Books on the Pros and Cons of Different Educational Models

There is no end to the writing of books on education and for every book pulling one one way, there is another pulling differently. Although the best advice for finding what to do with your child, I think, is to start with looking at the details of which options are actually available to you as opposed to starting exclusively with the theory and a wish list of school qualities.

Nonetheless, here are the books that I think are the most useful for thinking about education from several perspectives. 

Disclaimer: I don’t endorse less than half of half the books on this list, and I do endorse more than half of half the books removed from it. 

There are no books on pedagogy here. Those will be for another time.

Books about Education and Learning

Why Knowledge Matters by E.D. Hirsch

Argues that a carefully planned curriculum that imparts communal knowledge is essential in achieving one of the most fundamental aims and objectives of education: preparing students for lifelong success. Hirsch examines historical and contemporary evidence from the United States and other nations, including France, and affirms that a knowledge-based approach has improved both achievement and equity in schools where it has been instituted.
The Schools We Need and Why We Don’t Have Them by E.D. Hirsch

Argues that, by disdaining content-based curricula while favoring abstract–and discredited–theories of how a child learns, the ideas uniformly taught by our schools have done terrible harm to America’s students. Instead of preparing our children for the highly competitive, information-based economy in which we now live, our schools’ practices have severely curtailed their ability, and desire, to learn.

The Case Against Education by Bryan Caplan

Why we need to stop wasting public funds on education. Despite being immensely popular – and immensely lucrative – education is grossly overrated.

Why Students Don’t Like School by Thomas Willingham

Research-based insights and practical advice about effective learning strategies.

Deschooling Society by Ivan Illich

Schools have failed our individual needs, supporting false and misleading notions of ‘progress’ and development fostered by the belief that ever-increasing production, consumption and profit are proper yardsticks for measuring the quality of human life.

Homeschooling

Designing Your Own Classical Curriculum by Laura Berquist

Home educator Laura Berquist presents a modern curriculum based on the time-tested philosophy of the classical Trivium—grammar, logic and rhetoric.

You Can Teach Your Child Successfully by Ruth Beechick  

This classic gives nitty-gritty help for each subject in each grade. Become an informed, confident teacher, free from rigid textbooks. Learn how to individualize spelling; how to use “real books” in history, reading, and other studies; how to make arithmetic meaningful; how to avoid the grammar treadmill; how to develop advanced reading skills; and much more.

The Well-Trained Mind: A Guide to Classical Education at Home by Susan Wise Bauer

How to give your child an academically rigorous, comprehensive education from preschool through high school―one that will train him or her to read, to think, to understand, to be well-rounded and curious about learning.

Home Education by Charlotte Mason

My attempt in the following volume is to the suggest to parents and teachers a method of education resting upon a basis of natural law; and to touch, in this connection, upon a mother’s duties to her children.

Hybrid School

Hybrid Homeschooling: The Future of School by Mike McShane

A quiet, readable, encouraging guide to parents and educators, filled with examples, anecdotes and first-person accounts, on what may be the fastest growing sector in American education.


Charter School

Charter Schoolsand Their Enemies by Thomas Sowell.

A leading conservative intellectual defends charter schools against the teachers’ unions, politicians, and liberal educators who threaten to dismantle their success.  

Public School

The Death and Life of the American School by Diane Ravitch.

An urgent case for protecting public education, from one of America’s best-known education experts.

Resources on The Content and Method of Classical Tutoring

Henrik the Great asked me to dust off what I know about the curriculum and practice of private tutoring. While I don’t know much, I do know the basics and the big names.

I assume you read my excerpts from Jesuit educational ideals already. which offers some pointers.

For a detailed example of an entire curriculum see Jesuit Education: Its History and Principles (1904) which, while a lackluster book for several reasons, does include a detailed course of study which would be fairly standard not just among Catholic but also Anglican and Lutheran teachers during the 17th – 19th century. For example, John Stuart Mill’s early education was very much in the same vein.

Here are the big works on pedagogy and curriculum:

Aristotle (all, but especially)

On Rhetoric

Roman

Cicero, Ad Herrenium, which lays out the entire course rhetoric and persuasion for the next 1800 years. It is also the first place that the use of deep memory techniques is briefly discussed. 

Quintilian, Institutio Oratoria, which reviews Cicero’s course and extends the ideas and practice.

Marcus Aurelius mentions in his meditations mentions the quality of teaching of many of his tutors, especially the method of writing dialogues on alternate positions. This method was popular enough that many early Christian writings are in dialogue form as well. 

Cassiodorus, Institutes of Secular Learning

Medieval

Peter Lombard’s Sentences were the standard method and textbook for 400 years.

Aquinas On the Teacher. Of course, Aquinas’s Summae tried to make a replacement for the sentences, but was not successful until well after his death (three centuries!).

John Buridan’s Summulae de Dialectica was a standard textbook on Logic and logical method for a couple hundred years.

I do not know of any medieval source who discussed and presented scholastic pedagogical method explicitly, although it was very influential. I need to check what would have been the standard reference.

Renaissance

Petrus Paulus Vergilius, De Ingenuis Moribus frequently translated as The New Education. Refocuses education on service to civic life.

Aeneas Silvius, On Education 

Erasmus De Ratione Studii, On the Method of Study, and Ciceronianus, which covers how he thinks schooling can excel beyond mere memorization and imitation.

I think it is easy to underestimate how much sway these older authors had on 17th-19th century education. They were giants.

I have some takeaways from these readings and my own experience being classically educated but am not yet able to fully articulate them.

Enlightenment

I am not well aware how tutoring curricula changed in the Enlightenment. I wouldn’t count the differences in method to be great, although the content certainly shifted to include more mathematics. The personal libraries of the great thinkers reflect remarkably little change from the interests of the Renaissance Humanists, as far as I know. Though, I am happy to be corrected.

