Entries from MathWars

That's not what the National Research Council says:

Executive Summary

Under the auspices of the National Research Council, this committee’s charge was to evaluate the quality of the evaluations of the 13 mathematics curriculum materials supported by the National Science Foundation (NSF) (an estimated $93 million) and 6 of the commercially generated mathematics curriculum materials (listing in Chapter 2).

The committee was charged to determine whether the currently available data are sufficient for evaluating the effectiveness of these materials and, if these data are not sufficiently robust, the committee was asked to develop recommendations about the design of a subsequent project that could result in the generation of more reliable and valid data for evaluating these materials.

[snip]

The Quality of the Evaluations

These 19 curricular projects essentially have been experiments. We owe them a careful reading on their effectiveness. Demands for evaluation may be cast as a sign of failure, but we would rather stress that this examination is a sign of the success of these programs to engage a country in a scholarly debate on the question of curricular effectiveness and the essential underlying question, What is most important for our youth to learn in their studies in mathematics? To summarily blame national decline on a set of curricula whose use has a limited market share lacks credibility. At the same time, to find out if a major investment in an approach is successful and worthwhile is a prime example of responsible policy. In experimentation, success and worthiness are two different measures of experimental value. An experiment can fail and yet be worthy. The experiments that probably should not be run are those in which it is either impossible to determine if the experiment has failed or it is ensured at the start, by design, that the experiment will succeed. The contribution of the committee is intended to help us ascertain these distinctive outcomes.

[snip]

The charge to the committee was “to assess the quality of studies about the effectiveness of 13 sets of mathematics curriculum materials developed through NSF support and six sets of commercially generated curriculum materials.”

[snip]

In response to our charge, the committee finds that:

The corpus of evaluation studies as a whole across the 19 programs studied does not permit one to determine the effectiveness of individual programs with high degree of certainty, due to the restricted number of studies for any particular curriculum, limitations in the array of methods used, and the uneven quality of the studies.

source: On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations (2004)
National Academies Press
Mathematical Sciences Education Board (MSEB)
Center for Education (CFE)
available online or purchase, pages 3 & 188

And I seem to recall something in NCLB about....evidence-based instruction?

Evidence-based instruction and receipt of federal dollars?

Yes?

I'm pretty sure.



nationalresearchcouncil

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AMathematiciansApology 13 Jul 2005 - 02:26 CarolynJohnston


I should explain first that "A Mathematician's Apology" is an in-joke -- it's the title of the memoirs of G.H Hardy, a mathematician who was at Cambridge in the last century, and who for a time was (according to himself) the "fifth best pure mathematician in the world". His Apology in the title is for the absolute inapplicability of the highest level of pure mathematics to real life problems.

The current Apology (by an anonymous pure mathematician) is not so much an apology as an explanation of why we really can't look to pure mathematicians as a whole for effective help in the political games surrounding the Math Wars. He's right; mowing over your average pure mathematician, politically, is like shooting fish in a barrel. In addition, the realities of the mathematics research and research funding game are exactly as he describes them; they do not reward political savvy at all; quite the contrary.

Lest I sound too jaded, this is a good time to recognize the efforts of those many pure mathematicians who have involved themselves in the effort to improve mathematics education at the K-12 level. David Klein, Ralph Raimi, Bas Braams, James Milgram, Hung-Hsi Wu, Fred Greenleaf, and many others have spent lots of perfectly good political capital fighting the good fight. As David says, thank goodness for tenure.

A bit of background: the AMS is the American Mathematical Society, the main professional society for research (pure) mathematicians. The MAA is the Mathematical Association of America, which as a group focuses on college-level mathematics education. The Notices are the newsletter of the AMS.
-- CarolynJohnston

Mathematicians are a diverse group of human beings and don't deserve to be stereotyped anymore than any other stereotyped groups deserve. However, society has already done a good job stereotyping mathematicians. There is usually a grain of truth in stereotypes and the mathematician stereotype might well be more accurate than most.

As a group, politics is not our strong point. I doubt that we have the normal spectrum of political smarts within our ranks but the whole spectrum has probably slid down to one side quite a bit.

There is not much in our daily work lives that develops political skills. Better an engineer or physicist who is used to politicking for zillion dollar grants and who cannot do their work without these grants. In math, if you lose your grants you can still plod along and get your work done.

It is worse than that. If a mathematician goes to Washington and raises a hundred million dollars for math in general, their chair won't give them a raise because they didn't do anything. If a physicist or a biologist does that, their lab is cranking out papers with their name on them all the time while they are in Washington.

Our "opposition" in mathematics education works in an environment where political skills are necessary to advance. They are a tough bunch.

A math Ph.D. in academia has two fundamental jobs after helping the institution run itself. One is to do research and one is to teach. Only a handful of academic mathematicians avoid teaching and only do research. On the other hand, probably the majority, far and away, are not doing research but only teaching. If all you do is teach mathematics, then it might be reasonable to be labeled a math educator as opposed to a "mathematician."

The MAA is not really a research mathematician organization. The AMS is a research organization and those in the AMS who gravitate towards the education committee are not your normal mathematicians (by definition).

I am at something of a loss as to why the Notices is so open to the rantings of the education folk. Perhaps it is Andy's way of trying to get mathematicians moving. I don't know.

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CompareAndContrastTopicThread 15 Jul 2005 - 21:31 CatherineJohnson


When you get a chance, take a look at the Archives organized by thread box Carolyn has been working on, above and to the right.

