Friday, February 2, 2007
Math Boot Camp – Talk Tape
Times tables, long division, square roots ... if you are of a certain age you'll remember these -- and probably not fondly. For many years, these basic drills were the nuts and bolts of elementary and high school math classes.
But that's no longer the case. A couple of decades ago, drills and repetition were overtaken by a focus on logic and problem-solving. It seemed like a good idea at the time. But Sherry Mantyka says it has led to what she calls "The Math Plague."
Sherry Mantyka is a Math Professor at Memorial University in St. John's, Newfoundland. And she says too many students are unable to apply basic math skills to complicated problems or to be ready for university-level math.
Our Newfoundland and Labrador producer Heather Barrett can count on one hand the number of successful encounters she's had with mathematics in recent years. But she nonetheless volunteered to go look into Professor Mantyka's concerns and the solutions that she is proposing. Heather Barrett was in St John's this morning.
(And by the way, Heather Barrett scored a stunning 95% on her last math test).
Listen to The Current: Part 1
How to Survive School Mathematics (Click here for excerpt from book)
As I read some of the comments it helped me understand why constructivist teaching is not optimal for both my kids – a 15 year-old boy and a 9-year old girl. It made me wonder, is constructivism anti-boy? Or, is it just anti-kids?
My son is a fast learner and typically wants "just the facts". He's often been bored in math, and I can see why. While the teacher may be engaged in discussing endless variations of a given concept and everybody gets to share their views, my son just wants to get on with it.
My daughter is a slower learner, easily distracted and very verbal. Since I successfully after-schooled her using Saxon I have seen that she does well with a logical presentation of material that sequentially builds upon previous lessons. It's curious, but the constructivist tendency (requirement?) to verbalize everything seems to act as a distraction to her learning by encouraging her to go off on tangents unrelated to the lesson. And spiraling simply offers many opportunities for her to superficially touch upon the subject matter without ever really mastering it.
The more I’m learning about direct instruction the more it makes so much sense.
BTW, our school is not currently using a constructivist text but I've observed many of the principles in practice.
Progressive education, by which I mean forsaking content for utility and a child-centered focus on creativity, also has a strong tradition in Britain. A. S. Neill, the famous progressive educator, founded Summerhill, the progressive school, in Suffolk, England, not Suffolk County, New York. But the progressive movement has not touched most British schools to anything like the degree it has penetrated in America. As Diane Ravitch, the academic and former assistant secretary of education, points out in Left Back: A Century of Failed School Reforms, a history of progressive education, America is now a nation of Summerhills. Most American teachers and principals frown on traditional schooling. Rote learning is out, as are American and European history and demanding math. Instead educators impart things they find fun or politically appealing. The attitude has become so ingrained that anyone challenging it risks being labeled elitist, even un-American. The New World, the message is, has never liked or needed Old World–style learning.This is the key passage:
This, as Ms. Ravitch shows, is a myth. American schools were not always anti-intellectual. As recently as 1910, half of those in high school studied Latin—even though many were immigrants who were also learning English. As recently as the 1930s, eight-year-olds in Philadelphia’s public schools routinely memorized biographies of Alfred the Great, William Tell, and Florence Nightingale. Grammar schools demanded that small children demonstrate a skill today not required of even Ivy-bound 18-year-olds—to answer questions such as “A harness was sold for three-quarters of four-fifths of what it cost. What was the percentage loss?”
Such knowledge was then deemed the best weapon to abolish class. “The famous simile of the educational ladder, with its foot in the gutter and its top in the university,” wrote one educator, “is a fact many times verified in the knowledge of every intelligent adult.”
Then, though, came the progressives, who argued that children needed living knowledge, not dead artifacts. They started small, by throwing out the Greeks and Romans, and worked from there. By the 1940s the schools in Battle Creek, Michigan, had halved the share of students enrolled in college prep classes, while introducing health studies and “basic living” courses. Schools replaced mythology and history with the more amorphous social studies.
