February 5, 2024

What the Romans Did for Us

Thinking about Rome?

By Amy Barr with The Lukeion Project

“Rome,” is now apparently a common answer to the question, “what are you thinking about?”
I agree that anyone hoping to better understand the modern world should look at Rome. The parallels are clear. Comparisons will lend insight to students of history. The best takeaways still serve us well today. Her worst ideas continue to echo through current events. Take five minutes to think about Rome. I’ll keep things brief.
The Romans were famous for adapting and adopting good ideas from other nations and then turning them into great ideas. Architecture, for example, was given a tremendous boost by the ancient Greeks. The Romans enjoyed their artistry and then tweaked the Greek post-and-lintel system by adding the arch. Adapting arches into barrel vaults and groin vaults allowed architects to craft massive structures like the Colosseum and Pantheon. If they tucked those vaults underground, they crafted effective sewer systems that allowed towns to become massive cities. Further adaptations meant Romans had fresh water year-round. This lead to all sorts of luxurious spa experiences that would fetch high prices today though they were usually free in ancient Rome.
The list of Roman contributions is long, and this blog is brief. Highlights include roads (many still used after 2000 years), Latin (still used today in all academic fields worldwide), cement, plumbing, reliable water pressure, good sanitation, heated floors, and hot tubs the size of swimming pools, and unforgettable sports venues. Rome got close to a global currency that worked just about everywhere (we have found Roman coins in India, China, and throughout Europe. Their legal system was sensible, reliable, and included basic human rights applicable to citizen and foreigner alike.
Neutral contributions include the introduction of fast-food restaurants with take-out, massive free public entertainment events that would last for days of blissful vacation time, and satire as a national pastime. The Romans had a relaxed lifestyle with delicious and readily available food but still loved to crack jokes about all of it. Such is human nature.
The Roman Republic was first established in response to the emergent need to topple a violent and dysfunctional monarchy. As is often the case in historical matters, the Romans had to quickly find a good way to prevent tyranny’s return through a decent political and legal system with plenty of checks and balances on her politicians (they considered term limits a great idea, for example).  Early American founders had much in common with early Romans. They too sought a better future for our nation when it became clear that none of us needed kings nor queens.
The Roman Republic worked very well for a little more than 400 years. It served the people and senate of Rome in practical ways while Rome grew from a swampy village to city-state, to nation, to world power, to mega power. Things went well until her politicians discovered loopholes in Rome’s systems of checks and balances. The last century of the Republic left the city in tatters and too much of her population dead. A lengthy period of civil war marked the end of the system. Her politicians had learned how to do whatever they wanted whenever they wished. Once laws are gone, tyranny is the result.  
Chaos diminished under the very strong leadership of Rome’s first emperor. In a series of astounding turns of events, the 19-year-old successor to Julius Caesar would overthrow his competitors and, after having united Rome for the first time in a century, he would rewrite the Roman constitution and then quit. The senate begged their new commander-in-chief to remain and power while they gave him a new name, Augustus. In a little over a decade he would change everything, all while heralded as a patriotic and traditional man-of-the-people. He did love Rome and her empire. He was quick to rebuild, reunite, and expand. Augustus had tremendous organizational abilities, but he also had two big problems. First, he couldn’t live forever. Second, though he was long lived, by the time he did die nobody could remember living under any other system.
Wanting a proper heir, Augustus promoted a disappointing stepson who lacked interest in Rome or her people. Under Tiberius, the whole system could have reverted to a Republic, but the Romans bypassed many opportunities because they were too busy attending sports events. They pressed on and installed a long series of truly dreadful emperors who were easily pressured and conned by those that worked for them. The Roman equivalent of the secret service/FBI/CIA (the emperor’s Praetorian guard) learned that they could easily manipulate any emperor who served. The Roman empire was barely beyond infancy when the Praetorian learned how to obtain whatever commands they placed on Rome’s weak rulers.
The most successful emperors learned how to appease the Praetorian guard with lavish perks and extra power, but it was difficult to maintain positive momentum during transitions to a new ruler. Very rarely was an emperor’s son a worthy candidate so success was limited to emperors chosen for practical skills and intellect rather than legacy.
The Roman empire became massive while her enemies became clever and powerful. They would learn to pick and peck at her boundaries while Rome slowly died of a thousand cuts.   
What caused the fall of Rome? That’s the subject of many books and theories. Rome fell when she outlived her own success by a couple of centuries. Once there were no more major money-making-wars to fight, she turned her attention to micro-managing the empire. Too much governmental oversight was disastrous. Towards the end, the powers governing Rome split her into quarters and made her rulers and sub-rulers bustle around in mobile command units as needed (or even not as needed). Rome as a city lost her identity as capital while new city-centers grew in importance for the sake of convenience.
Perceiving that the leviathan formerly known as Rome was aging and weakening, her enemies kicked at all her doors and windows until they were eventually invited in. Under the pressures of disease, overextended military forces, squandered taxes, under-performing leadership, and a disinterested population, Rome invited her enemies to join their rat race. They were invited to serve in her military and guard her boundaries. Such soldiers had no interest in a Roman way of life. Rome fizzled, sputtered, and died.   

