Mind Skills

Memorization Builds Brains

By Amy E. Barr at The Lukeion Project

 

    Charles attended his local gym every other day for months but nothing about him changed. He was no more fit and no more flexible than when he had first joined this ultramodern facility. To him it was a mystery! He attended the very epicenter of fitness and health so often that the front desk crew knew his name. He put in a full hour each weeknight. He put in two hours on Saturday. The other regulars knew exactly where to find him during his habitual visits. Charles made zero progress and saw no results but yet he continued to attend. His failure to make gains was no surprise to anyone who knew him. Charles refused to lift any weights, work on any cardio equipment, or take part in any swimming or cycling opportunities. 
    This sounds ridiculous. Charles paid the membership fee after extensive research looking for the right facility with the right coaches. He even bought a handsome exercise outfit which allowed full flexibility and to show-off any future gains. All this only to enter the gym and do nothing but see others lift weights, swim, exercise, climb, move, and stretch. 
    Charles attending an expensive gym for sizable parts of his week and doing nothing to improve his heart and muscles is very much like a student who plans to navigate 12+ years of education without once memorizing anything.
    Never being asked to engage one’s brain in this manner explains our public educational plight, at least in the U.S. though certainly the practice continues to spread to other nations. Never memorizing anything means that students live in the perpetual state of first steps and first impressions with no ability to climb the educational ladder to anything more complex. The brain is a muscle. It needs work and heavy lifting. Looking at charts, videos, and other students doing the work creates no benefit for yourself though it will certainly fill one’s day.
    Working memory, our superficial thoughts, takes any first exposure to new information and begins to engage the brain into a sorting exercise. The brain must decide if information needs to be stored short term, long term, or only briefly engaged and quickly forgotten. At best, working memory can keep around 7 items stored before everything gets jumbled. 
    If you look at your vocabulary flash cards for your Latin class only once or maybe twice before evaluating your retention, you’ll probably get around 5 to 7 things right and the rest wrong. If you enter a room to meet a bunch of new people, good luck. You might remember 5 to 7 names if the only thing people tell you is their name and nothing else like “nice to meet you” and “lovely day isn’t it!” Our brains are usually thinking up clever responses and we’ll not likely remember any names at all if we aren’t making a real effort. 
    Long term memory is what gives you the top score on your quiz and the ability to greet your new teammates when you see them again in a couple of days. Working memory is, at best, a tiny holding place for a handful of facts that will fade before the hour has ended. An educational system that is not built around developing long term memory skills condemns a student to live in mental deficit, like a case of amnesia. 
    Depending on how you prepare long term memory facts, you can store information in your mind for days to years to a lifetime. Learning the fundamentals of a subject for one year and then applying fundamentals the next as you add newer and more complex elements requires long term memory. This success requires memorization. If you’ve come from the vast majority of brick-and-mortar schools you’ve likely never been expected to memorize much. You’ve certainly never been taught methods to help yourself because “trendy education” has thought it old fashioned as our nation’s scores plummet lower than any other developed nation. The inability to develop topics over years means students limp through life with only a jumble of ideas temporarily stored in working memory and nothing more than hopes to look it up online.
    “When will we ever need algebraic formulae?” you might ask. Good luck moving up to more complex levels if you are juggling pages of facts you never learned but only saw. You can’t. Your brain can’t juggle working memory and the introduction of new concepts beyond that small group of 5-7 facts. You aren’t progressing because you are never learning. You are never learning because you have cognitive overload by asking your short-term memory to try to the job of long-term memory. Comprehension collapses. Your brain can’t juggle information and tires quickly, your learning slows, you get frustrated, and then you lose all motivation. 
    Listing the necessary outcomes of only using short-term working memory and never memorization sounds like a typical diagnosis of a learning disability: low comprehension, mental fatigue, delayed learning, frustration, disinterest, and low motivation. What if we didn’t need to hire all those classroom assistants? What if we started teaching students how to memorize and then expected them to progress beyond the basics by having long term memory functioning normally if not robustly?
    Let working memory do its job (juggling 5 to 7 new facts) but then move the important things into long term memory every night. The outcome makes an average student into a genius in today’s terms: increased comprehension (you memorized yesterday’s facts and can juggle the new ones today), increased mental stamina (you have sorted out how to process information efficiently and have confidence that you can keep doing it), faster learning (you don’t need to spend half your time looking up the things that you should have memorized but never did), and increased enthusiasm (look at that successful exam or project after the hard work paid off!)
    Having mastered what memorization can do for you, you get to move on to application (build that engine or complete that experiment or participate in that cool project), creation (apply what is known to new problems that must be solved), evaluation (swiftly sort out good ideas form bad ones to plan even better projects). 
    n the modern educational arena, too many have made a choice between memorizing a thing and understanding a thing. Use both as a tool to aid the other. 

