Paul Drake

“What’s a Trivium? And Who’s Plato?”- How to Speak “Classical” for Progressively Trained Educators

Posted on by Paul Drake

The way that classical educators think and talk about education is fundamentally different than the way most of us have been taught to think our entire lives. When training new teachers — who are rarely trained in classical education — we like to say it is like crawling out of the Atlantic Ocean, running across the continent and jumping into the Paci c. Teachers are changing educational oceans, and they have to come across a large, rocky continent of vocabulary, philosophy, psychology and experience to get there. Because so many teachers in classical schools come from progressive backgrounds, it is essential for them to understand three crucial differences: 1) who we teach; 2) how we teach; and 3) why we teach. New teachers — and those who train them — will leave this session with a rm grasp on some key vocabulary within classical education, as well as a clear picture of how it compares to the educational environment of the last century. We will also discuss a few practical pedagogical tools every classical educator needs in his or her repertoire. Lastly, we’ll discuss why what we’re doing matters, not only for the embodied souls of our students, but for the public good, as well.

Dusty Kinslow

Dusty Kinslow holds a master’s degree in educational leadership and has served as the Head of Austin Classical School since it opened in 2013. In the last five years, the school has grown from 13 to over 120 thriving students. ACS is a blended-schedule school that partners with families in the classical Christian education of their students, facilitating learning between days on campus and days at home. As such, Dusty also serves as homeschool mom to her three children within this unique model. She enjoys equipping teachers — both those in the classroom and those in their homes — with the tools to teach effectively, and she loves to come alongside educators to encourage them in the noble, difficult, creative and worthy endeavor of teaching. When she’s not teaching or leading, Dusty can be found sitting next to her husband while they cheer for their kids on the soccer field, watching reruns of The Offce or listening to any number of interesting podcasts while folding seemingly endless piles of laundry made possible by the aforementioned kids.

Paul Drake

Gravitas: The Lost Art of Taking School Seriously

Posted on by Paul Drake

It is quite remarkable that a potent paradigm gave birth to the classical education movement. Dorothy Sayers, using the word-pictures poll-parrot, pert, and poetic, made the abstract concepts of grammar, logic, and rhetoric concrete and memorable. These three stages have given structure and clarity to the long and somewhat inscrutable process of K-12 education, giving teachers and parents the confidence to start a revolution in education. Ms. Sayers also demonstrated the power of rhetoric: a simple truth expressed in an unforgettable way.

While we are still in the process of figuring out exactly how to implement these three stages, and how to flesh out the true potential of classical education, I would like to suggest we think about the unthinkable: adding another stage to our trivium trinity – the primary stage. The primary stage, K-2, has been traditional in education for many years, but it has not received the attention it deserves by classical educators. It has been more or less subsumed, mistakenly I think, into the grammar stage.

We would do well to focus on the primary stage to see how we can improve instruction and build a better foundation for the trivium that follows. Having taught everything from phonics to Caesar, I can affirm that skills acquired in the beginning years are of vital importance to the later years. If you are a high school teacher, you probably experience every day the results of inattention
to basic skills in K-2. Our students will not achieve the excellence we desire unless we come to a better appreciation of the primary school and recognize that life-long habits are formed here, good and bad.

I realized from the beginning that the primary school was very important and deserved special attention, so when I started Highlands Latin School I divided it into three levels, not those of the trivium, but rather primary, grammar, and upper schools. The primary school is K-2, the grammar school is 3-6 and the upper school combines the logic and rhetoric stages in grades 7-12. At each level students make an important transition, which at our school is made visible by an eagerly anticipated uniform change.

The classical curriculum begins in earnest in the grammar school, where students memorize the Latin grammar, followed by the logic stage in grades 7-8, where they study syntax and translation, and finally grades 9-12, where students read Latin literature. The trivium is a perfect fit for the study of Latin.

But the primary years don’t fit neatly in thetrivium paradigm – and they shouldn’t. At the time of the Renaissance, when classical education as we know it was born, students began their education at what was called a Dame School or Petty School, where students learned the rudiments of English before moving on to the Grammar School and the study of Latin and Greek. I think this is a good model for us today. Historically we have acknowledged the importance of this stage by giving it a name, so let us turn our attention to the content and goals of the primary school.

The first question that faces us in the primary school is what to do about Kindergarten, a transitional stage between preschool and real school. The five-year-old is not quite mature enough to sit still and focus at the level needed for real school. The solution for most schools has been
to intersperse academics with lots of play and preschool activities to fill out the day.

But a comment I overheard many years ago has always made this option unacceptable to me. I guess my ears have always been attuned to education, for I cannot account for why I should have noted, nor long remembered, a comment I overheard as a young child. A teacher, who had taught first grade for many years before the introduction of kindergarten in her school, complained to my mother that it was having a negative effect on her first grade class. The ears of this future teacher perked up.

The teacher went on to give the reason: the children who had spent a year in kindergarten enter First Grade thinking that school is play. As a result, teachers had to expend much time and energy in teaching children that school is not play, but serious work. She went on to explain that children used to come to First Grade in awe of school. Now they come, she said, with unrealistic expectations that school should be fun and that First Grade is not a big step in growing up, but just another year of school which happily involves lots of things, only some of which involve work.

