The Joy of Eureka! and Revelations on Common Core


If you’re looking for a decidedly pro or anti stance on Common Core (CC), you won’t find it here. Instead, you’ll find a little bit of both.

I’m seeking illumination, and, admittedly, the internet is a terrible place to seek it, being filled with information largely devoid of fact, wisdom, or truth. Denise Minger (Raw Foods SOS) characterized it best in her recent book (Death by Food Pyramid):

In case you’ve never tried to research something on the Internet before, it works something like this. First, you open a search engine and type the subject you’re interested in, such as “vegetarianism” or “the paleo diet.” If you want your subject to be a good thing, you add the phrase “is awesome,” “will save the children,” or “is supported by a large body of scientific evidence.” If you want your subject to be a bad thing, you add the phrase “sucks,” or “debunked.” Then hit search. You now have several thousand websites that will confirm whatever you want to believe.


So, while I normally blog about our experiences in home education, the topic of CC comes up often in discussion on other forums as well as in general conversation with other home educators that I might as well contribute to the morass. This is in no way a complete analysis, and is presented with statements of belief, anecdote, and metaphor; yet, the hope is that both the reader and I come away with a better understanding.

We proceed; but, not before passing along a little joy that lead me in this direction.

The Joy of Eureka!

There are those little moments during home education when you get to witness something great. Several of those moments happened the other day with Secondo (9-years-old).

As some of you may remember from our previous posts, Secondo’s auditory and language delays lead to a later academic start than his peers; however, in the last year Secondo has blossomed in everything from reading and writing to science and math, for all of which he is now on par.

At this point, Secondo is working through the equivalent of 2nd/3rd-grade math (the “old” math), slowly and begrudgingly. The main delay, however, appears to be rooted in boredom. The repetition in multi-digit addition and subtraction problems just garners a heavy sigh as he rarely misses one; and the simple multiplication problems (disguised as “skip counting”) are, similarly, just as easy.

Yet, those problems involving geometric shapes seem to light him up a little. This is not surprising when you consider the way he learns: kinesthetic, visual, etc.

InfiniteNumberOfCornersThe “cool” moment came when Secondo came running from the kitchen, where he’d been finishing up his “school” for the day, to announce “circles have infinite corners!“. Not being entirely sure what the excitement was all about I walked over to see what he was working on: a segment on identifying the corners and right angles of shapes. He pointed to the circle, “see?”

Yes! He was correct. In the limit, as the sides get very small, and the number of sides of a regular polygon increases, the aggregation of the those small parts approach a circle.

Congratulations, my child, you just invented calculus (tears in my eyes)…

It is this type of discovery that makes home education so exciting and demonstrates the benefits for a child that would have been assessed, labeled, and remediated by a public school as a result of his language (and motivation) delays.

As I suspected, the teacher’s guide was silent, showing only the Xs and Os on the shapes with definitive corners.

The Puzzlement

imagesThis is a problem I have, in general, with most textbook materials: if the answers are correct, they often present a limited view without discussion. Further, regardless of whether the teacher is a “professional” or a home educator, such limited (or absent) discussion would likely lead some to declare such observations (like Secondo’s) as “wrong.”  This would be especially apparent for educators uncomfortable with the materials.

After all, how can you teach something you, yourself, don’t understand?

Both GranolaGirl and I remember a time when our teachers had degrees in subject matter. Several even had Masters degrees, or “real-world” experience, who then went on to obtain teaching certificates. Now, it seems, we have students of education who themselves are being trained to approach these topics in a formulaic or cookbook manner rather than developing a deep understanding of the topics.

I started wondering if the understanding demonstrated by Secondo would be possible through the educational experiment that is CC. While I deplore any centralized intrusion into education (it deprives communities of the freedom to choose what is best for their local needs), I remain curious as to theory and practice of CC.

After all, proponents of CC state that the curriculum guidance is structured to improve understanding on concepts rather than focusing on procedure. The detractors point to examples of confusing instructions and convoluted procedures that make understanding all but impossible. Yet, I believe the real issues lay deeper.

I’ve been generally indifferent toward the debate, but I figured that I might as well look at it myself (especially since examples keep filling the spam box and Facebook timelines).

