‘A Recipe for Idiocracy’

What happens when even college students can’t do math anymore?

 

 

Disturbing piece in The Atlantic. 

For the past several years, America has been using its young people as lab rats in a sweeping, if not exactly thought-out, education experiment. Schools across the country have been lowering standards and removing penalties for failure. The results are coming into focus.

Five years ago, about 30 incoming freshmen at UC San Diego arrived with math skills below high-school level. Now, according to a recent report from UC San Diego faculty and administrators, that number is more than 900—and most of those students don’t fully meet middle-school math standards. Many students struggle with fractions and simple algebra problems. Last year, the university, which admits fewer than 30 percent of undergraduate applicants, launched a remedial-math course that focuses entirely on concepts taught in elementary and middle school. (According to the report, more than 60 percent of students who took the previous version of the course couldn’t divide a fraction by two.) One of the course’s tutors noted that students faced more issues with “logical thinking” than with math facts per se. They didn’t know how to begin solving word problems...

Things are not good. Read the entire Rose Horowitch essay. U.S. education at all levels—public and private—is increasingly enervated.

 

I'll quickly go back to some of my own experiences as a high school and collegiate student, from a prior riff on LLM AI and "fluency."

I was an unremarkable "B" student in high school (1960-64). Opted to not attend college and instead went out on the road as a guitar player in a bar band.

Sixteen years later I entered undergraduate school at Tennessee. Divorced, custody of my two daughters, nothing to put in a resume.Time to make a substantive change.

Upon enrollment I took the CLEP Exam (College Level English Proficiency), a lengthy multiple-choice "reading comprehension / vocabulary" diagnostic with an essay section (topic unknown to the examinee ahead of time). At the time (1980), the national 99% percentile was 920.

I scored a 965.

That simply had to be a reflection of my compulsive reading habit, which had gotten fully underway by 1967, when I arrived in San Francisco and became fully politically aware. Didn't hurt that I lived in North Beach a few blocks west of the venerable City Lights Bookstore.

Across my adult life since that time I have continued to read 2-3 books a week on average, a broad range of periodicals, and, increasingly, all of the internet-based written material now widely available to all of us (i.e, our LLM "training data").

My AI/LLM joke now is that "I'm a Carbon-Based Relatively Large Recursive Language Model," a "CBRLRLM." A one-man "Fluency Heuristic," I suppose.

Got my undergrad at 39 and moved on to the white collar world.

My initial undergrad goal was to obtain a degree in advertising. I'd become a fairly adept photographer and learned some basics in print layout technique from a colleague guitarist who also had a degree in architecture from Auburn. I read everything I could find on the topics at the Knox County library.

My precise interest was focused on "B2B," corporate / industrial communications. While I enjoyed courses in copywriting, ad design, commercial TV production, etc, the UTK Ad Department was totally consumer products and services oriented. I had little enthusiasm for selling shampoo, cars, food & beverage, or tobacco products.

Coursework in deductive logic, inductive logic ("lying with statistics" according to my prof), philospohy of science, the gamut of stats classes, and the breadth of psychology curricula diverted my attention, with an eventual concerted study in "psychometrics" (psychological tests and measures design and empirical validation).

Then in January 1986 I got my first day gig. Systems programmer and QC analyst in a radiation lab in Oak Ridge.

Go figure.

I eventually engaged in other technical writing fields...

The training of a CBRLRLM 

 

And then...

 

After getting my Master's, I got to teach collegiate "critical thinking" for 5 fun years (1999 - 2004) while living in Las Vegas (evening school adjunct faculty; my day gig was that of a credit risk analyst in a bank). I never really liked the curricular title. I'm likewise guarded about cavalierly using the word "idiot."

Too many of my students came in thinking "oh, cool, we're just gonna argue about stuff endlessly and get our gripes off our chests..." 

Also, "idiot" is not a dtrect synonym for "stupid," notwithstanding common invective usage. Greek "idios," aware of only one's self. Yeah, one could argue that such egocentric fixations are "stupid:" I suppose, but, dunno, brosdly.

As that goes to the current Atlantic article topic, I would repeatedly look out over my Critical Thinking classes and think "man, half of y'all need to re-take high school."

 

It was by no means irascible, cynical snark. UNLV had admitted that 60% of incoming frosh found themselves promptliy remanded to remedial English and math.