Because of that voice of experience so many years ago I have always thought that it is a good thing that young ones be in awe of the big step of going to school. So what to do about Kindergarten? One solution would have been to just eliminate Kindergarten, but I didn’t feel that I could overcome the expectation of this firmly established tradition of modern American education. So I decided to compromise by designing an academics- only kindergarten, but in a reduced two-day schedule. The content is academic and age-appropriate, and the limited number of days makes allowance for the younger age and limited attention span
of the five-year-old, who still has plenty of time for play at home.

Kindergarten has introduced into our education culture a profound confusion between preschool methods of learning and formal methods of learning. Play and exploration, are the way the pre-rational child learns. But the methods that are appropriate for the pre-school child, unfortunately, have been introduced up through the grades as if there is a continuum between preschool and school, and no difference in the proper leaning activities of the two.

The essence of the preschool learning model is the preschool explorer. The preschool child learns by play and random, non-systematic exploration of his surroundings. The essence of formal education, however, is just the opposite. Once the child is old enough to learn through reason, he is able to acquire the artificial, abstract tools of human learning: letters and numbers. The methods proper to formal education are not play, discovery, and exploration, but rather systematic instruction.

This progressive model of the happy preschool explorer eagerly investigating his surroundings and making discoveries through his own untrammeled curiosity is the rationale for the discovery method of learning. The progressive educator, just like Dorothy Sayers, uses word- pictures and rhetoric to convince the unsuspecting parent that only through continuing with these methods, can the joy of learning be maintained permanently in the education process.

This is the essence of progressive education and is the single most destructive influence in education today.
It has become the air we breathe and there are few, even among classical educators, who are immune to it. The romantic notion that the joy of learning characteristic of the preschool child is the model of learning for the formal education of the classroom is the siren song of progressive education. It is sheer nonsense. Until educators and parents realize this, we will never achieve excellence in education.

Think about the piano teacher or the basketball coach. Would any parent pay for lessons in which the teacher allowed the student to discover the principles of his skill on his own, claiming that method to be more fun and effective? What does the coach offer? Blood, sweat, toil and tears; and the kids line up for it. Young people want a challenge; they want to be taught. It is an insult to the child to have adults worried about whether they are having fun.

Instead of the mistaken notion of learning as fun and exploration, we must return gravitas to the classroom. Gravitas is the element most lacking in the K-12 classroom today. American culture today is so shallow and pleasure- sodden that we don’t really know what gravitas is anymore. It is not a word heard often. It is a sense of seriousness about what we are doing. Our work in Christian terms is a high calling from God. There is no better picture of gravitas than the Romans. The Romans had gravitas. As Christians we should have it too, but with the added element of joy.

What does gravitas look like in the primary classroom? Gravitas is not severe or grim, but it is serious. Our K-2 teachers are at the front of the classroom with a podium, like all of our teachers. The podium is not a place to lecture, but rather a place to put curriculum materials so the teacher can be organized and teach effectively. All desks face the front of the classroom, which has an absence of learning centers, since all students, instructed by the teacher, are working on the same skills together. K-2 students do activities and games to practice skills, but
the classroom is always quiet and orderly, because all are engaged in purposeful activity that is an efficient use of time.

Our students do have calendar time on the floor, but that is the only activity that takes place on the floor. (Sitting on the floor is the iconic image of the progressive classroom.) We have music, art, recess, and cut, color and paste for those small motor skills. We use materials and methods that are appropriate for the attention span and cognitive skills of the young child. But our Kindergarten is serious grown-up work, which, in fact, motivates the young much more than play. The child wants to do grown-up things; that is his motivation for coming to school. He wants to be like the older kids. He can play at home for free. Awe and wonder are the ideal attitudes for learning and we strive to maintain that awe in every grade, including and especially in the primary school.

It is only with gravitas that we can return awe to education, and at the same time make our primary years, as well as all of the trivium years, models of true excellence. Gravitas is concerned not only with the school culture but also with its content. I believe that gravitas in the primary school means that we take very seriously those important foundational skills of reading, writing, and arithmetic, the three R’s. I often tell my primary teachers that they are doing the most important work in our school, and all that we accomplish in the higher grades depends on what they achieve in those first few years.

Those foundational skills have a huge effect on the student’s academic career, and can, if poorly taught, turn into a huge impediment to success. The basics are so important that there is little time for anything else in the primary school, where students need an exclusive and concentrated focus on reading, writing and arithmetic, without the distraction of other “subjects”.

Because we classical educators are always thinking ahead about the high levels of achievement that our students will attain, it is tempting for us to overlook the importance of the basics and how fundamental they are to building the tower of learning. But a weak foundation will eventually crack before attaining that high level of learning we seek. All of the three R’s are equally important, but in the space remaining, I will address only one, the skill of writing.

By the skill of writing, I mean the physical act of writing, not composition. The skill of writing begins with the correct pencil grip and ends in smooth legible manuscript and cursive. Correct pencil grip greatly reduces hand fatigue and resistance to putting words on paper, and greatly increases pleasure in the physical act of writing. It is a huge asset for the student to be able to write rapid, legible cursive, with comfort and enjoyment.