Can't or Can?

Attitude Starts at Home

By Amy Barr with The Lukeion Project

Parents, I’ll keep this brief. All of you are busy. This week’s blog is all about modeling the attitude that helps propel a student through the most challenging academic trials. Since some of your children have not yet met many challenging academic trials, here’s your primer. The first month of academically challenging classes will be taxing but we have tips.

Survive the Drama – Everyone Hates New Challenges

It is your first week at a new job. You have a lot to learn, you don’t know anyone, you forgot your lunch, and you don’t know where to eat. As an adult, you struggle and stress tremendously when starting this new challenge, but you will likely wait until you get home to complain about getting lost while looking for the break-room and all the scheduled meetings. Sure, you are excited about new opportunities and certainly the gains in income, but starting new challenges is, well, yucky. This scenario is no different when you first start educating at home, only the lunchroom is sometimes easier to find. 

When your student starts a new academically challenging class there will be complaints. Everything is new, they want to do well but fear they won’t, and they don’t know all the answers nor understand all the expectations, they aren’t sure yet where to go. Yucky. We get it. For all of us, a good snack, hydration, and supportive words will help you and your student survive this dramatic start.

Praise the Effort, not the Smarts

Your student is putting in the time. All the signs are good because flash cards are in use, assignments are getting read, tasks are being completed. Praise all of this excellent activity because a growth mindset affirms that one can only get good at something after putting in some effort. You are fighting against the far more normal mindset of the undeveloped mind, namely that our talents are somehow already “fixed in place” (as in set in stone, stationary) at birth. Logic prescribes this isn’t so.

Don’t wait until that fabulous grade arrives on the first big exam to say, “well done.” The goal is steady consistent effort. Ever-improving grades are a nice bonus side-effect of putting in determination and struggle.

I like to use one of my son’s college experiences as an example. He’s now a gainfully employed physical therapist but his first class for his first semester of college was much the same as every other student who has grand plans for a medical career: anatomy and physiology. A&P lost half of the students before the drop deadline. Students who had luminous academic scores in high school were clawing towards scores in the low C range, the minimum to pass a course that is needed to move on in medicine. Another half of the remaining students didn’t pass and changed their majors. My son was pleased and proud to earn a low B (and retook it his senior year for an A).

An academically challenging course that was a career-do-or-die offered no chance for glamorous rewards but needed determination and grit. That score didn’t look particularly “smart” on paper, unless you too have been through this type of class. The work that really matters may not always look smart but sticking with it? That’s the prize!  

Don’t Foster an Addiction to Do-Overs

A trendy policy in public education right now is the habit of constantly allowing re-dos and retakes and do-overs and mulligans. In all the history of education, this was never normal, primarily because there is zero motivation for a student to study for anything. Enter that quiz and keep whittling away at a quiz score until boredom hits or you’ve toggled through all the multi-choice options and game the system. Consequently, we have millions of students who not only don’t need to study but now certainly can’t study if needed. Why would they?

This approach was introduced when personal devices became a major part of every classroom. Educators could put together a short multi-choice computer graded quiz online and leave it sit. Students can keep retaking the quiz until scores go up, the only goal (learning? Not so much).

The only type of quizzes that work for eternal re-dos are fairly basic by necessity. There isn’t time to grade, regrade, and re-re-grade complex assignments and projects with a room of 40 students. Material is kept at an artificially rudimentary level so it can be completely computer-graded. Now we have students who never learn to write under any type of pressure.

Offers of unlimited retakes give a student no pressure to surpass basic levels but why? If you must prepare a 20-minute well-researched speech to a group of esteemed peers, you prepare fervently. You never know what question the audience might ask! Nobody feels that level of concern over, say, an email in which you casually assemble your points and add important links then answer questions at leisure.

That stressful speech—just like a one-chance-only quiz, exam, or timed essay—pressures you to prepare. You want to present your case knowledgeably. Research, preparation, memorization, and practice naturally help. The reasonable response is subject mastery.    

Unlimited re-dos do not mimic real life. Mess up the quarterly report, your boss isn’t going to repeat the meeting. Tangle up holiday plans, you don’t get a second week of vacation to fix everything. Forget your college midterm, you don’t get to reschedule a week later after a second study period. Forget to pay the bills for two months? Good luck. 

Your Child Can Do This

Unless the faculty educating your student started teaching yesterday, he or she has had a lot of experience getting students from very limited experience in a particular subject to the point of proving very decent mastery. Constantly model confidence that your student can overcome, persevere, work hard, have determination, and ultimately succeed. Setbacks are expected! Occasional hurdles are required! Failure here and there? Normal! Failure is a teachable moment rather than shame but only if we allow natural heights of success and valleys of failure.

