Today's Question

Today's question is for all you National Standards folks.

Mississippi, despite being the poorest state in the U.S., is nearly as affluent as Finland.  Why is Finland capable of setting its own educational standards while Mississipi requires guidance from the Feds?

Waiting for Petrelli's Kids

Fordham's Mike Petrelli wants all you affluent people to send your kids to inner city public schools to improve them "overnight."

More recent, and more sophisticated, “peer effects” research (by the likes of Carolyn Hoxby and Eric Hanushek) finds much the same. Rick Kahlenberg has been shouting from the rooftops that poor kids do better in “middle class” schools–which is why, in Gerald Grant’s words, there are no bad schools in Raleigh

I've heard of Spike Lee's "Magical Negro," but I've never heard of Petrelli's "Magical Rich Kid."

Now Hoxby's paper is under lock and key (Five dollars for an electronic download? Really?) and Kahlenberg and and Grant are merely spouting opinion. But Hanushek's paper is readily available. Here's the conclusion:

On average the black share of school enrollment in Texas is almost 30 percentage points higher for black students than for white students. Elimination of this gap would reduce the proportion black from roughly 0.39 to 0.16 for black students and raise the proportion black from 0.09 to 0.16 for whites. Using the coefficient for blacks of 0.20 and the coefficient for whites of 0.10, such a redistribution of students would reduce the racial achievement gap by 0.050 standard deviations in a single year. The cumulative effect of such a reduction for grades 5–7 (the sample period) depends upon the rate at which knowledge depreciates over time. If the rate of depreciation were equal to one minus the coefficient on lagged achievement (roughly 0.4 for blacks and whites), the 3-year cumulative effect of racial composition equalization would reduce the race achievement gap by roughly 14%, moving it from 0.70 to 0.60 standard  deviations.

These estimates represent extremes in the possible changes in racial compositions because they would require significant changes in residences across districts and regions for blacks. More modest, and perhaps more achievable, changes still imply substantial closing in the test score gap.

So, at best we might possibly at the extreme see an 0.10 standard deviation increase in black student performance by sending your kid to an  inner city public school.

Notwithstanding Hanushek's assertions to the contrary, a 0.10 standard deviation increase is student performance falls far short of an educationally significant result (0.25 standard deviation).  Moreover, this kind of result, meager though it is, is only obtainable in the fantasy world of a data-mined economics study.  In the real world, we're not going to see anywhere near such a large effect.  Typically, educationally insignificant effect sizes don't show up at all in the real world.  That's why we have the concept of educationally significant.

About the only thing you can be sure of by enrolling your pampered suburbanite children in an inner city school is that they will quickly learn how to catch a beating.

(Note:  Even Checker laughs at this one.)

Obama: Old Text Books Are the Problem

Really?  Did he really just say that?

"Obviously, in some schools money plays a big factor ... ," Obama said, pointing out that schools in the poorest areas often don't have up-to-date textbooks.

I guess so.


I taught my kids how to read with a 20 year old classroom textbook.  They didn't seem to notice the difference.  I did this because I knew the 20 year old textbook worked.  I didn't have the same confidence in their school's much newer textbook.  Apparently, their school thought the same; they just switched to a different book.  I don't like gambling with my child's future.  Schools don't seem to mind so much whose future they're gambling with.  That's because they aren't gambling with their own futures.


My son is using a 30 year old textbook to learn algebra.  He's teaching himself.  He's in fifth grade.  The book was intended for high school students.  He can do it because he learned elementary math well.  And, that's all you need to understand algebra.


How about history?  The most recent history we covered in school was decades old.


Science?  Lots has changed in science and our understanding thereof.  But not much of that new stuff is taught in school either.

A Fool and His Money ...

Facebook founder, Mark Zuckerberg, just unfriended $100 million by giving it away to the Newark School District ($23,000 per pupil) with no strings attached.



Isn't it great the way capitalism has a way of voluntarily divesting rich idiots from their money?

Free advice to wealthy edu-philantropists:  Your educational consultants know as much about education as you do:  Almost nothing.  Therefore, you can't trust the "means" they are advocating.  Have they ever run a successful school or school district getting successful results with the demographic group you are targeting? I didn't think so.  So, if you can't trust the "means," you can only trust the "ends" - does the reform actually work?  Where does this leave you? With a contest of course.  take your $100 million, find a cooperating city, and hold a contest.  A tenth of the prize goes to the first group that can achieve the results you desire. The remaining 90% is awarded when the reform can be successfully scaled.  Now go cruise around on your yacht.

