overlook the importance of integrating the essential building blocks of algebra in pre-K–8 curricula, especially during the middle grades. Work with patterns is probably overemphasized in some quarters as the defining component of algebra with younger learners, but early experiences with equations, inequalities, the number line, and properties of arithmetic (such as the distributive property) are foundations for algebra. Silver (1997) notes that integrating algebraic ideas into the curriculum in a manner that helps students make the transition from arithmetic to algebra also prepares them for what occurs later in algebra."

[So why does NCTM support curricula that don't meet these goals?]

"So is early access to algebra a good idea? Sure—for some—probably for many. More importantly, however, all students who are working to secure this valuable "passport" should begin their study of algebra with all the prerequisites for success, regardless of when the opportunity comes their way."

[They don't see that they have anything to do with this lack of preparation? They should have a big section called Focus on Algebra, not Focus on Data/Probability. Low expectations and blame shifting permeate this message from the president of NCTM. They lack any ability for critical self-analysis.]

My latest rant

Chi-square in high school?

Moonbat Math!

Follow the link.

NCTM standards of your very own

I'm so glad I finally made contact with Niki Hayes.

She just sent an Amazon link for the original NCTM standards!

from Niki:

You can get a 1991 reprint of the Standards. My copy is 1989, but it is the same as the 1991 book.

My copy is on its way.

why we need parent choice

The fourth comment in this thread tells you everything you need to know:

It is telling the Street, Lyon, and Moats don't identify their own bias for phonemic awareness instruction nor their full corporate embrace of publishing phonics-based materials. In essence, these individuals deny that the National Reading Panel was packed with advocates who believe that phonemic awareness, an oral language skill, must be mastered before children can learn to read.

[snip]

After the National Reading Panel was packed and the desired results published, the committees for adoption, and the Reading First program officials acted in collusion to exclude any program that did not fit the original prestidigitation of the NRP results.

[snip]

Lastly, you see Louisa Moats accusing Richard Allington of not being a scholar or a scientist. Anyone who knows Allington's publishing record in peer-reviewed journals and his success in textbook publishing is aware of Moat's dishonesty on this issue. However, the casual reader may not know of her affiliation with corporations that sell phonics-based and phoneme-based reading programs. She has a distinct bias that includes a failure to admit that the National Reading Panel research has been thoroughly repudiated. It was neither scientific nor scholarly.

This conflict will never be resolved, because we have no source of authority with the legitimacy to persuade whole language advocates they've lost.

The same could be said for advocates of SBRR reading programs (scientifically based reading research).

I'm strongly inclined to defer to scientific consensus, with the proviso that because scientific consensus changes with new discoveries I don't absolutely have to accept the prevailing wisdom if I think it's wrong. Occasionally, over the years, I haven't. And occasionally, over the years, I've been right and the consensus has been wrong. Once in awhile.

So I could question the importance of teaching phonics and phonemic awareness if the right person suggested that perhaps I should. As a matter of fact, the right person did suggest such a thing a few years back. When I met Thomas Zeffiro at a NAAR SAB meeting, he told me that in fact dyslexia can involve the visual system as well as the auditory system.

That was interesting, and I assume -- provisionally -- that he's probably right. So perhaps there's some kind of visual approach to teaching reading that the Reid Lyons and the Louisa Moats have missed.

The truth is, though, that while I recognize that the scientific consensus represented by Reid Lyon and Louisa Moats may one day change, there is no one in the world of education schools & NGOs who would cause me to doubt that consensus today.

So my mind is not open to education school evidence and argument, either -- not when it conflicts with NIH-funded, peer-reviewed scientific research. (I am open to, and interested in, personal accounts of experience inside the classroom from anyone, regardless of ideology.)

They can't persuade me, and I can't persuade them.

I remember reading a very nice Michael Barone article explaining why it was that the South abandoned racial segregation so rapidly in the wake of the Civil Rights Act:

In the meantime, Congress had acted. Chief Justice Warren had hoped that the unanimous support on the Court for Brown would move white Southerners to change their ways, but that didn't happen. In contrast, the long deliberative process between President Kennedy's June 1963 endorsement of the Civil Rights Act and President Johnson's signing of the bill more than a year later seems to have changed minds.

The nation watched on television as senators slept on cots during the Southerners' filibuster in the Senate. Opponents of the bill were given every chance to obstruct, but they could not prevent an overwhelming majority of the House from voting for the bill and a two-thirds majority in the Senate breaking the filibuster. Support was broad and bipartisan; contrary to what is often assumed today, a higher proportion of Republicans than of Democrats supported the bill. Its leading advocates included not only Democrats like Sen. Hubert Humphrey and Congressman Emanuel Celler but also Republicans like Sen. Jacob Javits and Congressman William McCulloch.