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BACK TO THE ATLANTIC PIECE 

...Many schools across the country have shifted toward making math engaging for students at the expense of evidence-based teaching practices. And due to funding shortages or misguided efforts to improve equity, many students are held back from taking the hardest math courses.

The pandemic supercharged the decline. Districts that spent most of the 2020–21 school year mandating remote learning saw students fall more than half a grade behind in math; districts that reopened earlier saw more modest declines. These difficulties prompted teachers to further relax their standards. “Everyone was just exhausted and challenged by the circumstances around the pandemic,” Joshua Goodman, a Boston University professor of economics and education, told me. “And I think one of the reactions to that was for everyone involved to say: ‘Let’s lower our expectations. Let’s make sure that we don’t fail students when they’re not doing their work, because the world is challenging right now.’” Many districts adopted a “no zeros” policy, forcing teachers to pass students who had little command of the material. One study of public-school students across Washington State found that almost none received an F in spring 2020, while the share of students who received A’s skyrocketed. Math grades have remained elevated in the years since.

Together, these changes meant that even as students’ math preparation was stagnating, their grades were going up. The UC San Diego report notes that more than a quarter of the students who placed into the elementary- and middle-school-level remedial course last year had earned straight A’s in their high-school math classes. Almost all of them had taken advanced math courses in high school.

At the same time, the UC system eliminated its best tool for assessing students’ academic preparedness. In 2020, system leaders voted to phase standardized-test scores out of admissions decisions. They argued that the tests worsened racial divides and unfairly privileged wealthy students. But SAT and ACT scores are the most reliable predictors of a student’s math ability, the report found. “It’s not really surprising, then, that you’re going to be admitting more students who aren’t ready for mathematics, because you removed the one piece of data that would have told you that,” Morgan Polikoff, an education professor at the University of Southern California, told me. That same year, the UC system dramatically increased the number of students it enrolled from under-resourced high schools. These students are much more likely to place into Math 2, the elementary- and middle-school-level remedial course.

The new report calls on the UC system to consider reinstating the use of standardized-test scores in admissions, and for UC San Diego to bring its enrollment of students from under-resourced schools back in line with that of other selective UC colleges. “Admitting large numbers of students who are profoundly underprepared risks harming the very students we hope to support, by setting them up for failure,” the report observes.

Bringing back standardized-test scores might help elite institutions get out of the remedial-math business, but it will not address the underlying problem of widespread innumeracy.

Standardized admissions tests remain frequently viewed as a component of the minorities-stifling "woke faux-meritocracy" academic canard. More on that in a bit.

 

CAM3 ASSOCIATES

 

At UTK, I signed up for undergrad "Social Psychology."

The instructor, Michael K. Smith, was a doctoral student GTA. I subsequently served long-term as as his principal undergrad research assistant. His PhD effort comprised a broad and deep study on the salient psych elements of "math anxiety" afflticting undergraduate students.

We became fast friends.

And then business partners in an "Exam Cram" A/V production company. Mike, who'd been doing a long side-hustle of exam prep courses (PSAT, SAT, ACT, GRE, etc) was the Prez & content developer.

I was co-counder, VP, Producer, Director, Editor, Ads & Packaging Designer, Office Mgr, Customer Service Rep, Shipping Clerk and overall gofer. I built our A/V studio.

We Princeton Review wannabees scuffled for 5-6 yrs, managed to break even at about $600k. We pretty much sold to Guidance Departments and libraries (never could accrue the $$$ Juice to go consumer-national). The experience was priceless. Mike remains one of my favorite people.

Hence my interest in the Horowitch topic. I've learned standardaized exam development, validation, and administration rather thoroughly. Power, speeded, recall, recognition, internal/external validity, the gamut.

 

They remain widely regarded as "aptitude tests." (e.g., tangential IQ proxies). They are in fact "achievement tests." You can in fact train for them.

 

What of salience the  examinees have usefully "achieved" is a separate, inadequately addressed question. 
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Also during my undergrad days, I took physics. The professor was from Greece. Final exam? Three physics problems. No formula sheets or other crib stuff, no partial credit. My young classmates were horrified. He shruggingly asked "would you feel comfortable driving across a bridge designed by an engineer who got through college on "partial credit?"

 

I had to laugh. He also recounted his college student days in Greece: "You attend university for 4 years, and at the end you take 2 weeks of general exams. Pass/Fail. They want to see whether you actually learned and retained anything."