The youth-centered 1960s gave the trend fresh life. Now old-fashioned, content-oriented education was deemed not merely useless but dangerously authoritarian. Schools sought to cater to children and offered, as one Michigan scholar wrote, “an endless list of subjects to attract and interest students, such as Girl Talk and What’s Happening.” The schools, the scholar noted, had “simply given up on any attempt to exert any moral authority relative to education.” By 1970, Neill’s book Summerhill, which promoted his experimental methods, was required reading at 600 universities, selling 200,000 copies. What had started as a tiny war against Homer and Herodotus had turned into a siege, a watering down of every part of the curriculum for all ages. Today even basic math skills such as long division and the division of fractions are under assault. Teachers explicitly dismiss them as outdated and hand out calculators to children in the first grade.
They started small, by throwing out the Greeks and Romans, and worked from there. By the 1940s the schools in Battle Creek, Michigan, had halved the share of students enrolled in college prep classes, while introducing health studies and “basic living” courses.Labaree on the 2 progressivisms & which one won
Progressive education wasn't just one thing; it was two things.
pedagogical progressivism (Dewey)
administrative progressivism (Thorndike)
The second thing we need to recognize about the history of this movement is that the administrative progressives trounced their pedagogical counterparts. Ellen Lagemann explains this with admirable precision: ‘I have often argued to students, only in part to be perverse, that one cannot understand the history of education in the United States during the twentieth century unless one realizes that Edward L.Thorndike won and John Dewey lost.’I get the sense that more than a few ktm readers, writers, and commenters see high school as the release from progressive ed. The evidence? It's in high school where tracking begins.
For my district and I'm sure for others, that's wrong. Tracking was invented by the progressive ed movement, and at the district level it's not about high standards for teaching or content.
It's about tracking.
It's about selecting an elite from amongst an already self-selected group of students.
[T]he main thrust of the social efficiency curriculum, with its emphasis on core principles of the pedagogical progressives. It mandated exactly the kind of topdown curriculum that the latter abhorred, imposed on students in order to serve society’s need for particular skills and knowledge, and forcing them spend their time in schools becoming socialized for the adult social roles they will play. This puts priority on learning particular subject matter instead of learning to learn; it elevates the interests of society and of school administrators over the interests of students; it makes the classroom a preparation for adulthood rather than an exploration of childhood; and, in the name of these social benefits, it risks extinguishing the child’s engagement in learning and curiosity about the world. It was, in short, exactly the kind of curriculum that Dewey deplored, ‘externally presented material, conceived and generated in standpoints and attitudes remote from the child, and developed in motives alien to him’.In our district what I think I see is John Dewey progressive ed K-5 replaced by Edward Thorndike progressive ed 6-12.
Not only did the social efficiency curriculum threaten the kind of natural learning process treasured by the pedagogical progressives, but it also threatened the values of social justice and egalitarian community that were central to their beliefs. This curriculum was radical in its challenge to traditional notions of academic education, but it was profoundly conservative in its embrace of the existing social order and in its eagerness to prepare students for predetermined positions within that order. It introduced tracking and ability grouping into American schools; it introduced ability testing and guidance as ways of sorting students into the appropriate classes; and it institutionalized the educational reproduction of social inequality by creating a system in which educational differences followed from and in turn reinforced differences in class, gender and race.
So far I prefer Dewey.
Jay Mathews, as it turns out, lived in Scarsdale and experienced "Westchester tracking" firsthand. More later.
spilt religion - Hirsch on progressive education & Romanticism
David Labaree on the 2 factions
Labaree on constructivism
Hirsch on Labaree
Hirsch, E.D., "Romancing the Child," Education Next, 1 (Spring 2001).
Labaree, David F., "Progressivism, Schools, and Schools of Education: An American Romance," Paedagogica Historica (Gent), 41 (Feb. 2005), 275–89. (pdf file)
Thursday, February 1, 2007
I came across this article on the APA website.
This question may be answered by David Klahr, PhD, a psychology professor at Carnegie Mellon University, and Milena Nigam, a research associate at the University of Pittsburgh's Center for Biomedical Informatics. They have new evidence that "direct instruction"--explicit teaching about how to design unconfounded experiments--most effectively helps elementary school students transfer their mastery of this important aspect of the scientific method from one experiment to another.
