How a Theology of Wisdom Undergirds Education

Posted on by Paul Drake

“Wisdom cries aloud in the street; in the squares she thunders!” (Prov 1:20). The figure of speaking Wisdom is more than just an interesting literary device. Jewish and Christian tradition saw in a theology of Wisdom a foundation for what we would call classical education. In this presentation I propose to show how the theology of Wisdom presented in Proverbs and later Jewish and Christian texts presents us with what I call a traditional and transcending pedagogy. This traditional and transcending pedagogy is the antidote to the fragmentation of the modern world of education, specifically to three problems: scientism, technicism and pragmatism. These three -isms share the feature of reductionism, i.e. they reduce the educational endeavor to less than it is. A theology of Wisdom, however, has the power to unite all the dissected ideals of education.

Jason Barney

Jason Barney recently joined the faculty of The Geneva School of Orlando as Upper School Latin and Greek Instructor. This last year he was the Director of Instruction for Languages and Faculty Development at Clapham School, a classical Christian school in Wheaton, IL. He served as Clapham’s Head Latin Instructor for the last six years. In 2012 he was awarded the Henry Salvatori Prize for Excellence in Teaching from Hillsdale College. In May 2014 he completed a MA in Biblical Exegesis at Wheaton College, where he received The Tenney Award in New Testament Studies. Jason’s research interests include: the foundations of classical education in the biblical texts, especially the Theology of Wisdom in Proverbs; the great philosophers of education from the classical era to the present (Aristotle, Quintilian and Aquinas are current favorites); and, in particular, the importance of Charllotte Mason’s philosophy of education for classical schools today.

The Liberal Arts and Human Flourishing

Posted on by Paul Drake

One encounters any number of reasons for the importance of a liberal arts education, both from within the Christian classical renewal and in the broader educational culture. In Christian classical circles one is likely to hear an emphasis upon the potency of the liberal arts as tools of learning, while in the broader culture the emphases one often meets range from vague notions of well-roundedness to pragmatic claims of employability. Thus the thesis advanced in the present article may appear to some as bold and somewhat surprising.

The best reason for pursuing a liberal arts education is not that it produces well-rounded persons, though the breadth of human experience it affords is expansive. Nor is it that the liberal arts foster or engender the kind of written, verbal, or critical thinking skills sought after by some employers, though the skills of persuasive writing and speaking and of interpretive reading and analysis indeed lie at the core of the liberal arts curriculum. Rather, the most compelling reason for pursuing a liberal arts education is the distinct claim that the historical, aesthetic, philological disciplines of the traditional liberal arts curriculum
cultivate the qualities of moral judgment, common sense (sensus communis), and taste.1 It is not only that the Western tradition has understood the distinctively human element of civilization to consist in the acquisition and exercise of these qualities, but also that they actually constitute the pre-critical conditions for human rationality itself. Put most simply, then, the best reason for pursuing a liberal arts education is that it cultivates the qualities necessary for human flourishing, both in terms of human reason and of human moral being in the world. It is also the most compelling because it is perfectly attuned to our own cultural moment.

Cultivating moral judgement, common sense, and taste

There is perhaps no single aspect in which a liberal arts education is more obviously unique than in its telos— the acquisition of moral wisdom or judgment. Earlier thinkers such as Plato or Aristotle would have called this virtue phronesis, practical wisdom. While our own culture is preoccupied with a plurality of incommensurable educational goals—rational mastery of a subject, technical proficiency, the ability to calculate, to deduce, or to process data—the ideal of a liberal education has always been wise and responsible action in the world. Phronesis thus unites the theoretical and the practical goals of education; we might say that it is the good sense to know what to do with truth. Honed through imitation and continual practice, it is the skill of living a good human life in the world.2

The question arises, however, if the liberal arts are primarily academic in nature, how does such an education cultivate this virtue of practical rationality? The most direct answer is that they do not and cannot do so on their own. Acquiring the skill of living wisely in the world takes practice— real choices, real actions, real consequences.3 However, the liberal arts provide irreplaceable imaginative resources for acquiring this skill. In fact, imagination is perhaps principal among these resources, for the poets and historians have bequeathed to us the great gift of literature—narratives historical and fictional—where one may observe the lives of the wise and the foolish, experiencing those lives vicariously by entering imaginatively into their stories. Through the study of literature the student gains the kind of experience in life necessary for moral formation that his or her young age does not permit. Hence, what one lacks in lived experience he can glean from literary experience. Cicero adds a further dimension to our understanding of this imaginative effect of literary experience in his famous oration Pro Archia Poeta. “All books are full, all words of the wise are full, and all history is full of examples,” he writes; “I have always kept these images in view when serving as a magistrate, shaping my heart and mind after them by meditating on their excellences.” For Cicero the study of history and literature afforded by a liberal arts education not only instructed him but compelled him boldly to act for the common good of his community. The experience gained from the liberal arts provides narratives for making sense of one’s own life and directs one’s affections toward what is good and noble and true. Potent resources indeed for acquiring moral wisdom.