Why do we still talk about the Black-White gap in education?

When it's pretty clear we should be more concerned with the Black-Asian gap. (And, the Hispanic-Asian gap , the Native American - Asian gap, and, what the hell, the white-Asian gap for that matter)

For one thing it would allow us to look at why Asians succeed better than all other groups.

It would also get us past the silly discrimination/oppression excuse when we use whites as the comparison group. Last I checked Asians suffered discrimination and yet that didn't seem to hold them back.

Lastly, if you're going to talk about gaps between groups, do it the right way -- express the gap in standard deviations not percentage difference.  Using standard deviations eliminates much of the mischief caused when percentile gaps are used to compared (more or less) normally distributed groups.

And, if you don't understand what I wrote in that last paragraph you don't have an informed opinion yet on education policy.

Obama: D.C. schools don't measure up to Sidwell Friends

The president, in a television appearance Monday morning on NBC's "Today" show, was asked by a woman from an audience whether a public school in his home city could measure up to the standards of his children's private school.

"I'll be blunt with you: The answer is no right now," the president replied. Obama said the D.C. schools are "struggling." There are "terrific individual schools" in the city, he said, and because he is president he could "probably maneuver" to get his daughters into one of them.

Nonsense, I say.

Take all the Sidwell Friends students and put them into a random DC public school.  Then take all the students from that DC public school and put them in Sidwell Friends.

(Don't forget the control group.)

Then cook for whatever period of time you think is needed for there to be observable results.

The result shouldn't be surprising to anyone who follows education.

The Sidwell Friends educated students will still perform as miserably as they did in their DC public school.  The Sidwell teachers aren't trained to and don't know how to educate the difficult-to-educate students found in the typical DC school.  Also, the curriculum at Sidwell Friends, is most certainly not accessible to the typical DC student.  Never has been.

On the other hand, the DC public school educated Sidwell students will perform about the same as they did back at Sidwell.  The quality of the teachers and the curriculum won't matter much.  It doesn't take a fabulous super-teacher to educate the kind of kids who go to Sidwell.  And, as far as the curriculum goes, what's being peddled at Sidwell is only superficially different (from an instructional basis at least) than the curriculum used in every other school.

Tuition-wise the DC public schools have about $26,000 per pupil to squander far more than it takes to teach students how to read, write, do basic math, and learn some content.  Sidwell is only about 20% higher and no one believes that money is needed to educate the students at Sidwell.  Everyone knows that tuition is high at Sidwell in order to keep out the kind of kids that typically go to the DC Public schools.

As far as the "terrific individual schools" in the city line goes, these are mostly magnet schools, i.e., schools that use the admissions process also keep out the the kind of kids that typically go to the DC Public schools.  Might as well call them Sidwell-lite schools.

The Problem with Most Edu-Commentary

In a simple picture ...

Still Overselling Play

I understand the allure of using play and games as a means of making learning more enjoyable for children.

I get it. I do.

These breathless stories never fail to flush out the educationally naive.  As if wishful thinking alone will improve the instructional value of children's play time activities.

This kind of child-centered learning has been tried  for a very long time and the improved learning has yet to materialize.  The technology is certainly there.  But no one seems to understand instruction well enough to use all that technology productively.

Even I find this surprising.

And yet a thirty year old critique of child-centered education techniques still remains valid today.

[C]hild-centered approaches have evolved sophisticated ways of managing informal educational activities but they have remained at a primitive level in the design of means to achieve learning objectives.

...

Child-centered approaches rely almost exclusively on a form of instruction that instructionally-oriented approaches use only when nothing better can be found.

...

This primitive form of instruction may be called relevant activity. Relevant activity is what teachers must resort to when there is no available way to teach children how to do something, no set of learning activities that clearly converge on an objective. This is the case, for instance, with reading comprehension. Although there are some promising beginnings, there is as yet no adequate "how-to-do-it" scheme for reading comprehension. Accordingly, the best that can be done is to engage students in activities relevant to reading comprehension-for instance, reading selections and answering questions about the selections. Such activities are relevant in that they entail reading comprehension, but they cannot be said to teach reading comprehension.