If you click on CompareAndContrastPosts you'll get a page containing every one of the posts that compare a constructivist text to a non-constructivist text.

A lot of us seem to agree that these posts are the single most effective argument against fuzzy math.

That's why they're all here, in one place.


ways to use the compare and contrast thread:

• send the link to friends, teachers, & interested parties
  http://www.kitchentablemath.net/twiki/bin/view/Kitchen/CompareAndContrastPosts

• pull up the thread on people's computers if you're in the midst of a conversation about math ed (I've pulled up Kitchen Table Math now on a couple of teacher's computers to show them what we're doing)

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MartinGrossColumn 21 Jul 2005 - 11:16 CarolynJohnston


Yesterday the Washington Times ran an article by Martin Gross, Weak U.S. Education Link, that is a broad-band indictment of public education.

He begins by quoting Greenspan's testimony from a recent Senate Finance Committee hearing.

In the long run, he accurately pointed out, our economic strength in the world market eventually rests mainly on one factor -- brainpower, measured by the quality of our education system. In that race, he emphasized, we are failing badly.

Why is it, Mr. Greenspan asked, that our fourth-grade students are superior in international competition, while our eighth-grade students have proven inferior? Also, why are 12th graders hopeless in the key disciplines of math and science? In the Third International Mathematics and Science Study, our high schoolers scored 19th out of 21 countries, beating out only Cyprus and South Africa. They scored 20 percent lower than the Netherlands, a nation that lives on its brainpower -- as America might one day have to do.

Asked why our students become more ignorant the longer they stay in our public schools, Mr. Greenspan's response was typical of America's uninformed leaders: "I have no idea."

Gross has an idea, though.

But for those of us who have studied public education, the answer is clear: Our educators, from teachers through superintendents of schools, are academically and intellectually so inferior that the fourth grade is apparently the outer limit of their teaching abilities. They are so poorly selected, poorly trained and lacking in general intelligence, that failure by our middle- and high-school students is foreordained.

How can we support such a potent indictment? Easily. All standardized exams confirm their shocking inferiority.

He also has some solutions to offer.

(1) Close all undergraduate schools of education, and eliminate the generally ignorant and gullible 18-year-olds from the system. Instead, adopt the system used by most European and Asian nations. They require teacher candidates be graduates of a liberal arts college, and have at least a B average. They spend one year in practical teacher training, not in studying outdated educational theories.

(2) High school teachers of calculus receive the same pay as kindergarten teachers, which is ludicrous. To get satisfactory high school teachers, we must select better and pay more. To save money, we should fire 50 percent of administrators and support personnel and bring the student-bureaucrat ratio back to where it was 40 years ago.

(3) Education is not now a free market, but a closed shop. Scholarly college graduates who might be more independent are purposely kept out. A Yale summa cum laude in math is prohibited by law from teaching math in most states because he or she doesn't have an "education" degree. But the Yalie can teach -- in private schools.

The answer? Change the law so teachers need no education credits at all. Superintendents should be able to hire better college graduates trained in a true academic field. Then mathematicians will teach math, scientists teach science, and historians teach history. For the extra money needed, see (2).

(4) The middle school and high school should, by state law, be separated from elementary school and headed by a separate scholarly superintendent with a Ph.D. in a subject other than "education."

In short, sweeping political reforms are needed; the beneficiaries are generally either vulnerable (children) or clueless (parents), and the opponents (teacher's unions and schools of education) are motivated and politically savvy. It's enough to make even me wonder about homeschooling...

Think about this. For every underqualified person teaching math in public middle and high schools, there is probably an overqualified person teaching math for $3000 per course as adjuncts to university or college faculty. The only thing keeping him out of the public schools is his lack of an education degree.

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WhitherAmericanTalent 22 Jul 2005 - 16:04 CarolynJohnston


In my line of work, we're already seeing the effects of the dwindling American-born high-tech workforce. It's not hard for us to find mathematically and technically literate people, so long as we are willing to take in people who are foreign-born, and we are. In our commercial business sector, we have Chinese, Korean, Austrian and Canadian employees.

But a certain segment of our business is done in the classified world, and there, we are hurting for skilled employees who are 'clearable'. It's not just us, either -- it's everywhere in this business -- and the problem is getting worse. I don't think the shortage of educated American-born high-tech workers is entirely due to dwindling educational standards, either, though they contribute. I think it's cultural, too, a result of our increasing wealth.

I noticed when I was a graduate student that people were pouring in to study mathematics disproportionately from the struggling, up-and-coming (or trying to up-and-come) countries with good educational standards. We saw a big influx of Chinese, and later Russians, and they all opted to stay (following both Tiananhmenh Square and the end of the Soviet Union, and who could blame them?). They caused the glut of talented academicians in the job market that was discussed in this recent thread. Notable by their absence were any Europeans. The mathematics talent was mostly coming from the 'second world' countries.

Bernie and I also noticed the same phenomenon on a smaller scale in American students. In the generation prior to mine, a lot of the technical talent came from Brooklyn and New York City and other big eastern cities with a lot of bright first-generation American kids. My dad came from Brooklyn, went to good schools and got to go to Brooklyn College for free in those years, and so the son of a bus driver was able to become a pharmaceutical researcher with a much better standard of living than he'd had while growing up. In that generation there were a lot of men like him.

