All About Arguments

How to Win

By Dr. Kim Johnson with The Lukeion Project

Of all the topics and ideas we cover in logic, the argument is certainly the star. Students may dream of outarguing their opponents in the courtroom, or winning an important political debate, or even proving their parents wrong about curfew, homework, or allowance.  Unfortunately, because of the nature of logical arguments, showing that someone has reached the wrong conclusion is difficult.

What makes an argument?

When logicians talk about “argument,” they don’t mean the typical immature argument between siblings (“Did too!” -- “Did not!”). The technical definition of a logical argument is “a set of premises which imply a conclusion.” That means that each argument has at least two statements, one of which is a conclusion.

Seems easy enough, right? Unfortunately, even figuring out which is the premise, and which is the conclusion, can be difficult. Consider the argument in the Declaration of Independence. Is the conclusion, “All men are created equal”? Or is it that King George had established tyranny? Or is it that it was necessary for “one people to dissolve the political bands which have connected them with another”? To discuss an argument, you need to know what is being argued.

To add insult to injury, sometimes parts of the argument are left unstated including even the conclusion. Arguments with unstated propositions are called enthymemes, from the Greek for “to keep in mind.”  Advertisements and politics are some of the worst offenders: “Open a Coke, Open Happiness.” Why?  Because Coke (according to the advertising company) is happiness. “My opponent hates cats. You would never vote for someone who hates cats.” Conclusion: Vote for me!

When faced with an enthymeme, your duty is to interpret the argument in the most favorable light for your opponent. The first reason for this is simple: treat others the way you would like to be treated.   The other reason is practical.  Responding to a command to “Surrender!” by saying, “You wish to surrender?  Very well!” is silly and soon no one will want to discuss anything with you anymore.

What makes a good argument?

Once you have found an argument, we can analyze its validity. In Lively Logician 1, we use the principles of categorical logic developed by Aristotle to analyze syllogisms, a specific form of argument with 3 terms, 2 premises and a conclusion. The logician’s favorite syllogism is as follows:

All men are mortal.

Socrates is a man.

Therefore Socrates is mortal.

In Lively Logician 2, we branch out into truth tables and use the laws of inference and replacement to judge whether an argument is valid. If each of the steps in the argument is made with valid principles, then the entire argument is valid.

Validity means that if the premises are true, then the conclusion must be true. The tricky thing is that validity refers only to the form of the argument, and not to the truth of the conclusion. Here is a valid argument (of the same form as above) with a conclusion that is obviously false:

All jellybeans are made of sugar.

All dogs are jellybeans.

Therefore all dogs are made of sugar.

What’s the difference between the argument with the false conclusion and the original one above? In the second argument, the minor premise (“All dogs are jellybeans”) is clearly false---so the conclusion is not guaranteed to be true.

Not only can valid arguments have false conclusions, but having a true conclusion and true premises doesn’t mean that the argument is valid. Here’s another syllogism:

All canines are mammals.

All dogs are mammals.

Therefore all dogs are canines.

The conclusion and premises are all true---but the argument is bad. If you’re trying to prove that “All dogs are canines,” you might want to get a different argument.  

Saying an argument is valid is a bit like showing that the structure of a house is solid and will stand. It makes no claims about the decorations on the house or the painting job or the light bulbs. Having a valid argument just means that if the premises are true, the conclusion is necessarily true as well. As we’ve seen, the implication doesn’t go the other way. A sound argument is much better.

Sound arguments start with true premises. This is not a requirement for valid arguments.  The argument in a sound argument is also valid. Thus, the conclusion of a sound argument is guaranteed to be true. If your opponent’s argument is sound, there’s not much you can do to counter it.

How can you prove someone is wrong?

This brings us to the goal: Show that your opponent (or parent, or friend) is wrong. Unfortunately, formal logic can only go so far with this goal. We can find fallacies in their arguments: ad hominem attacks, or circular reasoning, for example. Logic doesn’t have many tools to show that someone’s conclusion is false. They might need a better argument, but their conclusion could still be true.

The best way to vanquish your opponent is to create your own, sound argument including true premises and a valid argument plus a conclusion that is the opposite of what your opponent has stated. The best way to win arguments with friends and parents is not to prove them wrong, but to make your own, better argument.

 

The History of Zero

By Dr. Kim Johnson, The Lukeion Project (Check out Dr. Johnson's class Counting to Computers: Math from the Dawn of Time to the Digital Age)

It turns out that one of the greatest accomplishments in the history of mathematics is---nothing.