The Sound Bite

The following video takes a definitive anti-CC stance. While the point regarding unnecessary procedural steps is valid, the argument cherry-picks a particularly convoluted arithmetic technique as “proof” that CC, in general, is bad.

As we will see, such sound bites don’t really lend themselves well to any constructive debate since they decidedly omit the full picture in favor of evoking emotional reactions grounded in confusion, much like a magician’s slight of hand.

At the same time, the central argument should not be on a specific instance of a poorly constructed lesson, but rather on the political implications of allowing greater centralization (even in the form of “standards”).

The Theory

An example of the pro-CC side is presented by the Foundation for Excellence in Education (here) and an example of the anti-CC side is presented by the Truth in American Education (here). These are not the exclusive sources in this debate, but by way of these example I believe I can shed some light on it.

It is here that I will make a disclaimer; this section makes CC look bad. However, without revealing the content of the subsequent section, the story is incomplete.

The claim is:

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The mathematics examples (relevant to our moment of joy, above) present as follows:

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The assertions made in the “justification” are incorrect and incomplete. Firstly, both problems can be solved by either method: counting (adding) or recall of multiplication tables. Secondly, I would assert that demonstrating “recall of multiplication tables” in no way represents a deeper understanding of the topic; recall of multiplication tables simply demonstrates memory (a tool for efficiency), whereas knowing that $4 needs to be added three times, or that we need to sum six buttons seven times or seven shirts six times does demonstrate understanding of the problem (which is to find the totality requested).

Screen Shot 2014-04-05 at 3.11.31 PMAgain, nice try, but the assertions are incomplete. The CCSS question simply asks the student to compute the results of applying the same ratio four times. It is no less formulaic than the original question, with the only significant difference being the conversion between minutes and hours. More words in the question and additional computations does not demonstrate understanding of the relationship between distance, rate, and time; however, it does measure whether the student understands the relationship between hours and minutes.

A better measure of understanding would be to have the student describe, in words, how to compute any of the three variables given the other two: “A bird flew twenty miles in one hundred minutes. Describe, in words, how you would compute the time it takes for the bird to fly six miles, then perform the computation you describe.” Albeit a marginal improvement, at least we might assess that the student hadn’t simply memorized the formulae since the results requires articulation of concept in a separate symbolic form.

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The justification in the example, above, baffles me. If demonstration of reasoning is the goal, then this is not the type of question that can accomplish such demonstration. It simply asks the student to write two more equations that have the same value of y = 11/3; there is no significant process of elimination based on comparative logic being stressed in the exercise. Further, the question misses the more salient point that there are an infinite number of equations that result in the same answer. As such, the usefulness of such exercises is minimal without the constraint of practicable application.

A goal in sight?

While the Foundation insists that the new standard is “better” (by way of citing the Thomas B. Fordham Institute study) I remain unconvinced by the examples presented.

Still, the goal behind the attempt at standards is noble. It is important to establish some criteria to measure the effectiveness of education within specific topics.

Yet, I am inclined to argue that competitiveness via promotion of exceptionalism, rather than centralized normalization of mediocrity is probably a better instrument for seeking effective education. But that is just an opinion. In other words, we must ask ourselves “to what purpose?” What purpose does our education system serve? Are we promoting exceptionally creative problem solvers that directly or peripherally benefit the human condition, or are we attempting to corral both social thinking and behaviors for the benefit of some nebulous elite?

Honestly, I don’t know; it is possible the system simply feeds off itself as individual self-interests seek solutions requiring the lowest personal expenditure. I.e., it is competitive, but with goals of mediocrity (low effort) rather exceptionalism (which requires more work).

But I digress… An examination of actual questions and teaching methods aligned to these “standards” is in order.

The Implementation

The CC proponents are clear:

Screen Shot 2014-04-10 at 9.32.37 PM

So what does compliance with the standards look like (economic incentives notwithstanding)?

One example is presented by the Truth in American Education (TAE, here) in which various strategies for performing addition and subtraction are presented in a sample obtained from an elementary school. The TAE folks didn’t bother to actually comment directly, preferring to let “these speak for themselves.“; however, an analysis is necessary.