...

The contrast of sophistication in management and naiveté in instruction is visible in any well-run open classroom. The behavior that meets the eye is instantly appealing-children quietly absorbed in planning, studying, experimenting, making things-and one has to marvel at the skill and planning that have achieved such a blend of freedom and order. But look at the learning activities themselves and one sees a hodge-podge of the promising and the pointless, of the excessively repetitious and the excessively varied, of tasks that require more thinking than the children are capable of and tasks that have been cleverly designed to require no mental effort at all (like exercise sheets in which all the problems on the page have the same answer). The scatteredness is often appalling. There is a little bit of phonics here and a little bit of phonics there, but never a sufficiently coherent sequence to enable a kid to learn bow to use this valuable tool. Materials have been chosen for sensorial appeal or suitability to the system of management. There is a predilection for cute ideas. The conceptual analysis of learning problems tends to be vague and irrelevant, big on name-dropping and low on incisiveness.

...

Unless thinkers and experimenters committed to child-centered education become more sophisticated about instruction and start devoting more attention to designing learning activities that actually converge on objectives, they are in danger of becoming completely discredited. That would be too bad. Child-centered educators have evolved a style of school life that has much in its favor. Until they develop an effective pedagogy to go with it, however, it does not appear to be an acceptable way of teaching disadvantaged children.

The tools at educators' disposal have improved dramatically. And yet educators don't seem to know how to use these tools to improve instruction. It must be the pedagogy, the instructional know-how, that is lacking.  I can't think of any thing else.

Teaching beginning skills to children is often a mindless and dull endeavor.  Effective practice requires lots of repetition.  And, repetition is boring (at least for the adults teaching the skills).  You know what are good at mind-numbing repetitive tasks?  Computers.  It doesn't take a genius to see the potential.

The Continuing Irony of Alfie Kohn

In a long post criticizing value-added teacher evaluation, Alfie Kohn unwittingly hits us with this ironic gem.

I don't expect the founder of a computer empire like Bill Gates, or a lawyer like Joel Klein, or a newspaper editor to understand the art of helping children to understand ideas, or of constructing tasks to assess that process. I just expect them to have the humility, the simple decency, not to impose their ignorance on the rest of us with the force of law.

The irony of this statement is so dense it threatens to collapse upon itself into a sort-of black hole of irony.

I'm guessing Alfie favors his own ignorance based reforms instead of the current crop of ignorance based reforms.  But since the underlying purpose of government-run public education is to impose the will (or ignorance if you will) of those in charge politically, by definition politicians, on the rest of us with the force of law, only those politicians in charge get to pick the brand of ignorance being imposed. Those not in charge get to lament their fate and beg for humility and forbearance from those in charge.

It's the Progressive way of running things.  And, Alfie is a Progressive.  But, so is the current Administration.  Which should give you an idea of how long Alfie's brand of progressive education will be out of favor.

And, by the way, Alfie is right about the current crop of reforms being no good.  He just gets the reasons why (mostly) wrong.

The Half Billion Dollar Educational Buggy Whip

Behold.

File this one under misallocation of precious resources.

Or alternatively, under yet another reason why government should not run schools.

There's never a shortage of political reasons to justify building Taj Mahals like this.  But is there a valid educational reason?  So consider what trumped what in this case.

Stay Classy Now

Edublogger, Jim Horn, leaves the following comment on this three year old post:

Go fuck yourself.

A cogent and persuasive argument indeed.

Apparently Horn didn't like his mention in the last paragraph of the post:

P.S. Be sure not to miss the obsequious edu-blogger, Jim Horn, sucking up at the foot of the hungry master in the comments. "Thank you for your eloquent commitment to what's right for so many years ... A trusted lieutenant, should you need one. Jim Horn" What a jackass.

I'm guessing it was the jackass line at the end.

The Other Problem with Standards

"We took our licks, we got outvoted," [Republican Texas Board of Education member David Bradley] said of the last time the [Texas] standards were debated and approved in 1999. ... "Now it's 10-5 in the other direction. ... We're an elected body, this is a political process. Outside that, go find yourself a benevolent dictator."

I love the benevolent dictator part.

Standards, especially national ones, are a political beast. They will be politicized. And, about half the time your political party will be out of power. Politics are a zero-sum game. Deal with it.