Unnecessary hand fatigue and illegible penmanship have a very deleterious effect on academic progress. My public school experience teaching high school math and science many years ago taught me the importance of legible penmanship. Many of my bright, eager students could not read their own writing. They were woefully lacking in the basic humble skills that begin in the primary school. My students also had great resistance to putting anything down on paper. The physical act of writing was a chore they avoided, rather than a skill they could use with pleasure. I saw first hand how serious handicaps in learning resulted from poor instruction in the basics.

I don’t think there is any more visible evidence of the degraded state of education today than students’ handwriting. This struck me one day when a gentleman, seeking affirmation that his money was well spent at a private Christian school, gave me a sample of his granddaughter’s school work for my evaluation. The sample he showed me was one of those mindless online worksheets, filled in with writing that looked like chicken scratching. Not only was it not cursive, it was illegible manuscript. I mumbled some answer, but privately wondered if any of my students had such horrible handwriting.

I had always had my mind firmly fixed on the power and importance of Latin for the development of the mind, but I realized that I would look very foolish, if extolling, on the one hand, the benefit of a classical education, I was, on the other, overlooking the value of the humble basic skill of good handwriting. I vowed then and there to make sure that our students would be taught good cursive penmanship and pencil grip. What is interesting, in retrospect, is the power of the visual; that I made an immediate judgment about this school based on the penmanship of one of its students.

I have come to realize that little ones are growing and changing rapidly in K-2, and instruction that teachers think is solid and sure, is easily forgotten or ignored. Young ones have strong tendencies to experiment and change both pencil grip and letter formation on any given day and for no apparent reason. It takes years and much repetition to insure that good practices in all of our basic skills become firmly imbedded habits.

As classical educators we need to make sure we are not overlooking the primary school and the level of gravitas and attention to detail required to develop good habits that will last a life-time and ensure that our students have the foundation they need to be successful in classical education.

Paul Drake

The Formula Heard ‘Round the World

Posted on by Paul Drake

Revolutions tend to be noted for radical breaks with tradition and bold new courses set. However, the term “revolution” can also mean a return to an earlier position. Perhaps then, the most radical of revolutions combine elements of both by rejecting the cult of the new, spurning assumed progress, and breaking from the path not for new frontiers but a wise reclaiming of older customs and timeworn wisdom. Revolutionary or not, at the very least, if one finds himself on the wrong path, the only wise course is to simply turn around. The Christian Classical school movement is just such an example. American schooling has been on the wrong road for a very long time, and classical and Christian educators are attempting to turn around and return to wiser approaches to education. In this effort, a formula known as the Trivium has played, and continues to play, an essential part.

Surveying the physical and cultural destruction of Europe in 1947, popular author Dorothy Sayers composed and presented at Oxford her essay “The Lost Tools of Learning,” which shockingly argued that for Western Civilization to truly advance in education, it needed to return to the Medieval Age.1 Her essay emphasized the failings of modern education in preparing people to think and to learn. The abandoned tools of education to Sayers were encapsulated by the medieval commitment to the Trivium. Comprised of grammar, logic/dialectic, and rhetoric, Sayers believed the Trivium held the key for reviving an effective and proven form of learning. Though powerful and persuasive, Sayers’ essay and revolutionary formula would require several more decades before her advocated return gained much traction.

In 1991, Douglas Wilson published the book Recovering the Lost Tools of Learning and thereby effectively launched the contemporary Classical-Christian school movement.2 At the time of its publishing, Wilson had already worked to apply insights from Sayers’ essay into the private Logos School in Moscow, Idaho. With the publication of his book, many more would look to advance their own children’s education by returning to “old ways.” The Trivium as a formula for education was about to start a revolution.

Revolutions depend on revolutionaries; and, both Sayers and Wilson are essential to this revolution’s success. However, true revolutions are not ultimately defined, controlled, or contained by even crucial individuals and the Classical-Christian school movement is no exception, so it must be understood at the outset that Classical- Christian schooling is not restricted to the thoughts of Sayers or Wilson.3 Likewise, revolutions rarely respect history, even ones inspired by it. Here again, the Classical- Christian school movement follows this revolutionary law. Consequently, exactly how “classical” or “medieval” the movement actually is historically is up for significant debate. Socrates and Aquinas, just to name a few, would not necessarily recognize all that goes on at “classical” schools or even claim them as their own. Nevertheless, history, through the modern interpretation of Sayers and Wilson and others, has provided a very attractive formula for education, which has been enthusiastically adopted in a large and growing number of private schools. And so, to understand what is taking place at these classical academies, one should be aware of how the Trivium is being applied for it arguably remains the distinguishing mark of the contemporary classical school.

Interestingly, the Trivium as applied by schools today has actually taken three main forms. The most obvious and least surprising way is their embrace of the three official subjects of the Trivium. While it would be rare to find a modern public school labeling a course, or perhaps even a lesson, as grammar or logic or rhetoric, one will find all three at contemporary classical schools. Mastering the construction of sentences, memorizing logical fallacies, and effectively using words orally are not only skills emphasized within familiar classes on history or science, they are entire stand-alone courses, oftentimes taken at multiple grade levels, at classical schools.

