Study of Words

What is Linguistics?

By Dr. Kim Johnson of The Lukeion Project

Linguistics is defined as “The study of language.” It might seem as though human beings are experts in language. In every human culture across the globe, people communicate using spoken or signed language. There are around 7,000 languages of various types and relationships around the globe. Human beings typically speak and listen to language for their entire lives.

How do we think of concepts and then use our mouths to create sounds that are then translated into similar concepts in the hearer’s brain? How do the mechanics of language work? Why is the plural of mouse “mice,” but the plural of house isn’t “hice”?  Even when we make the plural the same way for two words, why do we pronounce the s in “dogs” differently than the s in “cats?” 

To study language we break it down into its component parts, mimicking how children learn to speak. We can talk about how to turn sounds into words, how to give words meanings, and how to turn words into sentences. In each of these areas, sometimes linguists focus on parts that are specific to one language and sometimes focus on universal traits of language.

How language sounds: Phonetics

The basic building blocks of language are the sounds we make using the tools of our mouth, tongue, throat and nose. Linguists have attempted to categorize all the sounds humans could possibly make according to what shape our mouth is, how the air is flowing, whether we are vibrating our nasal tract, and so on. Once we have these bits, called phonemes, we can study how sounds in one language vary across regions (accents) and how different languages use different sounds.

What makes a word:  Morphology

In The Lukeion Project’s word roots program, Witty Wordsmith, students join Wilbur as he examines words and their classical Latin and Greek roots. Word roots are one part of the area of morphology, the study of how we use words in a language.

There are more parts to words than just the roots, though. If I say, “I really flugged yesterday during class,” you would probably guess that “flug” is a verb. On the other hand, if I talked about flugition, you would know that flugition was a noun (and you would know how to pronounce it!) even though you wouldn’t have any idea what the word meant. The suffixes -ed and -ition are examples of morphemes, the smallest units of words that have meaning. The “s” that I added to cats and dogs is also an example of a morpheme. Studying how languages create words gives insight into how they work.

How language works: Syntax

In Barbarian Diagrammarian, students, along with the Barbarian Leland and his faithful Lemur, break down English sentences into their component parts and visually chart their relationships.

Syntax is how languages express relationships between words. Some parts of syntax are specific to a particular language but linguists also consider what is common to all languages. All sentences can be analyzed by breaking them apart into pieces which make sense together. For example, “The Lukeion instructor ate the delicious peach” can be broken down like this: “[  [[the] [[Lukeion] [instructor]]] [[ate] [[the] [[delicious] [peach]]]]”. To cut down on brackets, we can use trees or other ways to show the relationships between words.

In English, the constituents are typically right next to each other. In Latin the adjective “delicious” would belong to “peach” by virtue of its gender and case. Every language studied so far has two parts of a sentence: the subject and the predicate. Everything can be broken down into its constituent parts in different ways depending on the grammar.

And beyond!

In addition to these main building blocks, there are dozens of other areas that are parts of the subject area of linguistics. Linguists study the history and development of language such as how languages change and combine to make new languages. They also study how language is used in different societies and cultures. Psycholinguistics is the study of what is going on in people’s brains as they use language. Linguists study signed languages as well as spoken language. Any aspect of human interaction involves language, and therefore can be studied by linguists.

Why might you need linguistics?

If you are planning on learning more than one language, studying linguistics can help you make connections and highlight differences between languages. Knowing the history of how Latin morphed into Spanish, Italian and French can make learning those languages easier. Another joy of linguistics is learning about obscure or extinct languages and how their structure can be completely unfamiliar.

For those of you who are writers, linguistics can help you to create bold new languages for your stories. J. R. R. Tolkien is the premier example of a writer using language in his creation of a literary world. There are many other examples from Klingon (which is a language you can actually learn to speak) to even Parseltongue from the Harry Potter books.

These days, there is a great interest in trying to help computers understand and create language. It turns out that human beings bring a lot of complex background to understanding even simple sentences that cause computers a lot of trouble. To understand how to “teach” a computer to be better at understanding language, we must understand it better ourselves.

Of course, one of the best reasons to learn something is for the joy of learning something interesting and new. As I study linguistics to advise the Lukeion Linguistic Club, I am constantly amazed by the variety and complexity of the ways human beings communicate. My eyes are being opened to things that have always confused me but turn out to have rational explanations. Linguistics puzzles resemble mathematics puzzles in many ways. However, where competition math puzzles seem to rely on tricks and advanced knowledge, linguistics puzzles often rely on our human instinct as a speaker of a language.

What is the Lukeion Linguistics Club about?

Lukeion’s Linguistics Club serves a couple of purposes. First off, and importantly, it offers a space for students of Lukeion to get together in a less formal space and have some fun!  But that’s not all we do.