Induction is not Constructivism

(Update:  cleaned up a bunch of typos and reworded the post to clarify.)

Brian Rude asks a good question,

The induction model certainly makes some sense. But isn't it another name for constructivism?

I see how Brian got confused due to my oversimplified model, which conflates inductive reasoning with the inductive-like process of the learning metaphor I proposed.  And, since constructivism relies heavily on inductive reasoning, Brian's conclusion is a fair take-away.

So, let me clarify.  Take a look at this less over-simplified schematic.

The diagram shows how a learner converts an observation of some stimulus into a thought/memory. i.e., how the learner learns. I've re-labeled the induction process I was explaining in the previous post to a a sub-induction process and added on three primary super-processes of learning: direct memory, deductive reasoning, and inductive reasoning.  (Bear in mind that this is merely a hypothetical conceptual model, what is actually happening in the brain is still largely unknown.)

The point I'm trying to get across in the model is that the observed stimulus ALWAYS gets transformed as it becomes knowledge.  I could have used an alternate model and placed the sub-induction directly under the "direct memory" process and indicated that the "sub-inductive" process was subsumed in the "deductive" and "inductive" reasoning processes to get the same point across.  Something like this.

I think the first diagram is conceptually clearer.  The main take-away for either model is that there is no direct access into the brain.

The learning flow would go something like this:  1. learner observes stimulus, 2. learner processes stimulus via one of the super learning process, 3. learner  then the sub-learning process, and 4. then the extracted "knowledge" goes into the learner's memory.

How the observation is made or how the stimulus is presented to the learner determines what super-process the learner will use.  Let's look at some examples (now would be a good time to review these three posts on the nature of knowledge).

The teacher tells the learner the following fact (i.e., a verbal association): "The U.S. Constitution was written in Philadelphia."  The learner learns this fact via direct memory (I couldn't think of a better name, sorry).  However, the verbal statement does not merely get imprinted in the learner's memory verbatim (not that anybody seriously believes this in any event).  The fact gets abstracted by the sub-induction process into the learners existing knowledge, something like this:

The knowledge is the connection.

This knowledge could have been learned other ways as well.  Let's say the learner has been exposed to the following two facts: that "the U.S. Constitution was written at the constitutional convention" and that "the constitutional convention was held in Philadelphia."  From these two facts, the learner can use deductive reasoning to deduce that  "The U.S. Constitution was written in Philadelphia."

How about another one: learning a rule relationship.  Here's the rule: "the steeper the inclined plane, the less time it takes the ball to roll down the inclined plane." This rule can be learned deductively or inductively.

In the deductive method, the teacher might start off with: “The question is, Is there a connection between how steep an inclined plane is and how long it takes a ball to roll down it?”

The teacher then tells the student the rule-relationship (the steeper the inclined plane, the less time it takes the ball to roll down the inclined plane) and then show examples using inclined planes of different angles. These examples would confirm the rule. The knowledge of the rule is processed by the learner through the deductive reasoning process and then stored via the sub-induction process. (Sorry, no fancy connection map this time.)

In the inductive method, the teacher has the learner do an experiment by rolling balls down inclined planes of different angles, measuring how long it takes each ball to roll down, and then has the learner draw a conclusion.

This way requires more skills. (In the deductive method, the learner merely compares examples with the rule. “Yup, the ball takes less time when the angle is steeper.”) For example, the learner has to change the angles, measure the times, write the measurements, compare and contrast the instances, and figure out the connection. This means the teacher would have to teach these pre-skills before learners do the experiment.

The knowledge of the rule is processed by the learner through the inductive reasoning process and then stored via the sub-induction process. However, the learner takeaway is the same, that is, the connection mapping in the learner's memory is the same.

Which finally brings us 'round to constructivism.

Stripping away all the pedagogical blather, constructivism is merely a teaching pedagogy that favors learning through inductive reasoning as the preferred pathway.  Constructivists favor learning by experience or by doing. This means that the learner will be observing stimuli (examples and non-examples of something) and generating general ideas revealed by the examples and non-examples.  Hey, that sounds suspiciously like inductive reasoning.

Here's what I wrote about the inductive reasoning process that learners go through when they observe a stimulus during the learning process.

Knowledge is not directly transferred into a learner, but rather knowledge is acquired indirectly through an inductive process. Specifically, knowlege is typically acquired through an "inductive reasoning" process.

