Ludwig was helping me do calculus last night. I'm working on a bunch of things to upload, and I figured we could all do with a bit of a smile. I hope everyone is staying safe and healthy!

My original plan was to publish another long form rant, this time about the murder of Thomas Becket in 1170 (I have a soft spot for everything related to Henry II of England). However, with all the doom and gloom we have in the news, and because while we've been self isolating in our houses, spring has arrived, I figured I'd change gears today and head back to math activities. So we're heading back to Desmos.

One of my students is prepping for the SAT, and that prep includes prep for the Math SAT II. So I've been teaching her some topics that she hasn't yet gotten to in class (and I'm nervous that with all that's going on, she WON'T get to at all), and one of these topics has been things involving trig and polar equations of all sorts.

So for anyone with a little precalc background, let's talk polar roses and their cousins.

When we talk about sine, cosine, and tangent functions and their reciprocals, we are talking about what are called periodic functions, meaning that they repeat values at regular intervals. If you plot y=sinx or y=cosx on the Cartesian (x,y) plane, you get the familiar waves that are anchored on the x-axis. 

If we graph on the polar axis, we graph in terms of r and theta (the angle measure). The polar coordinate system looks like a series of concentric circles representing r centered at the origin. This opens up a world of possibilities because coterminal angles (π/2 and 5π/2, for example) will have the same value of cosine or sine, and instead of going on forever in waves, they will be bounded by those values of r and theta. With this in mind, we can make polar roses, cardioids, and lemniscates.

Polar roses can be created using the equations r = acos(nθ) or r = asin(nθ). Just as when graphing on the Cartesian plane, the variable 'a' determines the size (amplitude) of the curve. The variable 'n' represents the b term; 2π/b determines the period (distance between repetitions of the graph). Therefore, the 'n' variable determines the number of petals your flower will have; if n is odd, the flower will have n petals, but if n is even, it will have 2n petals. Above I graphed the rose r=3cos(6θ); see how it has 12 petals? If I were to have graphed sine instead of cosine, my graph still would have had 12 petals, but it would be tilted a little because sine and cosine are phase shifts of one another.

Cardioids are technically created by rolling a fixed point on a circle around another circle of the same radius (seen below). You get a heart shaped figure as a result with a single cusp where the point returns to the beginning. Cardioids can be created with the equations r = a(1 ± cosθ) and r = a(1 ± sinθ​).

Lemniscates are a class of figure 8 or infinity symbol shaped loops. They represent all of the points (locus) whose distances from two fixed points (foci) a distance of 2a apart, when multiplied together, equal a^2. The equation for Bernoulli's leminiscate, perhaps the "classic" lemniscate, is r^2 = a^2 cos(2θ​) or r^2 = a^2 sin(2θ​) (again, tilted due to phase shift). Another famous figure 8 leminiscate (and my personal favorite) is the Lemniscate of Gerono, which has the equation x^4-x^2+y^2=0.

So what can you do with all of this? PLAY! I challenge you to create flowers or designs of your own using these equations. Use different values for a, b, and n and see what you get. Change your + and - signs and see your graphs flip across an axis. Combine these polar equations and come up with designs as intricate as you want. Create your own bouquet or flowers and let your imagination run wild. One of the awesome things about math is that once you add different dimensions or ways of thought to your equations, you can make shapes way cooler than a simple straight line or parabola. If you found this brief introduction interesting, I urge you to research more about these types of graphs, what they mean mathematically, and different famous forms of graphs in history because I am barely scratching the surface here. Let's brighten these dark times with some geometric flora!

European history is filled with all sorts of scandals and intrigues—murders, romantic entanglements, near constant backstabbing—but few scandals in history rival England’s King Henry VIII and his six wives. After all, Henry managed (in a period of only twenty-two years) to see two wives beheaded, two marriages annulled, and the entire country of England excommunicated from the Catholic Church for his antics. The popular HBO series The Tudors romanticized much of what went on, but let’s look at what happened ourselves.

When we think of Henry VIII, I’m sure many of us harken back to (at left) Hans Holbein the Younger’s infamous portrait depicting an obscenely rotund figure crowding the painting, massive codpiece screaming out, “Hey! Look at me! I’m potent and powerful!” It’s easy to make fun of such a sight five hundred years later.  The real story, though, is, I think, much more tragic and certainly more complex.