In my generation, there were no longer as many kids from New York and the big eastern cities coming into the graduate schools. Other than Chinese and Russians, we had quite a few Americans from parts of America you never heard of; midwestern towns, and smaller towns in New York and New England. What happened? I'm not sure, but I think the kids from New York felt themselves to have options for getting ahead in life that didn't involve quite so much hard work. Probably the kids in Europe did too.

Anyway, I've gotten far afield from what I wanted to post, an article about some recent testimony about America's critical need for homegrown talent.

Current shortcomings in U.S. education could leave the next generation of Americans ill-equipped to combat terrorism, according to testimony given before the National Infrastructure Advisory Council (NIAC).

"The country's long-term security is tied to the quality of the workforce," Alfred Berkeley, a trustee of the Mathematical Sciences Research Institute said.

Berkeley's testimony before NIAC cited mathematics and science as key areas that need to be addressed at all educational levels. He stressed the importance of young adults being qualified to enter fields such as cyber security. However, Berkeley, who also serves as an NIAC member, said that current elementary education provides a poor foundation for the subsequent pursuit of these fields of study.

"The public has not embraced education as a priority. We must find a way to engage the public with a sense of urgency," Berkeley said.

Besides the problem of education quality, the United States is facing a shortage of students willing to study areas such as engineering.

According to a National Science Board (NSB) report released in 2004, "bachelor's degrees in engineering have declined by 8 percent and degrees in mathematics have dropped by about 20 percent" since 1990.

Check out the rest of it.

As a final aside -- where could the next great influx of American technical talent possibly come from, with birth rates in America falling and people so wealthy that a future in a technical job appears harsh by comparison with their other options?

Here in Colorado, we have a lot of Mexican and other immigrant Hispanic families. I understand that what we're seeing here isn't just local, but part of a larger trend in the U.S.. I'm thinking that their children, born in the U.S., would probably really appreciate the opportunity to make a good salary in a technical field.

If the schools don't let them down. Those families don't have a lot of money to burn on tutors and Kumon.


Whither American talent?
Congressional incentives for study of math
Paul Samuelson on the 'science gap'

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BarryGarelickAtEducationNews 25 Jul 2005 - 18:00 CatherineJohnson


Wow!

I just stumbled across Barry's op-ed, "Doing the Fox Trot with Cathy Seely," at EducationNews!

Go read it right now!

That reminds me: we have got to get a link up to Education News.

Also, for anyone who has tried to contact me via my KTM email address, it doesn't work. My 'home' email address works only sporadically; as a matter of fact I have just now discovered that I have been thrown off the NYC Math Forum mailing list for the 2nd time in as many months....

So, if you've emailed and I haven't answered, that's why.

update

It's great!

Cathy: Great! I think what you have in the U.S. is too much “Here’s the rule, now do the problem”; too much teacher instruction. The teacher should refrain from stepping in too early to provide students with answers or tell them exactly what steps they should use.

Me: I think I get it. I was thinking that students actually learn things when you teach them what they need to know. But you’re saying, first throw out the text books. Then instead of “Here’s the rule, now do the problem” you say “Here’s the problem, you figure out what the rules are”. How am I doing?

Cathy: Ummm; I think I probably confused you. The point I want to make is that there’s more than one way to teach.

Me: Ah! So sometimes “Here’s the rule, now do the problem” is OK and Singapore Math meets the NCTM standards? Or are you still looking beyond the textbook?

Cathy: Wow. Good questions. In Singapore and other countries they teach math differently than we do here. They teach it according to the NCTM standards.

Me: Uh, I wouldn’t say that. Singapore actually teaches content, and the content they teach actually matters.

Cathy: I don’t know why you think NCTM standards don’t emphasize content. The vision of Principles and Standards for School Mathematics paints a picture of the depth that we can achieve with all students.

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MissingKnowledge 25 Jul 2005 - 22:46 CatherineJohnson


More good stuff from Education News:

Today's math lessons, Armbrecht said, focus much more on "inquiry-based learning" than the math of yore. Students are given a problem, then asked to use their understanding of number structure, logic and math concepts to solve it. In Armbrecht's generation, most students were told to memorize facts instead of being challenged to understand the underlying concepts, he said.

Furthermore, today's math students use calculators, computers and hands-on objects more often than their parents did. So, like Wilmington resident LaMere Henderson, even well-educated parents aren't equipped to help their children with math.

[snip]

But math teacher Dawn Olmstead, recently retired from Alexis I. du Pont High School, said so many reach high school unprepared that remediation can't be avoided.

"What we're seeing is the kids don't know how to add fractions," she said. "Some don't even know what fractions are.

"When they come into ninth grade, they're supposed to be prepared for algebra, and they're not."

There are so many topics to cover, she said, it's a burden to teach them all by the time of the test, which is given in March.

"How about probability?" she said. "Why would I teach that in an algebra class? Because it's on the test. I have to do both: algebra and what's on the test."

For many kids, math is a low priority

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HighlyQualified 25 Jul 2005 - 00:48 CatherineJohnson


Some of you may be aware that a second provision of NCLB kicks in next year. Teachers must be 'highly qualified.'

I would be in favor of this provision if ed schools weren't in charge of definining who is and who is not highly qualified.

Case in point: One candidate certified in math submitted his application this month for a job in Howard County - less than two months before classes begin.

"He wasn't worried," Mascaro recalled. "He'll have six to seven job offers wherever he goes. There's a lot of competition."