The second way the Trivium is typically applied at a classical school is far more interpretive. Here, the Trivium is used as a formula for learning any subject. In other words, mastery of a topic will always need to move through three ascending stages of mastery represented by the subjects that comprise the Trivium. If one is to master U.S. history or biology for instance, one must begin by learning the “grammar” of the subject. This grammar is the basic facts, terms, formulas, and language needed to ultimately understand and converse on the topic. Once students have mastered the basic facts, they move to the “dialectic” phase that concentrates on grasping how these facts interrelate. Ideally then, the student moves from a base, or even rote, knowledge to understanding. Finally, mastery requires a concluding step, rhetoric. Here, students progress from understanding a subject for themselves, to being able to effectively communicate the subject to others. For anyone who has ever taught even the most rudimentary of skills, it is obvious that it is one thing to “know” something for yourself, but quite another to be able to explain it effectively to another. The rhetoric phase is an acknowledgement that true mastery of a subject requires that final step of ability. Furthermore, rhetoric at this level also means applying the knowledge (grammar) and understanding (dialectic) already gained across disciplines into practical life. Thereby, the Trivium, applied to any subject, can mark the crucial transitions from ignorance to knowledge, from knowledge to understanding, and finally from understanding to wisdom.

The final way the Trivium is regularly interpreted in contemporary classical schools is as a formula for child development. Simply put, this belief holds that the typical child goes through grammar, dialectic, and rhetorical stages on the road to adulthood. Implicit in this application is that both the teacher and school ought to work with, rather than against, these natural stages of life and learning.

In this child development interpretation, the child begins in a grammar stage that roughly corresponds to the elementary school years. The fact that elementary school used to be widely called “grammar school” is not considered coincidental. As noted above, to master subjects students need to know basic facts about the subject. Conveniently, young children have proven to be outstanding at memorization. Even more remarkable, young children like memorization. Even nonsense words can be mastered with ease and enjoyment by elementary age children, particularly if put to music or chants. For the modern classical educator then, such an opportunity is not to be missed. In contrast, the typical contemporary school philosophy assumes that elementary school students will have plenty of time to learn basic facts in the future or will just naturally learn them through time. Consequently, most elementary schools embrace “play” as the activity de jure for their charges. The classical school instead capitalizes on the young child’s affinity for memorization and gives him a solid diet of significant material on which to work. While unfairly and inaccurately derided as “drill and kill” by advocates of the “play” approach, classical educators seek to have students leave elementary school with a substantial amount of invaluable knowledge stored in their memories. Both history and now contemporary classical schools have more than proven that this knowledge can be mastered in an effective and even pleasurable way especially since the elementary years are the ideal times in which to do it.

In considering the dialectic phase, it perhaps helps to start with a cultural fact: junior high kids are insufferable little wisenheimers. Put more generously, one notes middle schoolers’ propensity for argumentation, contradiction, and verbal gaffes. While educators throughout time have frequently been tempted to deal with this phase by locking them in their rooms until humans can stand to be around them, the contemporary classical educator takes a different course. Though an obviously dangerous act, the classical educator insists that if one wants to argue, then at least one should argue well. So, this “dialectic” stage at the classical school is characterized by instruction in logic, reasoning, and argumentation. While undoubtedly parents must at times regret the arming of these young madmen with more effective verbal weapons, the child’s personality merely demonstrates that the time is developmentally right to do so. Not incidentally, if these young debaters have been brought up with the Trivium, they already have a vast store of valuable knowledge to consider, which makes their verbal wrangling much more palatable and productive. In contrast, their public school peers, who have played their way through elementary school, while still determined
to verbally joust, have nothing to tilt but pop culture windmills.

Finally, according to the developmental approach to the Trivium, after passing through the challenging dialectic phase, young adults arrive at the “rhetorical” phase. In sum, the mark of teenagers is their desire to “express” themselves. However, as one can sadly witness in every mall in America, they are not very good at it. This truth remains despite the fact there are few items that fire the hearts of the typical American public school teacher more than self-expression. However, to paraphrase C.S. Lewis, most high school instructors, though enthusiastic, are unknowingly urging the geldings to be fruitful.

Having never given or demanded knowledge of their charges, much less clear thinking in earlier years, most youth, have, like, you know, little to say. In contrast, the classical educator is not left with empty pleas to “express yourself,” since the student brought up in the Trivium has been given the knowledge and understanding along the way necessary for the development of wisdom worth professing. And, here again, the classical educator looks to work with, rather than against, the grain. With students eager to communicate, instruction at classical schools in these teen years focuses on effective expression through, among other things, the spoken and written word. As with the dialectic phase, if a student has been educated throughout in this Trivium model, this focus on expression is potentially delightful because the child actually has a vast array of knowledge and understanding to articulate. While the modern’s obsession with self-expression reflects the fact that essentially all educators desire to produce rhetoricians – wise, eloquent adults – it is the classical Trivium model that actually provides a workable and proven formula to produce them.

In considering the Trivium as a formula for learning and child development, it should be noted that these ought to be understood as broad, general categories not rigidly fixed lines. All courses at all age levels typically would contain grammatical, logical, and rhetorical elements, assignments, and emphases. Again, the Trivium approach argues that mastering any subject necessitates going through these three stages of learning so newly introduced subjects will always require grammatical essentials even for adults. The Trivium is a useful formula, not an inflexible one. Much of the Trivium’s revolutionary power lies in its simplicity and clarity, but also its versatility. Thereby, those seeking to be classical in contemporary times should not feel compelled to follow narrowly a fixed formula to qualify.