Sensus communis is closely connected to the skill of moral judgement. Although we often render this Latin phrase with the familiar words common sense, it is necessary to recall something of the technical meaning these words carry over from the art of rhetoric in order fully to appreciate their importance.4 Of course, we use the phrase common sense all of the time to mean an intuitive understanding of how to get along in the world, often contrasting it with academic or specialized knowledge.
(In fact, one is at times tempted to conclude that common sense is precisely the one quality many academics are lacking.) Although the ordinary meaning of the phrase is not identical to its technical sense, it happily flows from it. In classical rhetoric, sensus communis actually refers to that shared understanding of the world that a rhetorician can rely on when crafting his oration. It is not something he must prove, nor even that he will often state. Rather, it is that shared body of assumptions that invisibly bind together a group of people and, as writers from C. S. Lewis to Alasdair MacIntyre demonstrate,5 actually make moral reasoning possible in the first place. Since this quality was first marginalized and then suppressed during the Enlightenment, it is difficult for the contemporary reader to appreciate just how important the acquisition of common sense was to educators in the classical world.6 Aristotle notes in the Ethics, for example that the conscious transfer of the culture’s body of shared assumptions is one of education’s primary objectives.7

As a quality intentionally cultivated by the liberal arts curriculum, sensus communis is best characterized as a studied sense of the wisdom and insight (and indeed the prejudices and presuppositions) of previous generations. As such, it awakens us to that indefinably familiar atmosphere that breathes through the pages of the stories, shapes the historical narratives, and inflects the language of a people at a given place and time. It develops a conscious sense for what is commonly, though implicitly, held to be true. Common sense is thus closely related to what Edmund Burke famously coins the moral imagination in his Letter Concerning the Recent Revolution in France, and sounds remarkably like that distinctly human faculty-the chest-whose loss C. S. Lewis laments in the first part of The Abolition of Man. Philosopher Paul Ricoeur also seems to be invoking this sense of the common, when he speaks of the insight into life acquired via the “long detour” among the literary and imaginative works of humanity.8 He argues that what seems to be a detour is actually the obligatory path we must take if we are to understand ourselves and our culture. Failure to take this detour, to run along this path, is to guarantee the short-circuiting of self-knowledge. Interestingly, Ricoeur’s detour among the historical, aesthetic and philological disciplines is actually the well-worn path of the liberal arts curriculum—the study of history, literature, poetry, and language. The liberal arts connect us to our historical tradition by cultivating a sense for what is held in common throughout the history of that tradition.

The development of taste is something of an aesthetic analog to the cultivation of common sense. While it is not only artists who need to cultivate taste, reflection upon their experience is helpful in understanding its foundational importance. For to become a musician, fine artist, actor, or poet, is to take the long detour via the aesthetic achievements of humanity. The cellist works through the instrument’s received repertoire, the fine artist makes master copy after master copy, the actor rehearses the same lines countless other actors have performed for generations. I suppose we grasp intuitively the role tradition plays in the pedagogy of the arts. Lest we fail to recognize its significance, however, it is important to see that the specific claim of the arts in this regard is that creativity and artistic sensibilities are formed by attention to tradition. Picasso, to cite a somewhat dated but brilliant example, is highly original (to many of his time shockingly so); yet, without the tradition of European masters, there would be no blue paintings, no Guernica. Again, we grasp all of this intuitively; but how often do we fail to reflect upon the actual process of artistic formation when we wonder over much that is crass, tasteless, or vulgar in contemporary culture? The development of aesthetic taste, like the development of the adult palate, is formed by experience. As common sense is a studied sense for
the commonly held truths of a culture, taste is a sense for what is fitting or decent that is cultivated over time and experienced in the arts.

The liberal arts are more timely than timeless.

I asserted above that the most compelling reason to pursue a liberal arts education is that it cultivates the qualities necessary for human flourishing. To understand why this makes the liberal arts relevant to contemporary culture it is necessary to place our cultural moment within historical perspective. The last century witnessed a series of radical upheavals in the cultural and intellectual life of Western civilization. While one is tempted to think here only of cultural developments—the world wars, the advent of the nuclear age, or the sexual revolution—the intellectual landscape changed forever as well. Most importantly in this regard is the abandonment of what some intellectual historians have termed the Enlightenment project.9

To paint with very broad strokes, the Enlightenment is an episode in the intellectual life and culture of Western civilization, where on the basis of and in reaction to a number of factors—scientific, social, religious, and political—Western thinkers experienced an acute loss of confidence in central elements of human tradition and in the institutions which embodied and perpetuated that tradition. Where Western civilization had been maintained by a tensed harmony (at least in theory) of a number of incommensurable authorities—faith, tradition, reason, experience, community—the Enlightenment project is perhaps best characterized as the attempt to secure the goods of that tradition upon the putatively certain ground of reason. A brilliant illustration of this project
is Immanuel Kant’s 1784 essay An Answer to the Question: What is Enlightenment? in which he famously describes enlightenment as man’s emergence from self-imposed immaturity, an immaturity strictly defined as reliance upon such traditional mediating structures and institutions as books, doctors, priests, and judges in human intellectual, physical, religious, and moral life. To be enlightened, claims Kant, is to dare to think for oneself—sapere aude!— and thus his ideal human is a rationally autonomous subject for whom reason is the sole guarantor of human intellectual and moral goods. The notion that human flourishing is dependent upon anything more fundamental than reason is precisely what is repudiated here.