Henry VIII was the second son of King Henry VII, the first Tudor monarch and ruler of England after the tempestuous War of the Roses era. I’ll do more posts about this era and its illustrious personas; Margaret Beaufort, Henry VIII’s grandmother, for example, was a force of nature and deserves some recognition. As the second son, none of us should have cared much about Henry; if all had gone according to plan, he would have lived a life of relative luxury and little responsibility out of the way of political machinations of Europe at the time. Indeed, his elder brother Arthur was the child Henry VII placed all of his hopes on. In 1502, at the age of fifteen, Arthur was married to Catherine of Aragon, youngest child of the famed Ferdinand and Isabella of Spain, in order to establish an iron clad alliance between the two powers. Henry, by comparison, was a ten-year-old whose childhood was not well documented because he was just expected to be a kid.

Everything went horribly wrong less than half a year after Arthur and Catherine’s marriage. An outbreak of sweating sickness swept through England, and it claimed young Arthur as a victim. At the age of ten, Henry VIII became the presumed heir to the throne and assumed the title of Prince of Wales. His father Henry VII and the Spanish diplomats in England concocted a plan for Henry to marry his brother’s now-widow, but there was a problem with this plan: according to papal law, it was illegal for a man to marry his brother’s spouse. Fortunately, Henry was so young that this wasn’t a huge issue; the Tudors appealed to the Pope for a special dispensation with the law, saying that Arthur and Catherine’s marriage was never consummated and was thus invalid, and since Henry was so young, obviously nothing seedy had happened within the families. Because British and Papal interests were aligned at the time (remember, the Vatican was as much a political entity as a religious one at that time), this was not a big deal. By the time Henry ascended to the throne in 1509 at the age of seventeen, the dispensation had been granted, and he and the now twenty-three-year-old Catherine were allowed to wed.

By all accounts, Catherine and Henry had a good marriage—Henry was handsome and vigorous, Catherine bright and well-tempered. They apparently loved and trusted each other. Sure, Henry had his share of affairs on the side as was custom among the nobility of the time, fathering Henry Fitzroy with Elizabeth Blount, but all in all, the union was solid. Soon enough, they conceived their first child, but then tragedy struck. Catherine suffered a series of miscarriages, putting a strain on the marriage. Finally, in 1516, Catherine gave birth to a child who survived: the future Queen Mary.

By 1525, however, Henry was impatient with Catherine. He was now well into his thirties and still did not have a male heir. Since Catherine was older than him by a few years, the probability of the two of them having a male child was growing smaller and smaller. In the meantime, Henry’s wandering eye had been captured by Anne Boleyn, sister of Henry’s mistress Mary Boleyn. Anne, unlike her sister, was known for being highly shrewd and refused to give in to Henry’s sexual advances, saying she would never be a mistress. The stage was set for one of the greatest soap operas in European history. 

By 1527, Henry was desperate to find a way out of his marriage to Catherine so he could pursue Anne Boleyn. However, he had been able to wed Catherine only because of a papal dispensation; the pope was not exactly happy when Henry came to him asking for an annulment of said special marriage. Up until this point, Henry was a staunch supporter of the Catholic Church; he had even been given the title Defender of the Faith by the Vatican after publishing a fervent defense of the Church (remember, this is the time of the Reformation throughout Europe). But with the pope refusing to annul his marriage to Catherine (English and Papal interests didn’t line up quite as well by this time, so the Pope was less inclined to grant Henry’s requests), Henry found himself with his hands tied. He began a series of moves that separated the Church of England from the Catholic Church, and with the Act of Supremacy in 1534, Henry made himself the sole head of the Church in England. In 1532, he banished Catherine of Aragon from court and declared that marriage invalid. Soon after, he married Anne Boleyn, who gave birth to Elizabeth I just a year later. As a result, the entire country of England was excommunicated by Rome.

But alas, the marriage that was so hard fought for was not meant to be. Henry and Anne’s relationship was publicly tumultuous; Anne was intelligent and ambitious, and she was not going to play the role of subservient wife. The marriage was further strained by a series of miscarriages, the most notable happening in January 1536 after Anne learned of Henry’s severe leg wound as the result of a jousting accident. Conveniently, Henry took Jane Seymour as a new mistress at around the same time. Anne had become more of an annoyance than a help to the King, and she had to be gotten rid of. By that spring, reports were published that Anne was having multiple affairs, including one with her own brother. In sixteenth century England, this was considered treason, and in May 1536, Anne underwent a show trial, where she was found guilty of adultery and beheaded. Her child Elizabeth was, like Catherine’s daughter Mary, declared a bastard.

