note: as of October 20, 2005, I've moved this page to the homepage. Find Barry's letter & all Comments here

UPDATE: One day after the posting of the open letter below, the Commission changed the sample reading test that is available online. It no longer contains the question that I found offensive and which was the subject of the letter below. I thank the Commission for their prompt action.

An Open Letter to the California Commission on Teacher Credentialing

Part of the process of obtaining a teaching credential in California is passing a series of tests known as CBEST. At a minimum, one must pass the reading, writing and math tests. This is an open letter to the California Commission on Teacher Credentialing concerning an item on a sample CBEST test for reading:

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To the California Commission on Teacher Credentialing:

The CBEST web site contains a practice test in reading, mathematics and writing. I downloaded the reading test (http://www.cbest.nesinc.com/PDFs/CA_OPT_Reading.pdf ) and was extremely dismayed to find the following item on page 6 of the exam.

"Many people believe children will never learn mathematics if allowed to use pocket calculators. Having spent countless hours memorizing multiplication tables and doing long-division problems unaided by any mechanical device, many adults cannot conceive of anyone acquiring this knowledge without similar effort and practice. _______________________________________________ . What many people fail to understand is that mathematics is constantly evolving; it is not a fixed body of facts. Students must still learn basic skills, but they do not need to perform the endlessly repetitive exercises that calculators largely eliminate. Youngsters can better use their time—time they would have spent performing long-division problems—to learn mathematical concepts that will enable them to become better problem solvers.

"6. Which sentence, if inserted into the blank line, would best focus attention on the main idea of the passage?

A. It is true that mathematics is not the easiest subject in the typical elementary school curriculum.

B. Many of you have doubtless heard about the bitter classroom experiences of students who learned mathematics this way.

C. There is much to be said for instilling this kind of discipline in students.

D. Although it was clearly not fun, students trained in this manner rarely forgot what they had learned.

E. Such views, however, seem to reflect a resistance to change rather than a rational approach to mathematics instruction."

(Correct answer is given as "E")

I recognize that it is not necessary for test takers to agree with the opinion expressed above in order to pass the test. Nevertheless, I would imagine that the CBEST test makers would not include a passage that was derogatory or demeaning to any minority group, even though test takers need not agree with it to get the correct answer. This would not be done for fear of offending that particular minority group. The test makers evidently do not feel that the above passage is in any way offensive to any group, including mathematicians or teachers of the subject who actually care about making sure students learn content, skills and concepts. They also probably believe that the passage has educational and pedagogical merit. I question why it is included and whether in fact the Commission on Credentialling really believes what this passage imports? Furthermore, the passage implicitly argues against California's own state adopted math standards and policies. In particular calculators are not allowed on any of the California STAR exams, grades 2-11. The framework makes clear the importance of basic skills and the standards explicitly require memorization of basic number facts and proficiency in the standard arithmetic algorithms.

I would hope that this passage does not reflect how your Commission feels about this aspect of math education. For one thing, what does "countless hours" mean with respect to how long it takes to memorize multiplication tables? It is not an unthinkable amount of hours, and probably not as many hours as kids spend watching TV or shooting baskets on basketball courts. It is not that much of a burden when one considers that the payoff is instant recall of facts, allowing one access to the "higher order thinking skills" that enable them to "learn mathematical concepts that will enable them to become better problem solvers" as the above passage states as a goal. Multiplication and long division by hand also expose students to key concepts that play a role in understanding algebra, such as place value and the distributive rule.

Calculator use in the lower grades can be detrimental to learning these essential skills and concepts. If calculators are to be used in the lower grades, it should perhaps be in the context of helping to solve challenging problems, and used to save time on lengthy computations once it is ascertained that students have the facility to do such computations by hand. The correct answer (given in the answer key as "E"), suggests that those who resist calculator use do not have a rational approach to mathematics instruction. I would submit that the opposite is most likely true; that those who advocate for calculator use in the lower grades probably have a misguided sense of 1) what mathematics is about and 2) how it should be taught.

I recommend that the Commission consider removing this misleading and offensive passage from the practice tests and any real tests on which it may appear.