January 22, 2024

Think-Os

Stupid Mistakes

Dr. Kim Johnson, Logic (Lively Logician) and Counting to Computers with The Lukeion Project

I cannot tell you how many times as a mathematics teacher I’ve seen a student react to a question they’ve gotten wrong on a test or quiz by saying, “Oh, that’s just a stupid mistake.”  It seems as though calling something a “stupid mistake” or “careless error” allows students (and sometimes me) to dismiss the mistake as a onetime occurrence and go on to think about more pleasant things.

Celebrating your wins on tests or essays is crucial. But don’t dismiss the stupid mistakes out of hand---sometimes there is more to them than just carelessness.

Correcting “Think-Os”

A stupid mistake can also be called a thoughtless error. Sometimes I call them “think-os”. Like a typo, a think-o is something that you knew or understood well but wrote or typed incorrectly. Most often they stem from a momentary lapse in concentration.

Given that they are so fleeting, why should we not dismiss them and move onto something that is more important? The truth is, sometimes thoughtless errors turn out to be very important.

In 1999, scientists launched the Mars Orbiter with hopes that it would expand knowledge of the climate on Mars. Their hopes were dashed when, instead of exploring Mars, the orbiter crashed into the surface. The European scientists on the project used the metric system, the Americans used the English system, and so their calculations didn’t’ match up. This was truly a thoughtless mistake because every scientist in that group understood the difference between metric and English measurements. This thoughtless error cost millions of dollars.

“Fine,” you might say “…but I am not in charge of million-dollar projects, I’m just taking my Latin exam, doing some math homework, writing an essay, or taking a history quiz. A stupid mistake in these situations does not have any dire consequences. So why should you care?”

You should care because sometimes a seemingly innocent mistake hides a deeper misunderstanding. For example, if the instructor asks for one form of a verb and you give another, or if you are expected to give a number and you give a function, perhaps you never fully understood the difference and need to clear something up. It’s just a simple mistake---but it indicates that there is something you need to understand more fully before moving on.

Another type of worrying mistake is one that you make over and over. In working with students, I’ve noticed that each student has their own personal set of repeated mistakes. My personal set of mistakes is to lose negative signs and copy down digits in the wrong order. One friend misspelled the word “their” nearly every time he wrote it. Some students have particular facts that they always get backwards.

The best part about these mistakes is that you are not doomed to make them forever.

How To Avoid Careless Errors

Obviously, if you have a gap in your understanding of some part of the topic, work to figure it out!   Honestly appraising your work is crucial in clearing up misunderstandings. Without evaluating the mistake, you might think there is nothing left to think about and move on. The great thing about fixing mistakes which come from misunderstandings is that by fixing them early, you eliminate a whole raft of mistakes later. It’s kind of like killing a mosquito in the spring will eliminate thousands of mosquitos later in the summer.

Fixing mistakes that you make again and again can be slightly more difficult. The problem with trying to fix repeated mistakes is that they indicate a type of momentary blindness and inability to notice errors.

The first and obvious thing to do is to check your work. This involves a few things. First you must write something down to check. Have you ever heard your teacher tell you to “show your work?” This is why! Although an abacus or a counting table is a powerful tool, written work wins, hands down, when you are trying to catch errors.

Second, coming back to your work after a day or at the end of the test is another good habit. Even a few minutes can give enough distance so that mistakes become visible instead of seeming to be correct. When checking my work, I think of it like a “hidden picture” puzzle, or a “spot the difference” puzzle---each difference should be deliberate, not an oversight.