She added, "For the critical-needs areas, it's absolutely a teacher's market."

Adding urgency to recruitment this year is a requirement under the federal No Child Left Behind Act that all teachers in core subjects - English, reading, math, science, social studies, foreign language, economics, geography and arts - be "highly qualified" by the end of the next school year. Otherwise, schools risk losing federal funds.

In Maryland, recent data show that the percentage of classes not taught by "highly qualified" teachers has declined to 24.7 percent this year, from 33.1 percent in 2004. Suburban school systems tend to fare better than urban systems.

Hiring is tough task for schools

(Another thank you to Education News.)

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TheCourantInitiativeForTheMathematicalSciencesInEducation 25 Jul 2005 - 20:23 CatherineJohnson


from Elizabeth Carson, co-founder, with Bas Braams of New York City HOLD:

The Courant Initiative for the Mathematical Sciences in Education (CIMSE) is an activity in K-12 mathematics education, that has been informally in progress since 2000, involving a number of faculty members: Charles Newman, Director of the Courant Institute, Sylvain Cappell, Fred Greenle af, Jonathan Goodman, Alan Siegel, Arthur Goldberg, Al Novikoff, Mel Hausner and Edmond Schonberg.

The CIMSE mission is to help foster excellence in school mathematics education.

CIMSE will support activities to educate college and university Mathematics, Science, and Education faculty, K-12 educators and administrators,

parents, business leaders, education philanthropies and members of the community at large on a range of topics and issues in mathematics education, including instructional programs, curricula, standards and assessments, teacher training, research and development, and education policy at the local, state and federal levels, and internationally.

CIMSE is guided by the belief that an educated and informed community, and innovative partnerships between key constituencies of education stakeholders, can help transform the education enterprise to one where educational excellence in the mathematical sciences is part of the customs, practices, relationships and behavioral patterns of importance in the life of our schools, communities and society.

The Courant Initiative for the Mathematical Sciences in Education

EXECUTIVE BOARD

Chuck Newman

Sylvain Cappell

Fred Greenleaf

Elizabeth Carson

PLANNING AND ADVISORY COMMITTEE

To Be Announced

ADVISORY BOARD

To Be Announced


CIMSE year one plans include support and development for a number of NYC HOLD associated activities.

NYC HOLD Honest Open Logical Decisions on Mathematics Education Reform is a national grassroots mathematics education advocacy association of parents, K-12 educators, mathematicians and scientists working to improve mathematics education. NYC HOLD has established a partnership between Courant faculty and parents, teachers and administrators in the NYC education community, faculty at CUNY schools, and at NYU's Steinhardt School of Education. The partnership has grown to extend beyond New York City, to include parents and teachers in school districts across the nation and faculty at a number of universities including Harvard, Stanford, CalTech^?, Johns Hopkins, Emory, Brown, California State Universities, the University of Texas, and Rochester University.

NYC HOLD was co-founded in 2000 by Elizabeth Carson, a NYC parent advocate who currently serves as executive director. Founding members and advisors are listed at http://www.nychold.com/who-we.html

NYC HOLD activities include:

* NYCMATHFORUM and NYC HOLD news distribution and discussion lists * National e-newsletter * Mathematics education resources on the Web * Information and consultancy services to parents, teachers, university math and science faculty, education policy makers and the media

* National advocacy network * Education Forums and Conferences

Please show your appreciation and support for the work of NYC HOLD by making a contribution today.

Your donation may be made through CIMSE and is tax-deductible.

Suggested levels for Individual Support:

Associate $50 - $499 Advocate $500 - $999 Partner $1,000 - $2,499 Sponsor $2,500 - $4,999 Patron $5,000 - $9,999 Benefactor $10,000 - $25,000

Checks may be made out to:

New York University /Courant Initiative for the Mathematical Sciences in Education

and mailed to:

Courant Institute of Mathematical Sciences at NYU Office of the Director 251 Mercer Street New York, NY 10012

ATTENTION: CIMSE, Elizabeth Carson or Charles Newman

Please contact me with specific questions or comment, or for additional information.

Thank you !

Elizabeth Carson Email: ecarson@nyc.rr.com Tel/Fax: 212.529.1302 Cel: 917.208.7153

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TwoMathEdBlogs 27 Jul 2005 - 19:26 CatherineJohnson


Stephanie just sent me a link to a fascinating list of prerequisites for college math, which includes a terrific Comments thread, at Tall Dark and Mysterious, a blog written by "Twentysomething curmudgeon seeking employment teaching college math in BC."

And btw, these are not prerequisites for a serious college math course:

A year ago, I would have posted that list under a heading more along the lines of “Things Students Should Know By Grade Nine”, but alas, experience as extinguished such optimism on my part.

This is long, but it's so valuable I'm quoting the entire list, which I'll probably 'archive' over on....the 'math lessons' page? Another Content Question for the folks at Information Architecture, Inc. (Definitely read the Comments section as well):

Based on my experiences, students graduating from high school should, in order to succeed in even the most basic college math classes:

1.Be able to add, subtract, multiply, and divide fractions. Moreover, they should understand that the horizontal bar in a fraction denotes division. (Seem obvious? I thought so, too, until I had a student tell me that she couldn’t give me a decimal approximation of (3/5)^8, because “my calculator doesn’t have a fraction button”.)