Set Things Up for Success

Provide tools, time, and encouragement. Subtract distractions. Avoid too heavy a load but don’t be afraid to challenge your clever and competent student. A greenhouse plant will quickly perish in the sun and wind unless you acclimate that rose. A common thing that sabotages success at the start of each new semester is the desire to get in “one last” break. Some students can manage the stress of hurrying through the first couple of weeks of classes for a trip. Most can’t. Set things up for success might mean keeping things boring until your student gets on their feet.    

Don’t Fill in for Them

Unlike faculty who might have your student for just one semester, our program hosts students often throughout both their middle school and high school years. This means that we can see how they did at the start and compare that work to what they are able to do four, five, or six years later. Unless you are a homeschool parent (and many of you are, so this is a big benefit to home education) there will never be an educator who has the opportunity to see a student start with, say, Latin 1 and finish with Latin 5. All of this is preface to the following absolutely true statement: no student whose parents “fill in for them” ever make it to Latin 5 …or even Latin 2.

It is out of love and concern that we parents are tempted to help by doing a bit of this assignment or that assignment as good examples of how to get the assignment done. It is often very difficult once you help a student in this way to stop because all the prior struggles were lightened and all the necessary coping techniques were never mastered. Never do any of your students’ work.

Make It Ok to Not Be Perfect

Perfectionists struggle more than any other type of student. This form of self-torture will make even the most capable and clever student miserable to the point that they often give up. When questioned, perfectionists will claim their approach is the preferred one! Why shouldn’t one strive to be perfect?!

The problem is that there’s no such thing as perfect here on earth. We are all but shadows of the real thing if ancient Greek philosophy is to be observed and we have all fallen short according to the Bible.

Perfectionists often give birth to other perfectionists. Your task may not just be to help your child navigate towards a healthier relationship with struggle and failure. The fight might start with yourself and how you model perfectionism at home. The next time you mess something up—if you are like me that will be before you go to bed tonight—do your best to model healthy recovery with a little humor and old-fashioned live-and-learn attitude.

 

Don’t Let the Goldfish Win

Work Your Attention Span

By Amy Barr with The Lukeion Project

It used to be when somebody wished to insult your ability to pay attention, they would say you have the attention span of a goldfish. Naturally this inspired a number of studies that found the average attention span of a goldfish is in the range of 9 seconds. That is indeed a very short period of time. Observing the life of a goldfish, you seldom see them enjoy good literature, long conversations, introspective journaling, nor expressions through painting or drawing. 9 seconds is just enough time to remember that some food was sprinkled in the fishbowl or to swim a different direction to avoid your grumpy goldfish roomie. Neural research has also been done on average humans. Dr. Amen of Amen Clinics, who knows more about brains than almost anyone, estimates that most people in the U.S. have attention spans in the range of 8 seconds long.

The Goldfish are Winning?

As we examine all the splendid things people have done with their brains over the course of history, we must come to the logical conclusion that the average length of the human attention span was once much, much longer because our lives depended on it. Carefully guarding livestock, conscientiously weaving cloth, crafting, sculpting, cooking, writing, gardening, preserving, and inventing new ways to do all of these things better require much longer attention spans than 8 seconds at a time. Spoiled by the luxury of not living minute by minute to survive, most of us have more free time than our ancestors.

With free time came entertainment. A zillion things to grab our attention but very few things hold our attention. The luxury of the modern world makes it possible to survive a distracted lifestyle, mostly unharmed by our lack of attention. Some of us can afford to bounce back and forth between entertainments while we wait for our food to be delivered or our appliances to do the hardest chores. An attention spans less than that of a tiny fish seems like a setback in human progress. How do we do better?

Read Don’t Watch

The current generation typically doesn’t enjoy reading that much because it is difficult for them to maintain focus long enough to become engaged in a good story, much less good information. The average reader needs around 30 seconds just to read this far in this blog. Many will have stopped reading or have gotten distracted several times already. Consider the implications of how much educators might expect students to accomplish in a single assignment!

Around a third of people under the age of 20 consider themselves avid readers but admit that they typically read eight or fewer books per year even though they are enjoying a period of life that is uniquely suited to reading books as students. Self-described avid readers from older generations easily consume roughly twice as many books per year even with a more demanding schedule. Today, average high school students in literature courses with comparatively moderate reading assignments are overwhelmed by what would have been considered light reading five or certainly ten years ago. Most high school students never complete a single book and even fewer college students. Literacy is sliding backwards.

