QuoteNontraditional math decried as 'fluff' in Frederick
Changes in math curriculum don't usually stir parents to political action, but in Frederick County, the introduction of a new math textbook has caused a minor revolt by county residents, 600 of whom have signed a petition to persuade the county school board to return to a more traditional approach.
"Our primary objection is the lack of solid math content. It has been replaced with fluff," said Tom Neumark, a Frederick resident whose daughter will be a kindergartener next year.
The battle these parents are having with the county is just one part of a larger discussion taking place around the nation and among federal education officials over how math should be taught. Some education experts are calling for states to adopt national standards that would narrow the focus of the math curriculum and make American students more competitive internationally. Maryland is on the verge of reviewing its standards and deciding whether to make changes.
On the grass-roots level, Stacey McGiffin is part of the parents group that would like to see changes at the state level. She says her second-grade son is bored with the math he is doing in a new curriculum called TERC. She and other parents say the program requires teachers to spend too much time explaining why math works and not enough time having students practice how to do problems. "TERC takes discovery learning to an extreme. In trying to make math 'fun,' TERC fails to teach the fundamentals that will ultimately prepare kids for algebra and beyond," McGiffin said.
TERC uses an approach called reform math that has grown popular in the past decade. Used in thousands of classrooms, according to its creators, TERC stresses conceptual thinking rather than a more traditional approach of solving problems. Frederick County schools adopted TERC in its elementary grades this school year after having used it at Lincoln Elementary School for several years.
A number of school systems in the Baltimore area have chosen to use textbooks that attempt to blend both methods and have not chosen to use TERC exclusively as Frederick has. In Baltimore County, teachers supplement a more traditional textbook with TERC. Anne Arundel County uses a similar approach, approving TERC only as a supplement, but no schools there have chosen to use it.
Such programs have come under scrutiny as national leaders suggest that math programs in foreign countries where students are most proficient give students more practice at solving difficult equations, and they do them at an earlier age.
Those views were supported by a multiyear study done for the U.S. Department of Education that indicated that TERC was the least successful of four math programs studied. In fact, the results gave high marks to one reform math textbook series and to another traditional approach. TERC spokesman Ken Maher said the study used an early version of TERC and that the program may do better later.
The choice of textbooks, which is left up to local school districts, is likely to come under scrutiny if the state school board takes action this year to make the changes that are being pushed nationally.
Donna Watts, who is in charge of math curriculum for the state, said an outside group called Achieve was hired to review the math standards. Achieve's review was completed in February, but Watts had said the document would not be released to the school board until fall, after a full review. After The Baltimore Sun filed a Freedom of Information Act request asking the document to be released, the department announced it would make the Achieve report public after the state school board receives a copy at its May meeting.
Watts said the Achieve report is not calling for major revisions to the state standards but rather "polishing."
Frederick County Associate Superintendent Bonnie Ward, who was involved in the selection of TERC, said the county based its choice on the success it had at Lincoln, which saw scores move up significantly over several years. She said the county is holding meetings for parents to better understand their children's homework.
Nevertheless, some Frederick County parents say they will be teaching their children math from different textbooks so that they don't fall behind.
What is the typical US math curriculum like?
They are trying to dumb it down in Poland, too, btw. Back in my day, we've got trigonometry introduced in the fourth grade, and the calculus in the fifth or the sixth grade, and we liked it. :mad:
Just outsource math to the Chinamen.
Quote from: Martinus on July 11, 2009, 10:52:22 AM
What is the typical US math curriculum like?
For me, it was the basics for 1st-5th grade. Pre-algebra and geometry for 6th-8th with Algebra 1/2, Geometry, Algebra 3 and Trigonometry courses through high school.
I recently realized that though I was always between A and B in maths grades I have thankfully forgotten all about integral and infinitesimal calculus. :)
QuoteMajor Characteristics of TERC's Program: Investigations in Number, Data, and Space
1. TERC insists on the ongoing use of hands-on tools (manipulatives, "models," and calculators).
* They say concrete tools must always be available and regularly used.
* TERC strongly rejects the idea that children must eventually migrate from hands-on to abstract thinking.
2. TERC rejects the need for memorization and practice.
* They say that student's familiarity with single-digit number facts must "grow out of lots of experience with constructing these facts on their own." BA, Page 72 (emphasis added)
[Please click on References for the meaning of the BA code.] There's no additional gain in conceptual understanding associated with the task of trying to "construct" one more basic number fact.
o o TERC doesn't think it's possible to understand memorized information. But knowledge must first be loaded into the brain before it can connected to other knowledge and "understood." Explicit memorization is sometimes the most efficient way to get it there.
o TERC fails to understand that it's often desirable to move to automatic use of knowledge. The mind must be free to think at higher levels of complexity, without consciously revisiting underlying details. For example, the key idea of the standard algorithms is that multi-digit calculations are reduced to multiple single-digit calculations. If children don't have instant recall of the single-digit number facts, they aren't equipped with the essential pre-knowledge for easily carrying out multi-digit computations.
3. TERC fails to clearly define terms.
* They regularly state: "We don't ask students to learn definitions of new terms."
* They offer some "definitions," typically using multiple undefined terms to "define" a new term.
* They favor "natural language" and "personal language."
4. TERC emphasizes "familiar numbers."
* The "landmark numbers" are 5, multiples of 10, and multiples of 25.
o Landmark number are also known as anchors.