Quotes from Jesuit Educational Ideals

The following notes are from the book Ignatius’ Idea of a Jesuit University by Ganss 1957 without amendment, comment, or much formatting.

“Now we shall take up the advantages for the Society herself, for the extern students and for the nation or province where the college is situated. This is the utility which has been found through experience in colleges of this type. Even though part of this can be gathered from what has already been said:

  1. First of all, in the case of our own numbers, those who lecture gain profit for themselves and learn much by teaching others and become more confidently the masters of what they know.
  2. Our own members who hear their lectures gain profit to the care and continuous diligence which the teachers display in fulfilling their office.
  3. They profit not merely in regard to letters, but generally also in preaching, and the teaching of Christian doctrine. And they exercise themselves in the use of the means by which they must help their neighbors later on. And they are encouraged through seeing the fruit, which God our Lord allows them to see.
  4. Although no one may induce the students, especially when they are young to enter the Society. Nevertheless, they can win esteem for themselves by good example, conversation, and the Latin declamations about the virtues, which are delivered on Sundays, and they can gain many laborers in the vineyard of Christ, our Lord. These advantages are for the society itself.

The benefits for the extern students who come to profit from the lectures are the following:

  1. They’re occupied to a sufficient extent with their lessons. much care is taken that all learn through lectures disputations and compositions. Thus provisions are made for them to reap great fruit of letters.
  2. The poor who lack the means to pay the ordinary teachers or private tutors in the homes here find free, what they can only get with great cost and difficulty in their desire to become educated men.
  3. They provide profit in spiritual matters, through learning Christian doctrine and grasping from the sermons and customary exhortations, that which is conducive to their eternal salvation.
  4. They make progress in purity of conscience and consequently in all virtue, through confession every month and through the care taken, that they be decent in their speech and virtuous in their entire lives.
  5. In their studies, they draw much greater merit and fruits, since they’re accustomed to bring all persons to the service of God from the time when they begin to learn just as they are taught.

There are also the following benefits for the inhabitants of the country or province where these colleges are established.

  1. In temporal matters, parents relieved of the expensive of having teachers to instruct their children in letters and virtues.
  2. They keep their consciences free in the matter of instructing their children. Those who only with difficulty will find someone to whom they can entrust their children, even at their own expense. Will with all security find instructors in these colleges
  3. In addition to learning, they also have in the colleges, someone who can preach both among the people and within the monasteries, and who through administering the sacraments can very fruitfully supply great help, as is evident.
  4. They themselves and the members of their household will devote themselves to spiritual matters, with good example to their children. Likewise, they will grow fond of confessing more frequently and of living as Christians.
  5. They will have in our own members inhabitants of the country to inspire and aid them towards undertaking good works, such as hospitals, houses of reformed women, and such like matters. Their bestowing charity upon our members also entails their having a care of such good works.
  6. From among those who are at present merely students, in time, some will depart to play diverse roles, one to preach and carry on the care of souls, another to the government in the land and the administration of justice, and others to other occupations.
  7. Finally, since young boys become grown men, their good education in life and doctrine will be beneficial to many others, with the fruit expanding more widely every day.

I could elaborate this further, but this will suffice to set forth what is perceived here in regard to colleges of this common.

May Christ, the Eternal Life, guide us to serve him better. Amen.”

St. Ignatius to Father Antonio Araoz from Rome, December 1, 1551.

Pages 25 and 26.

The result which Ignatius aimed to produce in the students was manifestly, a carefully reasoned and therefore scientifically grounded Catholic outlook on life, which would enable and inspire them to contribute intelligently and effectively to the welfare of society. That outlook was the focal point towards which Ignatius directed all the branches in the curriculum, and all the elements his school contained. Since theology imparts whatever can be known from divine revelation about God and His creatures, especially man and his duties and destiny, it is the foremost indispensable source of this outlook. But obviously, it must be studied thoroughly and scientifically. So the student grasps the integration of its major sections and its subsidiary branches. Quite as one who has had a college major in physics must know all the principal phases of his subject.

PAGE 54.

Since schools have always been an extension of the home throughout their history, they too, no less than parents, have been concerned to teach something helpful towards a livelihood and towards satisfying intellectual curiosity. Their professors have noticed that their students are more strongly and spontaneously motivated to study hard a subject, which while being truly cultural, was simultaneously useful for living in a way characteristically and satisfyingly human and even for earning a livelihood.

PAGE 127.

Enthusiasm for Plato and for Aristotle, Cicero and Quintilian, and his successors, in whom many of his ideas reappeared with various modifications, was high among the Christian educators of the early Renaissance, such as Petrus Paulus Vergilius, Vittorino da Feltre, and Aeneas Silvius Piccolomini. Hence, they revived the ancient ideal of liberal education, Christianized it, and adapted it to their own age.

They conceived the aim of education to be that of producing the perfect man fitted to participate well in the activities of his day. As a means to train him, they worked into their theories of liberal education, numerous elements, the physical, the intellectual, the aesthetic, the literary with stress upon eloquence, the moral, the religious, and the social. As will be shown in greater detail, the ideals or models of education took the forms of the complete citizen and Christian gentlemen of Vitorrino da Feltre, the perfection of the man as a Christian citizen of Vagarius, the courtier of Castiglione, and in the northern countries of the Christian scholar of Erasmus. Other noteworthy ideals more or less outside the Christian current of the Renaissance were the prince of Machiavelli, the gentleman scholar of Thomas Eliot, Montaigne, and later on, after Ignatius’ death, of John Locke, still another ideal was the experimental scientist of Francis Bacon.

PAGE 140.

The means to produce this developed citizen are the liberal studies, which Vagarius defines as follows.

“We call those studies liberal which are worthy of a free man, those studies by which we attain and practice virtue in wisdom, that education which calls forth, trains, and develops those highest gifts of body and mind, which ennoble men and which are rightly judged to rank next in dignity to virtue only. For to the vulgar temper gain and pleasure are the one aim of existence, to the lofty nature, moral worth and fame.”