Barry Garelick -- BarryGarelick - 17 Oct 2005

Comments

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GAWD. I'm gobsmacked.

-- CarolynJohnston - 17 Oct 2005

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barry: thanks. you're doing important work.

-- VlorbikDotCom - 17 Oct 2005

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Good work Barry.

I have been studying the problems of education for over 5 years now and I am still amazed by what I read. I think that some teachers are truly ignorant of math and some know exactly what they are doing.

"What many people fail to understand is that mathematics is constantly evolving; it is not a fixed body of facts."

Has anyone checked what 7 times 8 is today?

"Students must still learn basic skills, but they do not need to perform the endlessly repetitive exercises that calculators largely eliminate."

This is a different premise that has nothing to do with whether math is or is not a fixed body of facts. They are saying that with calculators, you don't have to master multidigit multiplication and long division - perhaps even the times table.

"Youngsters can better use their time - time they would have spent performing long-division problems - to learn mathematical concepts that will enable them to become better problem solvers."

On the face of it, this sounds nice, but this idea is applied to much more than "long-division", which won't save you that much time. The real problem is that they don't replace that time with anything of real problem solving mathematical value. On top of it all, they slow down the coverage of the material and allow kids to slide from one grade to the next without mastering even a minimal amount of "naked" facts. That is why most schools supplement NCTM math with drills.

What about adding, subtracting, multiplying, and dividing fractions? How is the calculator going to help here? Their problem is not the wasted time doing long division problems by hand when there is a calculator available. Their problem is doing ANY "endlessly repetitive exercises". When the calculator can't save the day, what do they do? They say that practice and mastery is not necessary - only conceptual understanding. They water it down.

Their problem is NOT wasted time. Their problem is the hard work involved with mastery of skills. They say it isn't necessary; that there is no linkage. Only conceptual understanding is important. This has NOTHING to do with whether you use a calculator or not.

"E. Such views, however, seem to reflect a resistance to change rather than a rational approach to mathematics instruction."

This is arrogant, ignorant, and ruinous.

And, as an example of expository writing, I give it a 'D'.

-- SteveH - 18 Oct 2005

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but as an example of propaganda,
i give it an `A+' — in particular,
the fact that it appears under the guise
of neutrality ("which sentence ... would best focus ...")
is almost demonically contrived (and should be
respected — in the sense of "feared" —
accordingly): these guys aren't interested
in playing fair.

can we please just quit treating 'em with respect?
right now?

-- VlorbikDotCom - 18 Oct 2005

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Has anyone checked what 7 times 8 is today

Today it's still 56 but it is scheduled to evolve into 57 by 2010. So much for your useless facts.

-- KDeRosa - 18 Oct 2005

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Joanne Jacobs has a post on it today. Congrats!

-- SusanS - 18 Oct 2005

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I saw! Thanks. One negative comment from Chris Correa which I answered, FYI.

-- BarryGarelick - 18 Oct 2005

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What many people fail to understand is that mathematics is constantly evolving; it is not a fixed body of facts.

This one sticks in the craw. Can anyone give me one math fact that has changed in the past 100 years that has affected K12 math education? Just one. I can't think of any.

And, isn't this one of the main cards (the other being the calculator card) that the entire constructivist house of cards is built upon?

-- KDeRosa - 18 Oct 2005

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It's a poorly written paragraph that's for sure. It's not the facts of mathematics that are evolving, but our understanding of the subject. Hence new theorems are proven etc.

I don't know that the constructivist house of cards is built upon an assumption that the principles of math change over time. It's built upon an assumption that students should discover these principles on their own. Of course, since the constructivists like to think there is more than one right answer to a math problem, maybe they think that math facts change. To that end, maybe there is a highest number but no one has "discovered" it yet.

-- BarryGarelick - 18 Oct 2005

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Ok, let's assume they meant "our understanding of the subject" or "principles of math" instead of "facts," I'm not a mathematician (but many who read this site are), but I still can't think of one example of how a mathematic priciple or our undrstanding of math has changed in the past 100 years that somehow affects K-12 level math.