* The "familiar fractions" are limited to proper fractions with denominator equal to 2, 3, 4, 5, 6, 8, 10 or 12. Thus 7 and 11 are not familiar denominators. Perhaps TERC is opposed to gambling.
o Note: 12 is included because it's needed for TERC's clock face method for adding fractions.
* TERC doesn't believe in defining terms, so you won't find the preceding definitions in TERC materials. This is what they appear to mean by these phrases. We welcome their clarification.
* Although TERC rejects explicit memorization of basic single-digit number facts, they expect students to remember many non-basic facts about landmark numbers and familiar fractions.
5. TERC omits standard formulas.
6. TERC emphasizes estimation and many right answers.
* They suppress the concepts of precision and accuracy.
7. TERC proudly rejects standard computational methods.
* No standard algorithms for multi-digit computation.
* No standard methods for operations with fractions and decimals.
* No general methods for calculating with numbers.
* TERC emphasizes special case methods involving landmark numbers and familiar fractions.
8. TERC attempts to directly teach their shallow and misleading content.
* They claim to offer a "constructivist" approach where students discover math as they play games and carry out investigations. But they provide thousands of pages of teaching instructions and recommended scripts that identify the content they expect kids to "discover."
o Thousands of pages for the teacher, but no text for the student.
An example I found:
NYT article from 2000. This argument's been going on longer than I thought.
QuoteThe New, Flexible Math Meets Parental Rebellion
By ANEMONA HARTOCOLLIS
Three years ago, one of New York City's most adventurous school districts set out to tackle a nagging problem: the math phobia that afflicts many students, and the disparity between the test scores of white middle-class students and their poorer black and Hispanic counterparts.
The district, which stretches from the Upper East Side to Chinatown, embraced a new "constructivist" curriculum without textbooks. This approach preaches that it is more important for children to construct their own solutions to mathematical problems than to learn the standard rules -- from multiplication tables to the value of pi -- handed down through the centuries.
Long ranked near the top of the city in mathematics, the district has held its place, although there is still a disparity in test scores between the poorest schools and the more affluent ones. But the new curriculum has enraged many parents who find that their children cannot multiply easily or understand basic algebra.
One parent, Anna Huang, said her son, Mack, a fourth grader, "felt a lack of clarity" when his teacher insisted that he estimate answers, rather than compute them precisely. Another parent, Anne Cattaneo Santore, said she was troubled because her son, William, a second grader at P.S. 124 in Chinatown, spent months counting with coins and solving equations using "friendly numbers," for instance, converting 71 + 19 into the easier 70 + 20.
"Those strategies don't work when you get to larger numbers," Ms. Santore said, "and they have been doing those strategies all year."
Ms. Huang and Ms. Santore have joined other parents, mathematicians and many teachers in a rebellion that has shaken education from New York City to Plano, Tex., and Lincoln, Mass. As school districts from affluent enclaves in Greenwich Village to poor minority neighborhoods like East New York have embraced constructivist math, parents have formed e-mail networks and turned out in force at school meetings to protest what they say is "fuzzy math" and the systematic "dumbing down" of mathematics teaching.
"Parents are worried," said Elizabeth Carson, an actress, the mother of a seventh grader and a leader of the protest movement in New York City. "They're scared that their kids are not going to be competitive. The math is not in their bones.'
The new math has at its core a passionate belief shared by tens of thousands of teachers around the country that they can reach more children, especially low-achieving minority students, by dropping standard rules in favor of exercises that allow students to discover the principles of math on their own. Constructivist programs are being tried in more than half of New York City's 1,145 schools, Board of Education officials said.
Educators who support the new math say that old-fashioned teaching through memorization and rules produced generations of people who hated math and never deeply understood it. Indeed, the manifesto of constructivist mathematicians, the 1989 standards of the National Council of Teachers of Mathematics, urges teachers not to demand too much accuracy too early. Math should be "flexible," the standards say, and "reasonable" answers should be valued over a single right answer.
The constructivist movement has led to the widespread rejection of textbooks, in favor of exercises using blocks, beans and other materials. One popular program, MathLand, suggests that students count a million grains of birdseed to get a feeling for the size of a million. Another, Everyday Mathematics, teaches children an ancient Egyptian method of multiplication.
It also suggests that fourth graders measure angles with bent straws instead of protractors. Connected Mathematics, a popular middle-school program used widely in New York, teaches sixth graders to add fractions by folding paper strips into segments representing halves or fourths or thirds, instead of by converting to common denominators.
Lucy West, the director of mathematics at Manhattan's District 2, where the new math has been most aggressively adopted, said that old-fashioned math had been oversold. "There is a misconception that in the good old days everybody could add and subtract, multiply and divide really easily and efficiently," she said.
But professional mathematicians say the activists have set up a false dichotomy between conceptual understanding and basic skills. Parents chafing at constructivist math tell stories of their children coming home confused and dispirited by lessons in which getting the right answer to problems is devalued in favor of strategies that are often primitive, cumbersome and indirect. Used by inexperienced teachers who are weak in math, they say, the curriculum can be murky.
And tutoring services say that they are seeing an epidemic of children coming to them for basic math instruction.