Vagarius lists the subjects which he thinks can properly be classified as liberal.

“Amongst these I record the first place to history, on grounds both of its attractiveness and of its utility. Qualities which appeal equally to the scholar and to the statesman. Next, in importance ranks moral philosophy, which indeed in a peculiar sense is a liberal art, in that its purpose is to teach men the secret of true freedom. History then gives us the concrete examples of the precepts inculcated by philosophy. The one shows what men should do. The other what men have said and done in the past, and what practical lessons may draw therefrom for the present day. I would indicate as the third main branch of study, eloquence, which indeed holds a place of distinction among the refined arts. By philosophy, we learn the essential truth of things, which by eloquence we saw exhibit in orderly adornment as to bring conviction to differing minds. And history provides the light of experience, a cumulative wisdom, but to supplement the force of reason, and the persuasion of eloquence. For we allow that soundness of judgment, wisdom of speech, integrity of conduct, are the marks of a truly liberal temper.”

Other studies which he regarded as liberal are letters, especially poetic art and rhetoric, which lead to eloquence, disputation, or logical argument, gymnastics, music, arithmetic and astronomy.

PAGE 141.

Although it may seem at first a paradox or even a contradiction, it is now certain that during the Renaissance, the humanists as a body regarded classical and liberal studies as eminently practical. These subjects were indeed cultural, but they were simultaneously as practical as curricula in engineering, journalism or commerce are today. The humanists went to the ancient authors to find guidance for practical everyday life. Vagarius envisaged a practical objective, the citizen taking capable part in the affairs of the day, training for practical life was the leading purpose of Vittorino da Feltre, who approved Cicero’s statement, Virtutis laus omnis in actione consistit. Aeneas Silvius Piccolomini. himself, a practical man of action and affairs, approvingly quoted the same statement, and pointed out from the examples of Demosthenes, Aristotle, Caesar and Pliny that the study of literature develops administrative capacity. The study of antiquity, completed by its final course of ancient philosophy, was regarded as the finest preparation for law, medicine, or theology.

The Latin language too was learned primarily for utilitarian purposes, as it was during the Middle Ages. Further even skill in producing stylistic elegance in Latin had its utilitarian and economic values for two functions, the handling of official correspondence and the writing of speeches on solemn occasions. The humanists are indispensable as Latin secretaries to the multitudinous princes, nobles and civil officials and republics, and to bishops, Cardinals and Popes. Hence proficiency in Latin was the means enabling anyone, no matter how poor or from how lowly a social class to obtain the most coveted, honored and lucrative employments of the day. As we saw above, on page 39, the highest salaries in the Papal University of Rome paid to the professors of medicine and of rhetoric, subjects then studied only in Latin. Also, the humanists of Florence deemed the learning of literature, the best preparation for a career as a merchant or banker.

Page 164.

We shall spare ourselves much time and useless twinges of conscience by a resolution which would run somewhat as follows. There is no possibility of completely divorcing a liberal education from material considerations. In the light of a record which goes back to antiquity, it would be undesirable to make the attempt, for if it succeeded, it would result in a dilettantism, which would be denial of what a liberal education aims to do.

From James Marshall Campbell, Dean of the College of Arts and Sciences of the Catholic University of America

PAGE 171

The whole of the thought of the earlier humanistic educators is this that the people should be developed into the complete man those faculties trained to excellence or virtue in order that he may capably benefit the society of his day. The same central thought is present in Ignatius’ constitutions and procedures There is concern for the bodily health (this is gymnastic, at least in germ). There is training of the intellect through the whole curriculum of grammar, the arts, and theology. There is constant exercise in self-expression or eloquence and in disputation to meet the tastes and needs of the age. There is training of the aesthetic faculties and emotions through the study of ancient literature, including rhetoric, poetry, and history. If training in the vernacular languages and literatures had been part of the educational systems of the day from which Ignatius drew, he would no doubt have approved this training along with his other borrowings. It was not merely training of mind concomitantly acquired through mastering these studies but also through the crowning courses in philosophy and theology, the imparting of extensive body of knowledge which makes up a scientifically grounded theistic philosophy of life, a philosophy which gives true significance and worthwhile meaning to the life of man both in this world and the next.

There is constant encouragement of the student not only to moral and sacramental living, but also to the exercise of all the supernatural virtues which lead to the highest union with God. There’s constant insistence on the social purposes of education. There’s the equipping of the man not only to live as a Christian gentlemen, but also to earn his living in a way satisfying to himself and beneficial to society. For as we have seen the subjects taught in Ignatius’ curriculum in his day the surest road for a poor boy to achieve economic security and without such security even a highly trained man is little likely to function as a leader.

Page 176.

In this curriculum he made theology the most important and crowning branch and philosophy an aid to it, and the languages an aid to the learning and use of both. This last point was particularly true of Latin, but some attention was also given to Greek, Hebrew, and the vernaculars. Since the educated men of this period at a high admiration for Ciceronian Latin, Ignatius stressed practice and Ciceronian style. Since he wished the students to form their personal convictions, through much self-activity rather than through a passive absorbing of the professor’s views, and since his times were filled with public disputations in Latin, which Catholics held either with Protestants or among themselves, Ignatius stressed practice in declamation, disputations, and “circles” in which small groups of students held “repetitions.” Also in his curriculum, Ignatius did not limit the interests of his students in one area such as classical antiquity, or medieval culture, or the speculative genius of scholasticism, or the Renaissance, with its preoccupation with style and form. Rather, he widened the student’s vision to take in the hole of Christian culture. In his curriculum, there were not only Latin and Greek, and Aristotelian philosophy and Scholastic theology, but also scripture and positive theology, which included the Fathers of the Church. Hence his schools were a home in which the whole heritage of Christian culture was made an object of study, and was transmitted to future generations, with at least as much efficiency as in any other schools of the era. He was indeed eminently a practical organizer, choosing what was particularly useful to his end in his own times. All the elements in his system conspired to prepare the students to be and to do what they should to live well throughout this life and the next.