From where we sit today, the tools of mathematics seem so obvious that they hardly bear thinking about. It might surprise you, then, to learn that one of these everyday tools took thousands of years, deep philosophy and even controversy to become part of our everyday tool kit. What is this development that we use every day without even thinking about, and yet was so difficult for the most brilliant and advanced mathematicians in ancient times to grasp? The number zero.

Before Zero

In the mists of time, mathematics seems to have been used primarily for counting or measuring things. Whether you are counting the number of animals in your flock or the distance to the next town, the concept of assigning a number to “no animals” or “no distance” seemed unnecessary and overly complicated. After all, “zero cows” is the same thing as “zero apples,” while “one cow” and “one apple” are decidedly different from each other.

This is not to say that ancient civilizations never used any concept related to zero. The Egyptians had massive building projects which required sophisticated engineering: they used a number to refer to the ground level. They also had a concept of a “zero balance” when no money was owed. The symbol for these was called nef, which also meant “perfect” or “complete.” 

The Greeks had an even harder time with the concept of zero than the Egyptians. Pythagoras declared, “All is number,” but what he really meant was “All is ratio.” Numbers to him represented the ratio between two quantities or lengths. This is useful in geometry (recall the concept of similar triangles) and in music (the ratio between lengths of string that produce an octave is 1:2) but terribly difficult for the concept of zero--a ratio of zero is almost nonsensical. Aristotle, whose philosophy reigned over the western world through the Middle Ages, stated that, “Nature abhors a vacuum.” Not only was zero not a number, but philosophically speaking, it was impossible. The paradoxes of Zeno of Elia (490-430 BC) point out the difficulties that the existence of zero would imply.

The absence of the number zero became a problem for Babylonian computation. Unlike the Egyptians, Romans, and Greeks, the Babylonians had a positional place value system where each number meant different things depending on where it occurred. In our system, where the positions represent powers of 10, the digit 2 in 2,528 means either 2,000 (the first 2) or 20 (the second 2). In the Babylonian system different positions represent different powers of 60. The leftmost 2 would mean 2x(60x60x60) while the rightmost means 2x60. This is fine unless you need a number which contains a zero. For the Babylonians, 11 could mean 101, 1001, 110, and so on, depending on context. They eventually developed a place holder to mean zero, but it only worked in the middle of a number, not at the end. They could distinguish 202 from 22, but not 220 or 2200.

The Discovery of Zero

Fortunately for mathematics, something changed in about 300 AD. Indian mathematicians began developing the symbol sunya which referred to the number zero. Rather than just a place holder, sunya (first a dot, then a ring) was used as a number. It makes sense that zero should be developed in the context of eastern rather than western philosophy. The concept of nothingness or emptiness, anathema to the Greeks, plays a much larger part in Indian religious philosophy.

 

In the 7th century, the great mathematician Brahmagupta (598-668 AD) created a whole system explaining how zero worked with other numbers. Some of his rules included the fact that a fortune, take away zero, is a fortune; or a fortune multiplied by zero is zero. He did commit the mathematical sin of dividing by zero, but that concept remained difficult for mathematicians well into the modern era. Brahmagupta also talked about negative numbers with more comfort than western mathematicians would into the 18th century but that’s a blog post for another day. 

 

After Zero

It seems obvious to us now but zero took a while to catch on in the rest of the world. The first people to adopt zero—and see how useful it was—were the Arabs. Most notably, Al Khwarizmi (c. 780-850 AD) used Hindu-Arabic numbers as he was developing algebra at the House of Wisdom in Baghdad. He described zero, which he called sifr, in his book Algoritmi de Numero Indorum as “The tenth figure in the shape of a circle.”

Several individuals were instrumental in introducing zero to Europeans. One of the earliest, Pope Sylvester II (c 946-1003) had studied the Hindu-Arabic numerals when he went to Muslim controlled Spain to study mathematics and science. Because of his facility with these numbers (and probably for other reasons) he was accused of consorting with the devil.   

The next great advance in using this Hindu-Arabic numeral came when Leonardo di Pisa—better known as Fibonacci (c.1170-1240) wrote his great work Liber Abici. In addition to problems about rabbits, he introduced the numerals he had learned about when he studied in North Africa among Muslim mathematicians. He also introduced algorithms for doing basic mathematics including 28 pages about how to do long-division. We still use his method today.