THE MOVEMENT
Good Intentions, Unproven Theories
How schools got to this point is a saga of good intentions, unproven theories and a progressive education movement that has has had its most profound impact in reading and math. In many ways, the math wars echo the once ferocious disputes about reading between advocates of the intuitive "whole language" approach, which stresses acquiring skills through simple reading of books, and the phonics method, which stresses decoding of letters and words. Until "whole language" became a dirty word, constructivist math was known as "whole math." One obvious solution is to mix a bit of both. But while educators have called a truce in the reading wars, deciding that compromise is best, the math wars continue to rage.
The high point for new math advocates came last October, when a panel set up by the United States Education Department endorsed 10 constructivist math programs as "exemplary" or "promising." Within a few weeks, nearly 200 university mathematicians and scholars sent an open letter to Education Secretary Richard W. Riley warning that the 10 programs had "serious mathematical shortcomings" and would leave students ill-prepared for college-level courses.
R. James Milgram, a mathematics professor at Stanford University, analyzed three programs and found that they consistently neglected to teach basic rules of multiplication, division, addition and subtraction. The programs are typically one or two years behind grade level, he said, and aimed at what he considered underachieving students.
On April 12, the National Council of Teachers of Mathematics, the nation's most influential group of math teachers, made a gesture to the critics as it revised its 1989 standards for teaching mathematics, the closest thing this country has to a national curriculum. Though not abandoning its original constructivist agenda, the council put the arithmetic back in math, by adding language emphasizing accuracy, efficiency and basic skills like memorizing the multiplication tables. The chairwoman of the standards committee declared that the group's new message was "Get the right answer."
Still, there is ambivalence in the teaching field. When the national council of mathematics teachers endorsed more of a balance between basics and the constructivist approach at the group's annual meeting in Chicago, the president-elect, Lee V. Stiff, ardently defended constructivism. "If I only teach it the way I understand, then only students who understand it the way I do will be successful," he said.
The evidence to support the educational virtues of new math is inconclusive at best. Publishers have provided studies in which they compare the results in pilot schools that adopted the program to other schools that made no change.
But those studies have been challenged by critics who say improvements may be the result of better training of teachers, and the extra attention given to pilot programs.
District 2, which has a high percentage of affluent students, has long ranked near the top of the city school system. Last year, when a new math test was introduced, scores across the city declined, and District 2 was the only district in the city to remain stable.
Ms. West, the math coordinator, said that was evidence the program was working. And other officials noted that the new test was closely aligned with the District 2 curriculum, and many parents attributed the good scores to tutoring by professionals and parents. And they noted that the district had been spending $800,000 a year on training math teachers.
Even experience in the classroom can be ambiguous. Roberta Schorr, an education professor at Rutgers, is using a computer simulation of a frog and a clown walking back and forth across a plane to help teach the concept of velocity at Central High School in Newark. Ms. Schorr sees the simulation as an intuitive introduction to calculus that does not require what she called "formal symbol structure." But during a recent class, half the students seemed baffled, while Tieyon Hendry and Rahul Patel, the star students, told a visitor that they had arrived at the answer to one exercise by using a mathematical formula: y = mx+ b.
THE OPPOSITION
Unconvinced by Unconventional
As the new math -- a cousin of the "new math" popular in the 1960's -- entered the educational mainstream, first in California in 1992 and then around the country, it sparked waves of opposition. Hostility came first from conservative parents who opposed any change in education, then from university math professors who felt it was not rigorous, and finally from liberal, affluent parents who were worried their children were not getting enough math to succeed in school and in life.
In Plano, Tex., parents have sued the school district for refusing to provide an alternative to Connected Math. In New York, the opposition first emerged not in a failing school but in one of the city's best, Public School 234 in TriBeCa. Edgy schoolyard conversations grew into a parent Math Committee, which gathered members across the district, sending out surveys and making angry statements at school board meetings.
Parents said they were stunned as they talked to their friends and realized how many had hired tutors. Those who cannot afford tutoring tell of scouring educational bookstores for workbooks and textbooks to help them make sense of the new math.
Ms. Huang said she became alarmed when her son, Mack, a fourth grader at the Bridges School in Chelsea, came home complaining that he hated math. The emphasis on estimation, she said, was confusing him. She bought him workbooks consisting of straightforward calculations and he enjoyed the sense of mastery.
Constructivist teachers celebrate the unconventional exercises they use as a way of keeping weaker children engaged, especially those from groups that have historically lagged in mathematics performance, like girls and black and Hispanic students.
But some parents are insulted by them. Ms. Weinberg, a dentist, said she was appalled when her daughter, Kelly, a sixth grader at East Side Middle School, came home with assignments to write her math autobiography and to write about her favorite number. "She was being graded on grammar and spelling," Ms. Weinberg said.
Wilfried Schmid, a professor of mathematics at Harvard, became a critic of constructivist programs after his daughter, Sabina, began using one of them, TERC Investigations in Number, Data and Space, at her elementary school in Lincoln, Mass. When she started second grade last fall, Sabina knew how to carry tens and add two-digit numbers, Mr. Schmid said. Sabina's teacher, who is well-intentioned but too inexperienced to deviate from the program, Mr. Schmid said, told the child that she was not allowed to use this method; she had to demonstrate her work with blocks or by counting on her fingers.
"So Sabina is reduced to drawing 39 little men to solve problems like 39-14," her father said.
He worries that this rudimentary and tedious approach is quashing Sabina's spirit. "Last year, she would have complained that this is below her level," Mr. Schmid said, "but she doesn't rebel anymore."