By the mid-twentieth century, when the realization that the European Enlightenment had culminated in the most devastating (and efficient) elimination of human  life the world has yet witnessed—indeed, greater in quantity than all armed conflicts in human history combined—recognition of the Enlightenment project’s failure was widespread. Yet, it was not merely malaise or disillusionment that signaled the end of the Enlightenment. Throughout the twentieth century there was also a succession of insights—notably from the sciences— concerning the role historical tradition and community practices play in forming our philosophical outlook, the influence that religious (or anti-religious) presuppositions have in our reasoning, and the comprehensive effect that language and culture have in shaping our understanding of ourselves and the world in which we live. With this succession of insights has come renewed appreciation for the displaced notions of faith, tradition, reason, experience, and community. There has been renewed appreciation as well for the practices and ways of being in the world that gave these notions plausibility prior to the Enlightenment.

It is this new way of thinking about human rationality that provides a renewed context for liberal arts education, and the most compelling case for its contemporary re-appropriation. An Enlightenment view of reason has simply proved too narrow to account for human rationality, much less to secure the goods of human life. The historical, aesthetic, and philological disciplines of the liberal arts curriculum, however, are especially well fitted to the more robust understanding of what it means to be rational in our current intellectual situation.

Beyond the “well-rounded” student

Understanding this historical context also helps us to perceive the problem with the commonplace notion mentioned above that a liberal arts education produces well-rounded people. For it was precisely as an unquestioning response to Enlightenment rationality that the liberal arts were first defended as the means of making well-rounded persons. The rational and scientific disciplines, so the thinking went at the time, set the standards for what it meant to be well educated. The liberal arts are important for making one refined, cultured, humane. Thus, taste, common sense, and judgment were understood to be important subjective or intuitive qualities one should develop while acquiring an otherwise objective and scientific education. However laudable the intention, this notion is tragically mistaken for at least two important reasons. In the first place, rather than maintaining the liberal arts in something of a separate-but-equal status with the sciences, emphasizing their cultural or refining qualities actually served to relegate the liberal arts to educational window-dressing. In the age of science, urbanization, and industrialization, such accoutrement was superfluous—indeed, when it comes to making the automobile, not only history, but art and literature too, are bunk. In this brave new world of progress, the very notion of refinement was seen to smack of elitism and old-world aristocracy. Moreover, in light of the discussion above, it ought to be clear that the relegation of the liberal arts to
the periphery of the curriculum was philosophically naive. It was not apparent in the nineteenth century, but we see now that the qualities the liberal arts cultivate, much more than rounding out a practical, scientific education, actually play a fundamental role in the acquisition of human understanding as such. The liberal arts are thus essential to and not just an accidental element of education.

In The Abolition of Man C. S. Lewis writes: “And all the time—such is the tragi-comedy of our situation— we continue to clamour for those very qualities we are rendering impossible. You can hardly open a periodical without coming across the statement that what our civilization needs is more ‘drive’, or dynamism, or self- sacrifice, or ‘creativity’. In a sort of ghastly simplicity
we remove the organ and demand the function.” He is lamenting the failure of modern education to cultivate
the very qualities we have addressed all too briefly in this essay—moral judgement, common sense, and taste—not, we should note, critical thinking or academic rigor. Modern education rendered the cultivation of these humanizing qualities impossible because it displaced the liberal arts curriculum with what was imagined to be a more practical or more relevant curriculum. Chesterton once remarked that thoroughly worldly people never understand even the world. Perhaps we could adapt his words here and apply them to our discussion: thoroughly practical people never understand what is truly practical. So in its departure from modern education, the Christian classical renewal has come to understand that it is precisely the liberal arts curriculum—that seemingly impractical detour among the literary and imaginative works of humanity— that cultivates the qualities necessary for meaningful human action, and indeed true human flourishing.

What is Mathematics and Why Should Students Learn It?

Posted on by Paul Drake

When I am in the middle of a lesson, cooking along explaining things, working examples, perhaps rejoicing in the beauty of the subject matter (or my own perception of cleverness in thinking up a new analogy), there is always one question a student can ask that is guaranteed to throw me off my groove. That dreaded question is, “Why do we have to learn this?” As we get more seasoned and experienced as teachers, we perhaps learn ways to set things up in the beginning so that students are not tempted to ask this question. But even though I have been teaching for 16 years now, I still get it from time to time.

We may as well extend the question to all of mathematics. Why should students learn math at all beyond the simple skills needed to count change and pay bills? The need for learning more advanced mathematics may be obvious for students who will grow up to be scientists, engineers or financial officers. Naturally, one cannot do what an engineer has to do without a substantial background in advanced mathematics. But are algebra and geometry necessary for everybody? It is very easy to think, “Of course everyone has to take algebra! Everyone always takes algebra!” But our task is to see if this response can be justified.

For starters, we can probably all think of examples that illustrate just how challenging this question is. My own youngest daughter, now a senior in high school, struggles mightily with math and longs for the day when she can be done with it. She does feel bad about this, since I am her dad. Still, she wishes she lived in Jane Austen’s world, needing only to develop the “accomplishments” of a young lady, which happen to be the very things she loves— music, needlework, drawing, literature, and French. I, too, sometimes wish she could live in that world. That would be a nice life.