Page 178

  1. He regarded education as a means of attaining the end of his society, the salvation and perfection of the students in order that might promote the salvation and perfection of their fellow man, unless vigorously and intelligently loving the society with the spirit of the Kingdom of Christ. He hoped that students will learn how to live well, in this life and the next.
  2. In intellectual order, the end towards which Ignatius wished his curriculum to lead was a scientifically reasoned Catholic outlook on life. That is one which the student has thought through to his own personal conviction, in contrast to the memorized knowledge, which is characteristic of a child. That outlook was the focus of integration of all other elements in his system. It was what would enable as well as inspire the students to perfect themselves to contribute intelligently and effectively to the welfare of society.

Page 182

Questions about the Early Jesuits

Tyler is reading *The Jesuits: A History*:

Here is one passage that for obvious reasons caught his eye:

The Jesuits invested the lion’s share of their bureaucratic efforts in personnel planning.  We have already encountered the Society’s obsession with the quality, education, and development of its members several times — this passion was translated into bureaucratic procedures to an astounding degree.  Every Jesuit’s mental, spiritual, intellectual, and physical capacity was routinely evaluated.  The Society devised elaborate procedures for conducting such examinations.  Even the wording of these assessments was prescribed.  A kind of grading system with standard content was devised that was then used to answer about a dozen questions from each member.  Every three years, local and provincial superiors were required to prepare interviews of the staff under their authority, whom they were required to assess in table form.  These catalogues have justly been celebrated as an outstanding example of the bureaucratization of the modern period.

The 17th and 18th century Jesuits seem like a miracle of human capital formation.

Last year I read three books on the Jesuits for quite similar reasons. My thought was how did such a small organization create a culture of excellence that pushed the bounds of science, sociology, and politics so well (or did it? Maybe Jesuit mythos and reality are quite separate?), and what mistakes caused it to be suppressed?

The bureaucratic excellence might be one such reason. I am almost disturbed by the level of obedience these men had to superiors. The intense cultivation of ability combined with the “state capacity” to aim member’s abilities towards all manner of problems. That combination does seem frightening to anyone without such organizational competence. Don’t compete with this superhuman foe, the king and lords of Spain thought, shoot for suppression.

How much internal dissension was there? How was it dealt with? What were the most politically unwise or impolitic moves the Jesuits made in the 18th century? Who were the Jesuits enemies and why? How can we compare Jesuit accomplishments to the secular accomplishments of the day? What was the Jesuit role in the wars between the enlightenment secularism and the Catholic Church? Which Jesuits engaged with John Locke or Montesquieu?

I am not satisfied with any of the answers I have found, though I now know a fair deal more about Jesuit education. I need more nuts and bolts of Jesuit organization in the 17th – 18th century. I lust for more details.

Jesuits: a Multibiography (1997)

St. Ignatius’ Idea of a Jesuit University (1957)

Jesuit Education in Light of Modern Educational Problems (1904)

Towards More Popsicle Catapults: Statistics as a Branch of Logic

[This letter is part of the Little Letter Republic, a project whose purpose is to build community in St. Louis and beyond.]

Dear Sebastian,

I really enjoyed our discussion. In particular I’ve been thinking a lot about what you called statistics by logic or perhaps verbal statistics. When we spoke I noted that I’ve been thinking a lot about how computation has expanded the pedagogical frontier by allowing “learning by doing” for math & stats via scripting. More specifically I think discretization is an incredibly promising path for teaching a much wider population of students the core concepts of statistical thinking (and calculus and derivation, with statistics as the “practical application”). I’m not the only one thinking this way, see eg. Think Bayes, and of course this is precipitated by realizing that a tremendous amount of real-world computation is done via discretization and simulation.

However our conversation push me to think more broadly, not just about what could be taught effectively if a student learns a little scripting, but also what a student can learn simply through language and imagery.

I’m really coming around to the idea that the core basic ideas of statistical reasoning can be taught through discrete and empirical concepts such as histograms and empirical cumulative density functions. Not just univariate statistics, but multivariate statistics, which are critical for thinking about “real world” statistical modeling. Much of statistical modeling is about capturing the joint and conditional distributions of data, and what I call “F(X), g(F(X)), and F(g(F(X)))” – that is, distributions, functions of distributions, and distributions of functions of distributions (much of inference is about how functions of distributions are themselves distributed).

The more I think about it, the more I think that the foundational concepts for practical real-world statistical reasoning can be effectively taught to students with even a fairly low level of mathematical background, say addition/subtraction and multiplication/division.

To be clear I have in mind laying conceptual foundations, not teaching students how to prove results. The key to thinking about the world in statistical terms is the think about the world as full of potential counterfactuals, realizing that any such counterfactuals are inherently noisy, and understanding that ‘random’ doesn’t mean ‘hopelessly unknowable’ – rather we can (and do!) know quite a lot about randomness. The world shifts into probabilities, and decision-making shifts into “how much probability is needed before a decision can be made?”

The goal of this “conceptual foundations” instruction would be to ‘start with the why’ – “you’re going to be learning probability at some point (perhaps integration and derivation as well) – why?” The math of probability can be dry, the goal of this conceptual foundation would be to provide the motivation / inspiration to learn these.

I have in mind that ‘conceptual foundations’ could be something like a sequence, perhaps following the “F, g(F), F(g(F))” path – first basic distributional qualities (what a RV is, shapes of distributions, and percentiles, and concepts such as mean, median, variance, correlation + multivariate distributions), then functions of distributions (revisit mean, var, cov – ‘think back and notice – these are all functions!’, methods for capturing joint and conditional distributions {OLS, ML methods}), and then distributions of functions of distributions (all via resampling – revisit mean, var, cov, OLS, ML – “look, these are random themselves! what should we do about that? Well, go back to the beginning…”). Also, this naturally introduces the idea of counterfactual reasoning, though that could be introduced earlier and point to here.)