Klahr saw three main reasons to challenge discovery learning. First, most of what students, teachers and scientists know about science was taught, not discovered, he says. Second, teacher-centered methods (in which teachers actively teach, as opposed to observe or facilitate) for direct instruction have been very effective for procedures that are typically harder for students to discover on their own, such as algebra and computer programming. Third, he adds, only vague theory backed the predicted superiority of discovery methods--and what there is clashes with data on learning and memory. For example, discovery learning can include mixed or missing feedback, encoding errors, causal misattributions and more, which could actually cause frustration and set a learner back, says Klahr.
Yet discovery learning has persisted, he says, partly because of a lingering notion that direct instruction would not only be ineffective in the short run, but also damaging in the long run. Piaget thought interfering with discovery blocked complete understanding. More recent cognitive research, says Klahr, shows that "this is just plain wrong."
Study after study disproves the current "inquiry" approach to education, yet if you mention direct instruction among a significant portion of educators you might as well just call yourself a martian.
Barry just alerted me to the fact that this review (and post) sound anti-semitic.
This review appeared in Haaretz, which is the most prominent newspaper in Israel. This is an Israeli economist talking about the same stuff we talk about here, the miserable state of math ed in the schools.
from a review of Ron Aharoni's Arithmetic for Parents:
Once a year, Israelis wake up in the morning, open their newspapers, read reports about surveys comparing the level of knowledge in mathematics of our genius children with that of children from countries, which we more or less respect, and discover to our horror that we are slipping badly. Israeli kids, we sadly conclude, are just not all they are cracked up to be.
Since the level of knowledge in mathematics is customarily linked with intellectual prowess in general, the myth of Jewish genius suffers a massive blow. Since mathematics is customarily considered the "queen" of the sciences, serious doubts are raised as to whether the Jewish People of Zion can truly build a Temple of Academia and Science to which the nations of the world will flock. And since the quality of our human resources and technological progress are vital for the maintenance of our edge over those nations that are bent on destroying us, our very survival is threatened.
Reading this, I find myself shockingly not sorry about the fact that Israeli kids can't do math, either. Misery loves company.
Now if we can just do something about those Singapore kids.
What I Learned in Elementary School by Ron Aharoni
American Educator article by Ron Aharoni (ktm-1)
Ron Aharoni on teaching fractions (ktm-1)
Ron Aharoni on the fifth operation of arithmetic (ktm-1)
Ron Aharoni on reform math in Israel (ktm-1)
Maybe we need another term besides "math facts." They are much more fundamental than contingent facts like, say, dates when certain historical events occurred.That's a terrific point. The term "math facts" does lend itself to the view that "math facts" are on a par with historical dates.
Do kids still learn "letter facts" like the names of the letters and alphabetical order?
I'm going to start using the terms fundamental versus contingent to talk about the math facts.
(I guess we could call them math fundamentals...on occasion.)
Call them something exotic so the reformers at large will think it's higher order thinking skills. Call them theorems, because that's what they are. 3 + 2 = 5 is a theorem which can be proven using Peano's axioms. And like all theorems, once proven, it can be used without having to re-prove it, thus alleviating our kids from having to draw clusters and go back to first principles each and every time they add, subtract, multiply or divide lest anyone think they were doing things by rote.
I've never liked this either. I think it's a carfully-selected term used to degrade the importance of the knowledge. when I told my son's Kindergarten teacher (years ago) that I supported an educational approach that emphasized basic knowledge and skills, she said that I would like one of the second grade teachers who required each child to give her a "math fact" to enter the room.
They are just clueless.
From his first grade teacher I learned about "superficial knowledge". I wanted to tell her that it is fundamental knowledge.
Basic knowledge and skills are the foundation of education. You build from the bottom up rather than the top down. Somehow they think that education should be thematic or top down; that kids can learn basic knowledge and skills by osmosis.
Basic facts and skills require hard work.
Hard work is a filter.
The only point I would add here is that achieving expertise requires hard work and expert teaching.
I've been trying to make my way through the research on expertise, with limited success. It is vast.
However, I've managed to do some mighty skimming.
As far as I can tell, expertise is expertise; the mechanisms by which one acquires expertise are (largely) the same.
These days I think about athletics and athletes when I'm confused by an issue in K-12 education.