A completely different example is found in one of the great literary lights of the mid-twentieth century, Thomas Merton, author of The Seven Storey Mountain. Many of Merton’s formative years were spent in Europe, and as a youth Merton set his sights on studying at Cambridge. However, the very demanding exams he would have to take included mathematics that he had no talent for. He almost despaired of realizing his dream but then learned that he could avoid the math exams by even higher level achievement in the humanities, namely, studying his literature in the original languages and being examined accordingly. So, in addition to the classical languages he mastered and read Italian, French, and Spanish, passed the exams, and went to Cambridge.

It would be difficult indeed in contemporary times to design a school that can give prodigies like Merton what they need, and still be suitable for ordinary kids, as most of our students will be. I think I would be happy for any prodigy like Merton or Mozart to focus mainly on where his gift lies. I’m not going to worry about whether Mozart or Merton ever take algebra. But such prodigies are rare, and we must develop a rationale for our schools that applies to the other 99.999% of our students. The example of my daughter is probably a better example to challenge us as we address this question of why students should take mathematics. What about the ordinary kids? Why can’t girls be taught the way girls in Jane Austin novels were taught?

Before we develop a justification for including math in the curriculum, let’s pause for a moment to define the subject. To do this, I would like to make some observations about how the human mind works. Classical and Christian Education (CCE) schools typically emphasize the Trivium—grammar, logic, and rhetoric—and as a result students tend to exhibit above average performance in written and verbal expression through language. This is laudable, but interacting with the world and other people in the world through the written word represents only one part of human capability. The human mind is also wonderfully adept at imagining and discovering patterns, and communicating these symbolically. Moreover, as we have discovered during the past 400 years with the rise of contemporary science, our response to God’s creation is sometimes better facilitated by words, as in poetry or prose, and sometimes in the form of symbols, as in music and architecture. When the subject matter at hand deals with patterns, and with communicating ideas about specific patterns, communicating through the use of symbols is much more efficient than communicating through words.

This brings me to my definition of mathematics, a definition that is not original with me. I define mathematics as the study of patterns, a study that includes manipulating and expressing ideas about patterns symbolically and quantitatively. And though I will not be specifically addressing the Quadrivium in this essay, it seems to me that the key characteristic of the subjects in the Quadrivium, and the key thing to be preserved in education from the Quadrivium, is the centrality of searching for, identifying and describing patterns.

And now to our justification for including mathematics in the classical curriculum. Although it may sound strange to those espousing classical education, the first reason for teaching mathematics is the sheer practicality of well-developed mathematical skills. Please do not howl and stop up your ears; I am neither a modernist nor a utilitarian. But I ask, as I once was asked, “Should classical education be an ideal thing, or a realized thing?” Since we are here trying very hard to realize it at our schools, we must answer, of course, that it is to be a realized thing. Realizing any educational paradigm in any culture must involve the practical cultural question of who gets educated and why. In our culture it is not only the elite who get educated; it is everyone. This is a plain fact of democracy. We have no formal class system, we promote the freedom of the individual, and we have an educational system that has as its fundamental goal the broad education of the entire population so that every child has the opportunity to make his or her way in the world according to his or her own abilities and industry. In this country, in this century, education is for everyone and must serve the need for everyone to function in contemporary society. To do this, education must be practical. This means it will include living foreign languages, chemistry, and, of course, mathematics.

Practicality is defined by the age in which one lives. Practicality used to be about computing quantities of seed for planting, figuring sizes of parcels of land, or calculating exchange rates and unit quantities for commodities. Our high-tech age brings different requirements for the citizens. Nearly every job in the professional world, and many jobs in the trades as well, involve fairly sophisticated math. One doesn’t have to be an engineer to get into budget forecasting, statistical analysis of surveys, setting up spreadsheets, pre-tax paycheck deductions, network download rates, amortization, interest and tax calculations, cost vs. benefit analysis, the storage capacity of a back-up hard drive, and on and on.

Now, if practicality is one of the reasons for teaching math to everyone, it is also one of the criteria for determining what mathematics everyone should learn. When math is taught to everybody, practicality is a primary issue. This is why it is wise to require math studies to continue at least through Algebra 2 for all students possessing average or above average mathematical ability. Just as we expect everyone to gain a serviceable level of English proficiency for reading and writing, but do not expect everyone to be a writer, so in math we set the goal of a serviceable level of math proficiency suitable for life in the contemporary world, but do not expect everyone to be an expert in calculus. For many students this goal means that studies in math continue through Algebra 2, with perhaps some introductory statistics.

A student might reasonably argue that learning exponential decay functions or rules for powers and roots goes far beyond what is practical for most people. This is a reasonable point to make, and my response to it is two-fold. First, learning these more advanced skills in Algebra 2 is analogous to athletic training. Athletes train with arduous exercises, but this does not mean they will repeat these same actions in the game. The drills are demanding and are designed to get the athletes in shape so they can handle the actual game effectively. Similarly, we will expect that some mathematical topics and problems will be taught for their training value, and not because a particular type of relationship or function will be specifically needed in later life.

