What’s 1/3 + 1/4? Asked by a radio host, the president of the New York City teachers’ union said she couldn’t answer without a pencil and a piece of paper. Another guest, Marc Tucker of the National Center on Education and the Economy, supplied the correct answer, seven twelfths.

According to New York State standards, adding fractions with different denominators is sixth-grade work. But (Randi) Weingarten defended her lack of a quick answer. â€œI do it the old-fashioned way,â€ Ms. Weingarten said. â€œYou take your paper, your pen, you add it up, you get to the fractional whatever.â€

â€œAnd you show your work, right?â€ (host Mike) Pesca prodded. â€œSo a good teacher can give you partial credit.â€

Ms. Weingarten replied, â€œA good teacher will look at it and talk to you about what went right and went wrong.â€

When she negotiates contracts, it’s all about the decimals.

Via Chalkboard.

1. As an elementary teacher for over twenty years, I was frequently shocked at my fellow teachers’ lack of understanding of math concepts. If a teacher needs a pencil and paper to do a simple fractions problem, then that teacher doesn’t really understand fractions, and can’t teach kids to understand them.

2. allen says:

Ms. Weingarten is obviously of an age.

With the use of pencil and paper, she was describing the old old-fashioned way.

The new old-fashioned way is to claim an understanding of the process that will generate the right answer, regardless of the answer generated, and the currently-fashionable way is to claim that understanding the process of acquiring the skill is more important then being able to generate the right answer.

3. Chris says:

the shame is not needing pencil and paper … but in not having pencil and paper if that is what you need. But that doesn’t extend to caculators, I do draw the line at pencil and paper (if you’ll pardon the pun)

4. Barry Garelick says:

In this constructivist era, why didn’t they allow her the time to discover the answer?

5. old girl says:

I defend Ms. Weingarten’s right to use paper and pencil.

A piece of paper is extra working memory, and the simple act of writing out 1/3 1/4 on paper would probably jog her long term memory to find a common denominator. A good teacher, or radio show host, would give her a piece of paper and a pencil and a second chance with a similar question, e.g. 1/4 1/5.

The ideal of paperless mathematics, where it’s all done in your head like Brazilian street children selling candy and cigarettes and making correct change on the spot, is the ideal of constructivism. Although we would like suburban American children (and adults) to be able to make correct change in simple commercial transactions when the computerized cash register is down, that is a very specific goal that requires specific training and repeated practice. Drill and kill one might say. It would take time away from other mathematical training and practice we value more highly in our culture. There’s no free lunch.

What grade or subject does Ms. Weingarten teach right now?

6. Richard Nieporent says:

This proves that you donâ€™t need to learn how to do fractions to succeed. For example you can become the head of the teachersâ€™ union.

â€œI do it the old-fashioned way,â€ Ms. Weingarten said. â€œYou take your paper, your pen, you add it up, you get to the fractional whatever.â€

You would hope that she would be honest enough to just say that she didnâ€™t know the answer. Instead she not very convincingly lies. The factional whatever? Too bad he didnâ€™t give her a pencil and paper and say okay do it your way. It would have been interesting to see her try to wiggle out of it.

7. Ragnarok says:

old girl said:

“It would take time away from other mathematical training and practice we value more highly in our culture.”

Yes, like training to be beaten to a pulp by most of the world (see TIMSS etc.). Takes a lot of training, I don’t think.

“A piece of paper is extra working memory, and the simple act of writing out 1/3 1/4 on paper would probably jog her long term memory to find a common denominator.”

Let’s not make this trivial problem non-trivial. All you need is 4 x 3 = 12, so the result is (4 3)/12, or 7/12.

Bjut I’m willing to bet that Ms. Weingarten knows the meaning of ‘>’, as in more pay, more, more…

8. wayne martin says:

As a teacher of history at Clara Barton High School in Crown Heights, Brooklyn, from 1991 to 1997 ..

Weingarten holds degrees from Cornell University and the Cardozo School of Law. She worked as a lawyer for the New York firm of Stroock & Stroock & Lavan from 1983 to 1986.

Weingarten was chairperson of the Health Insurance Plan (HIP) of Greater New York and a board member of the N.Y.C. Independent Budget Office. She served on Mayor Michael Bloombergâ€™s transition committee following his election in 2001.

She is on the boards of directors of the Justice Resource Center and Council for Unity (both student-related groups); the New York Committee on Occupational Safety and Health (NYCOSH); the United Way of Greater New York; the International Rescue Committee; the New York Downtown Alliance and the newly formed Math for America. She is on the advisory board of Operation Public Education at the University of Pennsylvania. She is also a Democratic National Committee member.

