Cultivating the Intellectual Virtues

“Dishonesty, cheating, arrogance, laziness, cowardice—such vices are rampant in society, even among the world’s most prominent leaders. We find ourselves in an ethical vacuum, as the daily headlines of our newspapers confirm again and again. Central to the problem is the state of education…”

In his book Virtuous Minds: Intellectual Character Development, Philip Dow lays out a framework for how we can love God with all of our minds. He establishes that the recovery of virtue is not about doing the right things but about becoming the right kind of person.

Over the past several years at Paideia, Dow’s book has been instrumental in pinpointing for us the intellectual virtues that are lacking in today’s society and must be instilled in students. As your child’s teachers cultivate character in the classroom, we consider the seven virtues of courage, carefulness, tenacity, fair-mindedness, curiosity, honesty, and humility.


In To Kill a Mockingbird, Atticus Finch explains to his children why he took the controversial case: “I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. It’s when you know you’re licked before you begin, but you begin anyway and see it through no matter what.”

At Paideia, we want students to develop the intellectual courage to do hard things, to stand up for themselves, and to speak forth boldly. Whether it is raising a hand in class, inserting one’s self into a Harkness discussion, or declaiming a speech in front of two hundred people, we want our students to be men and women of courage.


The essayist Samuel Johnson once wrote that: “It is more from carelessness about truth than from intentionally lying that there is so much falsehood in the world.”

At Paideia we want our students to avoid being glib or heedless in their work, to eschew being sloppy or lackadaisical in both their thoughts and their actions. Instead, we want them to cultivate intellectual carefulness, remembering that, as Johnson says, error can creep in through carelessness as much as through intentional lies.


C.S. Lewis wrote that: “The only people who achieve much are those who want knowledge so badly they seek it while conditions are still unfavorable. Favorable conditions never come.”

Tenacity is what we want for our students at Paideia—to persevere past tiredness and despite distraction, to mine for understanding like silver and dig for wisdom like buried treasure. We want students who finish copying the sentence even when their hand hurts, who struggle forward in their math homework even when they failed the last test. We want students with the grit necessary to pursue knowledge even when the conditions are unfavorable.


Aristotle warned that, “it is better in fact to be guilty of manslaughter than of fraud about what is fair and just.”

Our human nature loves to be unfair and unjust in representing others we disagree with. At Paideia, we want our students to listen to others’ viewpoints and to represent those viewpoints fairly. We want them to fairly represent what a text actually says before stating their own opinion on the text. We want them to engage with real opponents rather than creating straw man arguments to knock down.


The Apostle Luke wrote: “Now the Berean Jews were of more noble character than those in Thessalonica, for they received the message with great eagerness and examined the Scriptures every day to see if what Paul said was true.”

We want our students at Paideia to receive the knowledge of the Creator and his Creation with this same eagerness, thirsting to search out more for themselves. We want them, as learners, to be in the role of an anticipator, making predictions where the lesson or text is heading, searching for additional information beyond the textbook, and discovering connections with previous learning.


In his autobiographical novel Little Britches, Ralph Moody records these words from his father: “A man’s character is like his house. If he tears boards off his house and burns them to keep himself warm and comfortable, his house soon becomes a ruin. If he tells lies to be able to do the things he shouldn’t do but wants to, his character will soon become a ruin.”

Our vision statement at Paideia states that we want students to build their characters as diligently as they sharpen their minds. A huge part of character-building is honesty—honesty to others and honesty to self. We want our students to have a commitment to truth that overrides all desires for convenience and gain. We want them to avoid self-delusion and tell the truth about themselves, about others, and about the world that God has made.


G. K. Chesterton wrote: “If a man would make his world large, he must be always making himself small.” The self that is puffed up cannot see the wonders that surround him.

Submission is essential to learning—the student must not think himself above the teacher, above the text, above the lesson. At our secondary campus, we have a banner in the hallway that says: “Humility before Honor.” Our desire is for students to achieve the honor that comes from the path of humility.


At Paideia, we believe, as G.K. Chesterton wrote, that: “Education is not a subject, and does not deal in subjects. It is instead a transfer of a way of life.” As students are immersed in the paideia of the Lord, in the culture and counsel of Jesus, these intellectual virtues will become part of their way of life.

Mastering Mathematics

One of the questions that sometimes surfaces from prospective families at Paideia is: “Do you teach Common Core math?” This question usually bubbles up from either a visceral loathing of Common Core or a nervous fear that students who don’t do Common Core will somehow be “behind.”

Before answering that question, I like to ask some questions of my own. “What does Common Core math mean to you? What do you not like about it?” Or alternatively, “Why do you think it is important?”