Second, contemporary issues constantly require citizens to think in quantitative terms, particularly in terms of a functional relationship between two or more variables. Mathematical relationships are now ubiquitous in modern society in every discussion of medicine, climate change, computer technologies, energy efficiencies, taxes, investments, survey results, profitability, trade, and so on. Exponential and power/root functions do come up all the time in particular fields of endeavor. But more generally, learning to handle them trains the mind to think in quantitative terms, with legitimate mathematical reasoning.

We are Americans living in America, and for 200 years Americans have been world-famous for their interest in practicality. If you want to get anyone’s attention in our culture today, including the professionals who are the parents of our students, you had better have a firm grip on the practical side of your discipline. Nowhere is this more true than in math and science. The competitive, high-tech, corporate-driven world we live in is unforgiving of weaknesses in math and science. If you can’t handle the math or the physics, there are plenty of students in developing countries who can, and they will take your place at the table and leave you to work your way up to an assistance manager’s job at Best Buy. Solid skill in math and science is very practical.

This brings me to one final point I wish to make on the practicality issue: without mastery (one of my favorite topics), no practical skill has been gained, and your efforts in the classroom have been in vain. Schools cranking out graduates that cannot do math are a dime a dozen. Our challenge in the CCE movement is to find a way to break through these decades of low performance into a new realm of proficiency and competence. Is this possible in a democracy? Ultimately, I do not know. But I think if we are wise in our efforts we will have our school families on our side as we do the hard work of developing a mastery-based curriculum.

So much for the practical value of teaching and learning mathematics. But while the modern world may be driven almost exclusively by the practical, for teachers in schools espousing a classical philosophy, the practical is not nearly enough. The reason for this is that as important as all the practical things are, they do not even come close to exhausting what being human is all about, and the core of the classical model of education is the goal of developing good human beings, not merely equipping people with practical trades.

Once we crack open the door on classical considerations for why we should study math we find that the reasons are just as extensive, if not more, as those on the practical side of the question. We could, for example, consider further my earlier point about the way the human mind works, and its capacity for expression in words as well as in mathematical symbols (as well as in the forms, colors and harmonies that are the raw materials of the arts). Or we could consider the matter from Plato’s point of view. In the Republic Plato taught that the proper subject for the education of a free man is that of being, the realm of the transcendent and permanent, as opposed to becoming, the realm of the temporal and transient. This was because he recognized in humans some kind of eternal, transcendent soul, and he viewed the proper task of education as feeding that transcendent soul. He saw mathematics as deeply connected to permanent, unchanging, transcendent truth, and thus a fitting subject for human beings to study. A third direction we could go would be to consider the Christian doctrine of the cultural mandate, and our understanding that Scripture charges God’s people with using Creation and all art, science and technology to improve the lives of fellow human beings, which is part of carrying out the Second Greatest Commandment. Finally, we could consider classical education from the point of view of pursuing truth, goodness and beauty as a means toward the development of wisdom and virtue.

For the present we will consider only the last of these possibilities, the pursuit of truth, goodness and beauty.

A good definition for classical education is the development of wisdom and virtue through the pursuit of truth, goodness and beauty. This ancient trilogy, reflected so vividly in Scripture in passages such as Philippians 4:8, focuses our attention on the deepest aspects of our humanity. G. K. Chesterton once wrote, “Art is the signature of man.” Creating or studying art requires the appreciation of truth, goodness, and beauty. Interestingly, so does making progress in fundamental scientific research. Let’s briefly consider truth, goodness and beauty and their relationship to mathematics each in turn.

The nature of truth has become clearer since the mid-twentieth century, for now we recognize that science and math are not so much concerned with discovering “truths” about the universe as they are modeling the universe. Students do not generally appreciate this until we lead them into discussion about it. Instead, they tend to take the findings of math and science as givens, as unchanging, eternal verities. But then we lead them to consider that science is not about discovering truth; it is about modeling the apparently infinite complexity of the natural world in an unending attempt to understand it better. And we lead them to understand that a similar principle applies to mathematics. The most glorious discoveries have
been realized through learning the language of nature, mathematics, beautiful structures that can only be described mathematically, such as Maxwell’s Equations describing electromagnetism or Einstein’s General Theory of Relativity describing gravity.

But we also know that the connection between mathematics and truth is elusive. Kurt Gödel’s 1931 theorem demonstrated that mathematics can be consistent or comprehensive but not both. And before that the nineteenth century realization that Euclidean geometry was merely one convenient geometry among many geometries, and did not carry truth about the structure of the universe the way people had thought it did since the days of Euclid himself, brought many a philosopher to tears. If Euclidean geometry was not true, what was it? A great question; one we continue to explore. As I said, students do not appreciate these things unless we lead them into the discussion. However, once we distinguish these studies from truth itself and begin to use the arena of mathematics and science as a field for the continuing pursuit of truth, a deep and fruitful discussion begins.