That is, the learner observes stimuli (examples and non-examples); (2) performs a series of logical operations on what it observes; and (3) arrives at (induces, figures out, discovers, “gets”) a general idea revealed by the examples and nonexamples.

In contrast, direct instruction relies more heavily on deductive reasoning pathway for teaching certain forms of knowledge, such as rule relationships. Using deductive reasoning, the learner goes from general (rule) to specific (examples). In the deductive method the teacher teaches the rule statement first. Then examples and nonexamples are then presented. Then the teacher tests all examples and nonexamples to see if the learner has learned the rule.

Constructivism can be faulted for many things, but its reliance on the inductive reasoning pathway of learning is not one of them. That is a perfectly valid pathway which proponents of direct instruction use (such as for teaching sensory/basic concepts). Constructivism's faults lie elsewhere -- over-reliance on the induction method of teaching and generally a failure to attend to the important minutiae of teaching for determining whether the learner has learned the intended knowledge and is retaining it. The latter is a self-imposed error based on ideology because constructivism makes it more difficult to get the minutiae right.

Common Core Standards Released

Here they go.  Ta Da.

I remain unimpressed.  Frankly, I don't see how these standards are going to be the impetus to improve any aspect of education.

As a lawyer I occasionally draft contracts and, let me tell you, you have to use much more precise language than this to actually get someone to reliably do what you want (and are paying) them to do.

I'd bet that all fifty states could adopt these standards, not change a single thing they are doing, and claim compliance.

Some of these standards are incredibly silly.

Take for example this one under print concepts for kindergarten (p. 16)

Demonstrate understanding of the organization and basic features of print. ... Follow words from left to right, top to bottom, and page-by-page.

This looked familiar to me and sure enough Minnesota had (has) a similar standard.

Follow print (words and text) from left to right and top to bottom.

Bob Dixon lampooned Minnesota's standard as being ridiculous and I'm thinking the same criticism applies to the Core standard.

Students should certainly do this when learning to read. My question is this: Before Minnesota developed this standard, was anyone there not teaching kids to read English from left to right and top to bottom? Apparently. The people who sat on that committee and collectively decided to write this out as a standard for the children of Minnesota—did they feel literate and scholarly and innovative when the final vote was tallied? I hope this standard makes a significant contribution toward correcting the problem with the way people used to teach reading in Minnesota.

This sentiment applies to pretty much all of the Core standards, even the less ridiculous ones.

In fact Dixon's criticism of the Standards movement is one of the best I've seen and applies to Core's standards.

These standards are harmful because they are, for the most part, meaningless verbal detritus on the one hand, but textbook publishers live and die off them, on the other. Even with respect to clearly incomprehensible standards, publishers have to come up with something to stick in a textbook that helps create the illusion that the textbook is aligned with some set of standards. I am empathetic with the publishers … to a point. The standards are a major incentive for the publishers to produce crap. Over the years, I’ve worked with several major publishers, and none of them has aspired to produce crap. They do it, though, because the market demands that they do it.

And standards and state tests, taken together, are very harmful. First, because the standards are so bad, it is nearly impossible to assess them. In short, the standards and the state tests don’t align, except in the most meaningless and specious ways. But here is the biggest problem of them all, and the reason the tests and standards are so damaging. IF the standards were really “good” according to some criteria that would make sense to the average educated person on the street, and if they were precise enough to be aligned with assessment tools that were actually technically sound, widespread failure would continue, unabated. Figure 1 shows Doug Carnine’s illustration of the problem.

The black box in the middle is the magic by which teachers start out with goals for students and end up with students performing brilliantly on tests that are valid and reliable. The black box is the instruction, and the states and just about everyone else are so clueless about instruction that they give it very little attention. With the best standards and the best assessments, the system is doomed to failure if, at the center of it all, we don’t have the best instruction. As it stands now, the standards are, for the most part, ridiculous, and few if any of the state assessments have been certified as valid and reliable.

So using the inductive learning model to judge the effectiveness of Standards reform, let's evaluate standards as an education reform.
 
