An extended mathematics metaphor:

Flowing
under the pre-K through high school curriculum, like the ever-widening
Mississippi, is a steady expansion of the number system and its
corresponding basic operations.

Important
milepost concepts and mathematical problems which are posed,
deconstructed and solved throughout those years are like the flatboats
and steamboats of Mark Twain's era which floated upon the Mississippi's
waters.

One
doesn't seek to control the river, because the number system and its
operations exist in nature, but we can select what floats on it and
where to travel. Choosing when and how to introduce concepts, what
problems to pose, and where they fit is the foremost responsibility of a
standards and curriculum developer.

## 2012-05-29

## 2012-05-18

### About the bloggers…

First, a pledge:

We should interpose that we are not salaried educators, we are not political ideologues, we have no personal vendettas, we are not self-absorbed egoists, we have no children in school, and we have no pecuniary interest in the future success or failure of various educational reform efforts. We are disinterested parties, and we are not selling any product or service. We own no stock in any education-related publicly traded company. (Did we overlook anything?)

Because we are unbeholden and free of conflicts of interest, we are able to speak truth to educrat-power.

Since it is impossible to expound on all that is right and wrong with Common Core in one fell swoop, we can only address issues piecemeal, at the risk of occasionally sounding incoherent, or even worse, looking likeWe, the bloggers, hereby affirm that we have a particular interest in improving K-12 mathematics education and will do what little we can to advance that worthy cause in the confines of this blog.

__bloviating ignorami__. We know that we may contradict ourselves at times. Writing a blog is difficult; kudos to you bloggers out there.We should interpose that we are not salaried educators, we are not political ideologues, we have no personal vendettas, we are not self-absorbed egoists, we have no children in school, and we have no pecuniary interest in the future success or failure of various educational reform efforts. We are disinterested parties, and we are not selling any product or service. We own no stock in any education-related publicly traded company. (Did we overlook anything?)

Because we are unbeholden and free of conflicts of interest, we are able to speak truth to educrat-power.

[It is remotely possible that someone will want
to hire us in some capacity to spiel on their (more heavily trafficked) website,
so some of the previous statements may have to be superseded. In the unlikely event that
happens, we'll be sure to let readers know. We believe in full
disclosure about any financial or other potential biases.]

We
have what we consider to be sufficient credentials to comment on the matter
(and we'll let readers judge that statement based on the content of our posts), but we remain anonymous to let our words
speak, rather than potentially being directly assailed or having our
credibility questioned. We wish to draw attention to the issues, not to ourselves.

## 2012-05-17

### Common Core: a national cop-out, not a national curriculum

A cautionary tale...

In the 1980’s, the combination of banking deregulation and lack of oversight allowed a breed of banks known as Savings & Loans to embark on a scheme of making risky loans using depositor funds. If the loans worked out, the S&L’s stood to profit, but if the loans failed, the deposits were insured by a federal insurance company (the FSLIC). For the S&L’s, it was a ``heads I win, tails you (the insurance company) lose'' situation.

***

In the 1980’s, the combination of banking deregulation and lack of oversight allowed a breed of banks known as Savings & Loans to embark on a scheme of making risky loans using depositor funds. If the loans worked out, the S&L’s stood to profit, but if the loans failed, the deposits were insured by a federal insurance company (the FSLIC). For the S&L’s, it was a ``heads I win, tails you (the insurance company) lose'' situation.

But it was
even worse than that.

When enough
loans went bad (of course they did, otherwise it wouldn't be a story), the
FSLIC was depleted and went bankrupt, taxpayers footed the $100 billion bill, and (although
we are not presenting the entire history lesson) these
events contributed to an economic meltdown that is commonly known as the
``

__S&L crisis__''.
What can we
learn from history? For us, it is when someone hands you a ``heads I win,
tails you lose'' proposition, be very, very careful before signing on the
dotted line.

***

## 2012-05-08

### Counting and its applications

Counting, notwithstanding the, er, tale of Clever Hans, is so basic that it seems to be an innate ability in several animal species, according to an article published in

[

Parents teach their youngsters to count to 10, or children learn it on Sesame Street, and there are numerous studies showing babies can conceive of small numbers and preschoolers can judge greater or less than without knowing exact numbers, but by understanding approximate counts.

In mathematical parlance, the counting numbers are also called the ``natural'' numbers, as existing in nature.

So how is it possible to teach counting, the most natural of mathematical skills, unnaturally? The worst way is to force memorization of numbers and number names before the concept is understood. What kindergartner do you know that owns 90 of anything, except maybe for Beanie Babies? Open a Scrabble set and look at the 100 tiles. Is that a number of objects that a kindergartner needs to comprehend in their child's world? Memorizing the names of numbers at the age of 5 before actually understanding the concept of the number is simply put, backwards. Mathematics should not be taught that way. A child should understand the number along with the name, before reading, and then writing the number.

If particularly anal parents want to push too-large numbers on their child at an early age for fear of falling behind, so be it, but the paranoia should not be systemic.

CCSSI standard K.CC.1 ``Count to 100...’’ carries into the next year's standard 1.NBT.1 ``Count to 120...’’ along with a few variations on the theme. We won’t pause long to chide CCSSI for such arbitrary parameters because there is a much more compelling standard in the parallel Measurement and Data strand that pertains to counting, which creates the potential for some real advancement of thinking and analytical skills in early childhood.

__Scientific American™ in September 2009__.[

*Clarification*: the word ``basic'' above is being used in context as ``fundamental'', not ``simple''. See tweet below linking to this blog post that missed the point.]Parents teach their youngsters to count to 10, or children learn it on Sesame Street, and there are numerous studies showing babies can conceive of small numbers and preschoolers can judge greater or less than without knowing exact numbers, but by understanding approximate counts.

In mathematical parlance, the counting numbers are also called the ``natural'' numbers, as existing in nature.

So how is it possible to teach counting, the most natural of mathematical skills, unnaturally? The worst way is to force memorization of numbers and number names before the concept is understood. What kindergartner do you know that owns 90 of anything, except maybe for Beanie Babies? Open a Scrabble set and look at the 100 tiles. Is that a number of objects that a kindergartner needs to comprehend in their child's world? Memorizing the names of numbers at the age of 5 before actually understanding the concept of the number is simply put, backwards. Mathematics should not be taught that way. A child should understand the number along with the name, before reading, and then writing the number.

If particularly anal parents want to push too-large numbers on their child at an early age for fear of falling behind, so be it, but the paranoia should not be systemic.

CCSSI standard K.CC.1 ``Count to 100...’’ carries into the next year's standard 1.NBT.1 ``Count to 120...’’ along with a few variations on the theme. We won’t pause long to chide CCSSI for such arbitrary parameters because there is a much more compelling standard in the parallel Measurement and Data strand that pertains to counting, which creates the potential for some real advancement of thinking and analytical skills in early childhood.

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