Common Core math was created because educators noticed students having a lack in critical thinking skills in mathematics. Students appeared to just be memorizing ways to do problems in a “monkey see, monkey do” fashion, rather than understanding the why behind what they were doing. Common Core was an attempt to build number sense into mathematical learning, teaching students to recognize patterns and reason out steps on their own instead of simply memorizing processes.

But although creators of Common Core math correctly emphasized critical thinking skills, they incorrectly identified memorizing as a negative and as being at odds with comprehension. Over the last decade, addition, subtraction, multiplication, and division fact fluency has fallen by the wayside as the importance of memorizing basic arithmetic facts has been steadily deemphasized and denigrated. Students being able to reason out the process for the problem has become more important than students actually being able to complete the problem correctly. “Because…we all have calculators now, don’t you know?”


At Paideia, we believe that both number sense and fluency in arithmetic facts are important. In fact, the ability to do arithmetic fluently can actually lead to far greater number sense. The student who has no difficulty adding 5 and 16 in his head, will not have an extra barrier to contend with when understanding how to move numbers to opposite sides of the equation in Algebra. The student who is quick with her multiplication tables will be able to see at a glance how she can factor numbers out of the polynomial.

Memorizing math facts is important. Understanding place value, identifying patterns, decoding word problems, reasoning independently, and explaining your solutions are also important. As one of our favorite books, The Liberal Arts Tradition, puts it, imitation must be joined with reason before the art of arithmetic can be achieved. It is essential to realize that math fact fluency and critical thinking work together to build a strong math student.


The approach to math that we use at Paideia targets both of these skill sets. Our Math-U-See curriculum is consciously designed to foster number sense. Some of the ways of doing addition and multiplication in our Math-U-See curriculum can seem strange to parents at first. Students learn to estimate for approximate answers before solving for exact answers. Students expand the notation for their multiplication problems to understand what each number means according to its place value. “This isn’t how I learned to do math!,” some parents might think. “So how can I help my child?”

We are here to assist you. If you have questions about “the rule of four” or “the same-difference theorem” or any of the unfamiliar methods in our Math-U-See curriculum, don’t hesitate to ask. Most of our teachers would likely tell you that they understand how numbers work far better after learning the methods Math-U-See uses.


Along with inculcating number sense, we are always working to build arithmetic fluency. At the beginning of each elementary class, students do a timed math facts page, mental Calisthenics to “warm up” for the practice that lies ahead.

In 1st-6th grade you will also see math facts on the at-home work checklist. It can be tempting to skip over these instead of making a daily effort to master them. (I know from personal experience that students who struggle the most with math facts are the most prone to shirk practicing them…) However, skipping math facts practice because they are hard for your child is counter-productive and ensures that your child will struggle with math all the way up through algebra.

Lean into the hard. Use strategies like breaking addition facts into small chunks and doing them over and over. Practice skip counting 8s first, and then time how fast you can do the 8s multiplication facts. Try to better your time the next day.

Think of arithmetic as any other skill that needs to be learned. When your daughter learns basketball, you don’t just teach her “the process of a layup”, you make sure she has the muscle memory to put the ball in the basket over and over again. When your son gets a new Chopin prelude, you don’t let him settle for “understanding how the chords work”, you have him play it over and over again until his hands transition fluently through each cadence. Math, like sports and music, is a skill that requires drill.


Giving our children the gift of mathematical reasoning and fluency is more than an attempt to make them successful in college or a bid to get them a well-paying career as an engineer. In a very real sense, it is an attempt to open their eyes to the order, design, and beauty of the world in which they live.

One of Isaac Newton’s most famous quotes is that “God created everything by number, weight, and measure.” Numbers are built into the fabric of our world, and the more we learn about the numerical patterns, processes, precision, and predictability of Creation, the more we learn about the nature of the Creator.

Proverbs 25:2 says “It is the glory of God to conceal a matter, but the glory of kings is to search out a matter.” Let us teach our children the glory of the search.

What’s in a Grade?

As the school year begins and students turn in their first assignments and take their first tests, it can be a helpful time to ask ourselves: “What’s in a grade?”

Grades are a feedback mechanism that let parents know how their child is doing in relation to the standard set by the teacher for that assignment or subject. Grades are not a goal in and of themselves. Grades are not a measure of how successful your child will be at age forty. Grades are not a measure of your child’s worth as a person. Grades are not a measure of how much your child loves God.

For those who are new to Paideia, a few notes about our grading system: In elementary (K-6th), we try to steer away from the typical percentage-based grade system of the modern academic system. (What makes a narration paragraph an 89 rather than an 88? Can you even put a number on an art project?) Instead of quantitative grading, we try to use qualitative grading, using the terms Excellent (E), Praiseworthy (P), Satisfactory (S), Needs Improvement (N), and Unsatisfactory (U).