I really do think that a lot of these things can be taught at a conceptual level with discrete distributions and pictures. Depending on the amount of time available, I think some of these things can be directly illustrated by exercises – for example, by playing games or having contests (even ‘against nature’). I think practical interesting projects where groups of students determine eg. which random process has greater mean than another could be run (eg. build little Popsicle-stick catapults, then measure repeatedly what their ranges are, then determine if their ranges can be told apart statistically – then have a game where you use the little catapults; nothing focuses the mind like a little competition! … or even simpler variations on this theme, see the Appendix below for even simpler ideas)

There are other practical experiences that could be incorporated – ‘eyeballing’ data and seeing if something looks strange; making forecasts, both informally (eg. as part of expected-value reasoning in real life) and formally (and assessing forecast errors for example). There are a number of things that can be illustrated visually, and broken down into discrete steps, such that it is accessible much earlier than usual.

Many of these ideas are taught at the college or graduate level (or beyond) – I think these key concepts can be taught at the elementary level.

To be clear, the goal is to teach the reasoning from elementary concepts, to give students a vision of what is possible, give them a ‘why’ for all the perhaps drier math and stats that they will learn in more detail in later courses. I personally find it much easier to learn a hard thing when I know why I’m learning it, when I’ve had some of the inspiration of seeing the power of a tool put to use – I’ve been able to plough through much more difficult material when I know why I’m doing it.

Beyond that however, I’ve found statistical and counterfactual reasoning to be incredibly powerful tools in making my own life decisions and learning about what is happening in the world. Statistics and data are increasingly the languages of knowledge, and this will only increase as we move towards the future. We also need leaders who can think in statistical terms, and the earlier we can teach the concepts the better.

Finally, I think these foundations can be extended – to return to my earlier idea that scripting can greatly extend ones learning ability, if what I have described above is “foundational statistical concepts”, a follow-up sequence could be something like “foundational statistical computation”, which uses textbooks such as Think Bayes, Cosma Shalizi’s Advanced Data Analysis from an Elementary Point of View, and Efron and Hastie’s Computer Age Statistical Inference to implement many of the concepts explored in the “foundational concepts” sequence (and may only require spreadsheets as a minimum). But that is conversation for another time…

Best, Nate

Appendix A – Some Ideas for Basic Concepts

I wanted to jot down some ideas about teaching basic concepts quickly.

I really do think that statistics can be “taught backwards” in a sense – start from higher-level concepts and and big pictures and trace out the major ideas first via illustration. For example I think that the concept of a distribution can be illustrated quite naturally with histograms (discrete distributions), and this can almost immediately be used to illustrate variance and correlations (for example a 2-D distribution of eg. age and height). Or even start simpler with extremely simple games played with dice before progressing to real-life data. Dice alone could illustrate a the ideas of randomness (one die), histograms (2 dice), mean, variance, covariance, and broad shapes of distributions (skew vs non-skewed). Those concepts could be taught first with things like dice and framed as a binary choices, “compare playing a game with a die that is normal, 1,2,3,4,5,6, vs an opponent who gets to use 2,3,4,5,6,7. Which would you choose?” Varying the mean could be made very explicit and varying the variance could be made very explicit, eg. comparing a game played with 1,2,3,4,5,6 vs 1,1,1,1,1,6 (lower variance not always better) vs 1,1,1,1,1,16 (“if all you care about was the average, which dice would you choose to play a game, or indifferent?” “If you liked a game with higher variance which would you choose?” …etc). Single and multiple dice would provide natural ways to talk about shapes of distributions (PMF of 2 regular dice is a symmetric distributions, vs eg. 1 regular die and a 1,1,1,1,1,6 die would produce a skewed distribution).

Depending on the ages of people taught and the time set aside for learning, students could actually play common games, but beforehand choose which of the dice or combination of dice they’d like to use – get a visceral experience of a “same mean but high variance” die vs a “regular” die, or skewed distributions vs symmetric distributions.

This could lead naturally to discussions about more real-world distributions – eg. population data, with marginal and joint distributions of height, weight, age for example. I’ve already been using histograms and demographic examples to causally teach basics of mean, variance, correlation, etc to friends and family, and it works quite well.

On more sophisticated modeling of joint distributions:

At the end of the day a lot of statistical modeling is about capturing joint and conditional distributions of data. When statistics was invented the profession had to use incredibly clever analytical tricks to do this; thus OLS regression is the BLUE of the conditional mean of a joint distribution. But with modern computation we can capture many of these things directly. Part of the success of machine learning has been through exploiting various ways computation can directly capture these joint distributions, and the construction of these estimators are often simpler to learn than the analytics and assumptions needed for understanding OLS. (For example K-nearest neighbors directly captures the idea of the conditional mean by simply taking a local average, rather than working through the tooling of OLS. Of course this requires big data and big computation, but we’re getting more an more of those every day.)

Again, I’m not the only one thinking this way – Cosma Shalizi’s Advanced Data Analysis from an Elementary Point of View points this out explicitly in the first chapter, and Efron and Hastie’s Computer Age Statistical Inference can be seen as the simulation-driven version of this idea for inference.

These kinds of “looks to the future” are important for illustrating an idea to an aspiring student – the “concepts” course wouldn’t endeavor to teach these things, but rather when the questions arises, “wait can we take the average in a way that incorporates many things at once?” – one can answer, ’yes, that’s what regression does, and that is what ML concepts do …quick illustration… and you’ll learn about that in a lot more detail in the future if you’re interested! Good question!”

But again, I think the main ideas of nearly all of commonly used statistics and inference can be taught with addition/subtraction and multiplication/division. The only other concept I’d add is “resampling” which is also I think very straightforward to describe.