2.Have the times tables (single digit numbers) memorized. At minimum, they should understand what the basic operations mean. For instance, know that “times” means “groups of”, which will enable them to multiply, for instance, any number by 1 or 0 without a calculator, and without putting much thought into the matter. This would also enable those students who have not memorized their times tables to figure out what 3 times 8 was if they didn’t know it by heart.

3.Understand how to solve a linear (or reduces-to-linear) equation in a single variable. Recognize that the goal is to isolate the unknown quantity, and that doing so requires “undoing” the equation by reversing the order of operations. Know that that the equals sign means that both sides of the equation are the same, and that one can’t change the value of one side without changing the value of the other. (Aside: shortcuts such as “cross-multiplication” should be stricken from the high school algebra curriculum entirely - or at least until students understand where they come from. If I had a dollar for every student I ever tutored who was familiar with that phantom operation, and if I had to pay ten bucks for every student who actually got that cross-multiplication was just shorthand for multiplying both sides of an equation by the two denominators - I’d still be in the black.)

4.Be able to set up an equation, or set of equations, from a few sentences of text. (For instance, students should be able to translate simple geometric statements about perimeter and area into equations. ) Students should understand that (all together now!) an equation is a relationship among quantities, and that the goal in solving a word problem is to find the numerical value for one or more unknown quantities; and that the method for doing so involves analyzing how the given quantities are related. In order to measure whether students understand this, students must be presented, in a test setting, with word problems that differ more than superficially from the ones presented in class or in the textbook; requiring them only to parrot solutions to questions they have encountered exactly before, measures only their memorization skills.

5.Be able to interpret graphs, and to make transitions between algebraic and geometric presentations of data. For instance, students should know what an x- [y-]intercept means both geometrically (”the place where the graph crosses the x- [y-]axis”) and algebraically (”the value of x (y) when y [x] is set to zero in the function”).

6.Understand basic logic, such as the meaning of the “if…then” syllogism. They should know that if given a definition or rule of the form “if A, then B”, they need to check that the conditions of A are satisfied before they apply B. (Sound like a no-brainer? It should be. This is one of those things I completely took for granted when I started teaching at the college level. My illusions were shattered when I found that a simple statement such as “if A and B are disjoint sets, then the number of elements in (A union B) equals the number of elements in A plus the number of elements in B” caused confusion of epic proportions among a majority of my students. Many wouldn’t even check if A and B were disjoint before finding the cardinality of their union; others seemed to understand that they needed to see if A and B were disjoint, and they needed to find their cardinality - but they didn’t know how those things fit together. (They’d see that A and B were not disjoint, claim as much, and then apply the formula anyway.) It is a testament to the ridiculous extent to which mathematics is divorced from reality in students’ minds that three year olds can understand the implications of “If it’s raining, then you need an umbrella”, but that students graduating from high school are bewildered when the most elementary of mathematical concepts are juxtaposed in such a manner.)

7.More generally: students should know the basics of what it means to justify something mathematically. They should know that it is not enough to plug in a few values for x; you need to show that an identity, for instance, is true for all x. Conversely, they should understand that a single counterexample suffices to show that a claim is false. (Despite the affinity on the part of the high school text I am working for true/false questions, the students I am working with do not understand this.) Among the educational devices to be expunged from the classroom: textbooks that suggest that eyeballing the output of a graphing calculator is a legitimate method of showing, for instance, that a function has three zeroes or two asymptotes or what have you.


also added to the list by commenters:

I would add estimation and verification to that list. Students should know the difference between a sensible and nonsense answer.

Another blog by a college calculus professor: Learning Curves

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ParentsTeachersNCLB 14 Aug 2005 - 22:05 CatherineJohnson


Interesting column from David Broder today, a follow-up to a June column in which he'd "questioned the educators' commitment to the goal of improving school performance."

The June column triggered mass protests from teachers & principals, so Broder wangled an interview with Secretary of Education Margaret Spellings to get her take.

The column was prompted by a survey for the Educational Testing Service by the polling firms of Peter D. Hart, a Democrat, and David Winston, a Republican. In it, three-fourths of the high-school teachers were unfavorable toward No Child Left Behind (NCLB), the 4-year-old Bush administration initiative Spellings helped design when she was on the White House staff.

More troubling, as I said, was the fact that teachers seemed skeptical of the basic premise of that law — that students, teachers and schools should be rigorously judged by a single standard. They were asked to choose between the statement that everyone should be held to the same standard of performance because it is wrong to have lower expectations for students from disadvantaged backgrounds, or the contrary view that they should not be held to the same standard because we should not expect teachers working with disadvantaged students to have them reach the same level of performance on standardized tests as can teachers in more-affluent schools.

More than half the parents in the survey favored the single standard, but only one-quarter of the high-school teachers agreed.

I agree with Broder; it's not good for 3/4 of teachers to be rejecting equal standards for poor and rich kids alike.

That said, this looks to me like a classic Polling Problem. The questions sound crude enough that parents, who aren't trying to teach poor kids in poor schools, can offer a strictly moral response while teachers, who are on the front lines, may be answering realistically instead of idealistically. (I don't know.)

What would the stats have been if you'd put the question this way:

In an ideal world, should poor children be held to the same standards as affluent children?

Here's one teacher's email to Broder:

Another teacher, with 20 years' experience teaching third and fourth grades in Ohio, questioned the notion that parents expect more of the students than teachers do. "I just cannot fathom where or how you obtain data that supports the thesis that parents are more likely than teachers to believe expectations and standards are set too low. I can say that certainly in my suburb of Sylvania, the exact opposite situation exists. Frequently teachers express the opinion that expectations and standards need to be raised, but the parents' complaints would cause the phones to ring off the hook!"