"I'm a professional mathematician, and I myself very often use mathematical methods that I understand only imprecisely," he said. "It is while I use them that I begin to understand. After a while, the use and the understanding are mutually supporting."
In their worst nightmares, parents fear that schools are producing a lost generation of math illiterate children. Bruce Winokur, a math teacher at Stuyvesant High School, New York City's most selective public school, says he is seeing more and more students who are gifted in math but unable to keep up with high school work. They understand concepts, he said, but have not internalized the rules.
THE FUTURE
Easing the Rules to Allow the Old
There are some signs of change.
Andrew Lachman, a spokesman for District 2 in New York City, said the district was responding to parent concerns. "We are not purists," he said.
California recently adopted new standards with a stronger focus on computation, and many districts will be putting them into place this fall. Some teachers, often the most experienced, have instinctively combined the old and the new.
The Daniel Boone School, in West Ridge, a tidy working class part of Chicago brightened by magnolia trees and the babushkas of Russian grandmothers, has been a laboratory for the development of TIMS Math Trailblazers, a constructivist program created by the University of Illinois. Math scores have risen since the program was put into effect. The principal, Paul Zavitkovsky, credits the program, but does not rule out increased attention to math, teacher training and collaboration.
In fifth grade the other day, Mila Kell, a Russian immigrant, taught a crisp lesson in probability, improvising riffs on the probability that the sun would rise in the morning and that she would fly to the moon. The class was enchanted.
Mrs. Kell said she loved the freedom and creativity of the new math. But on her desk was a secret weapon: a stack of worksheets -- the antithesis of constructivist math -- pages of classic problems in long division, the addition of fractions and reducing the sum of fractions to its simplest terms.
Quote from: Habbaku on July 11, 2009, 11:05:35 AM
Quote from: Martinus on July 11, 2009, 10:52:22 AM
What is the typical US math curriculum like?
For me, it was the basics for 1st-5th grade. Pre-algebra and geometry for 6th-8th with Algebra 1/2, Geometry, Algebra 3 and Trigonometry courses through high school.
Uhm, does it mean you didn't have geometry until high school? Wtf.
I remember we were calculating volumes of spheres and cones by the fourth grade. :huh:
That NYT article made me sick to my stomach.
QuoteMath should be "flexible," the standards say, and "reasonable" answers should be valued over a single right answer.
W + T = F?
Quote from: Martinus on July 11, 2009, 11:32:39 AMUhm, does it mean you didn't have geometry until high school? Wtf.
I remember we were calculating volumes of spheres and cones by the fourth grade. :huh:
And a lot of good it's done for Eastern European competitiveness.
Quote from: CountDeMoney on July 11, 2009, 11:21:59 AM
An example I found:
I think the second way is probally more how I would do it.
Much quicker and takes less paper.
Quote from: Tyr on July 11, 2009, 11:39:25 AM
Quote from: CountDeMoney on July 11, 2009, 11:21:59 AM
An example I found:
I think the second way is probally more how I would do it.
Much quicker and takes less paper.
Err, how does it take less paper? The examples there show that it takes more paper. Are you retarded?
Quote from: Martinus on July 11, 2009, 11:44:22 AM
Err, how does it take less paper? The examples there show that it takes more paper. Are you retarded?
Don't be retarded.
They're giving an example, they have to show everything. In practice you could just remember a number in your head though. (not that its really significant, I wasn't being entirely serious with that bit)
Quote from: Martinus on July 11, 2009, 11:32:39 AM
Uhm, does it mean you didn't have geometry until high school? Wtf.
I remember we were calculating volumes of spheres and cones by the fourth grade. :huh:
:huh: What does "Pre-algebra and geometry for 6th-8th" mean to you?
Quote from: Habbaku on July 11, 2009, 11:05:35 AM
Quote from: Martinus on July 11, 2009, 10:52:22 AM
What is the typical US math curriculum like?
For me, it was the basics for 1st-5th grade. Pre-algebra and geometry for 6th-8th with Algebra 1/2, Geometry, Algebra 3 and Trigonometry courses through high school.
Sounds about the same as we had.
That second example is how I do it too. And I like the idea of encouraging making estimates.
Yep, Catholic or private school is looking better and better in about 4 years.
The second is ok if you're doing it in your head.
I had calculus in high school, and I tested out of the first semester of university calc... Then I went into history.
Quote from: Pishtaco on July 11, 2009, 12:16:30 PM
That second example is how I do it too. And I like the idea of encouraging making estimates.
Fag. 2 + 2 = 5 does not deserve a ribbon. Asshole.
Quote from: CountDeMoney on July 11, 2009, 12:38:45 PM
Quote from: Pishtaco on July 11, 2009, 12:16:30 PM
That second example is how I do it too. And I like the idea of encouraging making estimates.
Fag. 2 + 2 = 5 does not deserve a ribbon. Asshole.
My doctoral thesis was about the circumstances under which n+n can appear to be the same size as n, for n a suitably large number.
I'm all for making concepts the prime target in maths.
I've met an awful lot of engineers that were able to memorize definitions and solve equations well enough to get their degree, yet can't solve problems in the real world.
I don't fucking care if you can ace an exam, if you are unable to create something new, you are worth nothing. I don't know if you can train kids for that, but it's certainly worth considering.