There's a reason you never, ever, see an Olympic athlete who is self-taught.
That reason is that expertise requires superb teaching.
I'm not sure whether the strong form of this statement is correct.* Certainly I've seen many people who are self-taught (I taught myself to write).
There must be a literature somewhere on self-teaching.
Nevertheless, the weak form of the statement is certainly true.
Our kids need expert teachers who themselves take the development of expertise seriously. Hard work isn't enough.
I would rewrite every school mission statement in this country to reflect this understanding.
I'd take out all the "lifelong learners" and "critical thinkers" and "all children can learn" foofaraw.
I'd insert the word expertise.
* One of the reasons why I'm not sure is that procedural learning and knowledge, which I believe is dominant in athletics, seems to follow a slightly different set of rules than declarative knowledge, which is dominant in academic disciplines.
Procedural knowledge seems to be much more vulnerable to error. Once you learn a procedure - a golf swing, say - the wrong way, you can't unlearn it.
As far as I can tell, declarative knowledge is less vulnerable. If you mislearn a fact, you can overwrite it in memory. I'm guessing it's possible to learn from error in declarative knowledge.
caveat: I don't "know" these things. This is what I surmise based in many years' surfing literature on memory.
Wednesday, January 31, 2007
Number and Operations
Understand whole numbers, including concepts of correspondence, counting, cardinality, and comparison;
Develop place value concepts and an understanding of multiple decompositions of numbers;
Represent, compare, and order whole numbers and join and separate sets;
Understand addition and subtraction and strategies for basic addition facts and related subtraction facts;
Develop automaticity of addition facts and related subtraction facts and fluency with multidigit addition and subtraction.
Understand multiplication and division, and strategies for basic multiplication facts and related division facts;
Develop automaticity of multiplication facts and related division facts and fluency with the multiplication and division of whole numbers;
Understand decimals as special classes of fractions, fraction and decimal equivalence and connections between fractions, decimals and common percents;
Develop an understanding of and fluency with operations on all rational numbers (i.e. addition, subtraction, multiplication and division of fractions and decimals, negative integers).
Define ratio and rate in terms of multiplication and division
Develop an understanding of and apply proportionality, including similarity
Write, interpret, and use mathematical expressions and equations
Analyze and represent linear functions and solve linear equations and systems of linear equations
Geometry and Measurement
Identify and describe shapes and spatial relationships and compose and decompose geometric shapes;
Identify measurable attributes and compare and order objects by using these attributes;
Develop an understanding of linear measurement and facility in measuring lengths.
Describe two-dimensional shapes and analyze their properties, including perimeter and area and understand and use these formulas;
Describe three-dimensional shapes and analyze their properties, including volume and surface area and understand and use these formulas
Analyze two- and three-dimensional space and figures by using distance and angle.
Data Analysis and Probability
Analyze and summarize data sets using descriptive statistics (mean, median, mode, and range)
Use theoretical and experimental probability
Essential Concepts and Skills Prekindergarten through Grade Eight
I gather this is to be considered a sequential list.
The ... topical lists were derived through careful analysis of state curricular standards in this country and also included review of the American Diploma Project Benchmarks and K-8 Benchmarks (Achieve, 2004, 2006), the intended math curricula for Japan, Korea, Flemish-Belgium, Singapore, Chinese Tapei, the work of William Schmidt with TIMSS and beyond (2002) and the recent work of the National Council of Teachers of Mathematics (2006).
- Cognitive and learning mechanisms are understood
- Most children in the U.S. do not achieve this
- Interfere with problem solving in which facts are embedded
most children in the U.S. do not achieve fast and efficient retrieval of math facts
I'm starting to think parents are underpaid.
Learning Processes Group
January 11, 2007
New Orleans, LA
Whole Number Arithmetic
Math Panel Update
Dave Geary, Task Group Chair
Jennifer Graban, staff
somewhere on another planet not my own
My fiance' Shannon found this great website from sadlier-oxford.
It has some great activities to use to help teach reading in grades K-5.
January 11, 2007
While there is agreement to the sequence of particular concepts and skills in PreK-8 mathematics (e.g. whole numbers), this is not true with algebra. Therefore the following list of essentials should not be considered a linear sequencing of these topics.