She's right. In the abstact, parents want high standards.

But in the real world, parents do not want their kids failing exit exams. Politically speaking, it's impossible to maintain rigorous high-stakes exams, because parents won't have it. This is why I believe none of us should rely on state tests. There is huge pressure--from parents--to dumb down the tests, and we can be sure dumbing down happens.

Parents need to do their own testing.

move to value-added testing?

More from Broder's column:

On one point, Spellings offered a significant concession. These teachers had argued that they should be rated on the year-to-year progress their students are making, and not just on their attainment of a particular standard.

Spellings said she has a task force, including teachers' union representatives, working on how measures of students' progress might be blended with performance standards in evaluating schools. "It is a complicated challenge," she said. "I think we were right to start with performance standards, but now that they are in place, we are working our way into more sophisticated approaches."

I have a semi-firm view on the question of value-added assessments.

Value-added means: how much more do students know at the end of the year? How much value has been added?

This relates to Carolyn's post about the huge amount of repetition in math texts from one year to the next. (I'm also going to track down my source showing that between 7th & 8th grades American kids learn nothing more about math at all!)

Value-added assessments strike me as a good idea, especially when it comes to evaluating individual teacher performance. It strikes me that value-added assessments get around the problem of high schools being declared failures because they didn't bring kids who were years behind when they arrived up to grade level overnight.

However, I'm strongly against replacing grade-level standards with value-added standards altogether. If kids fall behind, they have to be brought back up to grade level. Period. The schools have to do it.

what is the parent's responsibility? what is the student's?

One complaint about NCLB is that all of the responsibility for a student's progress falls on the schools.

Good point.

I'd be happy to see accountability schemes imposed on students and parents, too.

Of course, in the real world I once had an accountability scheme imposed on me by a school, and I instantly blew it off. This was Jimmy's & Andrew's autism school. The director, a terrific & talented gal, decided that parents weren't providing their kids proper support. So she set a requirement that we all had to visit the school to observe our kids at least once a month. Something like that. I forget whether there was a Consequence if we didn't. I do remember that they were going to keep score. Not only would our kids have permanent records, we would have permanent records, too.

Sounds reasonable, doesn't it?

Yes it does, and yet I remember saying, out loud, in the very meeting at which the New Regime was UNILATERALLY IMPOSED, that the director could go ahead and mark me down for 'zero' right now.

I'm incorrigible.

in conclusion

In conclusion, accountability schemes for parents may not......work.

Nevertheless, schools like KIPP have found ways to motivate and perhaps even compel parent involvement, so let's not go by me.

Schools can impose consequences on students, and they should. With parents, they can use incentives and mild social consequences--public identification of slacker parents, anyone?

My brain is still fuzzy. The fact is, I don't have ideas about incentives & consequences for parents, but I know other people do. Parents, students, and teachers all share responsibility for a student's education.

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GiftForPrincipals 15 Aug 2005 - 12:27 CatherineJohnson


I think it's worth posting the one reader review of Elaine McEwan's The Principal's Guide to Raising Math Achievement:

Having read this book as a parent and a school board member, I am giving it to both the principals in my district. This book explains both many of the things that are done badly in many schools in the country and shows the path for how to do them well. I found the comparisons with the Japanese and Chinese methods of teaching particularly helpful. This book was pleasant to read as well as enlightening in how to promote the effective teaching of mathematics.

That is not a bad idea. I was on the verge of buying a copy for our principal (whose wife is a high school math teacher) all year long. I didn't do it, ultimately, because the book is awfully pricey ($28 for a paperback).

It's still a good idea.


Principal's Guide to Raising Math Achievement
school starts soon

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GreatNewsAtTheInstructivist 15 Aug 2005 - 22:10 CatherineJohnson


Federal dollars to support peer-reviewed research in mathematics instruction.

As I understand it, the sole reason we have some phonics being taught in our public schools is that the NIH, under Reid Lyon, launched a major research project to determine how children learn to read.

When the results came in, showing direct instruction in phonics to be essential, Lyon toured the country giving speeches about the research to prevent the ed school establishment disappearing the findings, as happened with Project Follow-through.

At least once a week the words 'We need a Reid Lyon for math' run through my head.

Maybe we're getting one.

The simple fact that money has been withdrawn from the NSF and shifted to the Department of Ed strikes me as a huge victory.

update: 'I have never heard of it'

what you don't know can't hurt you



Ihaveneverheardofit
projectfollowthrough

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LetterFromJCobasko 02 Dec 2005 - 04:48 CarolynJohnston

I received an email today from Joanne Cobasko of Save Our Children from Mediocre Math (SOCMM). She drew my attention to a couple of articles, describing the improvement in California test scores after the new California standards were adopted.

I looked at the attachment and skimmed the second article. It's not a research study (i.e., it would not meet the WWC's standards of evidence for a well-designed study); but it is definitely one situation where Saxon went head-to-head with fuzzy math, and won.

Here's the letter (thanks, Joanne!):

Hi Carolyn:

Both these studies show fantastic classroom results achieved in CA classrooms which are attributed to Saxon Math. I believe Bishop & Hook down play the Saxon Math connection in favor of the "CA Key standards" so as not to promote any particular curriculum over another, they choose to promote the math standards employed.