Quote from: PDH on July 11, 2009, 12:23:40 PM
I had calculus in high school, and I tested out of the first semester of university calc
:yes: :hug:
Quote from: CountDeMoney on July 11, 2009, 11:16:05 AM
QuoteMajor Characteristics of TERC's Program: Investigations in Number, Data, and Space
1. TERC insists on the ongoing use of hands-on tools (manipulatives, "models," and calculators).
* They say concrete tools must always be available and regularly used.
* TERC strongly rejects the idea that children must eventually migrate from hands-on to abstract thinking.
2. TERC rejects the need for memorization and practice.
* They say that student's familiarity with single-digit number facts must "grow out of lots of experience with constructing these facts on their own." BA, Page 72 (emphasis added)
[Please click on References for the meaning of the BA code.] There's no additional gain in conceptual understanding associated with the task of trying to "construct" one more basic number fact.
o o TERC doesn't think it's possible to understand memorized information. But knowledge must first be loaded into the brain before it can connected to other knowledge and "understood." Explicit memorization is sometimes the most efficient way to get it there.
o TERC fails to understand that it's often desirable to move to automatic use of knowledge. The mind must be free to think at higher levels of complexity, without consciously revisiting underlying details. For example, the key idea of the standard algorithms is that multi-digit calculations are reduced to multiple single-digit calculations. If children don't have instant recall of the single-digit number facts, they aren't equipped with the essential pre-knowledge for easily carrying out multi-digit computations.
3. TERC fails to clearly define terms.
* They regularly state: "We don't ask students to learn definitions of new terms."
* They offer some "definitions," typically using multiple undefined terms to "define" a new term.
* They favor "natural language" and "personal language."
4. TERC emphasizes "familiar numbers."
* The "landmark numbers" are 5, multiples of 10, and multiples of 25.
o Landmark number are also known as anchors.
* The "familiar fractions" are limited to proper fractions with denominator equal to 2, 3, 4, 5, 6, 8, 10 or 12. Thus 7 and 11 are not familiar denominators. Perhaps TERC is opposed to gambling.
o Note: 12 is included because it's needed for TERC's clock face method for adding fractions.
* TERC doesn't believe in defining terms, so you won't find the preceding definitions in TERC materials. This is what they appear to mean by these phrases. We welcome their clarification.
* Although TERC rejects explicit memorization of basic single-digit number facts, they expect students to remember many non-basic facts about landmark numbers and familiar fractions.
5. TERC omits standard formulas.
6. TERC emphasizes estimation and many right answers.
* They suppress the concepts of precision and accuracy.
7. TERC proudly rejects standard computational methods.
* No standard algorithms for multi-digit computation.
* No standard methods for operations with fractions and decimals.
* No general methods for calculating with numbers.
* TERC emphasizes special case methods involving landmark numbers and familiar fractions.
8. TERC attempts to directly teach their shallow and misleading content.
* They claim to offer a "constructivist" approach where students discover math as they play games and carry out investigations. But they provide thousands of pages of teaching instructions and recommended scripts that identify the content they expect kids to "discover."
o Thousands of pages for the teacher, but no text for the student.
Even the TERC manifesto doesn't seem to like it. :(
I don't know which is the best way to teach math. As long as radically new methods are thoroughly tested before they are deployed all should be well.
I will however observe that the "teaching sciences" seem to be totally out of control. At least in Sweden students are several years behind their parents and grandparents when it comes to math. What used to be high school math has crept up into university courses etc. In other fields performance is usually increasing over time instead of decreasing. But in teaching? No.
Quote from: Pishtaco on July 11, 2009, 12:46:12 PM
Quote from: CountDeMoney on July 11, 2009, 12:38:45 PM
Quote from: Pishtaco on July 11, 2009, 12:16:30 PM
That second example is how I do it too. And I like the idea of encouraging making estimates.
Fag. 2 + 2 = 5 does not deserve a ribbon. Asshole.
My doctoral thesis was about the circumstances under which n+n can appear to be the same size as n, for n a suitably large number.
We're not talking doctoral theses here, Good Will Cunting, we're talking elementary level mathematics. A 9 year old doesn't need to learn that n + n = "not really". At their level, they need to know mathematics has a right answer, and a wrong answer, not an almost right answer.
Quote from: The Brain on July 11, 2009, 01:10:06 PM
Even the TERC manifesto doesn't seem to like it. :(
I haven't seen the "TERC Manifesto" but Bill Quirk doesn't seem to like TERC! :lol:
Quote from: Pishtaco on July 11, 2009, 12:16:30 PM
That second example is how I do it too. And I like the idea of encouraging making estimates.
Indeed. Estimation is not only a higher-level thinking skill (and thus useful in its own right) but essential to actual math success. If one sticks to the CountDeHeadInTheSand method, students cannot recognize when they have reached mpossible andswers unless the teacher tells them.
Having said that, I am not a fan of TERC itself. There are plenty of other programs that teach estimation and real-world problem solving that don't go as far as TERC from the need to actually memorize some aspects of arithmetic.
Quote from: grumbler on July 11, 2009, 02:09:07 PM
Indeed. Estimation is not only a higher-level thinking skill (and thus useful in its own right) but essential to actual math success. If one sticks to the CountDeHeadInTheSand method, students cannot recognize when they have reached mpossible andswers unless the teacher tells them.
4th graders aren't given problems with impossible answers. And what's with all this "higher-level thinking" and Pishtaco's PhD bullshit, anyway? Can we all wait until they at least reach puberty before we teach them higher-level math already?