Eleven days after Anne’s execution, Henry married his mistress Jane Seymour. By the end of the year, she became pregnant. Many believe that Jane Seymour was Henry’s favorite wife. It is certain that she was popular across England, pushing for Catherine and Anne’s children, Mary and Elizabeth, to be restored to the line of succession, and calming some of the unrest that Henry’s actions had stirred up. 

In October 1537, Jane gave birth to a boy, Edward VI. The labor was difficult; Edward was breech, and the labor lasted over two days. As the country celebrated the birth of the new king, Jane bled out, dying of childbirth-related complications merely days later. Henry was devastated; he did not remarry for another three years and allowed himself to become morbidly obese in the interval. When Henry died a decade later, he requested that he be buried in a grave he made himself next to Jane Seymour.

In 1539, Henry’s chief minister, Thomas Cromwell, pushed for Henry to remarry and supported a union with Anne of Cleves, a German Protestant noblewoman. Cromwell was a staunch Protestant and wanted the marriage to help solidify England’s Reformation. Henry sent painter Hans Holbein to Cleves to paint a portrait of Anne so that he could see if he wanted to marry her. Holbein completed his task, delivering Henry a flattering portrait, and Henry assented to the marriage. However, when Anne arrived in England, Henry was appalled. She was relatively uneducated, only able to read and write in German, and Henry accused her of smelling poorly and having saggy breasts. He went through with the marriage, but it was never consummated, and it was, in fact, quickly annulled. Thomas Cromwell was executed for treason for pushing for the marriage, and Anne was sent away from court with a handsome financial settlement. Over time, Anne was given the title of the King’s Beloved Sister, and they actually became friendly, but the union was not to be.

The day of Thomas Cromwell’s execution, Henry, now aged 49, married the eighteen-year-old Catherine Howard, a former cousin and lady-in-waiting of Anne Boleyn. Henry was suffering quite a great deal by this time; his leg wound from his jousting accident never healed (and was poorly treated by doctors at the time), he was fat, and he likely had diabetes. Catherine was young, and energetic, and mischievous. By 1541, Catherine was accused of having affairs with Thomas Culpeper, Henry’s favorite courtier, and Francis Dereham, to whom she may or may not have been engaged before marrying Henry. Love letters were found in Catherine’s handwriting addressed to Culpeper, and unlike Anne Boleyn, there is no doubt that Catherine did, in fact, commit the adultery that led to her downfall. Culpeper and Dereham were both executed at the end of 1541, and Catherine was beheaded only a few months later.

Henry tried his hand at marriage one final time when he married wealthy widow Catherine Parr in 1543. Catherine was instrumental in finally getting Mary and Elizabeth restored officially in the line of succession, and Henry trusted her. They would argue over policy and religion (she was a dedicated Protestant), and when Henry traveled to France in 1544, he made Catherine regent in his stead. They never had children together, but Catherine maintained strong relationships with Henry’s children. Indeed, when Henry died in 1547, Catherine married her ex-boyfriend Thomas Seymour (Jane’s brother), and the two of them actually allowed Elizabeth to live with them for a time (until Thomas made grossly inappropriate sexual advances on Elizabeth, causing a massive scandal in its own right). 

It’s easy to blame Henry for being a philanderer or for being fickle, but at the root of this soap opera is a very real desire to maintain stability within England. Remember, Henry VIII was only the second Tudor monarch (and a spare at that), and his father had ascended to the throne with a very tenuous claim to it at best. Yes, he could very well be portrayed as a tyrant or as a bad king, but his reign is highly reflective of the time during which he reigned. I wouldn’t call him a victim by any stretch of the imagination, but his character is far more complex than simply “Divorced, beheaded, died. Divorced, beheaded, survived.” Understanding that complexity helps us understand the monumental shifts that Henry and his court are responsible for, and hopefully, it lets us all be a tad less dismissive of others.

For more background on the Wars of the Roses and the era that Henry was born into, I highly recommend Dan Jones’s documentary series Britain’s Bloody Crown, which is available on YouTube. It ups the drama of the era maybe a bit more than necessary, but it provides decent context and will keep you or a student entertained. For more fact based research, I drew heavily from Peter Marshall’s Reformation England: 1480-1642 along with the work of David Starkey, Alison Weir, Susan Brigden, Robert  Hutchinson, and my own notes from multiple British history classes with Carl Estabrook (yes, I saved them all and have them) at Dartmouth College. The BBC also has good resources for biography and context (
https://www.bbc.co.uk/teach/what-did-king-henry-vii-really-want-from-a-wife/zh9s2sg, for example).