When considering accurate labeling, the Trivium has also served to justify the very naming of classical schooling. However, while certainly historically rooted, the Trivium as an organized system of learning is far more medieval than classical. However, no one needs a marketing department to tell them that calling for a return to medieval times proves a much more difficult sales job, so “classical” was, not surprisingly, adopted instead. Since the overwhelming percentage of classical schools are first and foremost Christian schools, this accommodation to modern sensibilities is at least mildly lamentable for it is the medievals who attempted to build a civilization infused with Christianity rather than the ancient pagans of Greece and Rome. Furthermore, while all truth is God’s truth, there is nothing inherently Christian per se in the Trivium especially if your emphasis is on its classical origins which again would mark it as the product of pagans. Nevertheless, because almost all classical schools in the United States are Christian, the terms“Classical-Christian,” or now the more appropriate “Christian-classical,” have become so conjoined that they easily roll off the tongue. Thereby, perhaps our Christian brothers and sisters of medieval times will forgive our snub, if our efforts to provide a truly Christian education to our children run true. And, applying the medieval Trivium to the specifically Christian nature of Christian-classical schools offers one final area of potential application.

Author Stratford Caldecott’s 2012 book Beauty in the Word: Rethinking the Foundations of Education argues that the Trivium actually reflects the triune nature of God, and he challenges Christian, and particularly Catholic, schools to incorporate this understanding into their schools’ organization and curriculum. Caldecott implicitly criticizes the “tools” metaphor both Sayers and Wilson associated with the Trivium by making the “central idea” of his book “that education is not primarily about the acquisition of information. It is not even about the acquisition of ‘skills’
in the conventional sense…. It is about how we become more human (and therefore more free, in the truest sense of the word).”4 Caldecott’s work suggests the Trivium’s value as a formula could easily surpass the three primary ways described above by helping students and adults
alike understand the nature of the Father, Son, and Holy Spirit. Caldecott, in fact, offers the following “eight threes” inspired from the Trivium for educators to consider and apply:

Mythos Grammar Remembering Music/Dance One

True Given Father

Logos Dialectic Thinking Visual Arts True

Good Received Son

Ethos Rhetoric Speaking Drama Good Beautiful Shared Spirit5

A detailed account of Caldecott’s argument for these “eight threes” is beyond the scope of this brief essay, but at a minimum Caldecott’s work demonstrates that the revolutionary power of this “simple” formula known as the Trivium shows no sign of losing its potency or applicability. As committed Christians continue to mine the wisdom of the past and the Trivium’s formulaic potential, the prospects for truly Christian education to flourish only brighten.6 As a productive revolution, the Christian-classical movement, with the help of authors such as Dorothy Sayers and Douglas Wilson, has helped many parents and concerned citizens recognize that American education is hurtling down the wrong path. Thankfully, the Trivium has served as a simple but powerful formula of return to a better and more proven course. Through the insights of Caldecott and others, the Trivium should continue to provide an even more robust vision of an education worthy of creatures made in the image of God.

Viva la Revolucion!

Paul Drake

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?

Paul Drake

Introduction to the Trivium

Posted on by Paul Drake

It was a return to teaching the Trivium arts (grammar, logic and rhetoric) that started the renewal of classical education nearly 30 years ago. In fact much of the renewal of classical education can be characterized as “Trivium-Based Education.” This seminar is designed
for those new to classical education who need to understand the origin, development and modern recovery of the Trivium arts. In this seminar we will discuss the important of the arts as verbal arts that impart the mastery of language, and explore the place of these arts in the broader context of classical education that includes the Quadrivium, but also musical and gymnastic education. Finally, we will discuss the various ways the Trivium is being adopted and deployed in classical schools around the U.S.

Christopher Perrin

Christopher A. Perrin is the publisher with Classical Academic Press, a consultant to classical, Christian schools and the Director of the Alcuin Fellowship with the Institute for Classical Schools. Chris has taught at Messiah College and Chesapeake Theological Seminary and served as headmaster of Covenant Christian Academy in Harrisburg, PA from its founding in 1997 until 2007. He received his B.A. in history from the University of South Carolina, his M.Div. from Westminster Theological Seminary in California and his Ph.D. in Apologetics from Westminster Theological Seminary in Philadelphia. He was also a special student in literature at St. Johns College in Annapolis. Chris is the author of the books An Introduction to Classical Education: A Guide for Parents, The Greek Alphabet Code Cracker, Greek for Children, and co-author of the Latin for Children series published by Classical Academic Press. Chris and his wife Christine live in Camp Hill, PA with their three children.