 

In the States we have kids slavishly honing their (ordinal metric) GPAs to 4 decimal places every quarter or semester.

 

Lordy. Yeah, right, that final one-ten thusandth of a GPA is gonna get me into Hopkins Med School or Harvard Law.
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UPDATE. AI IN THE COLLEGE CLASSROOM

 

'eh? 

 

Stay tuned...

Sentience? Perception? Cognition? Knowledge?

"Intelligence?" "Educability?"

   

WHAT DOES IT REALLY MEAN TO LEARN?
A leading computer scientist says it’s “educability,” not intelligence, that matters most.
Joshua Rothman, Aug 27, 2024, The New Yorker

... Arguably, it’s one of the tragedies of humanities education that so much of it occurs between the ages of eighteen and twenty-two. We don’t teach people to drive at twelve, when they’re carless; why should we make them read novels about life’s regrets when they have none? Yet there’s a theory behind the assignment of “Middlemarch” to sophomores: it’s that knowledge acquired too early gets stored away. Patterns of thinking established now will be retraced later; ideas encountered first in art will prime us for the rest of life. This sounds chancy and vague, until you reflect on the fact that knowledge almost never arrives at the moment of its application. You take a class in law school today only to argue a complicated case years later; you learn C.P.R. years before saving a drowning man; you read online about how to deter a charging bear, because you never know. In the mid-twentieth century, Toyota pioneered a methodology called just-in-time manufacturing, according to which car parts were constructed and delivered as close as possible to the hour of assembly. This was maximally efficient because it reduced waste and the cost of storage. But the human mind doesn’t work that way. Knowledge must often molder in our mental warehouses for decades until we figure out what to do with it.
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Leslie Valiant, an eminent computer scientist who teaches at Harvard, sees this as a strength. He calls our ability to learn over the long term “educability,” and in his new book, “The Importance of Being Educable,” he argues that it’s key to our success. When we think about what makes our minds special, we tend to focus on intelligence. But if we want to grasp reality in all its complexity, Valiant writes, then “cleverness is not enough.” We need to build capacious and flexible theories about the world—theories that will serve us in new, unanticipated, and strange circumstances—and we do that by gathering diverse kinds of knowledge, often in a slow, additive, serendipitous way, and knitting them together. Through this process, we acquire systems of beliefs that are broader and richer than the ones we can create through direct personal experience. This is how, after our first divorce, we find that we can draw on wisdom borrowed from English literature...

Interesting. Particularly in the wake of "The Death of Truth."

And head-scratcher stuff like this.

What?

 

Well, we can safely assume she's referring to human sensory cognition. What might this infer? ALL perceptions are illusory? Irrespective of organ input channel(s)? Across ALL iincoming topical information in need of accurate cognitive consensus resolution?

So, all perceptions are illusory? 'scuse me, but that stuff long been the tedious bane of undergrad Philosophy 102.

"There are no objective truths. Everything is subjective. Except, of course, for THIS assertion."

 

OK, then...

Necessarily assumes revealable truths?

…Recognizing that we process different belief systems in our brains in similar ways does not mean that they are to be treated as equivalent. There is no contradiction in an individual differentiating among belief systems as being worthy or not of their support.

Science as a Belief System
Fluency with belief systems gave humans the opportunity to develop the advanced technological civilization that we have. While the power of science is for all to see, the reasons it has been so productive in the past are not so self-evident. Even less obvious is what we need to do to keep the benefits of science flowing in the future.

Science is a belief system. A critical component of it is the idea that there are important patterns in the world that are not readily visible but are worth the effort to discover. That there is a moderate number of chemical elements and all materials on Earth are composed of these is not self-evident and had to be demonstrated through ingenuity and labor. Similarly, the bacterial and viral causes of disease are not obvious to the eye. The individuals who made these discoveries believed that useful but well-hidden patterns existed and could be found.

Science as a belief system, even when pursued by imperfect self-interested individuals, has strong self-correcting tendencies. An announcement of any significant result will prompt other scientists to seek to verify it by repeating the experiment or analysis. Also, there is usually wide agreement on the interpretation of an experimental result or an analysis with respect to a relevant question. These two facts in tandem keep the scientific enterprise on track, despite all the mistakes that may occur along the way. They also keep the incidence of fraud to a low level and the influence of any one such fraudulent act usually to a short duration…

…The reasons science works so well are more to do with the world to which it applies than the particular way humans approach it. Science might be compared to a gold mine where each field of science is a vein. Near each vein of well-established science, so much more new science can be unearthed. Venturing beyond these known productive veins gives less predictable results but can lead to new even more productive veins.