Desmos is a graphing program that's free to use online; chances are if you've got a high schooler, they've seen it. Today's educational way to stave off boredom is to draw a picture using functions! This one has been cooking for awhile; I'd love to make some sort of coloring book or paint by numbers that's truly a graph by numbers; if you plot things correctly, you get an image. It's less tedious to an artistic or creative mind.

Below is a poorly drawn cat. How I made it was by inputting multiple functions (here, mostly conics because I'm working on conics with one of my students, but there's a world of possibility; go nuts!). I restricted domains (the x, or horizontal, coordinates) using brackets. For example, the top of our feline friend's nose is a horizontal line, y=3.5. How I input the function so it didn't continue past where I wanted it was by entering y=3.5{3.5<x<4.5}, which told the program that I only wanted to see those specific values. You can restrict the range (or y values) the same way. This is a simple picture, but you can be as simple or complex as your heart desires.
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Drawing in Desmos has multiple benefits, especially for Algebra II/Precalc students. First, it allows students to really play with transformations (shifting up and down, left and right, making things wider or more narrow). Second, it reinforces the concept of domain and range. Third, it lets students draw what they want; the world is their oyster. Again, if anyone actually tries to make a picture by plotting graphs like this, I'd love to see them.

Parents with kids stuck at home:

I've seen a lot of posts being like "what do I do with the kids while they're out of school and not learning?!" I get it. I'm frustrated, too, and nervous for especially high schoolers whose entire standardized testing/AP exam plans are out of whack (I'm still working both in person and remote, so if you know of students who want to learn/prep for anything, send em my way because I am experiencing disruptions and am scared).

As an educator, I see this as an opportunity, though, to help reinvigorate that love of learning and creating that today's broken system has squashed. A few years ago, I started writing a book of salacious tales from history both well known and not. The idea was that I could tell the stories somewhat informally and then say "ok, if you found that interesting, here's where you can find more information". I didn't do anything with it yet because a) it's not finished and b) I'm a coward about putting my own work out there. But I'm going to start posting some of the stories here daily. It can give some kids something to research.

I'm also committing to posting activities that kids of all ages can do at home to hopefully learn something and have fun. Right now I'm starting with an oldie but goodie: The Fibonacci sequence.

We've all seen it before. I think my first encounter with the sequence was in a Babysitter's Club book when I was six or seven; recently it's reentered the popular imagination through the work of Dan Brown and really any TV show that wants to sound mathy. My boyfriend Erik reminded me this morning that Maynard incorporated it into Tool's Lateralus, and a quick Wikipedia search notes that the time signatures repeating reflects 987, a Fibonacci number. But what is it and why do we care about it?

The Fibonacci sequence has been around in scholarly works dating back to ancient times (India, specifically), but it is named after Leonardo of Pisa, or Fibonacci, who wrote about the sequence in his 1202 book, Liber Abaci. There, he used the sequence to model rabbit population growth, but it appears in nature all the time. Look at the swirl of a seashell or the center of a sunflower or the curve of a spiral staircase; all can be fitted to the Fibonacci sequence.

How does it go? Well, it's fairly simple. Each successive number in the sequence is the sum of the previous 2 numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...and so on. As the numbers get larger, dividing one number by the previous approaches what's called the golden ratio, or phi, which is an irrational number roughly equal to 1.618... You can use this ratio in many practical ways; it's used in economics to predict retracement. Hell, you can even use Fibonacci numbers and the golden ratio to loosely convert miles to kilometers and vice versa (21 miles is roughly equal to 34 kilometers).

So parents, what can you do with it today with bored students? The classic move is to draw the Fibonacci spiral. Get a ruler or some graph paper. Draw a square of side length of 1. Touching one side, draw another square of side length 1. Adjacent to both, draw a square with side length of 2, then one of 3, 5, 8, and so on (I've done my own below freehand because my ruler has walked off). Draw the spiral by connecting diagonals of each square (you can use a compass if you want to be super precise). Now with the spiral drawn, you can make a variety of art projects, both realistic and abstract. The kids can learn the sequence and let their imaginations run free. If anyone makes Fibonacci art, I'd love to see it.
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More cool images: https://sciencevibe.com/…/the-fabulous-fibonacci-sequence-…/

I've let this website go pretty much untouched because, frankly, I haven't needed it. Over the past few years, my tutoring has been frenetic and fortunately supported by strong word of mouth by some wonderful families that I work with. 

