Developmental Divergence
from Joseph Margolis, The Unravelling of Scientism: American Philosophy at the End of the Twentieth Century (Cornell University Press, 2003), p. 15

 . . . the great question of history's constitutive role in the formation and transformation of our cognizing powers is now largely ignored . . .  

from Stanley I. Greenspan with Beryl Lieff Benderly, The growth of the mind and the endangered origins of intelligence  (Addison-Wesley, 1997), p. 167

  . . . modern social institutions and much of the technology that supports them have come to threaten the conditions that nurture intelligence . . .
from E.D. Hirsch, Jr., “The Benefit to Equity,” republished in William Schmidt, Richard Houang, and Leland Cogan, “A Coherent Curriculum: The Case of Mathematics,” American Educator, Summer 2002.

“The learning gap. . .  in academic performance between American and Asian students . . . grows wider over time, putting American students much further behind their Asian peers by 11th grade than they were in the sixth grade.  The funnel shape of this widening international gap has an eerie similarity to the funnel shape of the widening gap inside American schools between advantaged and disadvantaged students as they progress through the grades."

from William H. Schmidt, "The Role of Curriculum," American Educator, Fall 2005, p. 11.

"Retesting in 1999 and 2003 found few gains. . . . By the middle grades, the top-acheiving countries do not intend that children should continue to study basic computation skills [as they do in the U. S.].  Rather, they begin the transition to the study of algebra, including linear equations and functions, geometry and, in some cases, basic trigonometry.  By the end of the eighth grade children in these countries have mostly completed mathematics equivalent to U. S. high school courses in algebra I and trigonometry.  By contrast, most U. S. students are destined for the most part to continue the study of arithmetic.  In fact, we estimate that, at the end of eighth grade, U. S. students are some two or more years behind their counterparts around the world."

Comment # 16 from Math Gains Reported for U.S. Students by Sam Dillon (New York Times, December 9, 2008)
I was raised in France and lived in Singapore for few years with my 2 children (8 and 12). So I have a different perspective than most. An anti intelectual culture prevails in the US (Sarah Palin)when my kids were in Singapore, they were highly interested in science and Math and ranked high among their peers in the 2 topics, within 2 years after our return to the US both kids lost all interest in Science and Math.
— Nacer, Seattle

TIMSS 1995 Mathematics


Minnesota 12th Grade Results, Trends in International
Mathematics and Science Study, 1995
The Missing Data: Why Was Twelfth Grade Testing Discontinued After 1995?

This chart compares the fourth, eighth and twelfth grade mathematics test scores of a number of Asian and northwest European nations with those of the United States, grouped into three regions as indicated by the graph. This study was conducted by TIMSS (see Wikipedia Trends in International Mathematics and Science Study) in the Spring of 1995. At that time this was the largest and most thorough international study of mathematics and science education ever conducted.

Testing of 12th graders was subsequently discontinued.  

Since PISA only tests 15 year old students, a major segment of relative decline of the United States, as indicted in the 1995 TIMSS results, is unobserved.

Periodically one gets news reports such as Students Make Gains in Testing on Science, by Richard Perez-Pena (NYT, May 10, 2012)

American eighth graders have made modest gains in national science testing, with Hispanic and black students narrowing the gap between them and their white and Asian peers, the federal government reported Thursday.

But this is only for eighth graders.  (And PISA only tests ninth graders.)  Until we get international comparisons for twelfth graders, we are left in the weakened position of having to make inferences from the 1995 data shown to the right.

continued below
Figure 1 is based on the Programme for International Student Assessment (PISA) math scores from 2000 to 2009.  I have used NCES data to estimate the United States (New England) and United States (South) PISA scores.  Note that data for Shanghai and Hong Kong was available only for 2009.  I entered the 2009 score in 2003 to 2006 to get my software to produce a usable result.

Any discussion of education must start with the data, on the one hand, and the various PISA reports, on the other.  The Program for International Student Assessment of the OECD is the gold standard of international educational evaluation.  (The refusal of the partisans of school "reform" to deal with these materials--see Candy Crowley below--is striking.)