We talk some each week about various aspects of linguistics. So far, we have explored the International Phonetic Alphabet (IPA), some ambiguous sentences, and how to build meaning from words and suffixes. We plan on talking about constructed languages, language acquisition, and some of the history of English.

We also spend some time solving puzzles from the International Linguistics Olympiad. These are logical-language puzzles that highlight aspects of language like word order, declensions, affixes, and so on. Homeschool students can sign up to compete in these national and international linguistics competitions. The puzzles are fun for their own sake---they involve languages from across the globe and many interesting constructions.

If any of this strikes your fancy, all current Lukeion students are invited to join us for linguistics club. We meet on Fridays from 1-2 PM (Eastern time). Email me to join the mailing list, class web page, and address for our Adobe Connect meeting room.

 

 

 

HOPE

Reboxing Pandora

By Dr. Sue Fisher with The Lukeion Project

Have you ever seen an unboxing? These are videos in which people will open boxes to showcase and discuss products, removing them one by one. They are generally calm, measured productions, designed to let you examine and consider each item as it comes out.

Well, the first unboxing from the ancient world was not nearly so peaceful or controlled. The story of Pandora, found first in Hesiod, Works and Days 53-105, is one known to many. She was the first female, created by the gods, who let all the evils into the world. Having been given a jar from the gods (yes, the original was a jar not a box) and an unhealthy dose of curiosity to go along with it, she was expressly told not to open it. As one might expect, she didn’t last too long and soon she had pried the lid off and out flew all manner of evils into the world. The story serves as an explanation (etiology) for how hardship, devastation, and disease came into the world. But the most interesting part of the story is the end, where Pandora slams the lid back on and manages to keep hope inside.

Was it a good thing that hope was kept inside, not lost into the world? Or do we need hope out there flying around with the evils to combat them? Moreover, what was hope doing in a jar of evils in the first place?

The 5th c. B.C. Athenian playwright Aeschylus might have answered this question when he had his Prometheus, chained to a rock in the Caucasus mountains, list hope as the first thing he gave to humans, even before the fire he stole for them and for which he was paying the penalty. Prometheus’ conversation with the daughters of Ocean (chorus), who came to visit him, is very enlightening: 

Prometheus: I allowed mankind to stop foreseeing doom.
Chorus: What medicine did you find for that disease?
Prometheus: I planted in them hopes that would obscure it.
Chorus: That was a worthy gift you gave to mortals.

(Aeschylus, Prometheus Bound 250-253)

Taken together, in these passages the ancient Greeks explain the plight of humankind but also offer a remedy. “What medicine did you find for that disease?” the chorus asks. The remedy is hope.

So how do you foster hope when the evils of the world are flying around? You can’t just stuff them back in the jar, after all. But you can fill a jar with all manner of good things. You make a good-things jar.

It’s so easy. Get a jar (or a box), and each week write down one good thing on a slip of paper or piece of index card and plop it in there. This can be anything. You heard a funny story – write that down and put it in there. You got a new puppy. That’s a super good thing. You saw a cool bird, or went mountain biking, or got to hold a newborn baby, or hung out with a friend. Perhaps you finally learned that concept or vocabulary word or measure of music that has been elusive up until now. It may be big, like you got your braces off or got the part you wanted in the play. Or it could be small, like you found a fantastic acorn. (I love a good acorn.) It doesn’t matter. If it’s good, it’s fair game. Put the date on it if you want; it’s kind of fun later when you go back and read them to see what date it was. But if you don’t want to, no matter – it’s YOUR good-things jar. If you want to do it every day, that’s great. But do it at least once a week, so they start to build up. 

As your jar starts to fill with good things, your heart will start to fill with gratitude and your hope will grow. And as your hope gets larger, the evils will diminish. This is the remedy. 

American poet Emily Dickinson knew the power of hope and described it like a bird that rests in the jars of our souls. Hope is the gentle but relentless and powerful force that asks nothing of us but holds up firm in any storm. No matter the evils, hope is still the remedy.

HOPE
Emily Dickinson

"Hope" is the thing with feathers
That perches in the soul,
And sings the tune without the words,
And never stops at all,

And sweetest in the Gale is heard;
And sore must be the storm
That could abash the little bird
That kept so many warm.

I 've heard it in the chillest land,
And on the strangest sea;
Yet, never, in extremity,
It asked a crumb of me.

Writing Projects

Creating Your Own “Final Checklist”

By Randee Baty with The Lukeion Project

For many of the papers that I have my college students submit, I first require them to go through a “Final Checklist” quiz that they must complete before submitting their papers.  Quick reminders of common problems in the form of a checklist can help every student, and you can create one to use with your papers based on common mistakes or issues that you know you are prone to.  Here are the types of questions that are useful to have on your own final checklist.