Elements of Algebra
Symbols and expressions
Geometric sequences and series
Arithmetic and geometric sequences and series
Fundamental relationships between linear equations and the graphical representations of such equations
Solving problems with linear equations
Linear inequalities and their graphs – to include compound inequalities
Graphing and solving systems of simultaneous linear equations
Factors and factoring of trinomials with integer coefficients
Factors and factoring of polynomials
Completing the square in quadratic expressions
Quadratic formula and factoring of general quadratic polynomials
Using the quadratic formula to solve equations
Quadratic functions – solve problems involving quadratic functions
Fundamental relationships between quadratic functions and their graphs
Polynomial functions (know graphs of basic functions)
Simple nonlinear functions (e.g. square and cube root functions; absolute value)
Rational exponents and exponential functions
Fitting simple mathematical models to data
Roots and factorization
Complex numbers and operations
Fundamental theorem of algebra
Binomial coefficients (and Pascal’s triangle)
Mathematical induction and the binomial theorem
Combinatorics and finite probability
Connections between algebra and other areas (e.g. linear functions and best fit in statistics; similarity relationships and distance in geometry)
– Francis (Skip) Fennell, Task Group Chair
– Larry Faulkner
– Liping Ma
– Wilfried Schmid
– Tyrrell Flawn, Staff
– Hung-Hsi Wu
– Joan Ferrini-Mundy
– Sandra Stotsky
– Outside Reviewers - several
(copied from the documents Lynn posted on the 18th)
The focus of the math night that I just had was on games that parents and children could play at home to work on math facts, just using decks of cards and things. These are things they can work on with their kids that are fun and easy to do. I don’t want to spend a half hour in class memorizing multiplication. We have far greater things, bigger things to think about.
Math Trailblazers (pdf file)
teaching math facts is brain surgery
somewhere on another planet far from my own
I was educated in Russia where school programs were also set by a central authority. I was in classes of 35 or 40 students. A sizeable proportion of my classmates had alcoholic parents. Many came from broken homes. Few of us were regularly read to, and some of our parents were virtually illiterate. Most of us lived below the poverty line by today's American standards. Despite all of this, we could all read by age eight, do basic math by ages nine or ten, and produce reasonably well written texts by fifth or sixth grade. Most of us had basic familiarity with major concepts in science, geography, and history. All of us knew some redimentary English. Our spelling, grammar, and sentence structure in English were better, in my assessment, than those of most of my son's American friends. As for creativity, I don't believe we are any less creative than our American-born counterparts. Most Americans of our age are impressed by the education we received and say they wish they had had the same opportunities.
When I hear educators talk about striving to reach a 70 percent achievement rate in standards that would be considered modest compared with those imposed on (and met by!) nearly all of my peers, I cannot help but see such efforts as naive, albeit well-intentioned, attempts to reinvent the wheel.
When I was growing up in Leningrad, there were two pedagogical institutes where future teachers received their training in how to teach. They learned, for example, that multiplication tables up to eight take second graders until April to master, if they practice four times a week for fifteen minutes and get three homework assignments on them a week.
four times a week for fifteen minutes + three homework assignments 'til April
That's the kind of info parents who have to teach their kids the math facts might find useful.
Too bad U.S. schools don't have any info like this.
Scholars and journalists have also ignored the odd and potentially harmful ways these [wealthy] schools have stratified their students. There is a class system imposed, without much thought of how well labels such as honors, regular, and remedial fit the children involved.
A district employee has told me - this is a quote - "Irvington is the most heavily tracked school district I've ever seen."
I've been talking for quite awhile now about the fact that when Christopher was in grade school he was tracked out of calculus in high school. He was 8.
He was tracked out of calculus in high school and no one told us he'd just been tracked out of calculus in high school. In fact, we were told that the tracking of children into "Phase 3" as opposed to "Phase 4" didn't mean anything at all.
Same deal with Honors courses in the high school except worse.