Paul Drake

Astronomy: The Cinderella of the Liberal Arts

Posted on by Paul Drake

If the three subjects of the Trivium are the presentable sisters of the liberal arts, astronomy is the humble stepsister (of the Quadrivial clan) who doesn’t get out much. Yet hidden under that maidservant’s garb is the smash of the ball. Astronomy is the oldest of the arts, and one even mentioned by the Hebrew Scriptures. Over the past three hundred years, its method has become the paradigm for nearly all of modern academia. Understanding the spectacular influence of astronomy requires piecing together disparate parts of the puzzle. But after viewing the subject holistically, the conclusion is nearly unavoidable: for better or for worse, astronomy has shaped our contemporary society more than nearly any other liberal art. For, the core of astronomy transmuted to become the heart of modernity. From ancient origins to its present dominance, the liberal art of astronomy holds great favors for those who recognize her.

The Egyptians kept astronomical charts since as early as the 3rd millennium B.C. They observed the stars, planets, and heavenly objects travelling throughout the night sky and kept meticulous records. For thousands of years, a body of knowledge about the regularity of heavenly motion grew, although the charts were chiefly used for astrological purposes. The constancy of the stars and planets fascinated the ancients, and they recognized the extraordinary character and significance of this phenomenon. Most ancient cultures, probably for these reasons, associated the stars and planets with divinity and mythology. The Hebrew Scripture walks an interesting tightrope between these two dynamics. It highlights the regularity of this motion and, in fact, mentions it as a source of knowledge. But it refrains from ascribing the stars and planets divinity. Instead, it suggests that these wonders point to a God even greater than the heavenly bodies which are His creation.

The heavens declare the glory of God; The skies proclaim the work of His hands. Day after day they pour forth speech; Night after night they display knowledge.

Psalm 19

Listening through the ages, one might overhear a dazzled Israelite mumble the million- shekel question, “But if the skies are talking, then what are they saying?” Of course they are declaring the glory of God. Yet even today the depth of that glory grows and continues to overwhelm the largest of telescopes. Not only do the heavens declare God’s immensity, but they also declare the genius of His creation. And this Psalm suggests one key to that genius. It lays down a core foundation for both science and astronomy in particular: observing the regular patterns of the created world will lead
to knowledge. It validates the empirical method. Moreover, the knowledge gained will declare God’s glory, as Newton reiterated 2,500 years later.

Let us also consider the more formal beginning of astronomy. The arts of the Quadrivium came to Athens through the Pythagoreans who called them mathemata, or lessons. Plato and Aristotle champion all of what will be known as the Quadrivial arts: arithmetic, geometry, music, and astronomy. The Greeks made the most decisive moves to search for that deeper coherence that was displayed in these arts. For the Pythagoreans, Plato’s Academy, and Aristotle’s Lyceum, astronomy looked for mathematical symmetries in the data. They were not content to simply observe the position of the stars and planets as the ancient Egyptians did; they were looking for mathematical implications that those observations necessitated. From the 3rd century B.C., Aristarchus, Hipparchus, and Eratosthenes, among others, made stunning conclusions. Firstly, they all recognized that the earth was spherical and not at as often caricatured, though they proceeded far beyond that. Eratosthenes calculated the circumference of the earth to within a very small margin of error using data obtained during the summer solstice and triangulation. Aristarchus also used an early form of trigonometry coupled with measurements during eclipses to ascertain the relative sizes and distances of the earth, moon, and sun. Although his error was greater than Eratosthenes, his method was perfect, and only the inaccuracy of his tools hampered him. Hipparchus developed the trigonometrical methods used in these measurements. Even looking at these three early astronomers, the pattern of the liberal art emerges. Astronomy is concerned with taking observations of the stars and planets and using mathematical reasoning to find the necessary relationships between these observations. The scholarly tradition sometimes refers to this process as “saving the appearances”. It is mathematical empiricism.

Ptolemy, the astronomer from the 2nd century A.D., is the chief exemplar of this process. He wrote the definitive work of astronomy for the ensuing 1400 years. Though popularly known through its Arabacized name, the Almagest, its original name, the Mathematical Collection, emphasizes the intertwining of observation and mathematics in his work. Aristotle is often associated with empirical thinking, but his approach to science and observation wasn’t dominantly quantitative like modern science is. Although not a hindrance in biology, it severely limited his physics as a ustered Galileo points out. Aristotle appealed to experiments to justify his physics, but they were either never done or completed with so little quantitative measurement as to be abjectly wrong. Thus, for the ancients, astronomy was the chief locus of the mixture of mathematical and empirical thinking. Although Archimedes did some applied mathematics, as in engineering, he did not found a liberal art upon his work. But as Copernicus, Kepler, and Galileo continually point out, when it came to the liberal art of astronomy, Aristotle valued the method of the ancient astronomers and encouraged the pursuit of the mathematical conclusions born out from the observations. These scientists contend that Aristotle would have agreed with them because he upheld their method of mathematical empiricism for astronomy.

If the liberal art of astronomy was, therefore, an empirical mathematical approach to the motions of the heavenly bodies, it was exactly this that birthed the Scientific Revolution and with it an empowered modernity. Newton, standing on the shoulders of Ptolemy, Copernicus, Kepler, and Galileo (the giants), called his groundbreaking work the Mathematical Principles of Natural Philosophy or Philosophiae Naturalis Principia Mathematica. In this he unified the principles of celestial motion and terrestrial motion under his three laws by employing his four rules of empirical reasoning and his newly developed calculus.