I’ve copied the pages to a gallery, below (click on any of the 13 pages to see more detail). The gallery is in no particular order other than as I found it, so I will refer to the image numbers, below, as ordered here.

I cannot find anything particularly troubling about most of what is presented. I.e., other than the terminology and the volume of information presented, the pages simply demonstrate numerous strategies for performing addition and subtraction.

At one point or another in my life I have used or “invented” each one of those “tricks” to find an answer to a problem. I’ve noticed, in the past, that Secondo used to look at the clock when working some addition and subtraction problems. There is nothing wrong with learning different ways of doing things. If I have to count using my fingers and toes, I’ll do it: I am a rocket scientist, after all.

Some solutions are more efficient than others. The point is to find reliable means for computation at which point one can clearly demonstrate an understanding.

So, is there a problem with the material? Debatably.

The terminology changes (“old language” and “new language” in Image 10) do nothing more than complicate the relationship between child and parent, to whom the child should turn with questions. I suppose it depends on the purpose of the change, for which I simply don’t have insight.

These language changes likely will not add clarity for some children; the more options there are to name things that lack apparent distinction, the less clear things become. It is not the same as describing “red” in its numerous forms as “scarlet, vermilion, crimson, ruby, cherry, cerise, cardinal, carmine, wine, blood-red; coral, cochineal, rose; brick-red, maroon, rufous; reddish; rusty, cinnamon, fulvous; damask, vermeil, or sanguine.”

Such distinctions are based on sense, perception, and experience; so while counting via addition and subtraction can be approached with the senses, mathematical concepts tend toward the more abstract end of the knowledge spectrum. Something that should be as intuitive as counting takes on the appearance of something more difficult than it is when multitudes of terms and procedures are presented.

But this is mathematics, for which the language should be precise with a common and concurrent lexicon. Children will naturally associate other terms with the actions performed, so there is no pressing need to throw this language monkey-wrench into this mix as a formality of education.

As for the number of different strategies, the impact will depend on the individual student and target age. If this paperwork is meant to represent a single lesson, I believe it is far more likely to create confusion; it’s simply too much at once. The material presents itself in an ironically formulaic manner; i.e., it seems to contradict the stated goals of seeking an understanding of the concepts.

But, other than that, there is nothing egregiously wrong with the material; it certainly approaches the topic much better than the Foundation examples did.

It’s actually possible that, in such an environment, inspired answers like Secondo’s would be explored rather than discounted. But that does really depend upon the personality, training, and experience of the teachers involved.

Which I believe gets us back to the central issue.

So, what’s the real issue?

Frankly, I like standardization; i.e., there is a need to be able to compare things and people to each other. Standardization is a means for reducing cost, realizing efficiency, and building confidence in the quality of a product.

If I believe, for a moment, that a child’s mind should be treated like a product, then standardization in education may be one way to assess the outcome. E.g., How do I know if someone does well in mathematics, or has aptitude for advanced physics, or art, or would be an ace auto-mechanic?

Having a sound basis of structure and measurement makes that possible. But there are other questions that must be asked: how does the standard get implemented? Is it the correct standard? Is it or should it be a universal standard?

Remember the claim?

Screen Shot 2014-04-05 at 2.38.35 PM

A standard, by itself, can’t do what is claimed above; i.e., in order to “make sure” students are meeting the standard, an infrastructure or central authority is needed to certify or verify compliance. This is no different than establishing full faith and credit in a fiat currency; it only has value because we say it does, and standards applied are done so with clear governance with the muscle to back it up.

And that may well lead to the principle issue: the inevitability and impact of centralization through standards. I will assert that such is a mechanism for the degradation of true diversity (the intellectual kind, not the superficial kind).

“But, no child is average!

bellcurveRelated to our discussion, the sentiment that “no child is average” was  overheard from a parent who was perturbed that her child was assessed to be an average performer.

Getting beyond the mathematical realities of averages, the take-away here is that, to some degree, every child has the potential to excel at something. I say potential because the reality is human capacity and achievement exists on a spectrum. I say something because the topics of speciality are multivariate to an uncountable degree (at least larger than I can count on my fingers and toes). Children will exist at both ends of the spectrum and points in between.

And this is a good thing.