You will find references to the curriculum in their write ups though.

http://www.nychold.com/talk-hook-040404.pdf
http://www.nychold.com/report-wbwh-040619.pdf

There is also a great district comparison of standardized test results from Manhattan Beach, CA and Palos Verdes, both well to do communities (the comparison was provided to me by Martha Swartz from Mathematically Correct). [Note: Joanne points out that Manhattan Beach uses Saxon Math, and Palos Verdes uses Everyday Math. -- Carolyn]

Palos Verdes has the edge with a 26% Asian population, and one Kumon or other type tutoring facility for every 429 grade 2 - 6 elementary age student (the tutoring info was my informal review of the school population per the state testing info and a print out from the Kumon & other centers indicating their locations within a 5.22 mi radius).

Manhattan Beach, with a 7% Asian population and only 1 KUMON facility in town for 2,1113 grade 2-6 students, outscores Palos Verdes on the 2004 test scores.

Jo Anne Cobasko
Save Our Children from Mediocre Math (SOCMM).

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FightingTheGoodFight 22 Sep 2005 - 02:46 CarolynJohnston


ChrisAdams sent me a link today that I really needed to read, just right about now. I'm bone tired, and nervous about going to bat for Ben later this week; going to bat is not my strong suit.

But read this article. Here are the last couple of paragraphs (it's short):

Why do I spend so much time arguing against such obvious rubbish, which should be both self-refuting and auto-satirizing the moment someone utters it? Why not just go and read a good book?

The problem is that nonsense can and does go by default. It wins the argument by sheer persistence, by inexhaustible re-iteration, by staying at the meeting when everyone else has gone home, by monomania, by boring people into submission and indifference. And the reward of monomania? Power.

-- The Triumph of Reason?: why bad theories never die, by Theodore Dalrymple.

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ThePowerOfRepetition 25 Sep 2005 - 14:04 CarolynJohnston


Catherine posted a gem of a comment on this thread about the power of persistent repetition to change things. Here it is. The NAAR is the National Alliance for Autism Research, where Catherine was on the board for a number of years.

For me this blog isn't only about saving my own kid or Carolyn's kid or ktm readers' kids....politics takes all kinds of forms, and there's a distinction between power & influence (though I'm not the one to theorize what it is).

One thing I've learned about politics is that effective politicians, inside any organization, don't usually attack something head-on (though this is my inclination). They....form alliances, make horse trades, frame issues in ways that work for them, set agendas, and sell, sell, sell.

I think that's what we have to do. Because we have kids in the school system, we are, ourselves, inside the organization.

For most of us, our most effective tack will be to engage in organizational politics, if that's the term.

This is why I do a lot of 'visual' politicking. I carry my Russian or Singapore math books with me to every meeting; they are major conversation starters. I continually press the issue of Singapore's kids being best, and/or of KIPP's 8th graders having a higher percent passage rate on the Regents A.

Spaced repetition works.

At NAAR I used spaced repetition all the time.

I remember back when I first joined the organization, I was reading a book called BRAIN REPAIR.

BRAIN REPAIR, at that time, was far too radical an idea for the people who had founded NAAR. For a variety of reasons, all realistic and many having to do with the politics of autism science & NIH funding, they were willing to speak at most of treatment and prevention. The word 'cure' wasn't even included in the original NAAR literature.

So I was out there on my own, freelancing the message 'research for a cure.' People used to look at me like I was mad.

Early on, I suggested NAAR sponsor a conference on brain repair.

Here's how those suggestions went.

I'd say, 'Why don't we sponsor a conference on brain repair.'

Whoever I was talking to would look at me blankly, then return to whatever it was he/she had been talking about before I'd said, 'Why don't we sponsor a conference on brain repair.'

I kept inserting the words 'brain repair' into conversation anyway.

About 4 or 5 years into my stint at NAAR, I discovered that NAAR was sponsoring a conference in FL on....guess what?

Brain repair.

Nobody even remembered I'd spent 2 years hawking the idea.

(End thought from Carolyn: I think this also demonstrates the value of a good, catchy, repeatable marketing hook such as brain repair).

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TourDeForce 11 Jun 2006 - 12:41 CatherineJohnson


Engineering school is a rude awakening for most college freshmen. Many students are surprised to learn that their previous thirteen years of formal schooling have not adequately prepared them for the rigors of engineering school. Sadly, about 2/3rds of them, some very bright motivated students, won't make it through the program. This is what you learn by the end of freshman year:

1. You had been coddled the past thirteen years by your K-12 teachers. You were mostly spoon fed the material, at a slow pace, and then tested on how well you could regurgitate the exact same material back to the teacher in the exam. Rarely, if ever, were you required to apply the knowledge you had learned to solving new problems you hadn’t seen before. As a result, you could, and probably did get by, without mastering the concepts as well as you should have. You are finding out the hard way that most of your knowledge is still at the inflexible stage. This would be most apparent in...

2. Algebra: A course you took four years ago and didn’t learn well enough is coming back to haunt you now in calculus. Calculus seems much more difficult than it did when you took it last year in high school. This is because the pace is twice as fast and the exams require more than a regurgitation of what was taught (or rather won't be, see below). You see, mathematics is brutally cumulative. Calculus is really 10% calculus and 90% algebra (which includes a healthy does of trigonometry and geometry); and, the calculus step isn’t all that difficult usually. Most of the difficulty lies in either setting up the calculus step or finishing the problem after the calculus step. Calculus isn't all that difficult provided you've mastered algebra.