In secondary (7th-12th), we do use the standard A, B, C, F grading system (more because we need our high school transcripts to be comprehensible to the world at large than because we love that system). We don’t have a “D” grade.

Another note about our grading system to keep in mind: grades are always relative. This does not mean that the standard changes in regard to individual students (that would be unjust!), but it does mean that depending on individual aptitude and gifting, the same grade can mean two different things for two different students. Grades must be interpreted based on what you know about your own child.

A “B” in Chemistry for an extraordinarily bright student with excellent number sense could be a mark of coasting and laziness. That same “B” for another less mathematically-minded student who worked his tail off puzzling out the homework problems and studying for the test, is a mark of high honor and achievement. In the same way, an “S” in penmanship for the first grader who sloppily rushes through his work means something very different that the “S” for the first grader who struggles with dexterity and erased and rewrote his copywork three times, each time making it slightly better.

The important thing, then, is not perfection but faithfulness. “Were you faithful with the time and talent God gave you when you earned this C? Then rest in what you have done.”

As our students continue to grow over the months and over the years, their efforts increase their abilities and their skills develop and change. Our calling as parents and teachers is to seek to continually know our students so that we can interpret their grades fairly, encouraging them to reach their full potential while refraining from overburdening them with impossible expectations.

Jesus speaks in one of his parables about the servant who buried his talent in the ground instead of putting it to use, illustrating this maxim: To whom much is given, much is required. Let us require our children to fully redeem the time and talents that God has given them, and let us love them well as they do it.

How We Teach: The Harkness Method

One of the fundamental principles of the Classical model is that it teaches with the grain of childhood development. Students in the Grammar stage love to sing, chant, recite, listen to stories, and in the elementary years we teach them accordingly. Students in the Logic stage love to debate, argue, take things apart, and fit them together, and they get their chance to do this when they enter seventh grade.

In our tenth grade classes, the students have entered the Rhetoric stage or, as Dorothy Sayers called it, the Poetic stage. Their skills at analyzing and evaluating have been sharpened by formal logic and they continue to hone these skills as they learn to present their arguments with politeness, poise, and polish.

In the high school grades we have started using Harkness discussions regularly. Harkness discussions are similar to Socratic discussions in that both require students to do most of the thinking and discussion. In the Socratic method, however, the discussion involves the teacher asking the students a series of questions to lead them to a desired realization. With the Harkness method, the students lead the discussion, asking questions of the text and themselves with minimal intervention from the teacher.

To prepare students for a Harkness discussion, I assign them a text to read on their own. (In our Ancient History class, we recently read a portion of the Egyptian Book of the Dead.) I tell the students some things they should be looking for in the text. (What is the Egyptian view of god? How does this compare to the Sumerian prayer we studied last week? How does it compare to what we learn in the Bible?) I encourage the students to make notes on specific places in their text as they are reading. (For books they are not allowed to write in, they use post-it notes.)

On the day of the discussion, I remind them what knowledge we are seeking to obtain and then seat myself in the background to allow them to discuss with each other. With a mature class, I rarely need to intervene in a discussion to get them back on track. Occasionally, I lob a new discussion question into their midst when a subject needs to be further explored. (What would daily life be like in a culture that has this view of god?)

After the discussion is over, I provide the students with feedback. Here are some of the positive feedback points I give students:

  • Asks good questions of the text
  • Refers to text regularly
  • Refers to text thoughtfully
  • Connects ideas to previous learning
  • Connects responses to other student comments
  • Disagrees respectfully with another viewpoint

You will note the primacy of the text in this feedback. The mature student asks questions of the text until he makes the text comprehensible and then uses textual evidence to support his own assertions about the text. The students are good about policing each other in this area. A student who makes a blanket statement is prodded by his fellows to demonstrate where he is getting that from the text. A student who offers a shaky interpretation is challenged by her peers when she tells them what line she is basing her assumption on.

You will also notice the importance of subject integration in this feedback. The mature student is the one who can tie in what he learned last year in science and last month in Bible class to this week’s discussion on Herodotus’ Histories.

And finally, you will notice the importance of the group interaction. Learning is a communal activity, and it is the fellowship of the classroom that stimulates, nurtures, and enhances learning. Students learn that they can and must learn from each other as well as from the teacher. This group interaction can only occur when we ask questions of each other and respond with respect and fairness.

The benefits of the Harkness discussion method are legion. Not only do my students now understand the crushing weight of perfection prescribed by the Egyptian Book of the Dead in contrast with Biblical grace, they also understand how to interrogate a text, how to integrate multiple facets of the world, and how to hold civil discourse. The Harkness discussion leads students away from unsupported opinion and teaches them to journey together on the quest for truth.

Book of the Dead
Panel from the Egyptian Book of the Dead (British Museum)