 

 

“These are the nine figures of the Indians 9, 8, 7, 6, 5, 4, 3, 2, 1. And so, with these nine figures, and with the symbol 0, which is called zephyr in Arabic, whatever number you please can be written, as is demonstrated below.”

Even after zero came to be used in the west, it wasn’t immediately accepted by the public. Financial institutions in Florence banned the use of zero in 1299. They felt that there were too many opportunities for fraud because someone could use place value to change the values on the checks that were being written. Even today we write “seven hundred fifty and no/100 dollars” on our checks---perhaps as a deterrent to adding zeros and increasing the value of your check.

The medieval philosophy textbook Margarita Philosophica (Gregor Reisch, 1503) shows a picture of a contest between someone computing with the old counting board on the right, and the new-fangled Hindu-Arabic numerals on the left. You can see who is happier. The Hindu-Arabic number system eventually won out, including its use of zero.

Zero has proven useful beyond allowing a more efficient number system. Zero eventually became the star of the number line and of the Cartesian plane, invented by Pierre de Fermat and Rene Descartes, and used to visualize algebraic functions and equations. Zero is essential in the invention of calculus. Newton and Leibnitz use infinitesimals to find a tangent line to a curve, quantities that are almost zero but not quite. Don't forget that zeros make up about half of every binary computing system.

The history of zero spans thousands of years, multiple civilizations and continents---and yet it is something so simple that we use it every day.

If this story of the connection between math and culture piques your interest, you might want to sign up for the course Counting to Computers: the history of math from the dawn of time to the computer age. This course is appropriate for strong pre-algebra students through high school students taking higher math.

Wheedle-dee-DON’T

Try not to Bug

By Amy Barr

Ever heard someone say, “there’s no such thing as a dumb question”? Ever hear the old adage, “it never hurts to ask”? Do you think these statements are true all the time? 

Over my quarter of a century as an educator, I have a small collection of truly dumb questions that people have asked. Don’t be concerned. The normal sorts of things you might ask in any class are far from dumb. To put you at ease, I’ll tell you that the dumbest question I’ve ever heard is when an adult in our group asked if the sand in the Colosseum of Rome was still wet with the blood of the gladiators. This question almost caused our tour guide to choke.

I also have in mind several occasions in which it does indeed hurt to ask a question. Life can be difficult to navigate to, today, I’m letting you in on a little life secret about how to avoid future difficulty if you tend to ask certain types of questions, namely wheedling. No, despite my picture I'm not talking about a weevil which is a type of bug. Wheedle is a verb that means “to influence or entice by soft words or flattery.” When it comes to classroom habits, we educators encounter people who naturally lapse into wheedling to obtain desired results in the form of extra favors, added point values, extensions on deadlines, upgrades to course grades, excuses for being late or missing assignments.

So, what’s wrong with asking for these things? Grandma always said it never hurts…but does it?
Just like asking a tour guide if the sand of the Colosseum is supernaturally soggy almost 2000 years after the last gladiator fight, asking questions leaves an impression of you on others. Most of the time, questioners are simply seeking clarity when information you've heard (or not heard) is incomplete. Such questions show you are focused on getting things right in your mind and in your schedule. I’m certainly not discouraging questions. I’m encouraging you to consider your motives for asking certain types of questions.

Are YOU a wheedler?

1.    If you regularly ask for exceptions to policies spelled out in the syllabus, you might be a wheedler. When you wheedle for an extension on deadlines or whatever else your instructor has set in place as necessary for the class to flow smoothly, you are wheedling for special treatment that you alone might obtain.
2.    If you regularly ask for your educators to bump up your score “just this once” because maybe you didn’t quite understand the prompt, or you don’t think your grader should have deducted a whole point, or you didn’t quite put in the time but really want or “need” a better grade, you might be a wheedler.
3.    If you didn’t put in the study the first time but want extra credit after the semester has ended, you might be a wheedler.

What’s at risk?

Wheedlers leave certain unfavorable impressions when they regularly ask for favors or quibble or fractions of scores. They come across as a person who needs special attention and rewards that their peers won’t enjoy. They seem inattentive because, by asking for exceptions to clearly stated rules like deadlines, they appear to be unaware of the basics spelled out in the syllabus. They give educators the sense that they’d rather quibble over minor points adjustments than put in the effort towards mastery and improvement. 