In high school, they allowed you over the algebra bridge without paying the full toll and you’re paying the price now, especially if you hobbled over on your graphing calculator. Anyway, you’ll need to know calculus and algebra cold if you expect to pass Physics I next semester. But this is going to be close to impossible because...

3. Your professors don’t teach and you can barely understand your TA’s poor English. This is more of an expectation problem; you’re still expecting to be coddled like you were in high school. Now you are expected to read the new material on your own and attempt to solve the problems before coming to class. This is a feature, not a bug.

By teaching yourself, you will be forced to understand and master the material, assuming you are doing the homework problems beforehand. Which you haven’t been doing because there just isn’t enough hours in the day to teach yourself and then do every problem assigned in every class. So you dutifully copy down the answers that the TA gives you during the class review all the while thinking “hey, that wasn’t so hard, now that someone’s showed me.” But, “understanding when explained by others” is not the same thing as the “ability to explain to others” which will become brutally apparent...

4. When you fail your first exam. The first test you’ve ever failed in thirteen years. You crammed the whole night before, but the test was too hard and too long. Goodbye unearned self-esteem; hello magic number 7. Seven is the number of things you can hold in working memory at one time. Partially learned knowledge uses more of these seven slots and takes longer to process than fully mastered knowledge. Your brain is being tested to its capacity for the first time and it's not prepared. You’ll become casual acquaintances with magic number 7 this semester and good friends next semester in Physics I because...

5. All those damn physics equations. Your brain is full. It feels like every time you learn something new it’s pushing something else out – like your name and your address. Spring semester brings with it Chemistry II (which requires you to remember everything you learned in Chem I), Calculus II (also brutally cumulative with Calc I), Computer Programming (learning new languages isn’t easy, especially when that language is C++); English Composition (your only easy class, too bad you have to do a term paper that’s twice as long as anything you’ve ever written before); and lastly Physics I, which will be...

6. The course that you’ll blame when you transfer to business school. Physics I – the rock upon which many engineering education ships have foundered. Two reasons – word problems from hell and the magic number seven. Physics is your first real test in your education career. It tests how well you are learning not only physics (under a withering course load of other difficult courses), but also how well you previously learned algebra and calculus. It is the latter two that will be your demise because you need every brain cell you can muster to learn physics today.

If you’re expending too many brain cycles recalling how to do the necessary calculus (most likely because you don’t sufficiently know the underlying algebra) sooner or later you’re going to meet the magic number seven. Meeting the magic number seven is like running out of active memory. You become overwhelmed and inefficient. Eventually, it all ends in tears (or an extra year of college after you’ve transferred to a nice soft major like human resources, communications, women studies, etc). So you lash out and look for someone to blame...

7. Like your college engineering department. Wrong. The train was slipping off the tracks well before they came into the picture, most likely sometime in elementary school. Don’t blame them because the train finally derailed at their station. Don’t be like the drunk who’s looking for his lost keys under the streetlights because that’s where the most light is. A career in engineering or in one of the hard sciences was effectively foreclosed to you by the 8th grade,. Most likely, you would have been none the wiser had you stayed in the soft fuzzy land of almost every other undergraduate field of study. Everyone would have been happier too because, well, you don’t know what you don’t know. Anyway, you can at least find solace in the words of Homer Simpson when he said to Lisa and Bart after they failed: “Kids, you tried your best and you failed miserably. The lesson is, never try.” But why blame yourself when you can blame the real culprit...

8. Your rotten K-12 education. Oh sure, they meant well; but look what happened. You see, you’re not part of the lower half of the bell curve who probably shouldn’t be pursuing a career in engineering or the hard sciences anyway. Nor, are you part of the two standard deviations and above gang that have the ability to succeed and compensate for a rotten education. No, you’re part of the curve that needed a good education to succeed and you didn’t get it.

And, it wasn’t a single chop that lopped your head off; rather it was death by a thousand tiny paper cuts. The accumulation of thirteen years of inefficiencies and unsound practices that prevented you from mastering and over-learning the material you needed to succeed in a rigorous college curriculum. Instead of teaching you content and facts and making you practice until automaticity, your well-meaning teachers were feed a bunch of scientifically and cognitively unsound educational fads -- constructivism, discovery learning, child-centered education, and social promotion to name a few. They all sounded so lovely in theory, yet in practice have consistently failed to adequately teach students as you have just found out. The hard way.

This advice may have arrived too late to help you; but it is not too late for that kid who just started kindergarten who lives down the street. This article is really for his or her parents, but they probably need to hear your story first before they begin to take it seriously. After all, you believed everything your K-12 educators told you and your parents, and look what happened.

- contributed by Kenneth DeRosa, October, 2005
(Note from Carolyn: this essay has been rewritten slightly, by its original author, with links added -- Carolyn).

That's going straight into the Math Writing Hall of Fame.

update

the magical number 7, plus or minus 2


Confessions of an engineering school wash-out
more confessions of an engineering school washout
the Terminator, or 'the magical number 7, plus or minus 2'
On Having a Math Brain (by Carolyn)
Wayne Wickelgren on mastery of math & on creativity & domain knowledge
late bloomers in math & Wickelgren on children's desire to learn math
math brain debunked (by Carolyn)
math professors versus computer science professors
Wayne Wickelgren on math talent
grandmasters and the magical number 7