There is a lengthy, top-secret admissions process requiring students to write and submit an application essay. [update 7-2007: it's possible now that the student's teacher selects the essay to "submit"]
The admissions process is so lengthy and so top secret that parents now have to sign letters stating that they know their children have decided to put themselves through it, a requirement obviously intended to ward off parent fury when our kids get shot down. If we don't sign our kids can't "apply"; when our kids don't get in we can't get mad because we signed. [update 7-2007: although the parent sign-off is indeed a rule, my neighbor was not asked to sign a consent form acknowledging that her son was "applying" to 9th grade English honors for next year]
The admissions process creates an elite consisting of, I'm guessing, perhaps 25% of the class.
These kids will be prepared to take SATII subject matter tests when the time comes.
The rest of the kids will not be prepared to take SATII subject matter tests when the time comes. Or so I'm told by other parents.
If a parent asks, "What if my child didn't get into Honors but wants to take the test?" the guidance counselor gives him a look that says, "Why would he want to do that?"
So that's the plan. Twenty-five percent of each class, I'm guessing, will be prepared to take SAT II subject matter tests.
more fun with guesstimating
The reason I'm guessing is that the selection and rejection numbers are secret, too.
No one knows how and why one student is chosen over another, including the middle school teachers.
If a parent asks a middle school teacher what his child can do to improve his learning and performance to a level that will get him into Honors, the middle school teacher will say she doesn't know, and she doesn't.
This year a middle school teacher told a parent that she had no idea how the admissions process worked, adding that, "Frankly, some of the choices surprise me."
There is no public value, none, placed on hard work, ambition, and striving. None.
Hard work, ambition, and striving are the quintessential properties of the pushy parent, so blech.
yet another irony
The irony of our situation is that our school discourages and devalues the precise qualities of character & temperament that got the parents "where they are today." All of the wealthy parents here are working rich; the dads, and not infrequently the moms, are extremely hard workers and always have been.
Meanwhile the "non-working" moms aren't out shopping. They're 24/7 raising kids and shouldering the volunteer work for school and town.
Many of these moms and dads started out middle class and attended middle class schools, public or Catholic.
The dads often have stories like this one.
Ed grew up in Levittown, PA, which was at that time a factory time. A lot of the other dads were steelworkers. He was a smart kid, but he didn't like to read or work too hard in school. He liked to play outdoors with his friends. When he was in 6th grade his teachers complained to his parents that he wasn't applying himself.
When he got to high school he went into some Honors courses, but decided not to take Honors English because it was going to be too much work.
The teacher of the regular-ed class threw him out.
He told Ed he had no business taking the easier class; I think he may have actually walked him over to the Honors class and deposited him there.
So Ed took Honors English. Better than that; Ed got serious and took Honors everything. Maybe he would have gotten serious on his own, maybe not. His school made sure he did. In the vernacular, his school had "kicked his butt." I think he used to do as much as 4 hours of homework a night every night. When he was a senior he applied to Princeton and got in. He's been building on his Princeton education ever since, and he owes his Princeton admission, at least in part, to his Levittown schools.
My neighbor's husband has the same story, only for math.
He decided to take regular math instead of Honors math.
The teacher said, "You aren't going to get out of Honors math just by taking my class."
Then the teacher gave him extra work - hard work - to do for the whole school year. (Talk about differentiated instruction.)
Another friend told us that the nuns shaped him up. He was an athlete - would have played college ball if not for an injury - and his working class family wasn't the Waltons. He was spacy and disorganized to boot.
In high school one of the nuns collared him, sat him down, and told him he had to get his act together.
Then she worked one-on-one with him every day after school until he did get his act together.
So today he has a life. He has a life because his school saw he could do a lot better than he was doing and then worked with him until he did it.
More than a few of the "pushy parents" here in Irvington, the ones who get their kids into courses where they don't belong, managed to get to Irvington because back in the day their schools pushed them.
That's the irony. I have never heard this story in Irvington. Never. I don't expect to.
In this wealthy, successful district no child is ever pushed up.
More than a few are pushed down.