If you suspect you are a wheedler but are shocked that you might have left a bad impression, consider this your aha! moment. You may think you had no egotistic intentions with your requests for special favors because you simply never thought about it that way. Most wheedling is innocent until it is a habit. Suddenly, your educators stop giving you any benefit of the doubt. Suddenly they never accept your reasons for needing extensions, even in emergencies. Maybe their grading has gotten even firmer, not easier as you progress. Your wheedling habits will always wear thin on those who are the recipients.

Wheedle not! You never want to wear down your educators, peers, parents, employers, or friends with constant requests for exceptions and extra advantages. Maybe you never thought this was much of an issue –after all,  you heard it never hurts to ask—but now it is time to give it a little more thought.

Popcorn Brain

Do You Have It? How Can You Recover?

By Amy Barr

Do you have popcorn brain? I bet you do. I certainly do. I didn’t invent this disease. It is an affliction that causes problems for most of modern humans. It is a pervasive affliction that causes daily troubles for all of us. Popcorn brain can drastically change one’s life trajectory and damage our relationships even though most don’t know they have the problem.

Popcorn brain is not caused by a pernicious virus. We can’t blame too many sweets, too few vitamins, too much food dye, nor even popcorn. The main symptom of popcorn brain is that you are easily distracted and will have difficulty focusing on one task at a time. You’ll find it is impossible to put aside technology, even for one or more waking hours. 

The average sufferer plays music while he is trying to perform an intellectual task like homework, studying, writing, or reading. If the list stopped there, that's not so bad. Now he adds a constant stream of notifications from social media accounts, playing apps, sharing funny videos, watching TV, and grabbing snacks during the few hours set aside to get work done. 

Popcorn brain feels productive because we are so busy. Popcorn brain fools us (and others) into thinking we are getting stuff done when we are not. Besides doing a poor job on mental tasks you also suffer from an intolerance for being bored even for a moment. Even the smallest lapse in activities means you will get distracted from even your distractions. 

Popcorn brain means you may never have a single creative moment in your life. All day long, your poor brain pops and pops and pops, looking for the next imposed impulse from a dozen sources simultaneously. You will constantly feel overwhelmed, over-scheduled, unproductive, and uncreative. 

What are the causes of popcorn brain?

There’s no way to soft sell this so you better sit down. Your sophisticated expensive time-saving technology is to blame. Those who don’t have computers (phones, tablets, whatever) don’t have popcorn brain. Their lives tend to be a full expression of focus, effort, creativity, and productivity. To remind myself that such a life is possible, I drive through one of the two Amish communities near my house. It is clear which houses are Amish and which are "English" not because the Amish have no power lines. Amish houses are dynamic, busy, well-tended, and full of life.They are able to easily accomplish daily chores with plenty of time for social time, community events, and opportunities for volunteer work. Their mental, physical, and spiritual health is robust.

Meanwhile popcorn brain spreads like wildfire in the modern world because the addiction is real. The mere thought of unplugging or living with minimal technological input likely made you feel uncomfortable or indignant. How horrible! Don’t they get bored? Unlikely but when they do, they also get creative unlike the rest of us.

How does popcorn brain change lives for the worse?
Drive through any modern neighborhood. You’ll find yards are empty and untended, playgrounds are sparsely used, and even joggers or dog walkers don’t just complete that one task. They listen to music, check texts at stop lights, and look to count steps, their heart-monitor app., and their social media.
Many studies and my own experience as an educator prove that that the average I.Q. is dropping, and our population is getting dumber by the day. Student assignments that should take 20 minutes now take 90 minutes between the constant distractions. Compare what an average high school graduate knows now and what was expected from an 18-year old 100 years ago! Visit parts of the world that enjoy limited technology and compare their productivity and personal skills with your own. Friends, it isn’t pretty. Popcorn brain is so serious that most of us will labor decades to master skills that non-tech humans can pick up at age 16 simply because our days, creativity, and minds are squandered for nothing.
How many artists, writers, and musicians will never develop their arts because they never once get bored enough to paint that mural, finish that novel, or form the muscle memory needed to become great at their instruments of choice? How many people that are wired to be carpenters, gardeners, inventors, linguists, dancers, or scholars will instead spend their lives doing none of that because they can’t find the time?   

How to Combat Popcorn Brain

If technology has caused this crisis, limiting, or eliminating it will cure it. Ouch.