1.      Have I read the assignment sheet one list time before submitting?

2.      Have I cited any information that I took from a source with both an in-text citation and a Works Cited citation? (Remember that citation always requires both!)

3.      Is my introduction interesting rather than bland and generic? (If you start a paper with, “In this day and age” or “Since the beginning of time” it’s time to rethink your intro!)

4.      Is my thesis statement at the end of the first paragraph?

5.      Does the conclusion show that I supported my thesis statement?  (This is actually a bigger problem than you might think.  I’ve had students submit papers that never addressed their thesis statement.)

6.      Does each paragraph have one clear idea that it addresses?

7.      Have I double-checked my formatting?  (Professors care more about formatting than most students realize!)

8.      Have I removed all unnecessary words, including unnecessary adjectives, adverbs, intensifiers, and modifiers?  Have I removed the word “very” from the paper?

9.      Have I removed all slang or casual language? (Cliches and platitudes also need to go!)

10.  Does my paper have the correct point of view? (If the assignment sheet asked you to write in 3^rd person but you have some 1^st person writing, you’re asking for trouble.)

11.  Have I done a thorough proofread?  (As I fully understand, many students don’t like to read back through their work once they consider it done.  Read back through it anyway.  A few minutes spent reading now could prevent having silly points taken off the grade for a small proofreading error.)

12.  Do I have the professor’s name spelled correctly in the heading?  (Yes, professors’ names get misspelled all the time. It’s not a good look for the student.)

Your own checklist may have different questions depending on the particular issues that you get caught on by your professors.  Don’t get point deductions for things you could have easily fixed!  After spending all the time and effort to write a strong paper, give it the best possible chance for a great score with your final checklist.