Reading for pleasure is the best test for a strong attention span. If you’ve never developed the habit, you should. You will at once encounter two surprising facts about yourself. First, you’ll discover that at first you will struggle to read for longer than a minute without getting distracted, even when you are reading a subject of interest to you. Extended reading is a muscle that must be worked and developed. Second, you’ll discover that once you can start reading with intensity, your life will be greatly improved. Deep engagement in excellent storytelling is deeply rewarding. Watching a story or hearing a story doesn’t work the same part of our brains as reading a story. Challenge yourself to consume entertainment in book form instead of screen or audio form.

Screen time (short-form entertainment, apps, games, TikTok, movies) have been designed for—and are much to blame for—the attention span crisis. Programming produced today is intentionally built around our 8 second attention spans to recapture our focus every few seconds with sounds, lights, and sound. “Older” movies from even a decade ago are considered unwatchable without the constant flash and glitter so there’s your answer about why companies remake so many classics. Recorded media is a little bit better (music, podcasts, books “on tape”) but still must multi-task instead of focus attentively. To extend your attention span, read rather than watch and if you must, listen with focus.    

Green Entertainment

I hope you like this term because I just made it up. Green entertainment always builds longer attention spans. How well does your soccer match go if the goalie has an eight second attention span? How does your hike progress if you can’t recall which direction to walk after a short break? How’s the chess match with your sibling turn out if you are staring at your phone instead of planning your next move? All of these are unplugged “green” entertainments.

If you grow your attention span simply by engaging in team sports, mentally stimulating logic games, gardening, hiking or a zillion other engaging tasks, you also enjoy the side benefits and gaining new skills, gaining physical strength, and maintaining appropriate distance from the snack drawer in your house. Want to double all of that benefit? Engage in green entertainment without electronic input of any kind. Yes, this means you leave earphones and devices at home. If you bring your phone “just so you can play some music” you’ll fall back into engaging mainly with your phone instead of your teammates or task. Engage your focus fully instead of splitting it with recorded media.    

Memorization Isn’t a Dirty Word

If you hang out in modern educational circles for even a few minutes, you’ll get hit with snarky comments about any educational approach that forces children to “merely memorize” material. Initially this was a reaction to approaches that never ventured beyond basics when the basics were the periodic table, the U.S. presidents, or the mathematical formulae of algebra or geometry. Sure! What’s the point of memorizing these things if you go no further? At some point, memorization was dismissed entirely, not because it is a thing that won’t serve us well as we educate ourselves throughout our lives, but because memorization became impossible in a world in which students have a shorter attention span than a goldfish.

Memorization is an excellent way to build your own attention span, but it is also a necessary skill to master anything complex. I assigned memorization tasks to my elementary age children to build that muscle. Do they still remember those poems, presidents, or geography? Probably not but when they move into the logic stage around age 13 and the rhetoric stage around age 16 or 17, they will prosper greatly having built that mental muscle and never letting it atrophy throughout life. Learn how to fill your brain with the intellectual ammunition you need to pursue more complex subjects.    

The Search for a Life Well Lived

Write Well, Speak Well, Think Well

By Amy Barr with The Lukeion Project

Completing a good education, we are told, must be the main goal for everyone under the age of 22. We can easily believe the lie that getting a good education is just a matter of ticking boxes, formatting a transcript, and getting into a “good” school at a price we are willing to pay. We look forward to college tours and narrowing down the list of possible majors in college only to repeat the process, albeit at more expense for four more years. Walking the college graduation stage means we’ve done it and “off we go” to obtain that career we’ve chosen or a seat in a graduate program where we repeat that check list a third time. Is this a good education? Will this give us a life well lived?

The opportunity to seek gainful employment after each level in this process passes the vaguely defined notion of a “good” education today. Soon, nobody cares if you made top scores in high school but watch for highest marks in college and then beyond. When is the goal reached? Eventually, most who have ostensibly obtained a good education wonder if life is more than earning institutional certification to continue to work hard.

Eventually we must all think about life as more than keeping a decent job with good prospects for promotion. This can cause a little confusion. The main impetus that occupied our first twenty-two or more years fades quickly as we “finish” our education. Is this it? Now what? We can presumably pay bills now but how do we go beyond that to have a good life? How do we discover the most direct path to that goal?

Defining a “good” life is the real riddle. It has been the subject of much philosophy and theology stretching as far back as we have written records. By comparison, choosing and then training for employment is easy. Keeping a job and becoming successful in that job is practically a no-brainer even though we use a quarter of our life on that one thing. Having and enjoying a good life is a profound mystery that few people solve to complete satisfaction having, in their view, run out of time before they “arrive” at that destination. Advice is mainly ignored by each new generation as though earlier ages didn’t quite work out the answers properly enough for their modern tastes.