Finally, one critical skill is being able to formulate an idea as implying prediction that can be measured, put down probabilities, and then measuring the outcome and checking your ‘forecast error’ – a major role of forecasting is imply framing your ideas in a way you can measure and learn from, an important skill to learn at any stage.

Ignore Ambition, Just do Good

[This letter is part of the Little Letter Republic, a project whose purpose is to build community in St. Louis and beyond.]

Dear CeltAtom,

You are curious about how to solve two problems. 1) What types of careers people should be encouraged towards and 2) How “ambitious” one’s career goals should be?

In the interest of first offering a more wholesome approach to the discussion, I think a discussion about “ambition” should come first. There is a perception around here that I am a super “ambitious” person. And from a certain perspective that is fair to say, but that is not how I frame the experience of my activities to myself. We could argue about Christian humility versus ambition, but I think this is a category mistake. We have talents, skills, insights that, having been freely given to us, ought to be freely and fearlessly used. If we begin by saying, how can I best use my current abilities and build my current strengths, then we have the right intention. When we are alert to opportunities to use these strengths, it is not ambition. It is looking for ways to conform ourselves to the Animating Spirit. Providence opens doors to us, and we have to choose whether to walk through them.

My friend Joe passed through St. Louis from Philadelphia last month. He was moving to Phoenix. And he told me the story of how he came into this job. He went down to a Benedictine Monastery in New Mexico for a week to pray and discern and seek peace after the current job he took turned out to be a disaster. He thought he was great at organizing and would be able to run this department despite the management issues. Instead, his boss gaslighted him, refused to delegate, and couldn’t be negotiated with. At the monastery, he and a monk repaired some broken down vehicles, the monk told him he should go to Phoenix and look for a job there. After his monastic stay, he drove a couple hours to Phoenix and applied for a few jobs, found a perfect fit for what he needed to develop himself more, and took it. It wasn’t a question of ambition, but of teachableness i,e, docility, the humility to drink the water offered.

I asked him the same question. Does he worry about ambition getting in the way of discernment? He said absolutely not. “Preparing oneself to do greater things is not pride; it’s preparation. God orders your path. If you try to force things to happen on your own, it is disaster.”

So, when I think about career and intellectual life. I think about moving along my current trajectory and making sure I grow the skills I can, so that I can put them to good use. By “good use,” I don’t mean career use either. Some things I do out an impulse of delight or exploration or familial duty, and those things are good use too.

One the one hand, “Be not anxious for your life, what you shall eat, or what you shall drink…” On the other hand, “There were ten virgins, five foolish, five wise…”. So be prepared to do what you are called to do, and you are called to do the great good you can see yourself doing. Does it help to be caught up in the question of whether some activity is “elite” or “ambitious” or not? These are socialized ways of thinking which are cover for the twin vices of vainglory or sloth.

If we try to do a great good thing and fail, we have still done right and should be willing to try again. If we are successful, it is not us that were successful, but rather things outside our control came together.

I find it intriguing that you both liked the advice in the two 80k articles but were repulsed by the conclusions they drew for what careers are appropriate. “This is a recruiting front for the California rationalists.” It seems to me that you agree with the principles of the two articles but find the general 80k implementation biased. You characterize this bias as being towards 1) expanding civilizational capacity and 2) elite concerns, as opposed to maintaining society and caring about local issues.

I think you are right that there are some important biases to notice here. Ryan Miller at University of Geneva recently wrote an article called “80,000 Hours for the Common Good: A Thomistic Appraisal of Effective Altruism.” In that article he cautioned that EA while it wants to be open to non-utilitarian ethical systems is also committed to a state-of-affairs analysis of ethics. But one can’t have both at the same time, he argues. And thus a Thomistic version of Effective Altruism will have divergent priorities from 80k. While I think that is basically true, I think the difference can be overstated, and what matters to me is the practical version of the question. In other words, what does a Thomistic Effective Altruism look like? Because as of right now, it’s only EA that’s systematically taking data and consequences seriously when thinking about career advice.

If we largely agree with the principles laid out in those articles, then we should still implement them.

But what are the practical implications for what careers people should be encouraged towards? You want to divide careers into two camps maintainer-careers and extender-careers. Let me offer a different framework, one that is more dynamic.

Skills get plugged into roles. Roles get plugged into industries. A person can move into the same role at a different industry, or a different role in the same industry. You do this throughout your career looking for the best good you can do. This process both maintains and extends civilization, and even if we get a few more people willing to switch jobs and think in this way, then will have a society where more people are flourishing. Different industries provide different value as do different roles, but it’s up to individuals to try and figure out where the value is and where their talents lie.

But, of course, people need guidance and culture to help inform them about what is valuable. The BLS tells you that words ending in “engineering” are valuable to society in the sense that they are well financially remunerated. However, the truth about most jobs that pay well is that everything is management. Technical skills get you hired, managerial skills get you promoted (or allow you to start something new). By intentionally trying to do good with one’s career, one is taking responsibility for his own life. Ben Franklin’s Junto or Leather Apron Club fulfilled this purpose in his Philadelphia. I think education (broadly conceived) must prepare people for freedom – and that means responsibility.

As a side note: this is also how an ideal polity works, people need to be able to both direct affairs and be directed for a democratic republic to function. Essential to freedom is responsibility.

There are more ideas to explore in this space. I’m out of steam for today.

Looking forward to more,

A Liberal Arts Approach to Economics

[This letter is part of the Little Letter Republic, a project whose purpose is to build community in St. Louis and beyond.]

Dear Nate,

Our conversation the other night provoked me to want to explain more how I teach economics. I have done two things this semester which make my economics class different from the run-of-the-mill class (not that the run-of-the-mill economics class is bad; even normie econ is pretty grand!).