Like many of you, I can’t get rid of the necessity for screen time because that’s how I make a living. Students are in the same boat until further notice, alas. I am working on some disciplines to limit myself.

Habits die hard so start with reduction. Diminish technological demands even while employing technology. Too many tabs, apps, videos open at the same time shrinks your ability to focus. If you give yourself an hour to finish an academic job, break it into 30 minutes and then close everything but your appropriate app and maybe some music to drown ambient sounds. Don’t play music with lyrics because your popcorn brain will tell you to sing along! At the 30-minute mark—if you have remained focused—enjoy a short non-technology reward or set the timer for 5 minutes to check texts, email, etc., before closing all those tabs again. Don’t go over that limit. Set the timer for 30 minutes again and repeat. Like learning to lift weights, you’ll need to build up to 60 minutes and then 90, 120, etc. 

Learn to MEGABATCH or work on getting a lot done in one time block. Now that you’ve tuned up your ability to go stretches of time with limited technology input, eliminate tech for longer stretches of time each week. Turn it all off and set a manual timer for 3 or more hours doing any one activity that needs no tech or maybe a single app. Do this at least once a week. At first pick something that you adore (reading, sports, garden work, painting) but do it for three hours with zero phone, tablet, laptop, or gadget anywhere near you. You are reconditioning your brain to go for longer and longer periods without the little addictive endorphin treats that you’ve trained yourself to seek. You’ll know when you have made progress when you can drag out a good book and read in silence for 3 hours. Soon you will need an alarm to force yourself to stop reading that good book. If you have popcorn brain, this is something you've not done for a long time.

After you’ve reconditioned your brain to focus on a single task you enjoy, now force yourself to spend three or more hours mono-tasking things you don’t like as much. Whatever you consider a chore, do it for three hours uninterrupted by anything but short necessary breaks. Make it a date with just you and that chore. You’ll soon find that something that used to take 3 hours will now take a fraction of that time. If you don’t need 3 hours, add several more chores to your list because you’ll likely get much more done.

To avoid relapses, if you mess up while megabatching by grabbing that device, reset your three hours and begin again. Your reward for making it through all three hours of mono-tasking is that sense of satisfaction over a big pile of finished projects.

More brain reconditioning behaviors:

• Don’t look at devices for the first 30 minutes that you are awake in the morning and the last 30 minutes at night.Work to extend this time as you recover from popcorn brain.
  
• When you do listen to podcasts, tutorials, classes, etc., force yourself to take notes with pen and paper instead of fiddling with 3 or 4 other things on your device.
• Take up any physical exercise that requires focus. I do yard work or gardening. Others might practice hitting a target, shooting a ball, blacksmithing, biking, roller skating, or building something.
• A little music helps improve focus, but set your device far away and pick a playlist that requires no changes. Once your device lands in your hands, popcorn brain will go pop, pop, pop. Go to great efforts to not touch tech during focus time. 
• Make room for social time. Quit (school or professional) work at a specific hour then find your family or friends to catch up on your day. Popcorn brain forces us to be unproductive until we give up or run out of time in our day. This means we miss out on much needed social interactions. Focus lets us schedule an end to work and enjoy personal time daily.
• Plan a tech-free weekend at least once a month. Avoid all screens from Friday night through Monday morning. Camp, paint, exercise, compete, create, write, read, build, garden. Focus will help you find yourself once more.
  

Students: Imagine & Invent Your Best Life

Consider Home Education in High School

By Amy Barr

"All of us have to learn how to invent our lives, make them up, imagine them. We need to be taught these skills; we need guides to show us how. If we don't, our lives get made up for us by other people." Ursula Le Guin

Ursula Le Guin was an American author known especially for her science fiction and fantasy series that spanned a 60+ year career in producing hundreds of well-loved pieces that included translations, poetry, and literature for children in addition to her main adult series. By all measures, Le Guin was a success at what she did. This quote is especially powerful in an age when so many fall under a trance and believe the lie that a good education should be standardized. Ursula Le Guin made history as a writer, but her education suggested she should become a French teacher. Instead, she learned to imagine a different life and then she invented it. 

Young people are expected to plot a plan for higher education followed by career. We adults ask them to choose their life road well before they know how to count the cost of taking that trip. With limited experience dealing with life (or the universe, or everything else), students are called on to complete a standardized course of study but yet—miraculously –emerge at high school graduation with exceptional interests, noteworthy personal assets, and ambitious plans to set them apart from all their peers who have also had a very similar course of study, the same standardized exams, and the same AP classes.