PISA 2009 Results

 Lessons from PISA for the United States, Strong Performers and Successful Reformers in Education, OECD Publishing, OECD (2011)

PISA 2009 Results: What Students Know and Can Do – Student Performance in Reading, Mathematics and Science (Volume I)

PISA 2009 Results: Overcoming Social Background – Equity in Learning Opportunities and Outcomes (Volume II)

PISA 2009 Results: Learning Trends: Changes in Student Performance Since 2000 (Volume V)

Top Test Scores From Shanghai Stun Educators   By Sam Dillon, New York Times,  December 7, 2010

What the U.S. Can Learn from the World's Most Successful Education Reform Efforts, McGraw-Hill Research Foundation.  Policy Paper: Lessons from PISA 

The bottom red line is the deep South of the United States (La, Miss, Ala).  This is the Trump zone--the socio-cognitive domain that forms the basis for the discourses of demonization and anti-modernism that have come to dominate the public sphere.  
New England (Conn, Mass, NH and Vt) is on a par with the OECD average, well below the high-performing nations of Singapore, Hong Kong, Korea, Japan, Canada, Finland, and Switzerland.  
Figure 1.  American Exceptionalism: PISA Math Scores, 2000 - 2009:
18 Nations + U.S. New England + U.S. South + OECD average
Time Magazine assesses the relative intelligence of its readers:
from The Daily Show with Jon Stewart, February 14, 2012:
TIME Magazine's U.S. Edition
"Evolution is theory, not fact," a key intellectual assertion made by the Right, should be placed  in the context of Figure 1 (PISA Math Scores, 2003 - 2009: 19 Nations + U.S. New England + U.S. South + OECD average).   The bottom red line (the U.S. South) is the Palin-Trump-Bachmann et al. socio-cognitive/rhetorical zone.  This is where the rhetorical performances of the anti-evolution crusade unfold.  (But this is only one of many expressions of anti-modernism and demonization, and is homologous with the entire set of right-wing "social issues".)

Hypothetically, one should be able to place this assertion--"Evolution is theory, not fact"-- as cognitive performativity in its correct place on the scale to the right.  Only one assumption is necessary: that correlated with higher test scores is a higher percentage of the tested population performing at the formal operational level.

It is critical to raise the question of formal operational cognitive performativity precisely because it is on the development of such competency that the fate of nations depends in the 21st century.  [James R. Flynn, What is Intelligence?  Beyond the Flynn Effect (Cambridge University Press, 2009)]  This excerpt from Cole is helpful.  For more go to developmental diveregence.

from Michael Cole, The Development of Children (W. H. Freeman and Co, 1996), p. 485

"R. Murray Thomas illustrates the difference between concrete operations and formal operations (which are said to appear in early adolescence) with the following two questions:

Concrete: If Alice has two apples and Caroline gives her three more, how many will there be?

Formal: Imagine that there are two quantities which together make up a whole.  If we increase the first quantitity but the whole remains the same, what has happened to the second quantity?  

What is striking about the rhetorical manuever "Evolution is theory, not fact," is that it is a radical rejection of the very sine qua non of modern (formal-operational) thought: abstraction and concept formation.  In the performative domain of the populist semiosphere, this amounts to the demonization of formal-operational thought as such.  The impact of this national crusade against not simply "science" but formal operational thought itself is evident in Figure 1.

Figure 1 is about more than education.  Formal schooling is only one moment in the unfolding of cognitive development, and data such as appear in Figure 1 therefore reflect the various forces that promote or retard development.*

*Pasi Sahlberg, "A Model Lesson: Finland Shows Us What Equal Opportunity Looks Like," American Educator, Vol. 36, No. 1, Spring 2012
from How the Finnish school system outshines U.S. education, by Stephen Tung (Stanford Report, January 20, 2012)

In the last decades, U.S. and Finnish education policies have appeared to be moving in opposite directions. While U.S. public schools moved to standardized testing, Finnish schools eschewed nationwide tests to evaluate teachers, students or schools, instead relying on sample-based testing and school principals to identify potential problems, Sahlberg said.

While U.S. public schools are locally funded, usually from property taxes, and rewarded based on high performance through programs such as the U.S. Department of Education's Race to the Top grants, Finnish schools are nationally funded based on the number of students. Schools are provided additional funding if they have a higher proportion of immigrants or students whose parents are uneducated or unemployed, he said.

Darling-Hammond, who wrote about the Finnish educational system in her book The Flat World and Education: How America's Commitment to Equity Will Determine Our Future, also contrasted America's test-based teaching to Finland's more flexible system.

"The [Finnish] curricula are very much focused on critical thinking and problem solving, project-based learning, and learning to learn," she said. "There is a lot of collaboration in the classroom."

[The article goes on to quote Pasi Sahlberg, a Finnish education expert and the director of the Center for International Mobility and Cooperation in Finland's Ministry of Education and Culture]

"When we compare teachers to other professions in society, we compare them to lawyers or doctors or architects," he said. "Not as here [in the United States], where they are compared to nurses or therapists, or something like that, that require lower academic training."

Teachers in Finland are required to obtain a three-year master's degree, state-funded, before teaching. These education positions are highly coveted, Sahlberg said. For example, only one in 10 primary-school teacher applicants are accepted.

"It's harder to get into primary school education than a medical program," he said.