Quote from: Iormlund on July 11, 2009, 12:51:01 PM
I'm all for making concepts the prime target in maths.
I've met an awful lot of engineers that were able to memorize definitions and solve equations well enough to get their degree, yet can't solve problems in the real world.
I don't fucking care if you can ace an exam, if you are unable to create something new, you are worth nothing. I don't know if you can train kids for that, but it's certainly worth considering.
:yes:
That our world is based so heavily on exams is a terrible system. I've met quite a few idiots who happened to be good at exams.
Sadly there's little better alternative.
Quote from: Ed Anger on July 11, 2009, 12:18:47 PM
Yep, Catholic or private school is looking better and better in about 4 years.
Too goddamned bad. Grumbler wants them to start working on advanced theory now.
Quote from: Tyr on July 11, 2009, 02:18:06 PMI've met quite a few idiots who happened to be good at exams.
It's not just reserved to engineers, but doctors, lawyers and Indian chiefs. A dysfunctional Rainman with Asparagus Syndrome is going to be an asshole, regardless of whether or not he is an engineer trained in traditional math.
Quote from: CountDeMoney on July 11, 2009, 02:22:25 PM
Quote from: Tyr on July 11, 2009, 02:18:06 PMI've met quite a few idiots who happened to be good at exams.
It's not just reserved to engineers, but doctors, lawyers and Indian chiefs. A dysfunctional Rainman with Asparagus Syndrome is going to be an asshole, regardless of whether or not he is an engineer trained in traditional math.
Nah, I mean literal idiots. People who are thick. Not just people I don't like.
Quote from: CountDeMoney on July 11, 2009, 01:39:54 PM
Quote from: Pishtaco on July 11, 2009, 12:46:12 PM
Quote from: CountDeMoney on July 11, 2009, 12:38:45 PM
Quote from: Pishtaco on July 11, 2009, 12:16:30 PM
That second example is how I do it too. And I like the idea of encouraging making estimates.
Fag. 2 + 2 = 5 does not deserve a ribbon. Asshole.
My doctoral thesis was about the circumstances under which n+n can appear to be the same size as n, for n a suitably large number.
We're not talking doctoral theses here, Good Will Cunting, we're talking elementary level mathematics. A 9 year old doesn't need to learn that n + n = "not really". At their level, they need to know mathematics has a right answer, and a wrong answer, not an almost right answer.
I totally agree.
It's amazing how stupid some of the responses in this thread are.
Quote from: Tyr on July 11, 2009, 02:18:06 PM
:yes:
That our world is based so heavily on exams is a terrible system. I've met quite a few idiots who happened to be good at exams.
I'm frankly getting sick and tired of this kind of attitude being prevalent in the modern day. Yes, idiots can also pass exams well. And yes, we are all unique and beautiful snowflakes who should be given an opportunity to blossom in our own unique ways. But if we took this road, we would not be able to tell a dysfunctional, useless, impossible-to-adapt-or-work-in-a-team moron (99% of people who consider themselves unique and thus fail to sit down and pass a simple exam even if they find it useless) from the true geniuses (1%).
Quote from: Martinus on July 11, 2009, 03:00:30 PM
I totally agree.
It's amazing how stupid some of the responses in this thread are.
:lol: I am also amazed by some of the stupid responses in this thread, but not at all amazed that you "totally agree" with them!
Quote from: CountDeMoney on July 11, 2009, 02:17:53 PM
Quote from: grumbler on July 11, 2009, 02:09:07 PM
Indeed. Estimation is not only a higher-level thinking skill (and thus useful in its own right) but essential to actual math success. If one sticks to the CountDeHeadInTheSand method, students cannot recognize when they have reached mpossible andswers unless the teacher tells them.
4th graders aren't given problems with impossible answers. And what's with all this "higher-level thinking" and Pishtaco's PhD bullshit, anyway? Can we all wait until they at least reach puberty before we teach them higher-level math already?
I don't know enough of human brain development, but I'd wager it would be far easier to introduce certain skills as a kid just as it is much easier to learn a language that way.
Notice that I'm not advocating this TERC thing, just saying memory alone (and I've got a fantastic memory) shouldn't be our sole focus when teaching (and not just in maths). I value the ability to come up with new, different answers or to gauge new approaches much more. And so does the real world. Hardest thing in my field is, for example, to estimate the cost of a new project.
Quote from: CountDeMoney on July 11, 2009, 02:20:11 PM
Too goddamned bad. Grumbler wants them to start working on advanced theory now.
Estimation is not an advanced theory. You'd be surprised how much smarter some kids are than you were at their age.
I am also surprised how popular speed math is, even amongst the kids that seldom win - and even more surmised that this includes girls who in fourth grade generally don't like competition..
Quote from: Iormlund on July 11, 2009, 03:34:13 PM
Hardest thing in my field is, for example, to estimate the cost of a new project.
Estimating expected answers in math is a different skill than estimating costs, though. Let's not get
too carried away!
Everything is described by maths.
Quote from: Iormlund on July 11, 2009, 03:38:31 PM
Everything is described by maths.
You didn't use a single bit of math to describe your assertion here, so I would say that your point is inherently self-refuting. :cool:
Elementary math does have a right answer and a wrong answer, but you can punch the problem into a calculator and get the right answer but not understand the math.
Generally speaking, using the right method to get the wrong answer is more useful for learning than using the wrong method to get the right answer.