Maybe All the Adults Have Lost their Minds?

No wonder anxiety and depression are on the rise with our teens. The conventional path toward adulthood consists of a maddening swirl of collecting good grades, getting a nice selection of AP classes, tossing in some music (art, writing, martial arts, basketball, etc.), marking a few hours in volunteer work, and maybe picking up a part time job. Don’t forget to spend much of ages 17 and 18 applying to colleges and scholarships while we fuss at them for not taking advantage of social or faith opportunities. 

This manic method is marketed as today’s fail-proof path to success. We ask them to do everything fast, furious, while taking top marks but we often send them into adulthood before most of them know how to use a bank account, cook a meal, clean the house, do laundry, mow the yard, or change a tire. That’s just how the first semester at college goes. Soon they’ll wonder why they don’t know how to pay taxes, save for a mortgage, work through a rental contract, deal with medical paperwork…stress!

How can students power their way through a standard transcript with standard classes (or accelerated versions of the same) but yet somehow emerge from their high school years as uniquely gifted and empowered individuals who have a strong sense of self when they’ve mainly only experienced no more and no less than their comparable peers.

What’s the solution?

Educating at home allows both parent and student to create a unique and personalized education for your truly unique child. Students who are excellent at a subject don’t need to slog their way through 4 years (5 days a week) of the same bland stuff if it can all be done in one year. Students who have more control over pace, content, and subject matter not only have a far better education in high school, but will have a far better understanding of self afterwards. 

Give your creatives time to be creatives from a young age. Give your STEM kids more time to problem solve and invent. Give your hands-on kids quality time working with hands!

Many families do a beautiful job of educating their own children right up to high school and then they put the student in a classroom for a “better standardized education.” While I know there are many more decisions at play in sending otherwise home educated students to a brick-and-mortar school for high school, in the end the biggest reason is that parents don’t feel they are up to the challenge. They lament that they don’t remember a thing about Calculus, French, or how to write a research paper! They wonder how to educate through high school. I can confirm, you home educators will do very well. Let’s talk about it why:

1.    Home educators are Resourceful.

Most of us didn’t remember all the names of the presidents, world geography, or even the basics behind geometry. We get through it thanks to the mountains of homeschool resources, and free (or at least affordable) online resources and friends. Once a student hits high school the game is unchanged. Go be resourceful to find the best approach to cover topics for your student. Includes a buffet of online offerings available for subjects you simply can’t or won’t be able to master.

2.    Home Educators Build Custom Educations.

Universities—at least the good ones—want to see students with unique educations and unique life experiences. Home educators often fear that their high school student will miss out on some opportunities, topics, and coursework if they don’t have “the” standardized approach.  On the contrary, most standardized education are as bland and lifeless as it sounds.

3.    Home Educators Are Their Child’s Best Advocates.

In our classes we often have students from conventional schools who are “allowed” to join a class or two by their school administrators. If they are very lucky, somebody up the chain of command will permit these students to enrich their education with a single class but only after much begging, paperwork, and hassle. My goodness! So generous! Consider home education. The only one “granting” permission about classes, passions, interests, and speed of study will be you and your learner. YOU are your student’s best advocate and you will make all the difference.

Classical, Trivium, Quadrivium, or Just College Prep

What’s the Difference Between Classical and classical?

By Amy Barr at The Lukeion Project

At TheLukeion Project we say we offer “Classical education expertly taught live online.” Our course topics typically relate to subjects stemming from the Classical world of ancient Greece and Rome or related fields. This includes Classical languages, literature, history, rhetoric, logic, and subjects that were dear to the hearts of people like Plato, Aristotle and Cicero. For good measure we toss in Classical archaeology and some classical literature (thanks, Shakespeare, Tolkien, and others). You’ll notice I employed a capital letter C with Classical. This was, at least until recently, the standard way of designating what we meant by the word. Classical with a "C" means, “of or relating to the ancient Greeks and Romans, especially their art, architecture, and literature; conforming to the artistic and literary models of ancient Greece and Rome; versed in the Classics.” We've been told it is now naughty of us to use a capital C but it does help us remain clear about what we mean by the word.