Standards aren't going to affect teacher or student effectiveness.  The  theory is that standards will improve curriculum effects.  But, I don't see that happening.  Standards, like the Core standards, that are easily subvertible will be subverted and educators will continue to do what they are presently doing -- because that's what they want to do.  And if NCLB 1.0 taught us anything, its that standardized assessments, even the high stakes variety, are simply not capable of improving student outcomes.  At best, improved standards and perfect assessments, might have a very indirect effect on curriculum and instruction.  Just because you write the perfect standard does not mean that educators will be able to teach it to the kids who they are currently unable to teach it to today without the standards.

Induction/Inferential Model of Learning

I've revised Downes' Induction Model of Learning schematic to incorporate my clarifications.

Specifically, I added the labeling for Teacher Effects (the top coil), Student Effects (the bottom coil), and Curriculum/Presentation Effects (the distance between the coils).

In the real world electronic circuit, current flowing through the top coil creates a magnetic field.  The magnetic field affects the bottom coil (depending upon the distance between the coils and the strength of the coils) which induces a current in the bottom circuit.

The model is not without its flaws; however, I think it is useful for conveying the simple notion that knowledge is not simply pumped directly into the student's head by the teacher.  Instead, the student observes the stimulus/data being presented by the teacher and induces "knowledge."  Hopefully, that "knowledge" is the  general idea revealed by the example(s) presented by the teacher.  Often it is not.

Anyway, the important take-away revealed by this model is that teacher effects, student effects, and curriculum/presentation effects are all interrelated and affect what the student learns, doesn't learn, or imperfectly learns.

A strong teacher and an average curriculum might only be able to induce the intended knowledge in a strong student.  Improving the curriculum will likely reach weaker students.  Improving the student, say by fixing his tooth ache which was causing a distraction, might also improve what the student learns.

Similarly, a strong teacher and a strong student might be hampered with a very weak curriculum.

Let me make three general statements regarding teacher effects, student effects, and curriculum/presentation effects based on my observations of our education system.

Teacher Effects:  We don't really know what makes a good teacher better than a bad teacher and we certainly cannot train a random teacher to be a good teacher outside the parameters of a specific curriculum.  teacher unions and tenure resist changes from the status quo.

Student Effects:  Have a hereditary/genetic and an environmental component, each contributing about 50%.  it is politically incorrect to even discuss the hereditary/genetic component so everyone pretends that there is only an environmental component.  Then everyone is surprised when environmental interventions directed to the student fail to achieve the expected benefits.

Curriculum/Presentation Effects:  To a naive observer there appear to be very many different curricula out there.  In actuality, most curricula are only superficially different and have little to no effect on what a student learns.  The few commercially-available curricula that have large effects are generally disfavored by educators for a variety of reasons (usually unrelated to student learning)

What do you think/

Next post will discuss education reforms and how they are explainable with the above model and why it is evident that most do not stand a chance of improving student outcomes

Why It's So Difficult to Improve Educational Outcomes

To understand the problems of K-12 education, that is getting students to learn what we think is important for them to learn, and the great historical difficulty we've had improving education outcomes, you need to look at ground zero of the learning process.

I like Stephen Downes' metaphorical induction model of knowledge of learning (with my clarifications).  If you haven't already, go read it and don't come back until you understand it. I'll reproduce the diagram below.

There are three important factors in this model. 

1. The top inductor representing teacher (or resource) effects.  Following the electronics metaphor, a teacher (or resource, such as a book) with more windings is more capable of transferring data to the student than a teacher with less windings.  The inductor windings represent teacher effectiveness.
2. The bottom inductor which represents student effects.  A student with more windings will be more capable of inducing a transfer of data from the teacher/resource than a student with less windings.  The student windings represent cognitive ability and other student factors.
3. The distance between the two inductors represents the presentation of the data from the teacher/resource to the learner/student.  I've termed the distance the "inductive gap."  The teacher presentation represents what actually takes place in the classroom that effects learning.  It is the curriculum, the classroom management, and pedagogy.  A poor presentation makes learning more difficult by increasing the distance between the teacher and student inductors.  A good presentation reduces the distance, making learning more likely.

The benefit of the above model is that not only does it capture most of the important variables, but it also illustrates that what the teacher intends to teach (the data) is not necessarily what the student has actually learned (knowledge).  This is because it it is difficult for the teacher to ascertain what exactly the student has learned.  Such feedback can only be ascertained indirectly with imperfect testing instruments.  This feedback must also be properly interpreted by the teacher. (The drawback of the model is that it relies on the reader's knowledge of the operation of a rather esoteric electronics circuit.)