Maybe this is true on the undergrad level and above. For example, I remember my old Dynamics teacher telling us how the concept of the vector was not around when he was an undergrad. But can someone give me one example on the K-12 level?

It's built upon an assumption that students should discover these principles on their own.

But isn't this assumption built on the assumption that there is no need to memorize or master the existing body of knowledge since it is subject to change? Students therefore need to discover the principles on their own so they can discover the new principles as they evolve, or something like that.

This is the danger of getting into an argument with an idiot (the constructivists). You start sounding like an idiot yourself.

-- KDeRosa - 18 Oct 2005

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I see your point.

I don't think the constructivists are arguing that the body of knowledge is subject to change. I think they argue that mathematical concepts are innately understood by each child, so it is a matter of "constructing" the knowledge one innately has through discovery. By God, I AM sounding like an idiot now.

-- BarryGarelick - 18 Oct 2005

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It's infectious.

-- KDeRosa - 18 Oct 2005

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"By God, I AM sounding like an idiot now."

I told my son a saying the other day. If you mess with skunks, you start smelling like a skunk.

My feeling about their use of the word change is that they are talking about technology and that technology allows teachers to approach math quite differently. I can understand this idea, but it falls apart when it comes to topics like manipulating fractions, which is not helped by calculators. They are trying to find justifications for eliminating all need for practice and mastery. This "not a fixed body of facts" is simply propaganda. I think we waste too many brain cells trying to make sense of it all. Things like this are made to sound good to others so they don't question them about the details.

-- SteveH - 18 Oct 2005

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Whether or not manipulating fractions can be done by calculators is irrelevant -- in fact, I believe there are calculators that can do it, i.e. manipulate algebraic expressions so as to get a "simplest" form, as if "simplest" was a clear-cut notion. I'm quite sure one can build a machine that will feed you without your having to use your hands; in fact such a machine is pictured in Charlie Chaplin's Modern Times. Chaplin's target in that movie is mass-production and its attendant dehumanization, not the topic under discussion here, but I recommend the movie anyhow, if only to remind oneself how soon social problems can mutate into newer, equivalent problems. The repetitive, mind-numbing job Chaplin had in the movie no longer exists, and has been taken over by a computer, but Chaplin's 21st Century counterpart is now afflicted with obesity. R.A.R.

-- RalphRaimi - 18 Oct 2005

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My point is not that you couldn't do fractions by computer. My point is that reform math does not use calculators or computers for this and they still do not require mastery of the knowledge and skill. My point is that calculators are not the main issue.

-- SteveH - 18 Oct 2005

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Oh my god.

I would like to see someone provide statistical evidence that today's calculator-addled students are learning math as well as, or better than, we luddites who, god forbid, memorized our times tables. Everyone I know who has taught math at the high school level or beyond has reported exactly the opposite.

As far as I know, even the staunchest proponents of calculators-for-all haven't even pretended to provide this data. I'd say that their views, however, seem to reflect an affinity for change rather than a rational approach to mathematics instruction.

-Moebius Stripper

-- KtmGuest - 19 Oct 2005

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Good work, Barry. I am really impressed that you got such rapid action!

-- CarolynJohnston - 19 Oct 2005

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wow. ralph raimi and moebius stripper.
everybody knows where to find KTM now!
musta been the joanne jacobs piece (10/18) or somethin'.
i'll have to start watching what i say ...

or not. meanwhile, welcome (from the fringe)
to all the newcomers (or delurkers) ...
and please stick around.
whatever else anybody might say ...
KTM is full of surprises.

never memorize a trig identity until you know
e^it = cos(t) + i sin (t).
i'm not kidding and i'm not crazy.

yours in the struggle.
the entity sometimes known as v.

-- VlorbikDotCom - 19 Oct 2005

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well, i am just now finding this Open Letter, on joannejacobs

where is my head?

why can't i use my own web site?

Open Letter

-- CatherineJohnson - 21 Oct 2005

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I just chanced upon Barry's open letter. I am speechless. The ignorance and arrogance of these progressive/constructivist ed propagandists is mindboggling.

-- CharlesH - 28 Jan 2006

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