No human activity or judgment occurs in isolation. They all occur in the context of some belief system. For any judgment or activity, one ought to declare the context in which it can be justified. For example, the perspective of this volume is the science belief system from a computational perspective…

The Scientific Revolution
While the gift of educability may yet bring humanity to its destruction, it has also led to great triumphs. Educability is a capacity that has taken a long time to have its impact. The possibility of accumulating knowledge discovered by others and creating new knowledge from it may have existed for hundreds of thousands of years. Eventually this gift spectacularly caught fire as the Scientific Revolution, which unfolded in the sixteenth and seventeenth centuries. Its principal protagonists lived in different corners of Europe, employed variously by universities, rulers, and religious entities, or living on personal wealth. They had Latin as a common language. They published their work in printed books, a technology invented not much earlier. They read one another’s work. Clubs and meeting places arose to bring together local groups of scientific researchers in Italy, Spain, England, Germany, and France. By the late seventeenth century, these had evolved into academies, including the Royal Society in London, the Académie des Sciences in Paris, and the Leopoldina in Germany.

Why this unique event, the Scientific Revolution, took place exactly when and where it did, some three hundred thousand years after the emergence of our species, is open to debate. The precipitating event was not a genetic mutation in fifteenth-century Europe…

…Humanity is finally exploiting the gift of educability in a systematic way and on an industrial scale. At the same time, it is enjoying all the benefits the new scientific knowledge provides.

It is quite possible that further improvements can be made in the scientific research process itself.4 A scientist needs access to previous knowledge, convenient ways of isolating those pieces that are relevant to the research question at hand, and new ideas. The sharing of information on the web and the use of search engines have already had important effects. Scientists can now more rapidly follow what is happening in their field, which will have orders of magnitude more participants than Kepler or Newton had to follow. Digital technology may well be launching a phase of scientific progress that is even more intense than before. This is not just because of all the opportunities computers offer for simulating scientific theories and detecting patterns in data, but more simply because digital technology offers another revolution in the dissemination of knowledge.

Equality
That “all men are created equal” was “sacred and undeniable” to Thomas Jefferson in his draft of the United States Declaration of Independence. With later editing, it became “self-evident” in the final document. While historians still debate Jefferson’s own intent, the continuing impact of his phrase prompts the question of how to interpret the words now. Can one justify Jefferson’s final wording as a statement of fact? Several religions support the concept of equality, and hence Jefferson’s choice of “sacred” would be more understandable. At no point in history, however, has equality been self-evident from looking around. Different social classes in the same region and the same classes in different regions have had different enough lives to make such a proposition counterfactual on the surface.

I suggest that the educability hypothesis fills a gap here in providing an angle from which to view our equality. Educability implies that humans, whatever our genetic differences at birth, have a unique capability to transcend these differences through the knowledge, skills, and culture we acquire after birth. We are born equal because any differences we have are subject to enormous subsequent changes through individual life experience, education, and effort. This capacity for change, growth, and improvement is the great equalizer. It is possible for billions of people to continuously diverge in skills, beliefs, and knowledge, all becoming self-evidently different from each other. This characteristic of our humanity, which accounts for our civilization, also makes us equal.

Perhaps the most serious challenge to the notion of human equality that came from modern science was the eugenics movement. The term comes from the Greek word for “well-born.” The adherents believed that inequality at birth was fundamental. The movement flourished from the 1880s to the 1930s in Europe and North America, driven by the eugenicists’ fear that if people with so-called “superior” genes reproduced at a lower rate than those with “inferior” genes, then humanity’s genetic stock would decline. The eugenicists proposed to take measures to discourage reproduction of what they considered the “inferior” genes. The criteria they considered as valid to discriminate between superior and inferior included measures such as IQ scores as well as membership of national and racial groups.

The reason for eugenics eventually falling into disrepute was neither the ethical issue it obviously raised nor scientific questioning, but rather the wide-ranging use of its tenets by the Nazi regime in Germany. Subsequently, in 1948 the United Nations General Assembly adopted the Genocide Convention, which included in its definition of genocide the imposition of any measures intended to prevent births within a “national, ethnical, racial or religious” group.