Complicating matters even further is that the model is different for each piece of data that the teacher wants transferred to (i.e., learned by) the student.  Thousands of these transferences must take place during the K-12 cycle.

Moreover, the model ignores student retention effects.  Just because the student has actually induced the intended knowledge from the teacher presentation does not mean that the knowledge will be retained by the student.  The ravages of forgetfulness are brutal and must be contended with by the teacher.  Often retention is ignore or, worse yet, derided by educators ("drill and kill").

As Stephen Downes puts it, what teachers are really doing is training a neural net in each student's brain.  That training does not happen instantaneously.  It happens over time and is imperfect.  See Willingham's article on inflexible knowledge. This makes the teacher's interpretation of the learner's feedback even more difficult as the neural network is being trained.

To help understand how the model plays out in the real world and it's implications for instructional design and how the "inductive gaps" affect the learning process, I'm going to provide a lengthy quote from Zig Engelmann's upcoming book.  In the passage Zig calls the inductive gaps "inferential  gaps."

[We] have learned from extensive applications that nothing may be assumed to be taught to at-risk children unless it appears on at least three consecutive lessons...When we apply this formula to the first draft of the material, we presume that when the program is field-tested, our estimates will be confirmed. However, we remain perfectly aware that in some cases the practice estimates are wrong. They may vary in either direction—providing too much practice, or providing too little. More frequently the error is in the direction of too little practice.

An important issue that we must address in creating a sequence of activities is how large the inferential gaps are between one exercise type and the next type in the sequence…

… If we were to unintentionally design a program with enormous gaps for teaching reading, we might first teach letter names, teach the short sounds for the vowels, and then require learners to sound out regularly spelled words like run and hat. Obviously, the gap between the exercise types is large because students haven’t been taught the sounds for the consonants, or how to blend the sounds together to identify words.

Although some bright students may be able to formulate workable inferences about how to derive the sounds from the names of some consonants, most students will fail the instruction because of the large gap between what they know and what they are expected to do. Discovery learning assumes that students are able to fill large inferential gaps between what they know and what they are expected to learn. Proponents of structured instruction believe that only small sequence-related inferences are appropriate.

Note that there will always be inferential gaps between exercise types. The only issue is how large they are. This is an empirical issue. If we believe that students should be successful, we would design instruction so the inferential gaps are small enough for students to succeed. If students do not succeed, their failure suggests that the inferential gaps are too large, which means that the sequence should be redesigned to make the gaps smaller. Direct observation of how students respond to a sequence is necessary because that is often the only way these gaps are identified. Typically students are progressing through a sequence well and then encounter an exercise type that is too difficult for them. If the exercise seems clear and apparently provides adequate practice, the problem is not with this exercise type, but with the sequence of activities. In other words, student performance implies that there is a gap in the sequence that is too large for the students.

As suggested above, the size of reasonable gaps is not the same for all students. The children we have worked with have ranged from those who could not take even the smallest imaginable steps without considerable practice, to children who drew correct inferences that were far in advance of what they had been taught.

At the extreme low end was a pair of twins who had spent the first four years of their lives with virtually no human contact and who could identify some real objects, like a shoe, a ball, and a cup, but could not identify any two-dimensional representations. Even when the teacher prompted the relationship by holding a red ball next to a picture of a red ball, the children could not identify the object in the picture. After many trials, they could identify pictures of balls, shoes, and cups without the corresponding three-dimensional object next to it; however, these children had to practice identifying more than 10 illustrated objects before they could generalize and identify an illustrated object that had not been taught.

At the other extreme are the highly talented students who make a mockery out of the three-lesson rule. They learn names of new things in only a couple of trials and are able to take great leaps from what they know to remotely related inferences they are scheduled to learn much later.

If the designer assumes that every minor variation in what is to be taught requires explicit instruction, the instructional sequence may be many times more laborious than it needs to be for the average learner who goes through the program. On the other hand, if the designer makes elitist assumptions that characterize analyses of Dewey and Bruner, the inferential leaps required by the program are so large that they may be made by fewer than one fourth of the students. For example, a math program that presents a single example of each problem type assumes that students will formulate an algorithm for solving the problem presented that will generalize to the full set of related problems that are not taught. In fact, possibly only one fourth of the average students will solve the problems or benefit from the experience of struggling with them. The percentage of low performers making this leap is virtually zero percent.