The other day I was discussing course options with a parent who was interested in a classical education for her child whose school program offered no Latin whatsoever. When you see lower case “c” classical (or today, any use of the word classical), what does it mean? Why do we talk about classical music and classical literature that has nothing to do with ancient Greece and Rome, or little to do with Latin or Greek?

If you are new to the world of home education, I invite you to visit any of the many bustling home school conferences available, at least in the U.S., throughout the spring and early summer months. You can’t make it through a vendor-packed isle without somebody touting classical education. In fact, we often attend these conferences as vendors and see that their speakers’ line-up features a “classical track.” We are never invited. We are Classical rather than classical, so we aren’t in the popular kids’ club. What’s the difference?

Lower-case-c-classical education can (not always) refers to an educational approach that was, at least at one point, inspired by the form of Classical education that worked beautifully for both the Greeks and Romans: the Trivium. 

Trivium comes from the same root as the English word trivial because both refer to three (tri) roads (via). Trivia is the sort of information one often gathers at intersections, water coolers, and crossroads where one might get the latest gossip. Trivium is a modern approach to education in which main subjects are graded and geared toward the three main stages of academic development: grammar, logic, and rhetoric.These levels correspond neatly to our traditional elementary, middle, and high school divisions in most U.S. systems. 

School/home education programs that call themselves classical often just refer to how their topics are taught and reviewed differently at the three different academic levels with, presumably, sufficient strength that their students are prepared for college. When classical is used in this fashion (I find it is the most common way you’ll see the term used at conferences), there’s no real relationship to the original tenets of ancient Classicism nor even the medieval concept of a classical education. It has become the modern alternative description for “prep school” which now sounds too stuffy for a good bottom line.

The concept of the classical Trivium, when applied to formal education, first appears in the Middle Ages, and was then further defined in the Renaissance in a work by Martianus Capella referring to Plato’s explanations about how grammar, logic, and rhetoric were essentials in a good early education. Plato would have preferred the world had remembered to include the Quadrivium which added arithmetic, geometry, music, and astronomy. Together the Trivium and then the Quadrivium formed the combined “Seven Liberal Arts.”

Today there are hundreds of programs, schools, and groups that maintain they are classical. Some of them truly sustain strong connections to the Trivium and might even toss in parts of the Quadrivium in upper levels. Throwing shade at classical, I can confirm that some schools and programs use the title classical for no reason besides how it spices up the top of a transcript. The term has also come to refer to the normal procession of subjects that were common 30 or 40 years ago in a public education with no connection to anything Classical whatsoever. Rhetoric gets a few hours in English classes while logic is rolled into a variety of math classes. Formal grammar is diminished to workbooks.

Most programs with classical in their title offer either a little Latin or none at all. You’ll not likely find Classical Greek anywhere but The Lukeion Project where we often have Classics majors in college come to take our history and literature courses because their college program stopped offering those types of things years ago.

If you are looking for a true Classical approach, The Lukeion Project is as close as you’ll find but, like many successful Lukeion families, you'll need to add your own strengths to our course offerings. Plato would assure us that we need to augment our program with music, math, and astronomy but we’ve made good starts in that direction. So many of our parents provide such robust alternatives in those subjects that the old philosopher would be proud! For the rest of the classical programs you find out there, caveat emptor, let the buyer beware.  

3 Things that Worked for Us

Basics to Our Home Education
By Amy Barr

My youngest of three children graduates from college in a few months. If you hang out with all three of my adult kids, you’ll find they are funny, reliable, and capable human beings with broad interests and firm opinions about restaurants. This officially qualifies me to offer some advice about homeschooling because my job as their personal educator is now complete. I’ve moved into an advisory role now.

I’ll now present with limited ado and a mild allotment of sarcasm, 3 things that were effective in the home education of my own children. Certainly, some will disagree with my wizened words while others will nod vigorously in union. Maybe these things will work for you too. Simply discard the rest. No need to email and complain.
I decided I would educate my children at home before I even had an interest in having children. When I was in college, I worked at a special collection library for education majors. I’ll save the specifics for my memoirs but, suffice it to say my experience was slightly traumatizing and my life was changed forever: I would never trust my (yet non-existent) child’s education to anyone else but myself and my (as of yet) undetermined spouse! Most people don’t have that lightning bolt moment to spur them on, but I did. The main benefit to this early decision was that I could start to build plans for how I might best educate a young mind. Here are three things. I have lots more where these came from.