Goodness is all around us in math and science for the simple reason that God declared his creation “good.” Thus, an element of our interaction with nature through math and science is the recognition that it is good that the apparent diameters of the sun and the moon as viewed from earth are nearly the same. It is good that the constant of proportionality in the relationship between mass and energy is simply the speed of light squared. It is good that the number of ancestors in each generation back from a given honeybee is given by the Fibonacci sequence. It is good that the planets’ orbits may be characterized accurately (though not exactly!) by Kepler’s Third Law of Planetary Motion. The double helix of our DNA with its multiple layers of instructional encoding and its capability for self-replication is inexpressibly good. So are the navigational abilities of migrating birds, the Doppler- shift detection capabilities of bat sonar, and the hexagonal shape of ice crystals. It is very good that all of nature displays a magnificent, sublime mathematical order that even non-Christian scientists have described as essentially miraculous. And it is very, very good that we humans have the cognitive ability to perceive and describe this order— these patterns—with mathematics. When students learn mathematics, the doors to see these things open before them. What could possibly be better than learning the language in which nature speaks to us, a language that enables us to behold the very goodness of God?

The third object of our pursuit as we develop wisdom and virtue is beauty. The relationship between mathematics and beauty is nothing short of mystical. It has been written about for ages, and illustrated in countless ways by countless writers, and yet we never tire of the subject. For many decades now scientists have recognized that the most valuable physical theories are those that are expressible in beautiful equations. Beauty has become a research tool, enabling us to probe the mathematical structure of the creation further and further. As with truth, leading students to see and appreciate the deep relationship between beauty and mathematics takes no small amount of effort. One has to begin by defining beauty. Then we have
to establish the criteria we all use, usually subconsciously, when we make aesthetic judgments of all kinds. Finally, we have to demonstrate how these same aesthetic criteria apply in the domain of mathematics. As I said in the beginning, mathematics is the study of patterns, and patterns amaze and enthrall us with their beauty, from the patterns in a carbon nanostructure to those in the endlessly fascinating Mandelbrot Set. It is worth the effort to lead students to the point where they can consider and ponder beauty through the lens of mathematics.

Why should students study mathematics? We have seen that the study of mathematics is eminently practical, as practical as knowing how to read and write. And we have seen how mathematics provides a forum and a framework for the exploration of truth, goodness and beauty, a pursuit at the heart of our humanity and at the heart of the classical understanding of how humans should be educated. So on the question of students studying math, I think at this point it is safe to ask, why shouldn’t they?

Abandoned Gifts

Posted on by Paul Drake

Carl J. Richard, professor of history at Louisiana University at Lafayette, has found a unique niche in the historical milieu. After receiving his Ph.D. from Vanderbilt University with a focus in early national American history and U.S. intellectual history, Richard has authored numerous books concerning the influence of the Classics on the Founding Fathers. One such book, Greeks & Romans Bearing Gifts: How the Ancients Inspired the Founding Fathers, superbly describes the importance of the histories and myths of the Ancients to the Founders of the United States. Richard correctly points out that the heroic stories of the Ancients which so influenced the Founding Fathers are virtually unknown to Americans today. Through his book Greeks & Romans Bearing Gifts, Richard attempts to remedy that problem.

In the introduction of his book, Richard admonishes current American culture for its abandonment of the ancient histories which so shaped the early United States. Indeed, he describes how unfortunate it is that the public is unaware of such stories, “for in neglecting [them] we neglect an important part of our own heritage.” Richard maintains that instead of looking to the heroes of the Founders for inspiration, Americans now look to the Founders themselves as the ideal American heroes. While venerating the founders of one’s country is certainly admirable, Richard calls for Americans to return to the Classics that influenced the Founders, for only then will Americans truly appreciate how the United States came to be as it is today.

Motivated by a desire to return to the stories of the Ancients, Richard devotes the vast majority of his book to just that: stories. Almost the entirety of the book consists of a chronological narrative of the foundings of Greece and Rome, as well as their respective falls. Richard understands the importance of telling a story well; he is a master-craftsman of tales, weaving colorful language and description throughout all of his accounts. In describing the stubbornness of Rome during the First Punic War, for instance, Richard constructs this vibrant sentence: “Rome was a pit bull that would not release its grip on the enemy’s leg, no matter how many times it was beaten on the head or offered the milk bone of peace.” Similar depictions abound throughout the book, making it an engaging and quick read. Yet such rich storytelling does not diminish the excellent historicity of Richard’s book in the slightest. He also provides a vast amount of detail, and includes an appropriate number of excerpts from primary sources, some of which the author translated himself. Richard constructs a delightful account of the stories of the Ancients, all the while maintaining the accuracy one would expect from his level of scholarship.

Richard does not simply leave his readers with mere stories, however. Instead, he supplements each chapter’s historical account with a “lesson.” Each chapter’s lesson describes explicitly how the stories found in that chapter directly influenced the Founding Fathers. After the chapter which recounts the Persian Wars, for instance, Richard notes that “[w]hen Jefferson wished to compliment John Adams, a staunch supporter of a strong American navy, he compared Adams with Themistocles, whose success in building the Athenian fleet had secured victory for Greece in the Persian Wars.” Such a comparison has true significance when placed after a chapter that devotes multiple pages specifically to Themistocles’ naval construction program. Without this historical background, however, the comparison would have been useless. Using the lessons at the end of each chapter, Richard bridges the gap for his readers between the Classics and their specific influences on the Founders, thereby demonstrating the Classics’ supreme importance.