You can develop a habit of going over your work looking for your most common mistakes. For example, my friend would search his papers for all instances of “their” spelled in his particular way, and I watch for lost negative signs. You can learn what errors you tend to make and look specifically for those mistakes. By focusing on and analyzing what you first dismissed as “stupid mistakes” you can find them and even get better at avoiding them.

Another strategy for catching foolish errors is to check with someone else. When mathematicians are working, they often work together. This is in part to generate more ideas, but it also allows them to catch each other’s momentary lapses in thinking. Even the most accomplished writers have editors. Software engineers review each others’ code to catch bugs. We can help each other reveal thoughtless errors.

Sometimes this is not allowed because of an honor policy, but even then getting another person involved can help. One of the best ways to catch errors is to explain the work to someone else. By going over your work out loud you introduce another sense---your ears can catch what your eyes do not. Pets are some of the most patient listeners. Even though your dog will never have to factor quadratic equations of conjugate Latin verbs, they will listen patiently and never judge when you find a mistake.

Get Over It

Finally, not all mistakes are signs of misunderstanding or part of a pattern. Sometimes a stupid mistake is just that. If that’s the case, your most potent tool is to just leave it behind and move on. Dwelling on mistakes takes mental energy that would be better put to use in learning new material and analyzing new ideas. Try pretending that you are looking at someone else’s work as a teacher or a scientist. Then you can judge more accurately whether the mistakes require further action or if they are not matters of concern.

Mistakes will definitely come, that is certain. Making mistakes is part of being human. Learning to deal with them appropriately---with honesty, attention, and grace---makes us better humans

November 6, 2023

Autodidacticism

You Have Everything YOU Need For a Good Education

Amy Barr with The Lukeion Project

The English word “education” comes from the Latin word educare, a verb that can refer to the process of bringing up children to adulthood or providing a wholesome place for animals or crops to grow. Modern usage would have us think that education is a commodity that we might purchase in the form of a book, a program, a class, or whole degree program. When we are done with one or all of these, we proclaim ourselves “educated.” The Latin word does not refer to any of these things, per se. Instead, one’s education is a matter of having a favorable environment or fertile soil for somebody (or something) to grow productively. Education, for much of human history, has been a personal choice and under our own control.

In the Roman world, those that worked on a subject very diligently might eventually be considered doctus by others, meaning they were well-informed, experienced, and clever. Doctus is a passive participle of doceo, a verb which means “teach” (a doctor was a teacher not a medical expert). Somebody who is doctus has been “taught” but not necessarily by others and certainly not in some established program. Remove your modern sensibilities about being taught. The English words we use to define doctus or docta have more to do with how one treats oneself as one builds one’s own learning environment. A well-informed, experienced, and clever person takes the initiative to self-educate regardless of one’s station in life.

The most brilliant men and women in history have been autodidacts who, until very recently, had zero framed diplomas hanging in their offices. Degrees, as such, didn’t factor into anyone’s career qualifications until the far more recent past. The notion of placing a measure (and certificate of completion) on one’s education was not something that most people thought about until public education compelled us to think in terms of something that could be measured, quantified, qualified, and marketed to the human race.

Greek philosopher Plato once said, “The first and best victory is to conquer self.” Aristotle, Plato’s student, listened carefully to his master’s words for 20 years and then reversed his opinion on most of Plato’s teachings to form his own thoughts. He famously said, “Through self-discipline comes freedom.” As he too would become an educator of famous people like Alexander the Great, Aristotle would also say “What lies in our power to do, lies in our power not to do.”

Education today is not something our Classical fore-bearers would recognize or condone. Today we view education as a set of stairs. We climb up some of those steps and celebrate when we’ve arrived at a certain stage while we earn a slip of paper that some institution has issued to say as much. Leaving behind all that was accomplished before, we climb a new set of slightly more difficult stairs and look for new affirmations of completion until, armed with seemingly enough certificates, we are deemed qualified. Those that didn’t climb those particular stairs are not authorized to form opinions or advice in that area. Such people are merely amateurs, a word that comes from the word for love (amare) in Latin. 

Modern education is a lucrative system that is jealous of all forms of competition. We are told we aren’t qualified to do our own research and we aren’t qualified to educate ourselves. Those who are home-educated must simulate a public education by jumping through similar hoops in hopes of being issued a graduation certificate which, despite numerous studies that prove that home education is the far superior method of learning, is often considered sub-standard by many secondary institutions. Many top universities are slowly understanding how valuable our home educated autodidacts are! The top skill mastered in home education is how to educate oneself, a skill that becomes a game-changing advantage in college, graduate school, career, and life. Those that don't want any part of that type of conveyor belt system are benefited as they teach themselves how to live the kind of life that interests them most. 