Think of this using a genetic model. While some species can persist via asexual reproductive means, the cloning process does not produce rapid, if any, adaptability. Sure, genetic coding can be activated to compensate for some preprogrammed conditions, but only spontaneous changes and luck would allow such creatures to remain robust to wider environments. Admittedly, some of the most robust creatures have been the simplest. I.e., bacteria and viruses, despite our best efforts, survive through the brute force of numbers in the speed at which they replicate. Yet, despite their robustness, they remain simple compared with species capable of building complex relationships because of sexual reproduction; the mixing produces multiple solutions to a wider variety of conditions.

So we have two strategies for survival: be simple, clone rapidly, and let chance kick a few genes every now and then, or mix large volumes of characteristics at a lower rate to produce multiple solutions (i.e., parallel).

Yet, I believe humanity desires more than mere survival, and it is this theme that I believe reveals the potential danger of standardization in education.

The Mixing Pot

stirThe growth in humanity (as more than just another organic creature) requires achievement; if we are to become more than monkeys with car keys, our species must also develop our minds through a diversity of ideas that mimics our genetic diversity.

What I can assess, however, is that segregation on any level simply weakens the human condition. Physical segregation reduces our genetic diversity just as cultural segregation perpetuates suffering through either stereotypes, bigotry, prejudice, and racism. But what I am talking about here is more than these superficial calls for diversity.

The irony is that the attempts to standardize education to improve our academic prowess actually leads to intellectual segregation through a coerced reduction in the diversity in what is considered appropriate or necessary instruction. It’s a big country with many needs and ideas, but nationalizing the approach to education simply suppresses intellectual adaptation to the economic and social needs of specific locales.

Left alone, I believe it would be more likely that as local control remains in smaller school districts, such systems will aggregate ideas to meet concurrent needs. It is a healthy mix of ideas rather than a melting or homogenization.

Concluding Thoughts

Our educational goals remain constant: to build individuals with sufficient diversity and skills competency that allows them to adapt to their needs while also benefiting the larger social needs.

So, is there anything about CC implementation that would improve the individual student experience toward such goals?

No. Although CC has raised, correctly, the issue that problem solving can be approach in various ways (as demonstrated by the mathematics examples), I’ll assert that administration of CC will likely make the student experience worse.

The implementation of CC does not directly change the student/teacher relationship; it looks like the implementation adds complexity in the form of state-required knowledge, rather than student-driven necessity. This complexity will likely drive education deeper into the group oriented “perform or parish” survival mode as districts seek to prove themselves relative to the  standards in order to be granted incentives. This application is at the expense of students who may not be not ready for, have no need for, or no interest in specific topics. In my estimation this means that the system will continue to cater toward the large scale averages, which benefits neither the remedial or exceptional student, and ultimately represses diverse ideas.

Simply put, the system just can’t deal with students as individuals.

Most people will never need anything more than knowledge of simple arithmetic; this is especially apparent in the type of economy we have. Most people will be able to speak and write well enough to communicate and enter agreements. Some knowledge, no matter how well we standardize its dissemination, is totally irrelevant to some individuals. Yet, at the same time, through this standardization, and its inevitable implementation of equality, we risk marginalizing the exceptional students and ideas.

So, this still leaves some other questions.

Are there national strategic interests that justify centralizing standards and providing highly suggestive and incentivized guidance to the states’ curricular design?

Are national, corporate, or state interests more or less important than individual interests?

Does this centralization implied by CC serve some interest other than the people’s individual and localized community rights?

Reading through John Taylor Gatto, Charlotte Thomson Iserbyt, and Murray N. Rothbard the answers to the above are obvious: special interests seek to stratify society through control in education. There is always someone who is or desires to be at the top; such power is only served by exclusivity that all but inhibits upward mobility and practically stifles lateral mobility. Nothing happens without some control place upon it. But, at the risk of being redundant, we know this.

And, I suppose that is why we home educate: we choose not to be subject to group experimentation by some nebulous group order; we choose to treat our children as individuals, to achieve in their special ways and further benefit society with their individual brand of brilliance. While we may be deluding ourselves into thinking we are putting up “the good fight,” we are at least doing something.

We choose to let our children recognize that a circle has an infinite number of corners, no matter what the books says, or doesn’t say.

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