But Sahlberg identified the biggest obstacle in the U.S. system as the same policy intended to revolutionize education. "If I could change one thing in policy, I would seriously rethink the role of standardized testing," he said in an interview with the Stanford News Service. "No high-performing nation in the world has been successful using the policies that the United States is using."
Until recently it was assumed that somehow cognitive development would keep pace with scientific, technological, and organizational change.  Increased demand from employers and institutions could somehow take for granted that the modern minds neccesary for modern work would be produced by modern society. [Flynn]      
Not so, Figure 1 suggests.  Far from being a natural and inevitable development, higher-order cognitive performativities are products of civilization and public policy, of cultural and social evolution, and of individual socialization.   Not only are such performativities not inevitable in their development, they are downright fragile.  This is because cognitive development is a subjective, conflict-laden process.  Outcomes are sensitive to a whole range of conditions of which socioeconomic variables, while important, miss much that is critical in shaping, obstructing, and perverting cognitive development among modern humans in postindustrial societies. (Ceci, OECD)

Figures 1 suggests that there are different developmental pathways for different subgroups of the world’s population.  These developmental pathways are systems-related restraints and inducements operating on the levels of psychology, culture, history and political economy.  It is in the context of such systems processes that minds emerge.  It is this systems approach that renders intelligible the actual process of cognitive development and intellectual performance, as well as the enormous developmental consequences of different configurations of inputs related to different socio-cultural and political-economic settings. 

Figure 1 ought to be viewed in the context of this excerpt from Calvin's A Brief History of the Mind.  
from William H. Calvin, A Brief History of the Mind (Oxford, 2004)

"It is just in the last 1 percent of that up-from-the-apes period that human creativity and technological capabiities have really blossomed.  It's been called "The Mind's Big Bang."  In our usual expansive sense of "mind," the history of the mind is surprisingly brief, certainly when compared with the long increase in brain size and the halting march of toolmaking." xiv 

" . . . there are emergent properties lurking in anything that produces a steep gradient. . .  I can imagine softwiring emergents in the brain intensively engaging in structured stuff at earlier ages.  The steeper gradients between rich and poor may produce surprising social effects unless we do something about the rich getting richer.  Emergents are hard to predict, and they are not all beneficial . . . " (pp. 177-78)

"Yet once our education has the techniques to incorporate what is being learned about brain plasticity and inborn individual differences, we are likely to produce many more adults of unusual abilities, able to juggle twice as many concepts at once, able to follow a longer chain of reasoning, able to shore up the lower floors of their mental house of cards to allow fragile new levels to be tried out, metaphors and beyond--the survival of the stable but on a higher level yet again."   183

"Such education, perhaps more than any of the imagined genetic changes, could make for a very different adult population.  We would still look the same coming out of the womb, would still have the same genetics, but adults could be substantially different.  A lot of the elements of human intelligence are things like that, while they also have a genetic basis, are malleable; we ought to be able to educate for superior performance."

"But at the high end, what might pump us up even higher?  If our conscisness is a house of cards, perhaps there are techniques, equivalent to bending the cards, that will allow us to spend more time at the more abstract levels.  Can we shore up our mental edifices to build much taller "buildings" or discover the right mental "steel?"" (p. 186)
Thus, instead of a cognitively homogeneous citizenry, there is developmental divergence (Nisbett, Calvin) producing fundamental differences in cognitive functioning among different historically and sociologially defined subgroups of the population.  These subgroups can be defined by the nature of their cognitive-linguistic practice, including inventories of basic expressions and rhetorical maneuvers, such as are seen in the Youtube videos of the Palin and McCain rallies, Tea Party protests, and the mass of political ads produced for TV, as well as videos of newscasts and talk show interviews. (see Part II theater of ressentiment)

The inability of American society to generate the advanced minds critical to the development of advanced capitalism is masked by the enormous inflow of skilled and educated Third World middle classes into the U. S. labor force, including those born here of immigrant parents. 

The current convergence, in the United States, of economic decline, attacks on teachers and on the public sector as a whole, and the evangelical crusade against science, might reasonably be expected to deepen this inter- and intra-national developmental divergence. Cognitive decline--the decay of structure and discipline in cognitive performativity--is well underway, and has been for decades.

The deepening crisis in cognitive development in the United States is indicated by this New York Times table ➞.  Note that as we move from the least abstract area (reading) to the most abstract (math), the relative position of the United States falls dramatically.


Such developmental divergence figures critically into understanding the rhetorical productions of political actors (town-halls mobs, tea party rallies, auto bailout Congressional debate).  The standard presupposition--that the set of all voters is cognitively homogeneous--is itself a key shibboleth of liberalism.  

Few consider the historicity, fragility, and reversibility of cognitive development.  Cognitive development is not a normative, inevitable process.  It is an effect of history as well as evolution, and can suffer reversal or collapse.  One might consider the 2011 Republican debates in this context.
bias to the abstract (math score minus reading score)

from U.S. Department of Education, Pursuing Excellence: A Study of U.S. Twelfth-Grade Mathematics and Science Achievement in International Context, NCES 98-049. Washington, DC: U.S. Government Printing Office, 1998.  Chapter 2.