In addition to teachers, the UFT represents classroom paraprofessionals, guidance counselors, school secretaries, nurses, social workers, psychologists and other non-supervisory personnel in the cityâ€™s public schools. Also belonging to the union are private sector workers in health and education.
—-

Weingarten is no longer a teacher .. she is a Labor Union Representative .. she is, however, a member of a group called: Math for America.

9. John Thacker says:

Drill and kill one might say. It would take time away from other mathematical training and practice we value more highly in our culture.

Except that I find that I had to take valuable time out of my calculus classes because students weren’t drilled enough in basics like those. So in my experience, the end result of old girl’s advice is that the students get more mathematical training in manipulating shapes and learning that there’s no right answer, but less in calculus and other advanced mathematical training. There’s no less amount of time learning the basics– they just learn them later on, such as in college from me or my colleagues, since they don’t get them in their earlier courses.

Not drilling the basics takes time away from other mathematical training and practice we value more highly, not the other way around, IMO.

10. What grade or subject does Ms. Weingarten teach right now?

None, as a previous poster stated.

And while those six years are on her resume, I do not believe Ms. Weingarten taught that long, and that most of this is “part-time.” How partial the time was I cannot say, but I’m told her full-time experience is closer six months than six years.

I’ve no doubt Ms. Weingarten’s primary occupation for those six years was being groomed for her current position.

11. Correction… I do not believe Ms. Weingarten taught that long, and I’m certain most of those six years were “part-time.” A Google search produced this:

http://www.heartland.org/Article.cfm?artId=12445

A curious reporter from The Village Voice examined attorney Weingarten’s teaching record and questioned whether she had actually completed the required two years of full-time service before she was awarded her teacher certification in September 1996. The Voice found she had taught full-time for only one semester during the five years prior to her certification, mostly teaching for only about 41 days a year.

12. wayne martin says:

http://topics.nytimes.com/top/reference/timestopics/people/w/randi_weingarten/index.html?inline=nyt-per

Wrong,Wrong and Wrong: Math Guides Are Recalled

March 25, 2005, Friday
By SUSAN SAULNY (NYT); Metropolitan Desk
Late Edition – Final, Section B, Page 3, Column 5, 624 words

DISPLAYING ABSTRACT – Math test preparation materials intended for New York City students in grades 3 through 7 are recalled after at least 18 significant errors are found; school officials contend city Education Department fact-checker failed to do proper job, but Randi Weingarten, president of United Federation of Teachers, criticizes department for lack of coordination with UFT, stating that department’s style ‘does not welcome or want input’; examples of errors cited
—-

Regardless of how she adds fractions, Weingarten clearly uses â€œthe old fashioned wayâ€ of Labor Union boss, whether or not she really ever qualified as a teacher.

13. While I personally don’t much admire Ms. Weingarten, she’s correct that the DoE does not consult teachers at all before mandating its nebulous touchy-feely programs, and God help you if you try to use them exclusively with city kids.

I think Ms. Weingarten would be quite upset by your description, and sees herself as quite modern. Many of us conjecture she expects Hillary to win the presidency and appoint her Secretary of Education. Then, people won’t complain about a non-teacher being Secretary. After all, no one can deny she sweated through those 41-day semesters.

14. wayne martin says:

> Many of us conjecture she expects Hillary to win the
> presidency and appoint her Secretary of Education

For those of us who post comments kindly disposed about the role and function of a Federal Department of Education, we need to keep this specter clearly in sight.

15. old girl says:

old girl said:

â€œIt would take time away from other mathematical training and practice we value more highly in our culture.â€

Yes, like training to be beaten to a pulp by most of the world (see TIMSS etc.). Takes a lot of training, I donâ€™t think.

â€œA piece of paper is extra working memory, and the simple act of writing out 1/3 1/4 on paper would probably jog her long term memory to find a common denominator.â€

Letâ€™s not make this trivial problem non-trivial. All you need is 4 x 3 = 12, so the result is (4 3)/12, or 7/12.

I’m arguing that old-fashioned mathematics training where children drill with pencil and paper on, say, finding common denominators, is superior to a constructivist curriculum that eschews pencil and paper in favor of paperless mathematics. Paperless, and missing the standard algorithms that require paper and pencil to execute. The justification for these curricula is always some version of “why can’t stupid American children do these trivial problems in their heads?” The failure of these curricula is “why are stupid American children taking so long to discover the distributive property embedded in rich contexts, and use their learnings to construct reliable and efficient algorithms?”