A good life is subject to individual definition after decades of living with or rejecting different modes. Each person must evaluate where to place energy and passion. Some stay forever focused on the pursuit of good looks and good money. Others prefer slower investments that yield life-long relationships and a support system of friends and family. Others prefer intellectual challenges and are happy with a good library, garden, and book.

How Do We Live Life Well?

My deepest apologies for my inability to summarize a well-lived life in this short blog. I wish all of you many productive hours searching for this answer in trusted, wise, and virtuous sources as well as novel ideas (as each generation prefers). Instead, I suggest three basic skills that will help you the most in your search. They aren’t the absolute secret to a life well lived but they are the best tools to pack for that journey: learn how to write well, speak well, and think well.

Write Well

The main thing that prevents people from expertly expressing themselves in creative writing or formal academic writing is inexperience. Usually, they’ve been asked to play a complicated game but are never taught the rules. Some trendy pedagogical approaches today insist there are no rules! Write whatever comes to mind! You tell your truth! Such writers quickly discover there are rules to be followed and good examples to emulate if one hopes that other human beings will be interested in what they have to say.
Many students miss the most basic fact, namely that writing is meant to convey meaning to others so that they not only understand you but might even come to agree with you. How does this apply to a life well lived?

Long before there were pricey college degrees and peer reviewed journals, there was The Great Conversation, the exchange of ideas that has been going on for thousands of years that have to do with God, relationships, truth, knowledge, life, hope, despair, and how we must live. Every great thinker, writer, and doer of deeds not only consumes materials written on these topics but also takes part in the conversation about those subjects. Nothing is new under the sun. No fresh idea is truly fresh. Ideas have been in refinement for as long as people have written words and thought thoughts.
If you want to earn the highest academic accolades or learn how to fix small engines, being able to communicate in written form is a top tool for a life lived well.

Speak Well

The other day I was having a friendly conversation with a friend who runs a humble country greenhouse. He has never considered himself well educated since he set foot neither in college nor any formal classroom. He easily discusses thoughts on a wide variety of topics and speaks skillfully. He would be as comfortable in a boardroom, lecture hall, or a greenhouse full of tomato plants chatting with a customer. He enjoys the close support of family and community, and the competent success of all his efforts is easy to see. He is enjoying a life well lived! His ability to speak at ease with anyone and everyone on all subjects is as useful a tool in a greenhouse or at a campfire in the Rockies while he serves as a hunting guide. His clients range from adventurous millionaires to widows on a fixed income looking for garden advice.

Learning to confidently and boldly speak to others is a worthy tool for the job of building your own meaningful life. Just like there are rules and correct approaches to writing, verbal communication also has rules. The aim is to fully understand those rules and integrate them with such polish and practice that both tasks come quickly and easily to you. There are classes like rhetoric to help you learn how to overcome the fear of public speaking, attract interested listeners, and persuade them that you have clever ideas. The best success in speaking well is by doing more of it.

Think Well

Humans get so busy working on what they must think that they never master how to think skillfully. Expert use of one’s brain incorporates the ability to evaluate, study, memorize, and master new concepts without the need to have others teach that material to you or at least being judicious about the help you do need. People who know they can learn anything with a bit of perspiration and persistence, do. Not only are such people seldom bored, but the richness of their life compounds yearly, monthly, and daily. Their words are interesting to read or hear because they love to learn new things. They need no permission and seek few accolades, but their lives get richer daily. Those that can think well do so because they’ve given themselves the ability to learn new things, the humility to recalibrate when corrections must be made, and the confidence to employ their brains well, even without lofty credentials and costly degrees. 

“Six mistakes mankind keeps making century after century: Believing that personal gain is made by crushing others; worrying about things that cannot be changed or corrected; insisting that a thing is impossible because we cannot accomplish it; refusing to set aside trivial preferences; neglecting development and refinement of the mind; attempting to compel others to believe and live as we do.”
― Marcus Tullius Cicero

Kim Johnson

Lukeion Faculty Interviews

What do you teach at The Lukeion Project?

I am the resident mathematician at Lukeion---the classicists make me welcome, even if I don’t always get their jokes!  I teach Logic and I have taught the History of Mathematics.  I also lead mathematical workshops, including Bizarre Ancient Numbers and Art and Math.

How did that subject first inspire you and what kind of education do you have as you develop and teach your beloved subject(s)?

There are two stories: first, how I came to study math and, second, how I came to teach at the Lukeion Project.

The high school I went to had Latin, and although I didn’t take it, many of my friends did. My senior year I took a class in Classical Literature, and based on that class and what my friends had told me about Latin, I planned on majoring in Classics and Philosophy in college.