Having a different approach, means more than having a different philosophy while following the old motions. It means truly different tactics. My overarching goal in teaching economics is not to teach students about financial flows, but to teach students about human choice. In this way, my outlook is broader, more humanistic, and less focused on the mathematics and more on the decision algorithms from which the mathematics is abstracted and given meaning. The math is important, but I care first and foremost about introducing the economic patterns which motivate the invention of mathematical insights.

Our standard curriculum consists of economics by McConnell, Brue, and Flynn and Marginal Revolution University videos and questions. But since we have academic freedom, we are not forcing ourselves in a speed run cram semester-long cram session to complete the entire AP curriculum. Instead, we have taken two high consequence detours. Likely a few more will follow.

The first is in expected value theory. What’s the value of this? Firstly, to think about just the simple application of algebra to normal life choices and situations. Secondly, to see that one can incorporate risk into one’s thinking about choices, and thirdly to pass on a surprisingly simple yet powerful and important mode for thinking through decisions. We calculated how many people you would want on a road trip to Juneau for cost sharing to be worth it, how to calculate the expected value of a military strike, and what the expected value of different driving habits are.

In morality, such a method is useful too. When deploying the principal of double-effect in moral decision-making after all the major hurdles have been crossed the governing issue of moral action remains prudence, to take proportional measures to achieve our goals in the face of uncertainty.  Expected value along with marginal thinking and causal diagrams (discussion for another day), I think should become standard equipment in the category of prudential thinking, which means I am also happily committed to a theory of virtue which requires using tools like these.

The second difference is the way I allow international trade to alter the course. From international trade we quickly run into issues of globalization and automation. MRU has a little curriculum on the topic called Globalization, Robots, and You, an essentially depressing look at how difficult it is to compete in a globalized and automated world. I noticed as the students worked through the ideas, they both made insights and at the same time felt somewhat powerless. As much as I like the lessons, they leave something to be desired: an idea of what civilization is for and how to offer a unique contribution. On uniqueness, we talked about the combinatorics. If there are 500 skills and you possess three without being the best at any one, you can still quite easily become the best person who has that set of three skills. (500*499*498).

I then offered the students another way of thinking: two articles from 80,000 Hours on high-impact careers and career stages. And then we close with a self-assessment “flower exercise” from What Color is Your Parachute which I think forces the students to engage with their own individual preferences in the context of trying to both do good (vis-à-vis culture) and do well (vis-à-vis civilization).

Then as we dive into discussions on labor economics, the students engage the questions from a place of curiosity and personal interest.

What I’ve outlined in brief is my liberal arts approach to economics education so far: an emphasis on passing on those habits of thought and intellectual tools which make for personally free and moral characters. Some people shy away from discussion of the moral import of education. I embrace it. Intelligence must meet action, and voluntary action must be directed towards good ends.

Inspiration from Alcuin

We live at the crossroads: a time of great pains and anxiety, a time of great hope and possibility. It is a time of international tension and international commerce, a time of technological tyrannies and informational delights. It is a time of national distrust, imperial loneliness, and meaning crises; and it is a time of artistic creation, community formation, and personal renewal. In short, it is a great time, like all times are, to invest ourselves in firming the bulwark, countervailing the ills, and extending the capabilities of civilization and rejuvenating the heart of culture.

In 793, the Vikings first made landfall in Northumbria, Britain. It was the first of 250 years of Viking raids. In that same year, Baghdad became the chief financial center of the world, connecting the Arabic speaking world to China, using paper promissory notes. While the civilized worlds of Baghdad and China connected themselves to each other, the small glimmers of high literacy in Ireland, Britain, and Italy were threatened by a black dawn of incessant raids in both the Mediterranean and northern seas. The legacy of the Roman Empire was scattered about in error-ridden, half-readable, near-rotting texts. A ‘big’ library boasted 100 books. The copying practices were so bad that the next generation of books would be nearly useless.

In France, one warlord, Charlemagne, was creating a vast Frankish empire out of military might, but although his political accomplishment was short-lived, he left behind an important cultural legacy: the preservation of knowledge and an end to the heedless destruction and abandonment of texts which characterized the previous 400 years (Mulhall). There is no text that we know was around in 793 in Western Europe, that cannot still be read today. Literate civilization did not backslide any further. To what can we attribute this ancient accomplishment, this new foothold on solid ground from which European civilization would one day leap? It was the monk of York, Alcuin. Alcuin, and the monks of Charlemagne’s court, who reformed the clergy, refined texts, created textbooks, and both taught and inspired a new generation, a generation who in turn taught another generation, passing on the skills of administration, counsel, and moral formation to the next cohort, until a more civilized world could be born.

 This process is not over. This process has only just begun, and it is ours to treasure. In Alcuin’s day a most important task was preserving and transmitting information so that individuals and society would not lose sight of their purpose and potential. In today’s world, another most important task is to sort, structure, manage, and marshal information, so that individuals and society will not lose sight of their purpose and potential. But our task is deeper than that. It is not a matter of mere ‘information’ storage and retrieval mechanisms. It is a matter of maintaining a sacred contract to see to it that the next generations do not fall into tyranny, viciousness, destruction, and obliteration and that they equip themselves with those values, skills, and relationships that identify and promote what is good and make life a wonderful adventure. This sacred interpersonal contract, written in the stones of what we choose to build, determines the future.

Letter on Culture and Context

[This letter is part of the Little Letter Republic, a project whose purpose is to build community in St. Louis and beyond.]

Dear Nilay,

You asked about “Context is that which is scarce.”

In our last conversation you expressed mild shock when I said that none of my students and almost none of their parents know what a private equity market is. So, consider this example: I want to explain to a high school student what an equity market is. The student’s parents and family neither run businesses nor engage in any active investing, nor do their parents’ friends. From the student’s perspective there are jobs which pay money and there are places to which one goes to spend that money, and that little model, for them, is the economy. Notions like a funding round, shares, ownership, ROI, and public versus private markets are foreign concepts. But more importantly, even if they are explained, they are quickly forgotten because the concepts do not map onto the student’s experience of reality. To bring a student from ignorance to starting see how this works would require knowing one or several people whose picture of reality is formed by this other context. Such a personal network would then be adjacent to their own, and they could quickly add any new information I provided to their map of reality.