It was widely expected that there would be massive resistance to the Act, as there had been to school desegregation. But that proved not to be the case. Within a few years, public accommodations were largely integrated in the South and workplace discrimination, widespread throughout the nation, was vastly diminished. I remember traveling in the South not long after the Civil Rights Act was passed and noticing that black diners were treated with courtesy by white waitresses: an astonishing contrast with the anger and violence that greeted the lunch-counter sit-ins and freedom rides only a few years before. The law was the law, and Southern manners took over. Integration was achieved about as rapidly as it had been in the 1950s in the military, where it was based on the president's command authority.

I ran this past Ed, who thought it made sense. (He's not an American historian, but I've found that the perceptions of historians about history, including history outside their own periods, are almost always better than the perceptions of journalists about history.)

The United States Congress had legitimacy in the eyes of citizens in the North and in the South. Once it spoke, the issue was resolved. We are all Americans.

I find that moving.

Nothing of the sort can occur with the reading wars or the math wars or any other war that rages in the realm of public schools.

Congress can't deliberate and declare phonics to be scientifically valid and supported by consensus.

At least, I don't think Congress can do such a thing.

Whether it can or can't, I'm certain that it won't.

Peer-reviewed, NIH-funded science simply does not hold the authority for most professors in schools of education that it does for the rest of us. That's why we see attacks on controlled research as "right wing;"^* that's why we have edu-websites devoted to action research; that's why the NCTM advocates a "variety of research methods." (pdf file)

We are simply going to have to agree to disagree.

Which means parents must have the power to choose for their children.

If I want my child taught basic skills via direct instruction, that has to be my call.

_______________

^* The author says that he uses the terms left and right "in their spatial and not necessarily their political senses."

Bill Gates testifies before Senate Committee

Bill Gates testified before the Senate Health, Education, Labor and Pensions Committee on March 3, 2007, addressing competitiveness in the 21st century: Written testimony is here.

Aside from his usual plea for more technology in the classrooms, there is this interesting paragraph in his written testimony:

"Our current expectations for what our students should learn in school were set fifty years ago to meet the needs of an economy based on manufacturing and agriculture. We now have an economy based on knowledge and technology. Despite the best efforts of many committed educators and administrators, our high schools have simply failed to adapt to this change. As any parent knows, however, our children have not – they are fully immersed in digital culture."

First of all, his chronology is off. Fifty years ago was 1957 and the US was very much interested in advancing its technology expertise, particularly after October 4 of that year when the Soviet Union announced the successful launch of Sputnik. Putting aside that major gaffe, does he think that high schools using IMP and other attrocities that pass for math (and which are being used in his home state) are really doing the job? And to be "immersed in digital culture" doesn't one still need to master basic algebra? And more importantly, if one doesn't have the sound mathematical foundation in K-8, all the graphing calculators and lap tops in the world will not make students technologically savvy--in terms of being able to solve mathematical problems as opposed to being a software user.

But it doesn't matter. He's Bill Gates. And when he talks, people listen; even more than when E.F. Hutton used to speak. He points to the declining number of science and engineering degrees in the U.S. and goes for the easy answer: smaller schools and more technology in the classrooms.

Yeah, like that's really been helping so far.

And of course, we need national math and science standards. Senator Dodd and Congressman Ehlers have introduced identical bills calling for these. The bills are endorsed by NEA and NCTM. And probably Bill Gates.

Oh, and one more thing. He's pushing for upping the limits on H1-B visas. We shouldn't be so parochial he says. Gee, I wonder why he suggested that!

a variety of research methods

An Integrated Study of Children's Construction of Improper Fractions and the Teacher's Role in Promoting That Learning

Ron Tzur

July 1999, Volume 30, Issue 4, Pages 390 - 416

Abstract:
In this constructivist teaching experiment with 2 fourth graders I studied the coemergence of teaching and children's construction of a specific conception that supports the generation of improper fractions. The children's posing and solving tasks in a computer microworld promoted a modification in their fraction schemes. They advanced from thinking about a unit fraction as a part of a whole to thinking about it as standing in a multiplicative relationship with a reference whole (the iterative fraction scheme). In this article I report an intertwined analysis of the children's construction of this multiplicative relationship and an examination of the teacher's adaptation of learning situations (tasks) and teacher-learner interactions to fit within the constraints of the children's mathematical activity.

Classification:
None

Additional Keywords:
Cognitive development, Constructivism, Elementary, K–8, Fractions, Learning, Teaching fractions

Now that I know the NCTM formally supports increased funding for "a variety of research methods," I'm wondering what the rules are for this kind of research.