The Nourished Brain

Your Brain is Hungry & Thirsty

By Amy Barr with The Lukeion Project

You need clean water, food, and plentiful nutrients to power your muscles, liver, blood, and body. When we have a highly active life, we get hungry because our body burns through our fuel quickly and requires proper nutrients to manage life’s challenges. Playing soccer for three hours will (hopefully) earn you a nice meal and a little sympathy for sore muscles. But when we sit with our books and flashcards, some might think we have not really “done” that much. We have been sedentary all day with our studies so no need for much nutritive support, right?
Our brains burn as much as 20-30% of the energy our body consumes each day. Our brains need some love, attention, good nutrition, plus a little sympathy. Being a student is a physical work out, not just a mental one, as if those two things are different. If you want a high-functioning brain doing what it must do during the active part of your education years, there are some basic healthy steps to take. Students should prepare their brains for learning just like athletes prepare the rest of their bodies.
I am not a doctor nor a nutritionist. Anything I say here is based on my decades of personal experience as mom, educator, avid brain-user, and researcher. Take what you like, leave the rest. I have a lot of suggestions if you know me but will limit this to easy starting points.
When I started graduate school, I worked far into the night translating long Latin passages. Funds were limited as was time. I ate poorly, I seldom got any sunlight, and I rarely exercised except when I walked to the department office every morning and back home each night. My first year was tough but I assumed all of this was par for the course. I was constantly tired and lacked the energy to do anything but stay up late grinding away at my work. I felt isolated and depressed because I did not spend much time doing anything but translating.
I had a bright idea at the start of my second year of graduate studies. I added exercise, drank more water, and started consuming more nutritious food. Voila! I needed less time to study because my brain had more to fuel it. I was also less fatigued during the rare hours I had off. I could add more social events because my brain became more efficient at accomplishing what I needed it to accomplish. All my scores and academic efforts improved so that my stress was reduced. Though I added activities to my schedule (gym time, farmer’s market, time outside, and better meal prep) I decreased my brain work time and my physical work time by adding more to my schedule. I decreased my food budget expenses while I bought superior food at the farmer’s market.
What does our brain really want for the best results?
Some might complain they do not have the time or money to eat better food. Every penny and minute counts! Start by getting a decent water filter (do your research because results really do differ) and change to water as your main drink throughout the day. Many who say they do not like the taste of water complain about it because their tap water tastes like a dirty swimming pool in most communities. That is just the start of the unwelcome news because the “stuff” that shows up in most municipal water supplies would keep you up at night. A good filter gets rid of many objectionable chemicals (and other nasty things) and improves the taste. I use one that takes out fluoride too, which I strongly recommend for brain and body health. Simply switching to water throughout the day gives your brain what it really needs while your family saves money spent on sodas, juices, powders, energy drinks, etc. Want some flavor in that water? Add a squeeze of citrus or a slice of cucumber. In only a couple of months, whatever money you spent on a good filter will be returned to you by making the switch from pricey things that come in bottles to decent filtered water.
While you are saving money, cut out junk food. Easy! Unfortunately, many people are so accustomed to junk food that they cannot imagine cutting it out of their diet. So ingrained are our habits that we cannot imagine leaving behind family traditions like breakfast cereals, chips, boxed granola, packaged mac-n-cheese. Over two decades ago, our family gave up every bit of it. If it came in a box, we stopped buying it. It took about a week to learn new habits but eliminating all of it at once is better than suggesting that only a couple of people in the family should just “cut back.”  If it is in the house, family members will eat it. Starting your day with sugar (breakfast cereal or pastry, for example) is poor brain care plus it will make you powerfully hungry all day.
If you think transitioning away from factory food is hard, wait until everyone can think clearly, concentrate for longer periods, and get along more agreeably with siblings! Such a huge bonus for deleting these pricey toxic things from one’s daily diet. Avoiding fast food restaurants, it is obvious, has the same positive effect and saves even more money for better food purchases and better brain power.
Now that you have cut junk out, add good things in. The rule about foods that serve your body and brain well is simple: Know what every ingredient is and what it does. Processed sugars, gluten, dyes, and glyphosate (which is sprayed on things we might assume are healthy) are horrendous for the brain. Become an expert label reader or just avoid prefabricated food as much as possible. Farmers’ markets are excellent if you cannot grow your own food because you get the cheapest, freshest, healthiest supplies while supporting your local food chain.
If you visit my kitchen, you will find that it is full of one type of thing: raw ingredients that I assemble for meals. “Who has time for that!” you might wonder. I cook dinner every night from scratch though I run a business (50-hour work week), run a homestead, and educated my family at home. There are bountiful supplies of things that can help you cook while you work or quickly prepare other things from scratch in only a few minutes.
The learning curve is a little steep and will initially take a bit longer than opening your door for nightly delivery. C'est la vie. You will find it is worthwhile plus everyone in the house can get involved by learning essential skills in food prep. Dinners usually take around 20 minutes for preparation before it goes in an oven, Crock-pot, or Instant pot. My garden, the Amish market, or a local farmer’s market guides my daily choices. A full spice cabinet makes it more flavorful. I preserve my garden excess as our only form of “fast” food. Some use even less time per day by doing weekly meal preps, but I like to spend my Saturdays differently.
Finally, the nourished brain (and body) needs air, exercise, and sunshine. Every semester I take a poll in my classes about favorite physical activities. Every year, the number of students who say they prefer to stay inside goes up. Everything from feeling blue to having the flu improves with daily sunshine and movement. Get in a pleasant half-hour or so of midday sun maybe as you enjoy your lunch! The dog sure needs a walk. The flowerbed needs weeding. Start riding a unicycle or skateboard! Maybe just do ANYTHING outside. Every inch of our body craves air, exercise, and sunshine. At least for now, all of that is free.
Your brain is hungry and thirsty. It craves authentic nutrients, rest, sunlight, and clean water. It craves a good dinner at the table with those you love. Give your nourished brain some TLC and sympathy. Your grades will thank you and your mood will too.

Helping vs. Hindering

Seek Balance when Students Need Help

By Amy Barr with The Lukeion Project

A new class has your child flummoxed. So many new things to sort out, assignments to turn in, links to click, passwords to remember, and study skills to sharpen. Most parents are eager to lend a hand. Did the instructor explain all of this in class? Is there a handout or homework? Are there difficult problems to solve? Parents always wonder how much help truly helps and hope to hit that delicate balance between supportive and “doing your child’s work.”  Where is the line between helping and hindering?
Knowing that there is a line which should not be crossed is the first chore. When parents take a substantial role in “helping” by completing a student’s course work or reading all their assigned passages so they can summarize for them, the student will soon learn the benefit of pretending to be helpless at the same time they internalize the idea, “maybe I really can’t do any of this.” Very soon that same student will actually be helpless, no pretense required. High marks on those first quizzes will diminish as the foundations were never built, the basics never learned. If the student has been reduced to a mere observer, the line was crossed and obliterated.
A student who takes no real role in necessary problem solving, detail work, or research assigned for a class while having a parent do all the heavy lifting (mentally) is doomed. In especially egregious cases, the student internalizes helplessness, and never fully recovers even as an adult. A few skirmishes are won but the war utterly lost.
The pendulum might swing too far in the other direction for some families. Students really can benefit from a little support when getting started in the foreign territory of a tricky new class or, even in subjects that are comfortable in a subject, they need a little help working out a winning study regimen. Parents with a fully hands-off approach in every area may wish that their student had felt more comfortable asking for academic guidance in, say, college when it has long term implications.
The right balance between helping and hindering must change every year of a child’s education. What is appropriate in first grade is inappropriate in 6th grade and disastrous in 12th grade. If the student has any special struggles, the variables increase but the dangers remain the same. Handing out too much accommodation convinces a student that she will not ever be able to handle the tough stuff. Offering too few might be damaging as well. Add siblings to the mix and, well, you get the idea. Parenting is tricky.
As a lifelong teacher, I have seen trouble at both ends of the spectrum, but I have seen worse damage done by the overly “helpful” parent who does not step back enough when the time is right. When in doubt, less is more. Here are five suggestions to help you get a little closer to that balance each year of your student’s education.