While Richard provides an excellent analysis of how the Classics influenced the Founders, his analysis unfortunately stops there. Very rarely in his book does Richard acknowledge any other sources that influenced the Founding Fathers, a fact that may cause some readers to draw false conclusions. On some level, one can hardly fault the author for failing to extend the scope of his analysis to include other authorities of significance to the Founders; for the most part, that task is outside the purview of his book. Still, the inattentive reader could easily mistake Richard’s thesis to imply that the Ancients were the only influences on the Founders. While Richard himself would almost certainly deny such an assertion, his book does little to ensure that readers do not mistakenly draw this false conclusion. Had Richard at least tipped his hat to some of the other formative influences in the Founders’ lives, his book would have been much fairer and more comprehensive.

Still, Richard’s overall thesis rings true. The Classics enabled the Founding Fathers to piece together the wisdom of hundreds of thoughtful individuals from throughout the ancient world. The “Spartan frugality, selflessness, valor, and patriotism,” for instance, provided Samuel Adams with a model for the ideal citizen he hoped America would produce. Similarly, the accounts of Livy, Polybius, and Plutarch demonstrated that virtue was of critical importance to the success of a republic. Armed with insights such as these, the Founders far exceeded what they would have been able to accomplish without such positive examples. Additionally, the Founders were able to use the mistakes of the Ancients to attempt to prevent cancerous errors from developing in the civilization they were trying to create. For instance, the tyrannical reign of the ambitious Caesars of Rome assured American leaders of the necessity of a strong system of checks and balances. Indeed, the Founders learned from the fall of Rome “to regard one-man rule as an absolute horror to be avoided at all cost.” Such preventative insights enabled the Founders to avoid mistakes into which the Ancients had unknowingly fallen, thereby providing them the means to craft a more successful society. As Richard laments over and over again, the wisdom and insight gained from the Classics have little bearing on American culture today. Americans bask in the success of the Founders, not realizing the careful study their forefathers labored through in order to create the society modern Americans enjoy so much. Soon, after abandoning the Classics for so long, Americans are liable to forget where they have come from entirely. History repeats itself; America is certainly not above continuing that pattern. Without the strong backbone of the Ancients to speak wisdom into the lives of modern Americans, contemporary citizens run the risk of undoing all that the Founders accomplished.

Books such as Greeks & Romans Bearing Gifts, however, provide a shining beacon of hope. The charming prose and poignant stories of Richard’s book are sure to delight interested laypeople with a wide range of familiarity with the subject. In time, by re-infusing American culture with the stories of ancient Greece and Rome, the lessons from such stories may once again provide modern American culture with the needed wisdom it has far too long gone without.

The Enterprise of Learning as Wonder Toward Wisdom

Posted on by Paul Drake

Throughout history it often has been said that the process of learning begins with a sense of wonder/awe. It also commonly has been understood that the goal of learning is not merely the acquisition of information but the development of wisdom. In this seminar we will examine what it means to have a sense of wonder and how we can cultivate such wonder in our students. We also will discuss what it means to aim all learning toward the development of wisdom and how we can foster a love of wisdom in our students. Particular attention
will be paid to what it means to be a lover of wisdom (i.e. philosopher) within a Christian framework that acknowledges wisdom as beginning with the fear of the Lord (Proverbs 9:10).

David Diener

Dr. David Diener began his formal post-secondary education at Wheaton College where he graduated Summa Cum Laude with an undergraduate degree in Philosophy and Ancient Languages. After putting his philosophical training to work by building custom cabinets and doing high-end finish carpentry for an Amish company, he moved with his wife to Bogotá, Colombia, where they served as missionaries for three years at a Christian international school. He then a ended graduate school at Indiana University where he earned a M.A. in Philosophy, a M.S. in History and Philosophy of Education, and a dual Ph.D. in Philosophy and Philosophy of Education. A er teaching for one year at The Stony Brook School on Long Island he moved to Fort Worth, Texas, where he serves as Head of Upper Schools at Covenant Classical School. He also teaches philosophy courses for Taylor University and Southwestern Baptist Theological Seminary as an Adjunct Professor. The Dieners have four wonderful children and are passionate about classical Christian education and the impact it can have on the church, our society, and the world.

Wisdom and Eloquence

Posted on by Paul Drake

I really enjoyed reading Wisdom and Eloquence by Robert Littlejohn and Charles Evans. This is a well-written book, with certain chapters that should be read and re-read by all educators seeking to provide a classical and Christian education. There is good information here for everyone involved in the work of recovering a classical and Christian education.

The book also exhibits a central pedagogical departure from the application of Dorothy Sayer’s insight in The Lost Tools of Learning. In order for me to set forth this departure appropriately, it is necessary for me to back up, and give some background history. When our founding board began discussing what kind of education we should seek to provide, we knew that we did not want a fundamentalist reactionary academy, and we knew that we did not want a compromised prep school. So we came up with the motto, “a classical and Christ-centered education.” The word classical excluded a truncated fundamentalism, and the Christ-centered excluded a compromise with unbelief. Somewhere in this process I remembered an article by Sayers that I had read some years before. We tracked down a copy, and, with the view that this represented considerably more wisdom than we knew about, we adopted it, and resolved to give it a try.