However, the past year has been chock full of changes, and as some of those students head off to college, I think it's the right time to refocus, refine, and turn my attention towards building something that is more stable and geared towards growth.

Over the past five years, I've been lucky that my beloved cat Ludwig's health has been stable and has been able to support two moves, first to Lynnfield, MA and then to Weymouth. I've had to deal with the loss of my beloved father suddenly in September 2018 and have been fortunate to begin building a life with my rock and partner Erik. Because he has an extremely strong nuclear family, I made the decision to relocate to the South Shore of Massachusetts, and I am looking to make it a home base of sorts. I'm not leaving any of my students in the North Shore/Metrowest areas, but going forward, I am going to be a little more firm in trying to schedule based on area to limit driving (I put 30,000 miles on my car last year--that is madness!).

As the summer carries on, I'm looking to take on new clients more locally, revamp this site, as well as FINALLY finish some test prep/college prep materials that I will list for sale on this site. For the rest of the year, I am offering 1 free hour of tutoring for any student on whose recommendation I book a new student/small class. I am also welcoming testimonials from students past and present to put on this site. On the music front, I am a part of a new band (www.facebook.com/honoriaband) that is in the process of writing, booking performances, and hopefully recording our debut release at the beginning of 2020. I tend to write lyrics based on historical concepts/people, so it's a nice amalgamation of interests.

Going forward, I will try to keep this blog updated bi-weekly with tips/concepts/interesting facts to keep you informed and educated. But for now, pleased to meet you again!

--Ashley

The school year and testing season is winding down.  Admittedly, I'm a little terrified since that means my student load is thinning out.  However, I am in the process of planning and publicizing some summer workshops and teaching.

The summer is the ideal time to get some extra tutoring and test prep in.  Without the pressure of schoolwork and myriad activities, summer tutoring can help spark/reignite a love of learning in all sorts of students.  I am offering low-pressure sessions in math, music, and research among others, so no matter what a student may be interested in or need a little refresher on, he or she can find something to suit his or her needs.  If not, I am available for one-on-one sessions as well.  Some offerings, such as music appreciation or music theory are appropriate for all ages.

I always feel a pang of guilt teaching SAT prep during the school year; with students inundated with homework, clubs, and sometimes jobs, having to spend time every week running through problems or remedial concepts simply seems unfair to me.  Therefore, I am offering special summer SAT bootcamps, both in small groups and individually for $700/person.  These bootcamps, running 3 weeks for 3 hours a day every weekday in the student's home, provide students with 45 hours of individualized SAT prep.  Similar programs through the bigger companies offer around 30 hours for a comparable and sometimes even higher cost.  I can afford to provide more for your money because, as a small company, I don't have the same kind of overhead those bigger folks have.  I prepare all of my materials myself and don't currently have any employees to worry about.  My goal is to help families through the tough latter part of high school with as much empathy, humanism, and high subject knowledge as possible--not to make a quick buck. 

I have taken the step of printing promotional materials; I need to spend some time posting them in public areas within the next week, but I am accepting bookings now

Gabriel Garcia Marquez died Thursday.  I admit, I have never been a rabid fan of his work (I probably never gave it the attention it warrants), but I have a massive amount of respect for his output and his legacy, which has reminded a large part of the literary world of the power of Spanish language literature.  All too often we forget that the modern European novel owes its genesis to Spaniard Miguel de Cervantes (yes, I know Garcia Marquez was Colombian), and I know I am guilty of being woefully ignorant of all other Spanish language novels despite being a voracious reader.  Part of this ignorance comes from my wish to read things in their original languages and I do not speak Spanish, but I read the Russians with regularity though I do not speak Russian (yet) and thus cannot count this as a valid excuse.  Author William Kennedy called Garcia Marquez's novel One Hundred Years of Solitude “The first piece of literature since the Book of Genesis that should be required reading for the entire human race” in a New York Times book review; perhaps it is time for me to stop making excuses and start truly appreciating a massive section of the literary spectrum that I have neglected.

I have had language in general on my mind today; I cannot figure out why.  Perhaps it was hearing the name of such a literary behemoth repeated across all of the news outlets.  Perhaps I have just been in a mood.  On a lark I decided to rewatch the Late Late Show with Craig Ferguson episode without an audience where Craig Ferguson and Stephen Fry simply sit down and talk. 