Then came the reality of the actual college classes! My first philosophy class was about the theory of knowledge and how do we know things? It was a fascinating class, but I found that I was always missing something in my arguments. I got average grades on my papers, but I didn’t know how to make them any better.

I enjoyed my first Latin class very much. We used Wheelock and covered the book over two semesters. The grammar came easily to me because it was just like math!  But the nuances of vocabulary sometimes seemed out of my grasp. I wasn’t enjoying my chosen majors as much as I had anticipated.

Then in the second semester of my freshman year I took a calculus class. Every class felt as though I was going on a new exciting adventure. We were studying some of the most difficult topics in the first year of calculus such as the techniques of integration, but they seemed like a walk in the park. Doing my calculus homework was a joy. It was not that I always got the right answer but rather that I was able to tell by the work itself whether I was right or not. I didn’t need an instructor to tell me. I majored in mathematics and went on to get a PhD in mathematics.

Fast forward about 30 years when I discovered Lukeion from our local homeschooling mailing list. I wanted some good courses for my middle schoolers that I didn’t have to drive to, and Lukeion offered the high quality, interesting, and challenging classes I was looking for.  I listened to all three of my students as they took Witty Wordsmith, Barbarian Diagrammarian, and Latin 1 and 2, and I was extremely impressed with the way the instructors made the classes come alive despite not being on screen and even though students only typed responses in the chat. My kids would be yelling at the computer to try to answer questions---it was just as well that there was no audio! They were constantly engaged and therefore learned a lot, even during the relatively short weekly class sessions.

My son was happy to join Lukeion for Logic when it was first offered in Fall 2019 with instructor Michael Haggard. Unfortunately, that spring Dr. Haggard was unable to continue teaching, and I wanted to help. Although I had never taken a formal logic course, I had been following along with my son as he took the course. I had also taught a unit on Formal Logic in a Discrete Math course as I taught as an adjunct after receiving my PhD in math. I used logic in mathematics all the time both in creating arguments and in understanding and critiquing arguments that other people had made. To help Lukeion out, I volunteered to be a Teaching Assistant to one of the other Lukeion instructors. My thought was that I would grade homework and answer emails, both of which seemed interesting and doable.

The Barrs came back and asked if I would be willing to teach the class. I swallowed and said yes. There were a few 60-hour weeks as I learned the curriculum from scratch and prepared to teach engaging and interactive lessons, but the years of listening and absorbing the Lukeion method for online teaching made the format clear. In addition, the topic was fascinating. Although I was not familiar with the specifics, the principles were the same as those I used in math throughout my career. 

The in-person classes I had been teaching that spring were cancelled due to Covid. My kids were growing older and were becoming more independent.  It seemed like a good time to try something new. I was honored that Lukeion asked me to return the next year.

What do you wish everyone knew about this cool topic?

The history and development of logic is fascinating.  We study two branches of formal logic at Lukeion: Categorical Logic and Propositional Logic.  The formal study of Categorical Logic was founded by Aristotle when he wrote the Organon: not a book, but a collection of books about logic. A classic example based on Categorical Logic is the following syllogism:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

Although it may seem that this type of argument is inflexible and only useful in obscure philosophical arguments, it turns out that many of the arguments we make every day can be rewritten as syllogisms.

Aristotle’s logic was taught to students for millennia. Then, starting in the 1800s, mathematicians developed a new type of logic intended to unite the fields of formal logic and mathematics. One of the pioneers trying to formalize how mathematics worked was George Boole, the son of a shoemaker. He used mathematical ideas like addition and multiplication to combine propositions, revolutionizing logic.

Then in the 1930s, Claude Shannon added electricity to logic. When he was a graduate student at MIT he maintained an analog computer which used switches and relays. His great insight was that you could use the digital switches to encode logical arguments using Boolean algebra. Thus, in the most influential masters’ degree thesis in history, the modern digital computer was born.

How would this class help you if you are a student with limited time?

Some areas of study are obviously connected to logic. All mathematics, whether geometry and formal proofs or applications in finance or physics, relies on making assumptions and reaching conclusions based on reasoning rather than guessing. Computer science is literally built on logic. Both computer hardware and software rely on the foundation of propositional logic. If a student is interested in either of these two topics, logic will strengthen their skills.

However, logic is ubiquitous. Analyzing words and sentences in Witty Wordsmith and Barbarian Diagrammarian relies on logic. When you are doing a Latin translation and are figuring out how the nouns and verbs fit together in the sentence, you are using logic. When you write a thesis statement for history or literary analysis and you support it, your argument must be logical, or your instructor and audience won’t believe you. Even rhetoric, which also uses tools relating to emotion or character, without logic, your argument can be easily disproved. Being aware of logic, its structures and rhythms, can help students in all subjects understand topics and communicate their ideas more effectively.