1.    Be Socratic

According to Plato, the ancient Athenian philosopher Socrates was best known for knowing nothing. In Socrates’ interactions with students, bystanders, and fellow philosophers, he would simply keep asking them questions. Instead of giving information and facts, somebody using the Socratic method asks students open-ended questions. This dialogue helps a student discover what she does or does not know or might only partly understand. When your child asks for help on academic work, do not give answers but do ask questions. The student is still responsible for the intellectual maturation needed to master a subject but can be guided through areas that need work past areas that are already understood. More importantly, once they have understood the way forward, they will not unnecessarily turn to you as a short cut. A Socratic parent guides, discusses, looks for trouble, but offers no shortcuts.

2.    Do not Offer Easy Answers

So, the answer is clearly 12 or 1962 or laudant or any other easy-to-you response. Your child suspects she can shave 5 minutes off the homework session just by asking you for that fast answer. You might be tempted to give that fast answer because you need the dining table cleared up for dinner. Instead of a fast answer go slow. Return to my first suggestion and be Socratic. A student that really needs help will be guided toward a better direction this way. A student who is more motivated to finish quickly will not develop the expectation that the parent is there to do the work but will be there to offer a little guidance about how the student can find the answer.

3.    Supply the Right Tools

When prepping for a new school year, do not forget essential time management and “executive function” supplies. Chief among such tools is an academic schedule/calendar. I recommend a paper version rather than a digital app. A phone or tablet already offers an abundant assortment of distractions, so it does not make sense to seek a remedy to being distracted on a distraction-device. A paper version should allow a student to see a whole week at a time as well as a whole month. The student needs to plot out a whole semester. Being good at time management starts with fully understanding what must be done, how much prep time is needed to get it done, and managing the amount of time allotted to the task.
Students must learn coping mechanisms to manage their own personal quirks such as being able to concentrate better at certain times of the day or managing any level of ADHD that might trouble them. No formal ADHD diagnosis? No worries! Almost everyone has “popcorn brain” and our collective attention span has shrunk down to the length of a TikTok video. Pushing out one’s attention span and focus into longer and longer periods takes time and intention.
Every successful day starts with a few minutes of reviewing what is coming up, how long a task requires, and what things need priority over others. Parents can help discuss the difference between tasks that require our best time of day by helping to sort through anything that is quickly accomplished. Any chore that can be knocked out in only a few minutes needs to be at top of the list. After that, pick the top three things that must be done that day and then take a do-or-die approach to all three.  
After your student hits middle school years, 6th or 7th grade and up, they must have the primary role. Grab some Post-it notes or a whiteboard to help track priorities. Spending quality time getting (and staying) organized always saves time.      

4.    Check in not out

As our children mature, we must give them more academic autonomy. That is normal and healthy. Students must discover they can do challenging things without somebody stepping in to save them every time assignments become challenging. By the time a student is ready for the end of their high school years and the start of their college years, parents should function exclusively as an advisor not a manager. This does not mean you need to check out. Be Socratic even in this area by being genuinely interested in what is going on in classes. We always accomplished this at the dinner table with discussions about a project they have been working on, that big exam that was last week, or the long research paper that needs more research. You do not need a full inquisition but just check in.

5.    Celebrate wins

Finding the right balance between doing too much and too little for our children as they mature into adults is tricky. Your child will not feel especially great about a top score if they did little of the work themselves. On the other hand, offering just the right amount of support without crossing that line gives the gift of true victory and confidence in personal academic success.  When that happens, celebrate. Sometimes that is just a pat on the shoulder to acknowledge your pride in their success. Let your student overhear your pleasure and confidence in their abilities, sure, but especially their tenacity and their hard work.
Getting organized and staying there is not easy even for adults. Everyone prefers to do enjoyable tasks first leaving less pleasant things for last, rather than prioritizing. Run through several techniques that will help your student stay organized but also produce ways to reward getting the tough stuff done. For my youngest son, a reward was getting to spend twenty extra minutes playing the piano. For my oldest, that meant she got to do something creative in her sketch book. My middle son would climb the tallest mountain if it means he got to spend a little extra time on a game he enjoyed. Rewards can simply be the liberty to do what a student already loves.