Jay Mathews on the class struggle
Jay Mathews column on wealthy schools, AP courses, SAT scores
are wealthy schools worse?
value added comes to Westchester
It required the students to answer questions such as:
6 x __ = 18
7 x __ = 28
Not so bad right? Except the directions explicitly told them to solve the problems by drawing clusters. In other words, the problems would be solved by the students like this:
6 x __ = 18 oooooo oooooo oooooo (3 groups of six = 18 so answer is "3" )
7 x __ = 28 ooooooo ooooooo ooooooo ooooooo (4 groups of seven = 28 so answer is "7")
I had my daughter do the worksheet without the clusters and wrote the following message on the paper:
"Christina will not be drawing clusters to solve factoring problems. I drilled her to learn her multiplication tables so she wouldn't need to use pictures to solve multiplication problems."
Monday, January 29, 2007
This is not to say that skill mastery is not expected in Everyday Math. Fact automaticity is expected and nurtured through various games and practice routines.Hmm. That appears to be the extent of the expectations for mastery. I don't disagree, except I think we need mastery on much more than the basic facts.
The final document with the word "mastery" in it from EM comes from the 2001 Algorithms in Everyday Mathematics. The paper states as a justification for the non-standard algorithm the fact that in one study (not identified), only 60% of US 10-year-olds achieved mastery of the traditional subtraction "borrowing" algorithm. Unfortunately, EM doesn't tell us how many US 10-year-olds achieve mastery of the alternative algorithms EM has used to teach subtraction for the past 15 years.
Anybody have any data on whether US 10 year olds are faring any better these days?
Based on the EM website, it seems that calling EM anti-mastery is probably a fair characterization. Discussion?
The primary enemy that educators had to fight then and now is evaluation, because evaluation reveals the discrepancies between the educational rhetoric and the effectiveness of the schemes based on this rhetoric.
Which is why NCLB has met with such resistance.
On bussing and the Coleman Report:
Like hermit crabs who have lost their borrowed shell, educational policy makers were denuded by the Coleman Report, and like hermit crabs, scurried to find security, regardless of how bizarre the shelter was. Their effort resulted in one of the more inhumane programs ever initiated—bussing. For educators, however, bussing was an ideal solution, because herding children into a bus did not require any kind of instructional expertise.
Because bussing was a non-instructional remedy to an instructional problem (the failure of the schools to teach children effectively), policy makers needed some compelling rhetoric to make busses symbols of progress. They fixed on history and redefined the performance problems of poverty blacks as a social problem, rooted in history and caused by discrimination against blacks. With this link established, policy makers could point to busses and declare, “There's your evidence that we are responding to the data. We are breaking down discrimination. Therefore,
we are addressing the fundamental causes of the poverty blacks’ performance problems.”
On social promotion as the inevitable result of bussing/affirmative action:
“We’re supposed to have standards here. We don’t do social promotions. So if I place black kids where they belong, more than 75 percent of them would be in special ed. If I put them in special ed, I’m a racist. If I leave them in the regular classrooms and flunk them, I’m either a racist or an ogre who doesn’t understand affirmative action. So what do I do, close my eyes, sell out our standards and socially promote them, or go to another school?”
On the origins of Constructivism:
One of the [program sponsors in Project Follow Through] was Lauren Resnick, then a behaviorist at the University of Pittsburgh, who wanted to use her site to develop an
approach to teaching classification, which she seemed to think was the end-all of instruction and would permit children to do remarkable things. We had talked with her before the meeting. Wes thought she was great. I thought she was quite smart but lacked sensitivity to the problem of providing a service for these children. She seemed far more interested in her model for teaching classification (which was neither analytically nor practically very sound) than she was in considering Follow Through children as more than subjects in her experiment. She would later become a non-behaviorist, the flag bearer of a failed approach called constructivism.
On John Dewey:
A distinguished white-haired man on the main floor stood up and gave a long, dramatic oration. He ended by saying in rising volume, “I hear talk of skills and sub-skills and sub-skills of sub-skills, but why is there nowhere in Mr. Engelmann’s presentation one word about [pause and dramatic point toward the ceiling] learn by doing and do by doing!”
Explosion of cheers, shouts, applause, which lasted probably more than 10 seconds.
When the place calmed down, I said, “Well, I promised Bob Egbert that I wouldn’t say bullshit, but I’ll try to answer your question anyhow.” I went on to explain that not only was the originator of slogans about learning, John Dewey, dead but that there was nothing to suggest that his slogans had much relevance to the problems facing disadvantaged kids. As I talked, the man’s face became so red I thought he would explode. After the meeting, Bob Egbert looked at me with a wry smile and
shook his head. I later found out that the man with the long question was
the director of math instruction in NYC.