One explanation for our low performance that has been suggested in the past is that, because of our diverse population, there is a greater range of scores among U.S. students, and the difference between our lowest-scoring students and our typical student is greater than in many other countries. These low-scoring students, it has been argued, "bring down" the U.S. average. Available information suggests that this is not the case in TIMSS.A

A Specifically, the difference between students with a median score (fiftieth percentile) and those at the fifth percentile is 129 points in the United States; looking at all countries, the average difference between fifth and fiftieth percentiles is 137 points. In addition, the difference between the scores of students at the fifth and ninety-fifth percentiles is similar in most countries. In the United States, 296 points separate these two groups of students, and the average difference is 292 for all 21 countries.

Development divergence is now a fundamental feature of postmodernity: the liberal-Enlightenment presupposition of a cognitively homogeneous citizenry collapses in the face of this data.  The three excerpts to the right, taken in the context of the comments of William Calvin above, are three moments in the unfolding of this developmental divergence.

The excerpt to the right provides some socio-economic correlates to this process of developmental divergence.  Nevertheless, the psychometric data qua quantitative measure does not provide a direct measure of developmental divergence, even though one may assume that the highest scoring groups have achieved the formal operational level (Flynn) of cognitive performativity, while the lowest performing groups are performing on only the concrete-operational and even the pre-operational levels.

To get at a direct measure of cognitive performativity requires a qualitative analysis of cognitive activity.  To do this we turn to the rhetoric of educational reform in the United States.  When this rhetoric is compared with the cognitive performativity of the PISA reports, the results are striking.  The U.S. rhetoric on educational reform not only does not achieve the formal operational level; it demonizes it (ie: 'poverty is no excuse').

To continue, go to Assessing the Rhetoric of Educational Reform

Former Congressman Pete Hoekstra's Super Bowl ad: consider it as an assessment of the emotional and intellectual maturity of his constituency.  


from Richard E. Nisbett, Intelligence and How to Get It: Why Schools and Cultures Count (W. W. Norton & Company, 2009)

"And we know that there is a lot of room for improvement in the plight of the poor and working class in the United States.  Their economic situation is substantially  worse than that in most developed countries."  79

"We know that the United States accepts lower levels of intellectual accomplishment for its lower-SES children than do other advanced countries.  We need to consider the SES gap in achievement in light of the unsually large economic gap between classes in the United States.  Income inequality in the United States is much higher than in most European Union countries or Japan.  Although the income per capita in the Uniteddet States is 25 to 35 percent higher than in most other advanced countries, workers in the bottom third of the income distribution are poorer than workers in the bottom third in the European Union or Japan.  And workers in the bottom 10 percent of the income distribution of the average European Union country earn about 44 percent more than Americans in the bottom 10 percent.  And even this statistic underestimates the disparity between the poorest Europeans and the poorest Americans.  Europeans have national health insurance and other economic cushions that most Americans at low-income levels either pay for out of their own pockets or do without." 83-4

"Reflecting the differences in income inequality, there is more skill disparity between the social classes in the United States than there is in most advanced European countries, as measured by literacy, mathematics, and science scores gathered by the Organization for Economic Co-operation and Development.  Americans in the top fourth of SES scored almost a standard deviation higher than those in the bottom fourth.  The comparable differences for the Scandinavian countries was less than two-thirds of a standard deviation.  Most of the difference is due to the better performance of Scandinavians in the bottom fourth of the socioeconomic distribution. The difference in reading and math skills between lower- and higher-SES groups in the United States is greater than than that for twenty-two industrialized countries that have been studied.  The difference between the United States and South Korea is even more marked: only a third to a half of a standard deviation seperates the average academic achivement of the bottom quarter on the soicoeconomic index from that of the top quarter.  84-85

"In fact, the achievement gap between the lowest 25 percent and the highest twenty five percent of Americans is more similar to that in developing countries than developed countries."  85
Best Education In The World: Finland, South Korea Top Country Rankings, U.S. Rated Average, Huffington Post Posted: 11/27/2012

Pearson's chief education adviser Sir Michael Barber tells BBC that the high ranking countries tend to offer teachers higher status in society and have a "culture" of education.

The study notes that while funding is an important factor in strong education systems, cultures supportive of learning is even more critical -- as evidenced by the highly ranked Asian countries, where education is highly valued and parents have grand expectation. While Finland and South Korea differ greatly in methods of teaching and learning, they hold the top spots because of a shared social belief in the importance of education and its "underlying moral purpose."

United States Lags in Top Math Students, Huffington Post, November 15, 2010