Now the heart of Sayers’s article is her application of the Trivium (grammar, dialectic, and rhetoric) to the natural stages of child development. Her argument is that the Trivium is foundational, giving the kids the “tools of learning.” Now at the time, we could not have told you anything about the history of the Trivium and its relationship to child development issues beyond what we had read in Sayers. But what we did know (from Sayers), we put into practice and the results can only be described as a roaring success.

As the years went by, we read up on what we were doing, and learned a great deal more about it. In other words, we started blind, but we didn’t stay that way. And so it turns out a lot rides on whether we describe what Sayers was advocating as her historical explication of the medieval practice or, instead of this, describing it as the Sayers insight—what somebody really ought to try sometime (for the first time). Littlejohn and Evans point out (rightly, in my view) that the historical application of the Trivium did not do it the Sayers’s way. In other words, I don’t think that little kids in 1352 were taken through the grammar stage (the way they are at Logos), and then on to the dialectic stage, and so forth.

In my book, The Case for Classical Christian Education (2003), I refer repeatedly to the Sayers insight, and this is the reason why I referred to it this way. I believe that Littlejohn and Evans are quite correct on the historical point. In other words, if we look to Sayers for information on how they were doing it “back in the day,” we are going to miss the mark. But if we look to Sayers for a valuable idea on how this approach to the Trivium could and should be applied to modern education, we will find ourselves cooking with propane and extremely pleased with the results. And that is exactly what has happened to us at Logos. There are numerous indicators that I could point to here—from stellar test scores to nationally-recognized accomplishments of graduates. We have won the state championship in mock trial nine years (out of twelve years competing), and sent a mock trial team to national competition ve times. In short, as the sage once put it, “if it ain’t broke, don’t x it.”

A proposed departure from this is a significant part of the argument presented in Wisdom and Eloquence, and the point is reiterated a number of times. In short, the central contribution that Sayers has to offer (in my view) is the major thing that Littlejohn and Evans take issue with. This is not the end of the world, and I am sure that both gentlemen remain very fine educators despite disagreeing with Sayers on this. But it does represent a significant disagreement within the classical and Christian education world, and every classical Christian school needs to decide what they are going to do on this point. Both are fine dances, but you can’t waltz and do the Texas two-step at the same time. For their part, Littlejohn and Evans want to “separate the arts from the question of cognitive development altogether” (W&E, p. 39).

There is a significant amount of agreement in this disagreement. I agree that child development was not in view eight centuries ago. But suppose we reject the Sayers point considered as historical exegesis but go on to accept it considered as a new proposed pedagogical paradigm. The people who tried this in the early eighties in north Idaho didn’t know any different, and so we just went after it. The educational results have been astounding, and so if it was all based on a mistake it was therefore a very happy mistake. And further, the mistake would have been ours for assuming that Sayers was talking about how education used to be, and not about how it ought to be. I am not saying that Sayers shared any of our possible confusion on the point.

There is also an additional argument against going back to the purist view of the Trivium. One of the central reasons why we should not just return to the Trivium “as it was in the medieval period” is because
it used to be a pretty confusing hodgepodge. The simultaneous inculcation of grammar, dialectic, and rhetoric (along with the Quadrivium) is something that could get away from you pretty easily, and in the middle ages, it certainly did. Reading this book by Littlejohn and Evans makes me think that they have it well in hand, but this is more than could be said for some early forms of it.

Just two final comments and I am done. The first is to make sure we keep this difference where it ought to be—as a matter of important emphasis, and not as a matter of fundamental substance. In other words, every advocate of a graded approach to the Trivium acknowledges that none of these three stages are “pure,” free from all contamination from the others. Spelling is taught in the grammar stage, and spelling is a rhetorical matter.

It is important for ACCS educators to recognize that it is not going to be “pure grammar,” and then “pure dialectic,” and then “pure rhetoric.” These are not watertight categories. Nevertheless the Sayers Insight means that we emphasize the grammar of all subjects in the elementary years, the dialectic of all subjects in the junior high years, and the rhetoric of all subjects in the high school years. But of course, each stage will have important elements of the others contained within them. Students in the rhetoric years still have to memorize things, and students in the grammar stage learn to make letters that stay within the lines, thus presenting a more pleasant rhetorical effect. For their part, Littlejohn and Evans retain an understanding of the importance of gradation—they just don’t tie it together with the language of the Trivium (e.g. pp. 130, 164).

Having said all this, I suppose it means that I believe that the Sayers Insight represents a better application of the medieval Trivium than was practiced in the medieval period itself. And it would follow from this that I believe schools that follow the Sayers Insight will enjoy richer educational fruit than schools that simply return to the practice of teaching all seven of the liberal arts at every age.

But this is just a disagreement, not a collision. I still recommend this book highly—there is much to be gained from it. Schools that follow the pattern suggested here will no doubt be superior to many of the typical American schools around them. At the same time, I do believe that ACCS schools should be encouraged to stay the course on this point. But of course I would say that—you don’t work for MacDonalds in order to sell Wendy’s burgers.