The only way to determine whether the program is highly effective with the intended student population is to provide an empirical test of the sequence. This test will not only identify the missing inferences but will reveal both their character and size. In other words, they provide the designer with precise information about how to address the missing inference.

I'm going to highlight one observation from Zig's passage:

The children we have worked with have ranged from those who could not take even the smallest imaginable steps without considerable practice, to children who drew correct inferences that were far in advance of what they had been taught.

This is the one that does quite a bit of educational mischief.  Educators draw all sorts of bad conclusions from the students who can draw "correct inferences that [are] far in advance of what they had been taught" and apply those conclusions to the students who cannot "take even the smallest imaginable steps without considerable practice." 

But I don't want to get too ahead of myself just yet.

In my next post I'll discuss how the various ed reforms are doomed to failure since their real world effects often fail to address or have limited effect on the real educational variables as illustrated in the above model.

A Bridge Too Far

Over at Bridging Differences, Deb Meiers writes:

That was an amazing and surprising find re. Milwaukee charters. I thought that at the very least they'd get the advantage of being in a more diverse (integrated) setting with more middle-class kids and that being chosen (even by lottery) would produce a kind of halo effect. Why it didn't is what should baffle the media. But it doesn't.

I comment:

Or perhaps, your implicit assumption that diverse (integrated) settings with more middle class kids confers an educational advantage which leads to improved student performance is invalid.


The assumption rests on shaky empirical support in the first place. So, one would think that this additional piece of potentially-negative evidence might lead an un-biased thinker to question her underlying assumptions. Why it doesn't baffles me.

PS: This might be one of the best examples of irony I've ever seen in an education blog.

PPS: It's also a good example of why we never make any progress in education. Policy thinkers become so wedded to their pet assumptions and will bend over backwards to discount contrary evidence. Classic Confirmation Bias.

Today's Cartoon

Same as it ever was -- continued

The Obama administration has posted "a series of documents outlining the research that supports the proposals in its blueprint for revising the Elementary and Secondary Education Act (ESEA)."

Here is the document for Career- and College-ready students analyzed in my last post.

Embarrassingly, the document doesn't appear to cite any actual research.  More embarrassingly, what the document sets out as research clearly isn't research.

I wonder if these documents were submitted to the What Works Clearinghouse for review?

From the Department of Huh?

Some cognitive dissonance from Secretary of Education, Arne Duncan.

The No Child law, passed in 2001 by bipartisan majorities, focused the nation’s attention on closing achievement gaps between minorities and whites, but it included many provisions that created what Education Secretary Arne Duncan on Friday called “perverse incentives.”


In an effort to meet the law’s requirements for passing grades, many states began dumbing down standards, and teachers began focusing on test preparation rather than on engaging class work.

“We’ve got to get accountability right this time,” Mr. Duncan told reporters Friday. “For the mass of schools, we want to get rid of prescriptive interventions. We’ll leave it up to them to figure out how to make progress.”

So, let me get this straight.  Under NCLB 1.0. states were permitted to set their own standards and assessments.  In other words, the Feds "[left] it up to[the states] to figure out how to make progress." And, many states chose to create "dumbed down standards" due to "perverse incentives."
 
Fair enough.  This time DoE wants to pressure the states into adopting national standards.  Clearly, the Feds with their long history of educational success know much better how to educate than the states.
 
But now when it comes to meeting those tough new federal standards, Arne wants to again "leave it up to [the states] to figure out how to make progress."  Even though they weren't doing such a good job of making progress towards their own dumbed-down standards. 
 
Reading First failed, not because it was too prescriptive, but because it wasn't prescriptive enough.  States got to figure it out for themselves how to select/develop interventions as long as they made it appear to to be based on evidence.
 
The game for states, in case anyone hasn't figured it out yet, is to appear as though they are doing something important, pretend to care an awful lot for the children, appear to follow the scientific evidence, let the chips fall where they may, wait for someone to come up with a new politically correct narrative to explain why some external factor caused them to fail, and agitate for a kinder,gentlerNCLB 3.0 
 
NCLB 2.0:  Reading First but with even less oversight and compliance.
 
Now that's what I call smart regulation and failing to heed history's lessons.