The Assignment Sheet

Instructions Should be one of Your Best Friends

 By Randee Baty with The Lukeion Project

Students, when a professor gives you an assignment sheet, he isn’t just repeating what he told you in class. The sheet will have lots of useful information and essential details that must be observed. Use it well to your benefit. Never adopt a “too long, didn’t read” approach to assignment sheets. That never pays off.
Professors put quite a bit of time into creating clear assignment sheets with everything he or she thinks you need to know to finish the assignment just as it needs to be done. Nevertheless, even good students continue to submit assignments that violate clear instructions and therefore lose points or miss out on learning lessons the teacher wants you to learn.
Along with the parameters of the assignment, the assignment sheet will have additional information, possibly including the rubric the professor will use for grading, issues they want you to specifically avoid, tips for completing the assignment correctly, and what they will look for as they grade. They expect assignments to be completed in a specified format and they always expect it to be published to the instructor using a particular file type or link. Guess what? This is vital information if you are concerned about your grade on that paper.
Here is my suggestion to students when using an assignment sheet. Read the sheet a minimum of three times. I don’t mean read it three times before you start. I mean read it at three different points in the writing of the paper.  
Obviously, read the instruction hand-out carefully before you start. Read it however many times it takes for you to understand what the professor wants. Once you think you get the idea, read it from start to finish again. Make notes on it if you choose. Underline and circle important instructions or tips. Email the professor at once if there is anything you don’t understand. Then start the paper. There’s nothing worse than finding out you’ve taken the wrong approach right before the deadline. Most of us can't afford to lose hours of work.
About halfway through the paper or maybe when you finish the first draft, pull out the assignment sheet again. Re-read it from top to bottom, beginning to end. Is there anything the instructions mentioned that you may not have done yet?  Anything they told you not to do that you are drifting into? Are you staying relentlessly on topic? Are you avoiding fluff and padding? Do you have citations in place if needed? It’s a good time to self-check before you spend a lot of time on something and then realize you had neglected a basic instruction or reminder.
Once the paper is finished and polished, read the instruction sheet again. Don’t hit “submit” (or click that submission link) until after that third reading session. The process of writing and polishing can drive other factors from your mind, and you might send in a paper that that took an immense amount of work but isn't at all what was assigned. If you ignore the instructions, there are not fairy-tale endings in which your professor is suddenly OK with a submission that is way off the mark, even if you spent many hours perfecting it.  A perfected error is still just an error. A big part of your grade is accounted for simply by following instructions.
When you are concerned about getting an assignment right, the assignment sheet is your best friend!  Hang out with it, spend time with it, get to know and understand it. Mark it up with notes and underlines. Your professor and your grade transcript will thank you for it.

The Summer Brain

A Season for Creativity and Inspiration

By Amy Barr with The Lukeion Project

Now that we are ending summer months in North America, we can all either reflect on a pretty good summer or we can wish for better chances next year. Depending on each student, family, academic approach, and region, summer means different things. For our brains, summer can be sustained all year, depending on how we allow it to engage with the world. Even for families that choose to “do school” all year ‘round, students should learn how to enjoy a summer brain. What's different about summer?

Engage with Nature

This used to be easy advice for everyone except those who suffered involuntary limitations. For my generation, engaging with nature used to be firm parental instructions to go outside and stay busy “until the streetlights come on.” Threats of backbreaking household chores used to be sufficient to keep younger people from venturing inside before the time was right.
Based on unscientific polls in my own classes, around half of my students have a strong desire to stay inside all year long. Aside from those that enjoy team sports and outdoor practice, only a small percentage of the rest feel compelled to go outside and enjoy (or suffer) all that the great outdoors has to offer unless (and until) they are deprived of one thing: technological entertainments. What a sad situation we are in. More people than not prefer to view other people’s lives in short fake (but entertaining) videos on social media. This means it might take some motivation to exchange indoor habits for outdoor ones.
Engaging with nature doesn’t need to be strenuous or painful nor, necessarily, buggy. Just find a good spot outside every day, get some sunshine (yes, you need some), and find some fresh air. Once you get good at the basics, expand the amount of time you are outside.

Engage with the Present

We spend most of our lives scrambling to get the next thing done. Especially as a person matures and experiences more complex periods of their education and then early adulthood, making and then completing lists becomes all consuming. There isn’t enough time in the day to finish most lists. Sometimes we get to set aside to-do lists for just a little while for a holiday or vacation. When your brain is overly stressed, try engaging with the present for at least a little while. The best way to do this is to try something creative like playing an instrument, creating art, completing a project (garden, woodworking, sewing). These activities force us to focus exclusively on what is at hand which, just like summer break, serves to refresh our brains by enjoying something that is exclusively for now rather than later.  