Start with the End in Mind

This was easy for me because I had strong opinions about how my own education had gone (not that great up to that point) plus I had interests in how people learn best. My children hadn’t been born yet but I identified several goals that were important. Your list might be quite different. Here is a short list of what I wanted for my children:

• to enjoy reading good books (plus have time to do so)
• to have the chance for creativity
• to be prepared for anything academic, even if they didn’t choose college
• to be able to express themselves well in a variety of circumstances
• to have a good grasp of the practical skills necessary to make life pleasant

While each of these goals deserves more attention than a list in this blog, I’ll start with academic preparedness which took a very specific form for our family because mom and dad were ourselves in the very academic field of Classical philology (Greek & Latin), archaeology, and ancient history. I wanted my children to write well, communicate confidently, manage research analytically, and—above all--know how to learn for themselves without helplessly waiting to be taught. Sharing their parents’ interests in old Greek and Roman things wasn’t even on the table. That’s good because none of them were interested.
If given the opportunity, time, and means, children will excel at things that interest them. Offer as many tools (and seeds) as possible to keep that garden of subjects and interests growing for them. Enjoyment is robbed from learning when only the transcript matters. Some of that is unavoidable as students mature and form goals. It is difficult to flourish when education is nothing more than a chore list. The beauty of home education reveals itself when we can offset academic duties with subjects that our students genuinely enjoy.   
One of my favorite bloggers (Homeschool Libertarian) once said, “The idea that a child reaches cognitive milestones at a predictable age is damaging. Books that give lists of what children should know and when they should know it should be approached with the caution usually reserved for eating pufferfish or cobra wrangling.”  
Truer words were never spoken. The worst damage is done by well-meaning educators trying to convey perceived benefits by lock-stepping a child’s education through arbitrary academic steps before (or after) they are ready for that material. Learning happens best in leaps and lags, peaks and valleys. Don’t sweat the details because you aren’t accomplishing their education in the narrow confines of a single academic year. An education will happen but via the ebb and flow of many years. Their isn't meant to be a heart pounding sprint. They aren’t in an exhausting marathon either. Education is more like a hike along the Appalachian trail with flat paths, steep rock climbs, a few nice cold waterfalls, and a few long breathers when the view is good.

Have Them Read Real Books and Lots of Them

My children all had to learn sentence diagramming, writing, spelling, and all the other details that educators categorize as language arts. Some of that was done more formally than other parts but we carefully avoided those graded readers, that pablum that publishers insist elementary readers must endure before they are ever allowed to read real literature. We just went right into real literature as soon as we’d gotten through the basics.
My kids were given or selected for themselves stacks of books that interested them. If the book that looked good to them was a bit difficult for their “reading level” (whatever that is), no problem! What spurred them on to grow their vocabulary and broaden their interests was decoding a fantastic plot line written by writers who knew their craft well. When an older sibling held court at dinner talking about a new book series, the younger sibling might be keen to try it or go a different direction, just as a point of pride. Today, few high school graduates have read even a single literary work cover to cover. Simply keeping a love of reading alive through childhood and into the teen years is two-thirds of the battle won. Do whatever it takes to foster that love of reading.       

Allow Them to Have an Acceptable Form of Procrastination

One of many fatal flaws in the modern academic system is the belief that we can shove absolutely everyone through an identical education yet still expect them, at age 18, to have unique strengths and opinions about what they’d like to do when they grow up.
I had only three to educate and they couldn’t be more different. My oldest was compelled to draw. My youngest was attracted to all things musical. My middle child wavered between architecture, cooking, chess, and figuring out puzzles. Since both mom and dad worked from home, we’d take turns sweeping through the house to find out how daily academic progress was going for everyone. The tacit agreement was that our artist was allowed to procrastinate with a bit of art before we could get her to focus on something else (I just kept buying stacks of sketchbooks). Our musician needed to pound out on the piano whatever piece he was learning before he could settle down and think serious thoughts (he was very keen on playing during the time allotted to algebra). Our middle child needed a spot of time on Minecraft or Rollercoaster Tycoon and then he could work his way through the next school project quickly enough.     
Today my eldest is a senior graphic designer and illustrator. My youngest is training to be a sound engineer and already enjoys working with state-of-the art equipment and big-name professional groups on stage. My middle child, who easily grew bored with puzzles once they were solved, is finishing his studies as a physical therapist (humans are unsolvable puzzles). We are happy that we always gave them the room to explore their own interests, even if a more conventional approach would have just called it procrastination.