I absolutely adore Craig Ferguson; I love his ability to navigate the waters of the absurd and the insightful.  When he is conducting a serious interview or professing a genuine opinion, he is masterfully able to make a point with an air of complete sincerity and surprising insight.  When he is goofing off with his robot skeleton sidekick or pantomime horse, he is ridiculous and uproariously funny.  And the whole while he gives off an enthusiasm for his job, his situation, America, and seeing his guests succeed that makes the rest of the world a bit brighter for the people lucky enough to spend the hour watching.

I also adore Stephen Fry.  I tend to watch a great deal of British panel shows, and QI anchors my television docket.  I feel a certain kinship with Mr. Fry; yes, he is Cambridge educated, but his persona as an academic seems to be more one of the autodidact.  He comes across as loving knowledge of all kinds and plays the role of the bon vivant beautifully.  I flatter myself that in this way we are quite similar; I tutor not to become rich (that is pretty much out of the question anyway) but because I love learning and I want to help others learn to love it too.  I work across subjects not only because I can but also because I have a genuine interest and aptitude across subjects and find that I enjoy experiencing the world more when equipped with a wealth of facts and knowledge.  I therefore follow Stephen Fry, his work, and his interviews fairly closely.

In this particular interview, Ferguson and Fry jump from topic to topic, but they spend a few minutes discussing language and specifically Twitter.  Both tout the poetry that can be found in being forced to condense communication into 140 meager characters, and both argue that the shorthand that has followed the Twitter and texting cultures (and indeed every form of communication where characters are at a premium) is harmless and indeed sensible.  I would not presume to argue that this shorthand does not have a place in society; Fry is correct in that the character limit forces people to self-edit, and there is a particular beauty in the stripping bare that modern social media and digital communication facilitates.

However, at the risk of sounding profoundly old-fashioned and perhaps closed minded, my admiration of "textspeak" is cautious at best.  The issue that happens when one tries to implement a new variant of communication is that the "proper" means of communication ends up being subjugated.  I see students on a daily basis struggle with writing papers or doing test prep because they have never learned proper English grammar; they cannot recognize comma rules or they mix tenses with no idea what they are doing wrong, and more worrying, they do not understand why this is a problem.  I see the same kind of behavior with my music students who try to bypass the basics of learning to read the staff, count quarter notes, or learn basic repertoire and history in favor of doing overcomplicated things or creating electronic pieces with no idea why certain pieces go together or how things work.  As a result, when I ask these students to actually join in discussion about their work, they are largely unable to express themselves in favor of "I just like it", which strips these students of their power.  These students tend to plateau easier and then develop self-defeating attitudes that stifle real ability and improvement.  There is an epidemic of trying to run before one can walk that makes me very uneasy with modern culture.

The English language is an utterly beautiful and complex beast, and I wish I could make more students see this in today's society.  The OED suggests that if we were to add together the modern lexicon, archaic or obsolete words, et cetera, the English language would contain roughly three quarters of a million words.  This number is only growing as English continues to evolve and draw from other languages.  This wealth of words allows us to communicate with extraordinary precision, and to me, this is more beautiful than the 140 character poetry of Twitter could ever be.  If we look at syntax and the parts of speech, we can use the same exact set of words to mean multiple things, thus affording us with incredible power. 

I am not saying that English speakers should adopt a florid, overly verbose style of speech (though I tend to be quite wordy myself); there is no reason to try to revert back to Elizabethan English or the winding euphemistic language of the Victorian period.  I simply become very uneasy when watching today's youth (and I include my own generation in this category) attempting to be conversant in a barebones version of English without being conversant in everyday written English.  Often things that are more laid bare require a higher level of facility and nuance than things that are more involved (look at the compositions of someone like Steve Reich versus some kind of massive Wagnerian composition with forty parts working together; there is nowhere to hide in simplicity).  By allowing students and young people to use text/Twitter style language in everyday use while not making a concerted effort to teach "proper" English, we are denying students important tools that they can use throughout life and propagate a culture of mediocrity that I have a very hard time accepting.

In 2003 the British network ITV ran a documentary series on English presented by Melvyn Bragg called The Adventure of English.  I watched it for the first time out of boredom maybe 4 years ago; I have seen it at least once a year since.  The series personifies the English language; the viewer is left feeling as though English is a living, breathing entity, affected by major and minor events much the same way as societies and individuals are affected.  It is a series created for popular consumption, and it accomplishes its goal very keenly.  I am half tempted to add it to the beginning sessions for all of my test prep students.  Language is a finicky, beautiful tool and cultural snapshot, and I wish it received more appreciation by today's youth and their teachers for all of its beauty and complexity. It truly is a living entity and holds a massive amount of wisdom for us all.