Engage with Exercise

The best part about summer is that you can find exercise that requires no special skills, tools, equipment, or anything else. Grab a friend, dog, or family member for a walk. Grow some glowers or a garden. Join an informal or formal team for some friendly competition. Learn some dance moves. Mow the grass. Go build something. Nobody feels good if they spend all their time sitting on a couch. A summer brain knows that the best way to get unstuck physically, emotionally, or even academically is to get moving.

Engage with Friends

In the last five years something truly unique in human history has happened. While it is historically important, it is socially devastating. Humans are no longer maintaining a variety of healthy relationships. Even during typically very social periods of our lives, extroverts are becoming more introverted. Introverts are becoming isolated. Academically focused students excuse their lack of social interaction by insisting they have their studies but to their detriment. Friendships and relationships are even more important than a nicely filled out transcript, though one need not preclude the other when accomplished cleverly. Humans must find their tribes or suffer from loneliness.
Kasley Killam, author of The Art and Science of Connection, suggests the 5-3-1 rule. Engage socially with at least five people each week. Intentionally foster friendships with your favorite three people by connecting with them a minimum of once a week. Spend at least one hour a day enjoying a quality connection with others.
What this could look like for you is that maybe you get involved with a sports team, a band, a dance class, or maybe a club in which you have quality time interacting with at least five other people. Parallel play (like watching a movie) or sitting on a bench staring at your phone next to a friend doesn’t really count. Find a way to interact cooperatively with at least five others.
Intentionally foster friendships with at least three people each week. Hanging out is best, phone calls are good, interacting on social media ranks low but will do in a pinch. These minimum of three will be your support system. Yes, siblings count! If you are an extrovert, you’ll have a hard time keeping it to three. If you are introverted, you’ll be hard pressed to find three. Shoot for three as a goal because that’s how many people most of us can manage well.
Finally, tally up at least an hour of socializing daily. It doesn’t need to be formal (though it can be). Maybe just a good discussion at the dinner table is enough to feel connected with other humans. If you don’t have the luxury of a family that takes meals together, don’t forget to link up with a bestie or sibling or relative daily just to talk things through. You’ll feel better when you do.  

A Blank Page

Educational Choices Are Actually Yours

Amy Barr, The Lukeion Project

The start of a new academic year has arrived. Some hate getting back to academic work as they are forced to abandon the relative freedom of summer activities. Others are keen to get back into the swing of things as they look forward to new challenges. Most see their yearly academic schedule as inevitable, something that must be done, boxes that must be checked, and time that must pass one way or another. Which kind of student are you?

I have found through over 30 years as educator that students who have some educational autonomy will have a better attitude towards each new academic year. Conversely, students who feel they are locked into a parade or generic classes and subjects tend to have less enthusiasm about the work at hand.

A person who works a factory job completing a repetitive chore may accomplish much in a single day but seldom looks forward to his task. Even if he manufactures something he loves, his enthusiasm for it will not last long. Humans quickly get bored with repetition and with a lack of personal challenge. Most humans avoid undertakings that offer no room for improvement, no challenges, no changes.

When I was in high school, I worked for a nice pizza restaurant. I picked that job because I loved the pizza there and thought it might be fun. Wishing to earn enough money for college, I spent most of my evenings for a full year making or selling that pizza. I saved carefully and did indeed pay for my own education with that money. I am glad I had that job, but I went from being a pizza-loving teen to somebody that still dislikes pizza many decades later. You can have too much of a good thing.

Most of us gravitate towards projects that allow us to improve and eventually excel if we choose to put in the work. Good health (both mental and physical) depends on the ebb and flow of seasons, changes, and challenges. If everyone gets the same grade no matter how hard they work or if every day looks the same no matter what you do, boredom will lead to apathy. Apathy will lead to resignation. Looking back at my high school pizza job, I know that my boredom was not just eating too much pizza but the constant sameness.

As you start a new academic year or semester, you might feel you have been given few choices about your classes because certain topics must be covered in the short span of a few years. That transcript is not going to finish itself! You may begin to see what is in store and learn to view it through the lens of sameness and respond with a bored yawn.

You may also see what is ahead and realize that your education is a blank page that you get to illustrate and fill out how you like. Yes, you need an English credit each year of high school. NO, that English credit does not need to be the same one that everyone else completes. Foreign language? Math? History? Science? Writing? Yes! Everyone needs those. Learn to tick those boxes and finish those requirements in ways that challenge you.

Your academic plan is all your own. Prepare yourself for a future that interests and engages you. Even if you do not feel you have a ton of choices over the types of things you are expected to study this year, retain control on how you prepare, the amount of effort you expend, and the level of mastery you achieve. You have more control over your current circumstances and your future than you might imagine. Even small investments towards excellence now will fill out the blank page of your education in ways that only you can control. Everyone has the autonomy necessary to become truly excellent at many things. Start today.Your education is not something done to you or for you but by you.