But if you're using the wrong method to get a wrong answer can make senator or head of GM. It's all good.
Quote from: grumbler on July 11, 2009, 03:35:32 PM
You'd be surprised how much smarter some kids are than you were at their age.
Nonsense. I am always the smartest kid in the room. Just ask me.
Quote from: Pishtaco on July 11, 2009, 12:46:12 PM
Quote from: CountDeMoney on July 11, 2009, 12:38:45 PM
Quote from: Pishtaco on July 11, 2009, 12:16:30 PM
That second example is how I do it too. And I like the idea of encouraging making estimates.
Fag. 2 + 2 = 5 does not deserve a ribbon. Asshole.
My doctoral thesis was about the circumstances under which n+n can appear to be the same size as n, for n a suitably large number.
1 million + 1 million ~ 1 million, versus 1, but not versus 2 million.
Quote from: Pishtaco on July 11, 2009, 12:46:12 PM
Quote from: CountDeMoney on July 11, 2009, 12:38:45 PM
Quote from: Pishtaco on July 11, 2009, 12:16:30 PM
That second example is how I do it too. And I like the idea of encouraging making estimates.
Fag. 2 + 2 = 5 does not deserve a ribbon. Asshole.
My doctoral thesis was about the circumstances under which n+n can appear to be the same size as n, for n a suitably large number.
This is certainly true in politics and public spending. :P
I can't complain about most of TERC's methods, since things like this
Quotesolving equations using "friendly numbers," for instance, converting 71 + 19 into the easier 70 + 20
and what was described in the image CdM posted are the methods I use to solve problems. In fact, I disagree with statements like this
Quote"Those strategies don't work when you get to larger numbers," Ms. Santore said
Maybe not for her, but they do for me. Which brings me to what I see as the glaring problem with TERC, statements like these:
QuoteOne parent, Anna Huang, said her son, Mack, a fourth grader, "felt a lack of clarity" when his teacher insisted that he estimate answers, rather than compute them precisely.
QuoteWhen she started second grade last fall, Sabina knew how to carry tens and add two-digit numbers, Mr. Schmid said. Sabina's teacher, who is well-intentioned but too inexperienced to deviate from the program, Mr. Schmid said, told the child that she was not allowed to use this method; she had to demonstrate her work with blocks or by counting on her fingers.
QuoteThe new math has at its core a passionate belief shared by tens of thousands of teachers around the country that they can reach more children, especially low-achieving minority students, by dropping standard rules in favor of exercises that allow students to discover the principles of math on their own.
The problem with traditional math education for some students is not the methods taught so much as that the methods are taught to the exclusion of others. TERC doesn't fix that problem; it just forces a different set of methods on students, which simply shuffles around who gets it and who doesn't. It does so in a more detrimental way; the "standard" methods came about because they work best for most people, while the TERC methods work best for a much smaller set. Which works best for who certainly has nothing to do with ethnic background or socioeconomic status, either.
I used to get flak in grade school because I didn't rigidly follow the standard algorithms. Fortunately, since I still got the right answer more often than my classmates it was tolerated, though I did frequently get reminded to "do it properly" if I did get one wrong my way. Many teachers nowadays, on both sides of this "new math" debate, wouldn't be so tolerant of it.
To preempt another condescending "unique snowflake" comment, I don't think every kid is unique. Rather, I think its a matter of sequential vs. spatial thinking. Sequential thinkers benefit from the traditional methods, while spatial thinkers benefit from most of the TERC methods (the ones that actually deal with solving problems, anyway, not that essay writing bullshit).
Oh, and of course there's the issue of not enough teachers, not being able to give extra help to the kids who really need it, and such. That (along with over-reliance on standardized tests) is the core of the problem, regardless of the curriculum.
Hippie.
iirc, isn't math one of those things you really can't explain how and why it works ontil you've actually learned math to a rather advanced level?
iic, you need to build the house before you can put down the foundations (to use the metaphor Pratchett used)
Quote from: Martinus on July 11, 2009, 03:05:54 PMI'm frankly getting sick and tired of this kind of attitude being prevalent in the modern day. Yes, idiots can also pass exams well. And yes, we are all unique and beautiful snowflakes who should be given an opportunity to blossom in our own unique ways. But if we took this road, we would not be able to tell a dysfunctional, useless, impossible-to-adapt-or-work-in-a-team moron (99% of people who consider themselves unique and thus fail to sit down and pass a simple exam even if they find it useless) from the true geniuses (1%).
Oh yeah of course, as I said there's not really much of a alternative out there, but that its the only choice doesn't really make the system a good one.
The only real alternative that I can think of is making things more coursework based- this is more representative of what students are capable of and more representative of the real world. Happily the world of education does seem to be moving in this direction.
I'd disagree with your 99% vs 1% there too (I know you didn't mean it literally but meh). People who actually fail exams despite being very bright are indeed very rare but people who can only manage relatively low passing grades despite being more capable than those with higher grades are quite a bit more common.
Quote from: CountDeMoney on July 11, 2009, 11:34:45 AM
That NYT article made me sick to my stomach.
QuoteMath should be "flexible," the standards say, and "reasonable" answers should be valued over a single right answer.
W + T = F?
The sentiment is not as crazy as it sounds. In many cases coming up with the ballpark estimate is what's desired, and requires some ingenuity, as further precision would be false. However, all these concepts should not be introduced so early, and instead of the basics. I think that's where New Math makes a fatal miscalculation.