In college, writing was not my favorite subject. If there was an awkward way to write a sentence, I would find it. I could have used Lukeion’s courses in my high school! However, I found that the logic I used in writing proofs and making mathematical arguments gave me power when writing papers. In essence, a paper is an argument. You are trying to convince someone that your conclusion is true. If you do this convincingly enough, your argument stands on its own without needing any teacher or professor to tell you whether you are right.

Tell us a cool story from your teaching experience in this subject.

One of the disappointing things about mathematics and logic is that you don’t need to travel to any foreign lands to study it, you can literally do logic anywhere and anytime. Its very transportability means that logic is everywhere.

In my class students complete a project called “Logic in Real Life.” Some of the places my students have found logic used are:

• Insurance documents: when is something covered by insurance, and when it is not
• Historical arguments: why did politicians and military forces act the way they did?
• Current articles: do the conclusions follow from the premises the writers use?
• Advertisements:  The conclusion of an advertisement is almost always, “Therefore you should buy our product.”  But does their argument make logical sense?
• Books: Characters make decisions based on logic, to some degree, or the story doesn’t hold together.
• Comic strips often use unstated premises or conclusions to create humorous or ridiculous situations.

Students find a huge variety of examples of “Logic in Real Life,” often relating to their interests. I love seeing how they take what they have learned in the classroom and apply it in real situations.

 

Why Take Academic Classes If You Aren’t Planning an Academic Future?

Educate Yourself

By Amy Barr with The Lukeion Project

 If you listen to university and collegiate advertising, getting a college degree is the golden ticket to life! Finish that degree and you’ll have a bright and carefree future, right? This might be the case for some, no doubt. This is often untrue as well. For some, college will be a very expensive experiment. Results will vary. Some move towards the end of high school years without any interest in following the crowd into college. Should this change how you approach your high school years?
Being undecided about college (or even being certain it isn’t for you) does not mean you should skip tackling academic subjects in high school. “Academic” classes are not just for students planning an academic career. Just like you shouldn’t spend your life stretched out on a couch because you never plan to hike Mt. Everest, never miss out on challenging yourself and your brain to master new things. The challenge of navigating life’s demands will be improved when you have trained yourself to learn, do, and know a wide variety of things.   

The Highest Grade isn’t the Greatest Good

The Lukeion Project has been offering challenging courses for 20 years. While most of our courses were on par academically 20 years ago, they are now considered relatively challenging. Today’s students haven’t changed. What is expected of them has. Consequently, some ostensibly bright students are choosing an easy path to ensure a perfect GPA and transcript. Horror stories abound about students who graduate from high school (even with honors) but have never read a book or written an essay. After some navigate 12 years of this type of “education,” they are — unsurprisingly — disinterested in playing the academic game any longer than necessary.  
Having a crack at academically challenging classes can be wonderfully fulfilling, even if you must work extra hard to enjoy rewards. Success is often won with less than perfect scores but more than adequate assurance that you have what it takes to complete tough mental missions. “What if” it doesn’t go that well for you? That’s the risk with anything, no matter your path. It is as important to learn how to navigate failures as it is to know you can overcome and conquer challenges. The highest grade is NOT the greatest good.

Tackling Academic Challenges Benefits Everyone

There are plenty of subjects that you’ll be asked to do that will leave you wondering if you’ll ever “need” to use that knowledge again. Does the average person need calculus every day? Does one need 14th century French history? What about playing a toy xylophone when you were 5 or finishing an Egyptology lesson in fifth grade?  
Education is only as good as the width and breadth of your experiences. If we only do things we think we’ll eventually need, we will limit ourselves to the smallest and narrowest possible existence since we have no clue what awaits. Challenges, victories, failures, and recoveries shape who we will eventually be and how we’ll use this life. Taking on tough subjects offers benefits to absolutely everyone. You don’t need to become a professor of archaeology or an expert in ancient languages to learn about them and love them. They will continue to enrich your life endlessly.

A Rich Education Is Something You Create for Yourself

Home educated students already know this fact well. Skipping the often random and perplexing requirements set by program dictocrats is the biggest advantage to pulling the plug on conventional education. Getting a good education is nearly impossible unless you, and hopefully also your family, know how to enrich your own education.
I had only two bright spots in my otherwise dull high school education: botany and Latin. Those two subjects have shaped my preferences, career, and hobby ever since. Finding something to light your mental fire and then going out of your way to pursue it will make all the difference, regardless of how dreary your educational prospects might seem now or in the future.  