Math ...History?

A Course on How Humans Have Used Math Through the Ages

At The Lukeion Project, we offer a unique course which covers the history of math. Students considering taking a math history course sometimes wonder if the course is a mathematics course or a history course. As with most good questions, the answer is complicated. 

It’s a Math Course

In Counting to Computers (C2C) we discuss many of the topics mathematics students encounter from the beginning of their math career to the end of calculus and beyond. Despite covering so much content, because these concepts developed in a natural way over time we cover them in a format accessible to students in algebra or are advanced prealgebra.

At the “dawn of numbers,” the only tools prospective mathematicians had were their brains and their fingers. It took thousands of years to build up the tools to do calculus and computing. In C2C, we begin where all children begin, with counting. Even counting turns out to be not so simple! 

Over the centuries people have come up with many different number systems which have different characteristics and strengths. The Egyptians developed fractions, but they only used 1 in the numerator (with a few exceptions). Instead of writing ⅔ you would have to write ½+⅙. The two forms are equivalent, but the second seems much more complicated. On the one hand that seems like a lot of work for a simple concept! On the other hand, for solving certain types of division problems, Egyptian fractions were much superior to the our simpler fractions.

In another example of crazy counting Babylonians developed a base 60 system for doing arithmetic. At first glance, base 60 seems much more complicated than our good old familiar decimal system. Why would they make things more complicated? As it turns out, when we use minutes in an hour or degrees in an angle, we actually pay tribute to the Babylonian system. For all its faults, the Babylonian system was miles ahead of Roman numerals.   

Some of the problems we do in the course come directly from problem sets developed to train ancient scribes and mathematicians. We can do problems from the Ahmes papyrus (1650 BC) and decipher cuneiform tablets found in the trash pile from a Babylonian school. Fibonacci’s Liber Abaci, originally written to demonstrate Hindu-Arabic numerals to merchants used to cumbersome Roman numerals, becomes a source for puzzles for homework.

Gradually the math that we discuss becomes more powerful. Even students who are a long way from trigonometry can look at the ratios created by Hindu mathematicians to talk about astronomy, or practice interpolation to find difficult values for sine and cosine using prealgebra techniques. We don’t have to do calculus problems, but we can practice the methods of Archimedes which were precursors of those developed in the 17th century by Newton and Leibniz. The key to thinking about these more advanced concepts is that they developed gradually and not all at once. By following along with the history, we can do the math along side the ancient mathematicians.

It’s a History Course

C2C is also a history course. At its most basic, any history course is a discussion of past events. We discuss events in the history of math such as the development of zero and the conflict between Leibniz and Newton over the development of the Calculus. We show how the development of mathematical symbols over hundreds of years makes the calculations we can do easier and more powerful.

However, there is more to math history than just the events in the subject of mathematics. We discuss how world events led to the export of the modern Hindu-Arabic number system to Europe. The development of the printing press helped spread trigonometry across Europe and made it useful for the scientists discovering how orbits worked and how the stars seemed to move.  In addition, understanding cultures and their motivations makes clear why the mathematics developed by one culture differs from others. The differences in cultures michte explain why the Greeks valued rigorous proof, while Indian mathematicians were able to see  the concept of zero, and Islamic mathematicians developed the idea of algebra. When we study the origins and history of mathematics, we see that mathematics didn’t arrive full blown in an Algebra 1 textbook, but was a gift from many places and times.

In addition to the events in history, we discuss the character and biographies of mathematicians. The people who do math turn out to be as interesting as the ideas they discover. We discuss what is known about the biographies of great mathematicians and why they became involved in mathematics, from Hypatia to al-Kwarizmi to Leonhard Euler. The personalities and culture of these mathematicians influenced what they thought of as important, and therefore what mathematics they developed.

It is a Mix of Both

The power of studying history and math together is that, no matter your background or preferences, there is something for every student.  If you would rather read an article on ancient history than solve a single linear equation, this course is for you.  If you love math and can’t get enough of it but really hate thinking about people, places and things, this course is for you.

Here are two comments from past students, first from a more advanced student (post geometry) and then from a student who is closer to the beginning of her math journey.   

"The history was the most useful part, because while I knew quite a bit of the mathematics, I knew very little of the history of those who discovered it. The brief overviews of the mathematics in the form of the homework was also incredibly valuable, because it helped refresh and cement mathematical principles and even teach me a few new things."

"I enjoyed the connections between math and history and the new math concepts like calculus and logarithms."

Mathematics informs history, and history informs mathematics.  There is no reason to be satisfied with just one or the other when you can get both in one course!