Autodidacticism (self-education) is and has always been the most reliable method to become well-informed, experienced, and clever. Our own interests and passions are a powerful tool to compel us to excel. Autodidacts are never sated with mastering a single body of knowledge. Having learned one and then two, self-educators are driven to learn by their own interests. They choose to master more and still more. While such people often go on to collect a variety of degrees because they are still constrained by our modern system, they will always continue their own learning process provided they have life and breath.

As Plato points out, your first task is to master as an autodidact is self-discipline. Rising above your own lazy instincts to sleep more or play more means you’ll have the ability to push on, to persist in your efforts to master some topic or skill. If you have enough self-discipline to persist, there are no limits to your goals or ambitions. This is true freedom. The choice falls on you. You have control over your own timeline, effort, and skill. Degree programs might require a set number of years and certainly a prearranged fee, but a self-disciplined autodidact has control of his own time, her own effort, and the quality of all outcomes. Armed with far more educational materials and opportunities than history’s brightest minds, the best education today can be free, or nearly so.

 

 

October 16, 2023

Think Three Things

Beliefs to Build a Better Brain

Amy E. Barr, The Lukeion Project

We humans are our own worst enemies in too many ways to count but, more specifically, we torment ourselves when we want to learn new things. We ask a lot from our brains daily but never more so when we are students. The truth is that healthy humans should always be students of something, even when we are not strictly enrolled or controlled by a schedule of assignments and a system of grades. Even healthy humans struggle to have a good learner’s mindset. We often try to talk ourselves out of our own success. Negative thinking, perhaps we suppose, is a way to soften the blow when success is temporary or diminutive.

What can we do to help ourselves out? Start by making three observations about yourself.

I have…

If you are reading these words, you already have a good track record at learning tricky things. You have already developed the mental power and sustained the practice necessary to master reading and writing, two skills that fewer than 1 out of 20 people possessed 500 years ago. Today, your literacy still puts you in a position for ongoing success. Unlike most of the population of the world thus far, you are likely also skilled in the basics of math, music, science, and even managing a computer device. Well done.  

Your track record proves you can learn what is set before you because you’ve already done so much already.  As you look at challenges ahead, remember to say to yourself, “I have already been very successful at learning difficult things in the past.”   

I can…

A growth mindset, the belief that a person's capacities and talents can be improved over time, is the best predictor for future intellectual success. The opposite, if there is such a thing in the real world, is a fixed mindset, a belief that dictates that you are born with a certain skill set which can’t be expanded much, even with great personal investment.

Nobody celebrates the poetic, athletic, or musical abilities of a newborn. Logically, we all know that the skills we have at birth will develop over time. It makes no sense that we spring into this world fully finished yet some of us still lament “I’m just not GOOD at ________” (fill in the blank).

You aren’t good at something that you have only just begun to learn. A growth mindset simply acknowledges that learning new material and acquiring new physical skills take time.  The first time you walked, you did a terrible job (even while your family cheered!). The first time you read a book, you did a terrible job: it took you a long time and you had to take a lot of breaks. The first academic paper you write? Terrible. The first speech you’ll make? Rotten. The first time you play the piano? Ugh.  The first time on a basketball court, dance floor, theater stage, or football field? Not so hot!

The first several times you do anything, you won’t rocket to stardom in doing it (unless your friend gets a funny video when you weren’t looking). But the hundredth time looks much different. Do something with a positive viewpoint enough times and improvement is guaranteed. Your hundredth try means…that’s a good speech, a great paper, a solid game, a proper recital! As you face future challenges ahead, remember to say to yourself, “I can improve with effort, practice, and time.”

I will…

Negative thoughts rob our time. Allow a few negative thoughts to grow and they’ll develop into fatalistic excuses like, “I’ll never be that talented,” or “I’ll never accomplish everything necessary to achieve my goals” or “I’m just not that …” (smart, coordinated, athletic, beautiful, handsome, popular, wealthy, etc.).