If I want to convince a student that starting their own business is something to seriously consider, their soul must grasp how this could work, but the soul can only with difficulty grasp what the senses haven’t experienced.

Consider another example found in “communities of practice.” What is the best way to become good at creating software back-end architecture? Reading a book? Certainly not, for a book cannot span all eventualities and quirks. For the most part, it seems, the best way to become good at something is to work on a problem and find people who have run into the same issues as you and talk with them or read their chats. Then, when you engage in conversation, they understand the context, or the context is shared enough that they grok the problem you describe.

A community engaged in similar practices encounters similar problems, but one cannot understand the problems or their possible solutions if one lacks the context to understand the problem in the first place.

When I dip into a work of philosophy, I can become gripped and absorbed into the text when the author is exploring a series of questions that I myself have contemplated. My “philosophical literacy” helps me see the point quickly about why a particular argument or line of inquiry matters. When I know what matters I am able to gain understanding. One needs cultural literacy to grasp the significance of any fact.

The point here is that knowledge is not a set of statements outside the mind but understanding within our intelligence about what matters and why.

We live in the information age, but it’s context that is scarce.

Here’s a trivial example. Let’s say I have had a fever for a few days, I text you, “I feel like Raskolnikov.” The information contained in that statement can only be unlocked if one has the cultural passkey, knowledge of Crime and Punishment. The most difficult part of this idea that the scarcity of context is so ubiquitous that we hardly notice the phenomenon, except by example or the experience of total confusion.

If I had to explain to my mom what I have been thinking about recently, it would take many hours of discussion before we were on the same page. The implication is that it is very hard to induct people into one’s own thought and problems unless they already share significant amounts of context with you. Nonetheless, my mother and I share other things, and so can connect on those.

There is a tragic loneliness in the scarcity of context. If I have something great to offer others, but they can’t understand it, then I will languish in obscurity. Sometimes I think about the people, the websites, the communities that I would love, that I know exist out there, but that I cannot find. I could wait for someone to link me there. But the human person is not a passive receptacle of experience, but rather a creator of context, a crafter of relationships and worlds. And so whenever we interact and build something together, we are creating context.

I hope some of that makes sense.

Yours sincerely,

A Curriculum Story

When I enrolled at Wabash College, the faculty had just voted on retiring the Cultures and Traditions course, a two semester sophomore seminar on the great texts of ancient and modern history. Such a course was meant, I presume, to serve as an introduction to at least some of the foundational texts of civilization. Arranged mostly chronologically the texts would be an introduction to some of the big ideas of humanity. But intellectual balkanization took the day, and the course was replaced with a freshman second semester course called Enduring Questions.

With all due apologies to the chief architect behind the course, Dean of the College Gary Philips, who, despite being an excellent professor for my section, fathered this disaster. EQ was a smorgasbord, The product of many kooky cooks in one claustrophobic kitchen. Some of the items on the menu were not even food. It was as though a gaggle of drunk undergrads were appointed to the curriculum committee on a Saturday night and immediately proclaimed, “For dinner we will be having strawberry gravy over Hot Wheels cars with a side of Papa John’s Red Pepper Flakes. As an aperitif, gentlemen, indulge yourself with this fine wine from an origami sippy-cup.” The course consisted of all the greats, that is, one sexist page from Aristotle, a bit of a book on freedom by an educational philosopher, In Defense of Dolphins arguing for the personhood of these ocean tricksters, a good Black experience novel, several movies (Bladerunner, Orlando, City of God), some holocaust literature, and The Power and the Glory. Despite, Gary’s heroic attempts to create a single thread holding this course together, the entire college suffered severe intellectual indigestion.

My soured relationship with Gary (would it weren’t so! He and I really should have been friends, but I spent half my college career trying to overthrow the administration, i.e. Gary and the President) met its ultimate end at an EQ course section reunion dinner three years later during senior year. As we circled around each other in conversation, looking to slide the rhetorical stiletto into each other, another student committed a terrible and crass faux pas. He ended our soft barbs with a cannon blast, a direct insult on the Dean. How could he not know to whom he was speaking? Could a senior have really been so ignorant that he did not know that Gary designed the EQ course? Did he not realize we were at that moment eating delicious vegetarian cuisine in our host’s vegetarian Victorian home? Maybe it was the light sparring that Gary and I engaged in that egged this student on? Or yet perhaps a desire to be noticed for having formed a wise and considered opinion after years of liberal arts reflection? Whatever the cause, heavenly compulsion or earthen desire, he managed to cruelly insult our host. Silence would have been golden, but instead: “Do you all remember In Defense of Dolphins?” he asked. Then continued, “Yeah, that was a really stupid book. I didn’t get it. Why did we have to read that?” So shocked was I, that I had to look at Gary and give him the reassuring I-swear-I-didn’t-put-him-up-to-saying-that.-He’s-obviously-just-really-sincere-and-heedless-of-the-fights-that-have-been-going-on-the-last-three-years look.

In any case, a course which lacks coherence will neither be absorbed nor respected by the student years hence. And that is the lesson of EQ: courses are better when are topical, coherent, and lead somewhere.

It is possible to error in the other direction, but I hesitate to even bring it up, since our schools are so far away from making this error. Nonetheless, for the sake of symmetry problem do arise when one only reads the great seminal texts. My mentor in bibliophilia Mike Martel, a Thomas Aquinas College graduate, and the most nurturing text lover I have ever met, always advocates for reading the texts themselves before the scholarship. But in our back and forth for seven years, we have moved closer to one another in the proportion of scholarship to primary texts on should read.