I would be the last person to jump in and stomp on Ms. Weingarten. I say: give her a pencil and paper. She was lucky enough to grow up at a time in America where teachers stood at blackboards with a piece of chalk and taught children how to find a common denominator. Holding a pencil and writing down the problem may jog her memory. Is she an example of the failure of traditional instruction, or an example of the trade-off we accept as a culture, for less facility with mental arithmetic in favor of more facility with written arithmetic?

No fraction problem is trivial. Fractions are a thing of beauty. They only seem ordinary after you have mastered them. Fractions are the stepping stone to algebra and to to all of the higher mathematical learning that our culture values, and so we should also value the training — the drill and kill — of paper and pencil mathematics in the elementary school.

If Ms. Weingarten hasn’t found the common denominator for two fractions with unlike denominators anytime in the last thirty years because she has been working with cost of living increases expressed completely in ones, tenths, and hundredths, she may well pause before she can work out what is a third plus a fourth.

16. old girl says:

Look, I shouldn’t have used the phrase “drill and kill” because the “and kill” part is meaningless to me, but it raises hackles.

It is deeply ironic that constructivists gain traction when we laugh at Ms. Weingarten’s troubles on the air, and yet this paves the way for a constructivist pedagogy in our public schools. Constructivists say they value mental arithmetic and “fluency with math facts” but they will refuse to drill children on single-digit multiplication facts, let alone multidigit multiplication and division. Any drilling happens at home, or at Kumon.

If you want adults to be good at mental arithmetic, drill them on it every year. Write it into Ms. Weingarten’s contract. If you want children to get ready for algebra, you drill them more in written arithmetic and less in mental arithmetic because there is not enough time in the school day for both. In fact, in a traditional sequential mathematics program the drill on mental arithmetic will be built into the drill on written arithmetic, for instance in the way written long division drills children in estimation, multiplication, and subtraction.

17. wayne martin says:

The last posting got me to thinking that maybe I was missing something. A quick look on the NET produced a number of hits on â€œconstructivismâ€ and â€œmental mathematicsâ€. A snippet from one posting is provided below:
—-
http://www.acurriculumforexcellencescotland.gov.uk/images/Mathematics_tcm4-252174.pdf

Qualitative study in Mental calculation strategy
Murphy, C.: 2004, How do children come to use a taught mental calculation strategy?, Educational
Studies in Mathematics, 56, pp. 3â€“18.

As we have seen, Kingâ€™s college research team found that â€˜the area of greatest improvement noted by
schools and teachers was in pupilâ€™s mental mathematicsâ€™ (Millett, Brown and Askew, p. 184). This is
particularly interesting since this is also an important issue in Scottish mathematics education. Here, we
extend our review on this topic by referring to a research paper that used a qualitative approach. The paper chosen here was recently published in Educational Studies in Mathematics, one of the most
important journals in mathematics education.

Murphy explored in more detail how children interpret mental calculation strategies taught
through whole class instruction. In particular, the compensation strategy was chosen. This strategy is
described as a sophisticated method, for example, â€˜12 9 would become 12 10-1. In this way a known
fact, such as 12 10, is used to derive an unknown fact such as 12 9â€™ (Murphy, 2004, p. 5). The research
design was interesting. First, the author chose three children aged 8 to 9 who were considered to be
average ability in mathematics, and who demonstrated contrasting spontaneous calculation approaches,
through diagnostic interviews. Then these children attended in a session to learn the compensation
strategy. Finally, post-teaching diagnostic interviews were carried out a week later (ibid, pp. 5-7).
Findings of this research is very interesting, but it might be rather disappointing for those who strongly
believes the effectiveness of direct teaching of mental mathematics, i.e. â€˜The children did not use the
strategy consistently as taught and suggest contrasting interpretationsâ€™ (ibid, p. 12).

I wasnâ€™t aware that these handy tricks had been hijacked by the â€œconstructionistsâ€, so I better understand how this conversation is drifting now.

I canâ€™t remember when I was introduced to the concept of adding fractions. Once introduced to the concept though, Iâ€™ve always been able to do these simple computations in my head. Iâ€™m certain that my teachers always had us do the work on paper (if only to be able to demonstrate the thought/work process) and never promoted the idea of only doing this work mentally. Iâ€™m actually a little surprised that â€œeducation theoryâ€ has gotten so off-keel that it would promote mental calculations over paper-based techniques. The two are exactly the same, just a little mental gymnastics required for the paperless version; however, in the â€œreal worldâ€, the numbers very quickly become too large to work with in oneâ€™s head. Calculators and Computers are necessary to do work of any complexity with the goal of obtaining accurate and timely results.

Without a sound understanding of the techniques, one probably wouldnâ€™t be able to do mathematics effectively.

Sometimes one wonders if â€œeducational theoristsâ€ donâ€™t have far too much time on their hands.
—–

18. speechless