Scientists conducting controlled studies face massive constraints on their activities, not least of which is the requirement that they pass IRB (Institutional Review Board) review.

Do "narrative researchers" have to submit research proposals to IRB review?

IRB: Ethics & Human Research

found: NCTM unicorn

RE: NCTM & constructivism

Constructivist Mathematics and Unicorns

by Lee V. Stiff

Constructivist math is a term coined by critics of Standards-based mathematics who promote confusion about the relationships among content, pedagogy, and how students learn mathematics....

Like unicorns, "constructivist math" does not exist.

Apparently someone didn't get the memo.

The Math Plague - in a nutshell

The Math Plague by Sherry Mantyka

• uses analogies to football (numerous quotes from Blanchard and Shula's The Little Book of Coaching.)
  
  
• Three ideas which are relevant to mathematics: (a) capacity limits performance - mathematical performance will eventually break down as task difficulty is increased; (b) capacity is used in performance - adding more components to a problem will use more capacity and increase task difficulty; and (c) demands on capacity are less for individuals who have higher levels of relevant skills. (29)

• Over-learned skills can be directly retrieved from memory rather than constructed (Logan, 1988) (68). Cognitive pychology clearly states that you cannot problem solve effectively if you have to simultaneously use working memory to process basic skills (87)

• If a learner experiences difficulty learning some bit of mathematics explicitly, he or she has to imitate the pattern of the technique as many times as it takes to be able to successfully duplicate it without error. (118)

• Modern textbooks that emphasize problem solving over skills do not contain enough problems of a similar type to allow the implicit learner to develop the sense of rhythm of the technique that comes with repeated practice. (119)

• The Math Plague slams NCTM's Curriculum and Evaluation Standards for School Mathematics. It is easy to see that a curriculum that is guided by these standards is unlikely to produce students who will be able to compute without the aid of a calculator. (84)

at NYC HOLD: Decline in Student Performance in Math by JHU math professor Steve Wilson

Stephen Wilson, a math professor at Johns Hopkins, has written a paper on the decline of students in their math abilities based on a statistical analysis that he conducted. He gave a group of students in his Calculus I class in fall of 06 the same final exam that he gave for the same course in 1989. He then compared the SAT Math scores for each of the classes and found that while the SATM scores were the same on average, the average final exam scores were lower by a statistically significant amount for the 06 class. Among his astute conclusions are the following:

Nineteen eighty-nine is, in mathematics education, indelibly tied to the National Council of Teachers of Mathematics’ publication, Curriculum and Evaluation Standards for School Mathematics (1989), which downplayed pencil and paper computations and strongly suggested that calculators play an important role in K-12 mathematics education. My 2006 students would have been about two years old at the time of this very influential publication, and it could easily have affected the mathematical education many of them received. Certainly, one possibility is that mathematics preparation is down across the country, thus limiting the pool of well prepared college applicants.

There is nothing that universities can do to correct the lack of preparation of their applicants. However, it is difficult to believe that there are not enough students to fill our classes with 1989 quality students. One of the major gate-keepers, the SATM test, is oblivious to this significant shift in preparation. Universities can certainly demand a more effective SATM test.

To misquote Bob Dylan's Ballad of a Thin Man: "Something is happening, but you don't know what it is; do you, Mr. Fennell?"

essay on NCTM Focal Points on NYC HOLD

Stanley Ocken, a mathematics professor at the City University of New York has written an essay on NCTM's "Focal Points."

He states that:

"The NCTM Focal points are issued at a time when many parents are appalled by the lack of quality and content in their children's math programs. The Focal Points in grades 6 to 8 seem reasonable. But in earlier grades, they fail to disqualify very weak programs, still in use, that derive inspiration from and are consistent with the 1989 Standards.

"In Grades 1 to 5, the Focal Points fail to explain that sustained experience with nontrivial multi-digit arithmetic problems is critical to success in algebra and higher mathematics. They omit all reference to memorization. They do not admit the interpretation that skills can be developed first and understanding filled in later. Some content material is vague or weak. Indeed, the description of whole number division activities with multi-digit dividends suggests that the hardest problem that students need to handle is 99 divided by 9, while the description of place value fails to name numbers above 1000. That is unacceptable. The NCTM authors should have incorporated existing documents, most notably the State of California's Mathematics Content Standards, which provide a crystal clear grade by grade delineation of computational and symbolic skills appropriate to a content-rich elementary math program."

Check out the whole thing.

math panel update

The National Math Panel just posted a bunch of stuff on their website. Transcripts are now available for the November 5th and 6th meeting in Palo Alto, here and here.

Also, there are Progress Reports for task groups from the January meeting in New Orleans. Here are the reports for Conceptual Knowledge and Skills, Learning Processes, Instructional Practices, and Teachers.