This work culminates in a paean of praise in the General Scholium, where he lauds God as Lord Omnipotent who alone could so wisely create such a grand universe. Still, with reverent awe, Newton unveils an incredible mathematical structure that God has given to the universe as he explores it through a long tradition of empirical observation. From here, it is a settled matter that modern science for the next couple hundred years is nearly synonymous with Newtonian science. Even the social sciences adopted the model of the hard sciences as their paradigm. Economics, sociology, and political science all rely on observation and mathematics (often statistics) as their fundamental methodology. For these reasons, I contend that the dominant model of the contemporary university, mathematical empiricism, for better or for worse comes from the liberal art of astronomy.

Of course, an inherent critique exists in this story. What about the trajectories of the other liberal arts? As in the tale, when Cinderella was all dressed up she was the hit of the ball. As long as she did not overstay her appointed hour, everybody loved her. The paradigm of astronomy has also occupied center stage for the past three hundred years. But alas, this sister didn’t know how to get o the dance floor in time. It seems that the postmodern reaction to an overly empirical and mathematical approach to all knowledge has turned the coach of Scientism into a pumpkin. Though a war between the humanities and the sciences rages on, even within the hard and so sciences, there is a breakdown. An appropriate understanding and restoration of the other liberal arts will help as the empirical mathematical paradigm of astronomy buckles under the weight of a load it cannot carry. But in order to restore the paradigm properly we must know what it is. Thus, teaching not only the content of astronomy but also its method and its story are critical for understanding the chief headwaters of our contemporary culture. And though she flees the party, looking like a wind-swept village girl, she still has her glass slipper. So if our little star- crossed Cinderella can get home and regain her wits, she may yet marry the prince and live happily ever after. And if so, it will probably be in a castle built by Christian Classicists.

Paul Drake

Taking the Trivium to the Marketplace

Posted on by Paul Drake

As Christians, we are directed by Christ to take the gospel to all the world. It is intuitively obvious how the “Christian” part of classical, Christian education supports our obedience. Do we understand, however, what a powerful tool the “classical” part is in furthering the Great Commission?

Several years ago, David Hicks, author of Norms and Nobility, spoke at the SCL summer conference. He argued forcefully that our students should study the classics and perhaps only the classics so that they can understand the depth of the truth of Solomon’s words in Ecclesiastes that, “There is nothing new under the sun.”

Our culture not only neglects history, we exult in our belief that history holds no relevance to the modern man. Twenty first century man only looks forward, straining for the “next new thing.” We live in a “new age.” We have a “new economy.” Every boom is the result of a first-time creative insight and every bust prompted by some never before experienced event.

For example, our headlines today scream about the hundreds of billions in bailouts necessitated by the real estate market, which has increasingly left behind the basic understanding of supply and demand. Speculation fueled an exponential rise in home prices when there was no parallel rise in incomes. This real estate market bubble was further exacerbated by a mortgage industry that ignored common sense and 90 years of mortgage practice with respect to the level of debt that could be sustained by any given income. Individuals took advantage, hoping against rational belief that the spectacular increase in real estate prices would continue indefinitely and save them from any imprudence. We are told that what made this volatile mix finally combust, however, was not the age old effects of unbridled greed but the “new” sophisticated financial instruments called mortgage backed securities. These hitherto unknown investments were “too new” and “too complex” for anyone to appreciate their destructive potential.

The overwrought headlines bring to mind some background work my eighth grade literature students did when we read Alexandre Dumas’ Black Tulip a few years ago. In the early 17th century, the tulip bulb was introduced to Holland from the Ottoman Empire and quickly became the rage. Demand for the tulip bulb increased so rapidly and so consistently for several years that fortunes were made. As more and more people entered the tulip market, speculators looking for even greater profits introduced a new, complex financial instrument, the tulip future. Tulip-mania became so pervasive that, as one 18th century commentator writes, “even the dregs of society entered the tulip market.” Between the months of February and May 1637, the bottom dropped out of the tulip market. People were left holding virtually worthless securities whose risk they had not appreciated at the time of purchase. Though modern historians debate the depth and breadth of the impact of the crash the parallels are striking.

So, there really is nothing new under the sun.

But our culture needs more than economic insight. Last October, the Pittsburgh diocese of the Episcopal Church became the second diocese to leave the church, a reaction, in large part, to that denomination’s stance on homosexuality. Other dioceses are expected to leave as well. As I listened to Bishop Katharine Schori lamenting the split in a radio interview, the argument was familiar: biblical statements on homosexuality cannot be literally applied to our modern culture. The Bible is an ancient document to which our reason must be applied in order to keep it relevant. Of course, the conservative response was simply that the Bible is the inerrant Word of God. It cannot be altered to suit modern whims. It struck me that in this exchange two lines were drawn in the sand. There was no basis for any further discussion. One group asserts its “belief” in the proper way of reading the Bible. The other group asserted an opposing “belief.” No one was pleased but the moral relativists who are perfectly happy to let us each entertain our own private “beliefs” as long as we don’t presume to have any actual facts.

What answer might a classically trained student offer? A student whose analytical thinking skills had been honed along with his understanding of history and literature might ask simply, “How?” How does our cultural situation differ from the culture of biblical times on the issue of homosexuality? Modern man, divorced from any depth of historical understanding seems to have a vague notion of all morality pre-dating Woodstock as a cross between Victorian prudery and 1950s conservatism.