The history of eugenics deserves study as an example where the self-correcting tendency of science was not in evidence for a long time. Several of the creators and primary movers of eugenics were among the most prominent scientists of their time. Some of them laid the foundations of modern statistics. Users of statistics will recognize their names and the statistical techniques they contributed: Francis Galton (regression to the mean, standard deviation), Karl Pearson (chi-squared test, principal component analysis), and Ronald Fisher (tests of significance, maximum likelihood testing).

It is now widely thought that these statisticians were mistaken in their belief in the primacy of human inequality at birth. How could such a group have been so wrong? Their published papers were chock-full of data, and they were applying their scientific expertise—statistics—for analyzing the data. Their statistical methodologies continue to be the basis for understanding data in the empirical sciences to this day. My suggestion is that the data available to them did not provide much information about the power of educability. They had little systematic data on individuals of different classes, cultures, ethnicities, and gender being subject to the same educational opportunities over an extended period. Human educability is a surprising and amazing phenomenon that these statisticians—and their contemporaries—failed to detect. Some would explain the eugenics movement by saying simply that the participants were biased by the beliefs of their times. The power of beliefs is, of course, a central theme of this book—but beliefs come from somewhere, and one should try to understand their origin.

For many measurable traits of plants and animals, scientists have sought to distinguish the effects of nature and nurture by assigning percentages to each of these sources using statistical analysis. Such analysis by itself provides no understanding of the mechanisms by which nature and nurture influence the trait. For cognitive traits, such analysis is particularly problematic if we accept that education plays a role in the development of the trait. Educability allows the influence of the environment to be quite enormous. The essence of educability is the unique and extreme power of this influence.

The answer to the eugenicists’ fear is that the capacity to change through experience and education is at the very center of the architecture of the human mind. Fortunately for humanity, the main social development of the last century has been the worldwide expansion of education. We are still in the middle of this expansion. Improvements in education and in the numbers receiving it have overwhelming potential. Pursuing this potential is the most rewarding focus for anyone aiming to improve a society.

Worldviews
Belief systems that are broad enough to suggest positions on diverse issues have been called worldviews. Religions are examples. Political and economic systems are others. Throughout human history there have always been widely held and wildly different belief systems about race, class, and gender, about who is the enemy, and about who is fully human.

Worldviews continue their struggle for acceptance every day. In each epoch various worldviews have been particularly influential. It is customary to be smug about one’s own worldview and dismissive of those of others, especially those of earlier times. Educability offers, among other things, an onlooker’s vantage point on this struggle.

Currently, a worldview with much influence is science. I think this is good. Nations that include most of the human population are teaching science to their young and putting resources into exploiting it for the benefit of their citizens. The proven success of this enterprise is one thing that we can be sure about and would do well to further. A scientific consensus on the nature of the Civilization Enabler may be impactful. Some convergence on what defines us may promote commonality among the ruling worldviews.

We therefore have opportunities.

What about the threats? What guarantees do we have that the ruling worldviews will not follow trajectories that most would currently regard as undesirable, such as returning to widespread human sacrifice? The answer seems to be none. Humans are just too facile with absorbing and applying arbitrary belief systems, and we seem to have much weaker countervailing abilities to evaluate the consequences or validity of our beliefs. This volume shows that one can discuss aspects of belief system acquisition and processing with some precision. Much remains to be discovered. What makes an individual commit to a belief system? What makes an individual maintain their commitment or give it up when it is challenged?

There is little evidence that our civilization is securely on an upward slope. Wars and oppressive political regimes persist and continue to attract supporters. I see no guarantee that belief systems that are worse, or much worse, than those that currently dominate around the world will not displace them. The only actionable defense I see is to seek a better understanding of how we process beliefs. Understanding our critical capacity could help guard against its worst dangers.

Educability is an information processing capability that humans have. It has enabled us to stand on each other’s shoulders and build the edifice of beliefs that is our current civilization. Our power to generate and adopt new beliefs has few limits. The beliefs we adopt govern how we act and have consequences without end. One would hope that if educability is recognized to be the defining human capability, then the search for a deeper understanding of it would become a unifying quest. Surely, we can direct our power of being educable at ourselves, to better understand the nature of this power and set a steadier course…

Valiant, Leslie. The Importance of Being Educable: A New Theory of Human Uniqueness (pp. 217-225). Princeton University Press. Kindle Edition. 

See what you think. I've really just begun my close study of this book.

More shortly...

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