Once you start wallowing in negative thinking, like a pig loves a good mud puddle, you’ll tend to stay there until you realize what you’ve done to yourself. Your future is unknown both to you and everyone else. Your negative thoughts hold no truth whatsoever. There is no virtue in having them and they serve no purpose. Negative thoughts are random weights that you collect until the weight of them forces you to stop everything. They are lies you tell yourself about yourself. Once you make a habit of negative thinking, you’ll guard your pile of lies like a dragon guards his gold.

One by one, recognize each of these lies you tell yourself and replace them with improved action plans. Instead of thinking you can’t, won’t, or shouldn’t, you must say “I will!” or “I can!” Remember that you already have a record of achievement, you are perfectly capable of continuing this success, and you will overcome the challenges that life puts in your way.

 

October 9, 2023

The Mathematics of Grades

How to Focus on the Things that Matter

Dr. Kim Johnson with The Lukeion Project, educator for Lively Logician

Did you know you can flunk a final and still perhaps get a B in a class?  What matters more to your grade: quizzes or homework? Grades are a part of life for almost everyone at some point in their schooling. They seem simple: it’s just a number (or letter) that tells how you did in a class. Because teachers don’t want to fall victim to favoritism or arbitrariness, we turn to mathematics to help us assign fair, transparent grades. However, many students (and some teachers) don’t understand the mathematical implications of the way they grade.

The Grading System

For most teachers, the goal of a grading system is to provide a symbolic representation of learning. The tool we use is called the grading system. Grading systems reflect what the instructor finds important for you to know and to be able to do.

A grading system assigns weights to various aspects of the course. Typically, a demonstration of knowledge, usually in essays, papers, or quizzes, is the most important part of your grade. Also important is a demonstration of behaviors that lead to better a understanding of the material through participation, attendance, and homework completion. You can see what parts are most important to the instructor by what weight the instructor gives to that section. It is interesting as well to see what parts have equal importance in the instructor’s mind.

Some examples of grading schemes:

  1.  

Item

Percent

Attendance and participation

10%

Homework credit

20%

Vocabulary quiz

20%

Grammar quiz

50%

 

  1.  

Item

Fraction

Quiz average

1/3

Paper average

1/3

Participation

1/6

Final exam

1/6

 

  1.  

Item

Percent

Quiz average

70%

Homework completion

20%

Attendance and participation

10%

 

  1.  

Item

Percent

Quiz average

35%

Homework completion

15%

Fallacy homework

10%

Attendance and participation

10%

Logic in Real Life project

10%

Final exam

20%

 Mathematically speaking, note that all percentages and fractions add up to 100%.

Percentages do not reflect the number of assignments: for example, in chart B the final seems to be worth less than the quizzes---but there is only one final and 14 quizzes. In the last example, there are 7 quizzes each semester, so each is worth 5% of your grade. The final exam is worth 4 times as much!

Grading schema can be used in a calculator to figure out your course average at any point in the class. Plugging this calculation into an online calculator (such as Desmos) will let you easily replace potential grades in each area and see what your grades might be. You could enter a calculation of your final grade like this:

(Weight of area 1 *grade in area 1)  +  (weight of area 2* grade in area 2)  +  weight of area 3 * grade in area 3)

You should use the weights as percentages: remember that a 25% weight is equivalent to the decimal 0.25. Also note that your grades should be averages---if you get 45/50 on a quiz, that score should be written either as 0.90 or 90 (either way provided you are consistent).

A little algebra will allow you to see what grade you need in an area (such as the final) to get the grade you want. Your needed grade in area 3 is this:

Use grades out of 100. The weights should be percentages which add up to 1. Both of these formulas can be generalized to different courses with more or fewer areas.

Don’t Sweat the Small Stuff

The grading system helps us figure out some quandaries students and instructors have when figuring out grades. One of the most common grading questions instructors deal with is individual points on assignments, quizzes, or finals. It is surprising to most students how little effect an individual point has on their grade but it is not surprising to most of your educators who know that most point-wheedling is counterproductive in every way.

To begin with, from a grade perspective it is never worth arguing points with your instructor on an assignment graded for completion. If you completed the assignment on time and conscientiously, you got 100% credit for the assignment. No amount of argument will benefit your grade in any way.

Even on a quiz, arguing for a few points rarely makes a difference in your grade. If the quiz is worth 5% of your grade, changing a few points will only change your final grade by tenths or even hundredths of a percent. If quizzes are worth ⅓ of your grade, but you have 12 quizzes, each individual quiz is worth ⅓*  1/12=2% of your grade. If the quiz has 100 points on it, getting two more points will raise your grade 0.04%---going from an 85% to an 85.04%.