The classical student, however, might recognize that the ancient and classical worlds were far more comfortable with homosexuality than even our culture today. A student of history or literature might recall that of the first ten emperors of Rome, only one, Claudius, was believed to be exclusively heterosexual. He might also recall the famous defenders of Thebes, a military regiment exclusively populated by homosexual couples renowned for their valor. A reading of The Iliad might raise an eyebrow. In the Bible itself, Sodom and Gomorrah hardly seem to be homophobic societies. Even a student’s exposure to the bawdy side of Chaucer and Shakespeare would suggest that for centuries before the modern era, sexuality was viewed quite liberally. The assertion that our higher level of comfort with homosexuality justifies reinterpretation of the scriptures seems far from self-evident.

There is still nothing new under the sun.

But what good to the culture is our students’ historical foreknowledge, analytical thinking and insightful ability to connect the lessons of history or literature to today’s headlines? Are we simply raising students with the academic superiority to brag, “I told you so”? Do we believe that we can intellectually badger someone into accepting Christ, or even Christian morality?

There is one more tool that a student gifted with a Christ-centered, liberal arts education should possess: the heart of Christ broken on behalf of the lost. The arrogant belief that we are a new man in a new time no longer subject to the old rules opens a door to deception, oppression and destruction. The classically trained student with a heart for the lost has old tools, long forgo en, with which to open the eyes and build up the defenses of those around him. He is not only willing, but eager to enter the debates even when he isn’t certain in advance that he can win. He knows that the pleasure of pursuing truth is greater than the pleasure of winning an argument, and he invites those around him to join him in the pursuit. He also believes Christ’s words, “I am the way, the truth and the life.” So he knows that those who join his pursuit of truth, in whatever arena, pursue Christ, whether they recognize it or not.

Paul Drake

Teaching Grammar Well

Posted on by Paul Drake

Grammar ain’t easy. It is abstract and complex. So, how should we teach it? Philippians 4:8,9 indicate that we learn by meditating and by imitating. Practically, that means grammar must be taught both indirectly (imitation) and directly (meditation).

First, grammar must be taught indirectly through imitation. An atmosphere indifferent to language cripples a child’s vocabulary and syntax, disabling his ability to think effectively and confidently. Everyone in the school must be committed to correct grammar. Otherwise, students will see grammar as merely a school subject, not a serious priority. Our goal should be that the school will be full of powerful vocabulary, sound expression, and complicated syntax. This takes effort, but, if we honor the God who gave us language, we have to give it the time it takes.

Grammar should also be taught indirectly through writing, Latin or Greek, and every text the students read. They learn by imitation.

Second, grammar must be taught directly, through meditation. While the environment provides models to imitate, the classroom provides practical instruction.

We train students to meditate on grammar by applying the three stages of the trivium to any particular lesson. Here’s how it works:

We come to understand ideas when we see them embodied in particular expressions:

Grammar: you see particular examples of something (say, a dog), then another, then another.
Logic: you compare the specifics with each other. Pretty soon, you come to understand what is true of every particular instance – what makes something the kind of thing it is. Rhetoric: You understand and express the idea. Now you can describe a dog and distinguish it from a cat.

It is easy to see this with concrete things, like dogs, cats, and books. It works the same way when we want to know an abstract thing, like justice, freedom, or a verb. We come to know justice or freedom when we see them in particular situations or people. We come to understand what a verb is when we see specific acts in a sentence.

First, be very clear about what you want your students to understand. Get this right and the rest falls nicely into place.

Suppose you want your students to understand that a sentence is a complete thought. That’s the idea.

Now provide examples. “John sits.” “Lauren laughs.” “Noah built an ark.” Tell them that these are sentences. After each, ask: “Does this make sense?”

Next, write some incomplete thoughts: “John…” “Lauren….” “Noah built…” “Mickey hit a home run and then…” Re- mind your students that these are not sentences.

After your students have seen enough examples, ask: “How are the sentences the same as the non-sentences? How are they different?” Get plenty of ideas and be patient while they answer. At this point the students are meditating on grammar. If their first thoughts are inaccurate, that’s just part of thinking.

After they’ve made enough comparisons, ask: “What is a sentence?” If they can tell you that a sentence is a complete thought, you’ve succeeded. If not, back up.

When they tell you what a sentence is, they are ready to apply the idea. Provide practice exercises: “Write five correct sentences.” “Complete these sentences.” “Which of these sentences are complete and which are not?” etc.

You can teach any idea following this model of the trivium: examples (grammar), comparisons (logic), expression and application (rhetoric). For example, every sentence has a subject and a predicate, the predicate is what you are saying about the subject, etc.

Here’s the additional good news: if you can teach this way, you can adapt any curriculum. You may find that the easiest curricula are old ones— prior to the 1950’s. I like Harvey’s Grammar, though it needs to be supplemented. Rod and Staff, Mother Tongue, and First Lessons in Language are used in quite a few classical, Christian schools and seem easy to adapt, especially Mother Tongue.

The bottom line: you can use any program, but your students can only come to understand one way: by meditating on examples of the idea taught.