Quote from: Martinus on July 11, 2009, 11:44:22 AM
Quote from: Tyr on July 11, 2009, 11:39:25 AM
Quote from: CountDeMoney on July 11, 2009, 11:21:59 AM
An example I found:
I think the second way is probally more how I would do it.
Much quicker and takes less paper.
Err, how does it take less paper? The examples there show that it takes more paper. Are you retarded?
With the second way it's easier to do some steps in your head. The second way is how I do mental math.
So this fuzzy maths thing got me looking up things. Can anyone tell me if there's maths for describing the / in 0/1? I would need the 101 version for morons. I don't ask much.
CdM, stick to your conspiracy theories and leave education to the experts like grumbler and Tim. :P
Quote from: Martinus on July 11, 2009, 11:44:22 AM
Quote from: Tyr on July 11, 2009, 11:39:25 AM
Quote from: CountDeMoney on July 11, 2009, 11:21:59 AM
An example I found:
I think the second way is probally more how I would do it.
Much quicker and takes less paper.
Err, how does it take less paper? The examples there show that it takes more paper. Are you retarded?
The 'new math' is for retarded kids. Jos digs it.
Quote from: Tyr on July 12, 2009, 11:19:29 AM
I'd disagree with your 99% vs 1% there too (I know you didn't mean it literally but meh). People who actually fail exams despite being very bright are indeed very rare but people who can only manage relatively low passing grades despite being more capable than those with higher grades are quite a bit more common.
People who fail exams are by definition not bright. They are stupid.
Quote from: grumbler on July 11, 2009, 02:09:07 PM
Quote from: Pishtaco on July 11, 2009, 12:16:30 PM
That second example is how I do it too. And I like the idea of encouraging making estimates.
Indeed. Estimation is not only a higher-level thinking skill (and thus useful in its own right) but essential to actual math success. If one sticks to the CountDeHeadInTheSand method, students cannot recognize when they have reached mpossible andswers unless the teacher tells them.
Having said that, I am not a fan of TERC itself. There are plenty of other programs that teach estimation and real-world problem solving that don't go as far as TERC from the need to actually memorize some aspects of arithmetic.
You're just too much of a faggot to employ the time-honoured educational tools of our forebearers: Beatings. Is it any wonder that society has collapsed, given that we refuse to beat our children when they fail?
Quote from: Neil on July 18, 2009, 05:13:03 PM
Quote from: Tyr on July 12, 2009, 11:19:29 AM
I'd disagree with your 99% vs 1% there too (I know you didn't mean it literally but meh). People who actually fail exams despite being very bright are indeed very rare but people who can only manage relatively low passing grades despite being more capable than those with higher grades are quite a bit more common.
People who fail exams are by definition not bright. They are stupid.
So you must think I am stupid then.
Quote from: Jaron on July 18, 2009, 08:22:12 PM
Quote from: Neil on July 18, 2009, 05:13:03 PM
Quote from: Tyr on July 12, 2009, 11:19:29 AM
I'd disagree with your 99% vs 1% there too (I know you didn't mean it literally but meh). People who actually fail exams despite being very bright are indeed very rare but people who can only manage relatively low passing grades despite being more capable than those with higher grades are quite a bit more common.
People who fail exams are by definition not bright. They are stupid.
So you must think I am stupid then.
I would imagine so.
Quote from: Neil on July 18, 2009, 07:46:23 PMYou're just too much of a faggot to employ the time-honoured educational tools of our forebearers: Beatings. Is it any wonder that society has collapsed, given that we refuse to beat our children when they fail?
As grumbler teaches at an all-girl private school, if he adopted beatings it would introduce an entirely new dynamic to the education system. A sublimely erotic dynamic with oh so naughty, naughty girls.
Quote from: Neil on July 18, 2009, 08:23:22 PM
Quote from: Jaron on July 18, 2009, 08:22:12 PM
Quote from: Neil on July 18, 2009, 05:13:03 PM
Quote from: Tyr on July 12, 2009, 11:19:29 AM
I'd disagree with your 99% vs 1% there too (I know you didn't mean it literally but meh). People who actually fail exams despite being very bright are indeed very rare but people who can only manage relatively low passing grades despite being more capable than those with higher grades are quite a bit more common.
People who fail exams are by definition not bright. They are stupid.
So you must think I am stupid then.
I would imagine so.
Fool!
Maths are down to numbers. There is no Whitey or Black maths.
Maths are the one remaining thing that keeps Africa down. They can still calculate a trade deficit.
I used to hate maths. Nowadays, doing statistics kind of turns me on. :D
Quote from: Jaron on July 18, 2009, 10:57:44 PM
Quote from: Neil on July 18, 2009, 08:23:22 PM
Quote from: Jaron on July 18, 2009, 08:22:12 PM
Quote from: Neil on July 18, 2009, 05:13:03 PM
Quote from: Tyr on July 12, 2009, 11:19:29 AM
I'd disagree with your 99% vs 1% there too (I know you didn't mean it literally but meh). People who actually fail exams despite being very bright are indeed very rare but people who can only manage relatively low passing grades despite being more capable than those with higher grades are quite a bit more common.
People who fail exams are by definition not bright. They are stupid.
So you must think I am stupid then.
I would imagine so.
Fool!
Next time, try harder, and maybe you will be more successful.