Perhaps you are one of the few people in the class whose grade is an 89.99% (an occurrence that is extremely rare) and you wish to get up to an A. Arguing for a few points on some assignment somewhere in order to increase your grade is not worth it---your time would be better spent making sure you fully understood the point of the question and studying for the next test.

When Small Stuff Makes a Big Difference

It is clear that niggling about points on a quiz will not mathematically change your final grade. But there are some small acts that have an outsized impact on your grade: completing homework on time and participating in class.

Suppose you are a decent student in a course and your grades on the quiz and final average is about 94%. You learn the concepts easily without having to turn in all the homework graded for completion: you only get about half of those turned in, and you sometimes don’t pay attention during class plus you tend to arrive late so your participation grade is lower than it should be. Here is your final grade computation if quizzes are worth 70% of your final grade, homework 20% and participation 10% (note: I wrote the quiz, homework and participation average out of 100):

 70% * 94 + 20% * 50 + 10% * 50 = 81.5%

Despite your grades on quizzes and the final, you only get 81% in the course! On the other hand, if you are a conscientious student and diligently complete homework and participate actively in the online class sessions, but only manage an 86% on your quiz average, the participation and homework grades will raise your grade in the course:

70% * 86 + 20% * 100 + 10% * 100 = 90.2%

Although it seems as though homework and participation are insignificant acts compared with doing well on quizzes, they can make a big difference in your grade. Of course, the real reason to turn in assignments graded on completion and participate in class is that instructors have noticed over the years that doing these things are a reliable way to improve your quiz scores and your understanding of the subject matter. It is worthwhile to be conscientious in these acts even if you think you understand it all perfectly.

Zero vs. 59%

There are multiple ways to fail an assignment. In students’ and parents’ minds, there is no difference between a zero and a 59% because both scores are failing. However, as far as the grade calculation is concerned, there is a big difference.

Suppose you have 5 quizzes which contribute equally to your quiz grade. Here is your quiz average if you get 85% on the first four quizzes, but don’t turn in the last one:

  (85+85+85+85+0)=68%

On the other hand, if you do your best and turn in a bad quiz (along with an email to your teacher explaining your new improved study system) you will get

  (85+85+85+85+59)=79.8%

Instructors know that things come up so in many classes, your educator will drop your lowest quiz score. Making a habit of not turning in quizzes that you might do poorly on will hurt your grade much more than turning in a quiz you “fail.”

Peace of Mind

One way the grading system can help students is to give them peace of mind before an assignment or the final. Even though a final exam or paper may be a large portion of the course grade, its effect on your final grade is mitigated by what you have been doing all semester. Suppose you are a student in the Lively Logician with only an 85% quiz average but have been diligently and conscientiously completing all the other assignments as well as attending and participating in class. Up until the final, your grade looks like this, with question marks for the last paper and the final exam.

If you are worried that an alien will abduct you and erase all your knowledge, or perhaps the wifi in that giant python (the one that swallows you on the last day of the semester) will be insufficient and you will not submit your final paper, you can plug these into a calculator and compute your grade so far. Even if the remaining 30% of your grade is not submitted at all (and gets a zero), the lowest grade you can get is a 64% (though you will still have to deal with residual complications from being swallowed by a python).

If space aliens only destroy half your knowledge (you get a 50% on the final and the paper) your grade goes up to 79%. If you get a few more points on the final (perhaps one of the questions is about aliens) and you get 53% but your course grade goes up to a B. Realistically speaking, your grade on the final is likely to be around 85% based on what you have done before. And so you can go into the final knowing that there is a very small chance you will get anything lower than a B. On the other hand, you can compute that if you can do slightly better than your earlier average and get an 89%, your final grade in the course may go up to an A.

The most amazing thing about these averages is how “sticky” they are. If 70% of your grade is already completed as a B, everything from a grade of 53% to a grade of 88% on the final assignments will get you a B---that’s 30 percentage points difference! This means that you can go into the final with confidence, ready to demonstrate your knowledge instead of panicking about a question here or there. It also shows that there is no point in arguing with your instructor about a few points here and there. Remember that your conscientiousness about homework assignments and participation really pays off in the end.

What the Romans Did for Us

Thinking about Rome? By Amy Barr with The Lukeion Project “Rome,” is now apparently a common answer to the question, “what are you thinking ...