Under the heading of "Reading." there was listed the skill:
Uses a variety of decoding strategies
His grade was a P for Progressing. First of all, don't get me started on the wacky grading scheme E (Excelling), P (Progressing), I (Improving with support ), N (not Progressing). It doesn't matter what code gets used, parents (and likely students to0) are going to automatically equate E, P, I, N with A, B, C, D/F. So what's the point, except perhaps to soften the blow when little Johnny comes home with a bunch of C's.
In any event "uses a variety of decoding strategies" is also code. Code for "whole language."
A quick review.
There is one legitimate way to decode text--using phonics skills to match up the graphemes (symbols in print) with the phonemes (the speech sounds they represent) to decode (i.e., identify) the written word and then, hopefully, extract meaning from it (i.e., match it up with a word in the child's oral vocabulary). Whole language proponents mistakenly believe, however, that text can be decoded using context cues such as word order, word endings, tense, intonation, phrasing (syntactic cues) and using the meaning of what has just been read (semantic cues) to identify an unknown word in text. In first grade, what this means is that when a child comes to a word that is unknown he is encouraged to look at the picture on the page (context cue) to guess at the unknown word. Since the text is designed to be predictable ("The cowboy rode on his horse" matched with a picture of a man dressed like a cowboy riding a horse.)
The mistake is that skilled readers don't use context and syntax cues to identify (i.e., decode), they use these skills to determine the meaning of words they have properly decoded but whose meaning is unknown. Whole language educators mistakenly conflate the decoding and meaning parts of reading with the inevitable result being the creation of children with poor decoding skills once the pictures are taken away (fourth grade) and the text becomes less predictable.
In any event, we had instructed my son not to use context cues when he's reading at home; however, when he's reading for his teacher at school and comes to a word he doesn't know it's OK to look at the picture to make the teacher happy.
So while I would have preferred to see an N (Not progressing) for this "skill" on his report card, I was satisfied with the P (progressing) since he had learned a very important school skill -- keep the teacher happy.
“In many critical disciplines, particularly in math, science and engineering, 50% or more of the post-graduate degrees at U.S. universities are awarded to foreign nationals.”I learned of Compete America from a newscast reporting on an immigration story. This story centered on a proposal to lift the cap on the annual number of H-1B visas issued, currently at 65,000. H-1B visas apply to foreign professionals who may work in certain occupations -- such as engineering, biotechnology and computer science -- where enough qualified Americans are unavailable.
From their website:
Compete America is a coalition of over 200 corporations, universities, research institutions and trade associations committed to assuring that U.S. employers have the ability to hire and retain the world’s best talent. America’s race to innovate and produce the next generation of products and services for the world market requires highly educated, inventive and motivated professionals. While many of the world’s top engineers, educators, scientists and researchers are citizens of the United States, a significant number are not. America’s scientific, economic and technological leadership has been aided by the many outstanding contributions of foreign nationals. Compete America believes it is in the United States’ economic interest to provide world-class education and job training, while maintaining a secure and efficient immigration system that welcomes talented foreign professionals.
Members include Microsoft, Intel and NAFSA; Association of International Educators (not sure who they are).
Their website includes state by state statistics on foreign students enrolled in graduate university programs.
Here’s another provocative fact:
By 2010, if current trends continue, more than 90 percent of all scientists and engineers in the world will be living in Asia.
Is this an indictment of the quality of our math education? Regarding the often quoted statistic that approximately one-fourth of US college students require remedial assistance, how many of those remedial students were educated outside the US? For math, probably none.
Sunday, January 28, 2007
Chapter 1: Before Project Follow Through (January 22)
Chapter 2: Project Follow Through Begins (January 29)
Chapter 3: Follow Through Continues (February 5)
Chapter 4: During Follow Through (February 12)
Chapter 5: Follow Through Evaluation (February 19)
Chapter 6: Follow Through Aftermath (February 26)
Chapter 7: The New Millennium (March 5)