Many Rewarding Fields are Looking for Great Minds not Great Diplomas  

If life, the universe, and everything stays exactly as it is right now, there are many fantastic life paths that require zero college degrees. I propose, dear reader, that most things about the modern world are about to change radically due to innovations in quantum computing and in AI applications. My prediction is that society will soon be divided into two groups. The old model separated the educated and the uneducated in terms of social mobility and earning potential. Very soon, those that can think with swift clarity, and those that cannot, will be marked for distinct career paths.
Making top grades in easy classes then finishing a fast degree with community college dual credits used to be a simple and affordable route to a diploma. Your little diploma could open a variety of doors in your choice of 40-hour work week fields. Unfortunately, those are the jobs that may soon be completed by AI in a fraction of the time and money a human needs. Those who can teach themselves the new rules of the changing AI landscape will do very well. Four-year degrees will still be necessary but only for very specific fields. Train your brain to learn and memorize, train yourself to communicate precisely in both speech and in writing, train your tastes to crave a broad scope of knowledge and topics. There has been no better time for taking academic classes even if you think you will not want to pursue an academic career.  

Your Own Personal Education

Passive vs. Active Approach to Building a Life

By Amy Barr with The Lukeion Project

Which do you enjoy best: a tough game played without directions or goals, or the same tough game but with access to instructions, tips, and a clear view about what you must achieve to win? Those that even have interests in challenging games typically prefer to have the basics in place so that they can enjoy the game with a reasonable hope of succeeding. The toughest games in life can be your own education.
Most of us begin well before we know we are playing and, mid-game, are expected to excel before fighting the “final boss” graduation. Many decide to endure bonus rounds with apprenticeships, college, internships, or graduate school.
Some of us love this educational process and rally around the various challenges and opportunities! Some of us look at the future and despair. So many variables! So much work! It is easy to become prematurely weary about all the demands and expectations.
Students come to love the game of education more when they are given directions and have relative control over their goals. On a scale ranging from a rigid education (like a boarding school) to a fluid education (like unschooling), any approach that gives the student increasing autonomy and self-determination works best to bolster focus and optimism for the future. A student who has room to make choices about classes and topics will enjoy more opportunities to try things they might want to do for a living before they pay for college. Students who had a rigid earlier education will struggle to know what interests them enough to study further. Though most eventually find their path, they might change majors and careers many times since they delayed the process of test running new things until they became an adult.      
When framing goals, start by exploring your general interests to see if they mesh with any realistic goals. You don’t need years in botany, medicine, or art to know that those things light your fire.
 Depending on your life experiences, you may wish to continue what you already enjoy (art, music, writing, science, sports). This first tricky step is where many of us stall out. It is FAR more normal to have no idea what we want to be “when we grow up” until we are really pushed to make some type of decision. Over-thinkers worry they won’t be good enough at something they like to do, or they have concerns that their choices are unattainable, or that others won’t agree that their chosen path is worthwhile or realistic.
Instead of pushing non-stop over top academic marks and taking impressive academic courses that aren’t particularly interesting to you, be intentional about trying classes (or camps or workshops or programs) on topics that interest you. At all stages of our education, diversions from the programmed educational path are called electives, classes we picked “just” because we liked the subject. I can’t imagine a better topic to pursue than one we enjoy. How many geniuses would have remained anonymously unimportant if they’d rigidly stuck to the regular program?
There’s a lot to navigate before you might be willing to talk about your educational path with others. Some students don’t enjoy much choice. Perhaps family expectations make it clear where you’ll end up. Maybe your family boasts several generations of engineers or maybe everyone graduated from the same school. Perhaps a family business dictates where you’ll work once you graduate. Sometimes what you enjoy plays no role in what you must do educationally.
I had a friend in college who was happily finishing a degree in information technology when his mother insisted that he apply to medical school. Though he had no interest in medicine, she was willing to cut off all communication if he didn’t choose a medical path. On the other hand, I’ve known many who receive no guidance at all. Families can be a bit tricky to navigate.
Once you explore your goals, run your ideas past the most dependable people you know. Some public and private schools have guidance counselors when dependable people are in short supply, but I recommend you find somebody who knows you well and will be honest with you. Perhaps you see yourself becoming an online influencer but the person who knows you best might suggest a path that gives you multiple options. Getting a background in public speaking, marketing, journalism, and even graphic design would foster such interests without giving you too narrow a goal. Don’t despair if your objectives remain elusive. Sometimes your “aha!” moment arrives serendipitously. Observe yourself when you get excited about a particular subject or skill. Do more of that and see how things shape up.
Once you envision a path, take an active approach to your education from that moment on. Most of us, for very practical reasons, are very passive about our education until, one day, we want to take the steering wheel. Whatever you like to do, work diligently at being the best at it and you’ll never lack opportunities.