WWTK: Summer Fun with Math!

Nobody likes doing homework in the summer. It’s just a fact of life. My advice to students who want to stay sharp during the summer is to inject fun into your work and work into your fun. Find a way to connect your personal fun time back to the subjects you’re learning in school. The best way to accomplish this, in my opinion, is to look for school skills in unusual contexts. If you’re interested in maintaining your English or writing, you can join a book club or arrange one with your friends. Take this summer as an opportunity to read that book you’ve been dying to get to, and while you’re reading think about it critically and talk about it with others. I’m part of a “Bring Your Own Book” club right now, where each month we are given a topic and have to find and read a book that fits the topic. BYOBook clubs are a great chance to see a broad range of interpretations of a given theme and think about your reading in a larger context (what does the topic “animals as main characters” mean to six different people?). If you’re organizing the club, start with various genre selections and move on from there (Sci-fi night, horror night, etc.).

Finding math in unusual contexts is a bit more difficult, but for me it’s a lot more fun. There are plenty of seemingly-unrelated skills and activities that actually involve a great deal of math, and if you look for it you can learn to think about math and its impact on the world in a broader context. Here are just a few examples of fun activities that involve math.

Dungeons & Dragons or other tabletop Role-Playing Games
Dungeons & Dragons is the most well-known of a genre of games known as Tabletop Role-Playing Games (RPGs). In a D&D game, each player creates a unique character using a complex chance-based generation system involving rolling dice to determine various statistics. The game is full of math, including but not limited to multiplying to find base stats or critical damage, or adding and subtracting various modifiers. Dice are rolled on the fly and numbers tallied up and called out, resulting in the need for quick mental math. Playing D&D can be a great way to practice your mental math skills without it seeming like drudgery. Plus the game itself is a great lesson in problem solving and algorithms, as you figure out which patterns of addition and multiplication are needed for which actions and very naturally arrive at your most optimal workflow. The storytelling aspect of the game can be helpful for creative writing practice as well, as you think about how best to phrase your statements or work together to figure out the solution to a puzzle.

Knitting and Crocheting
Knitting and crocheting are great for math practice. Learning the basic stitches is an act of problem solving and devising algorithms, as you figure out how to hold your work and where the various parts of the stitches go. Once you have the basics down, you’ll still need to count your stitches, follow patterns for lacework, and even use math to figure out how fast to increase or decrease. For a real math workout, though, you should go through the gauntlet of altering a pattern. Use a different weight of yarn than the pattern calls for; you’ll need to figure out your stitch ratio and then use lots of multiplication to figure out how all the numbers will change. It’s a complex process, but incredibly rewarding.

Want a fun afternoon of geometry- and physics-based fun? Head out for a round of mini-golf! Navigating around the obstacles requires planning and forethought – can you figure out how to predict where your shot will go before you start? Banking off of the sidewalls provides an exercise in angles of incidence – can you avoid the obstacles in the first place with a carefully-lined-up shot? How are you deciding which tee to use, and how do the bumps and hills affect your ball’s trajectory?

Writing Rundown: Finding Your “However”

It takes practice to find your writing style, whether it be in fiction, research papers, or analytical essays. The best piece of writing is both grammatically correct and organized, but also contains the essence of the person who’s writing it. When I correct students’ papers, I try to avoid suggesting alternate sentences in their entirety, since a paper written by you shouldn’t sound like one written by me. Even if we are answering the exact same prompt in the exact same way, the tone and character of each paper will be distinct, unique to each of us. Finding your style is a slow process, and generally comes about organically as a result of experience. Write more papers and you will begin to zero in on what makes a paper sing for you.

This is not to say that there aren’t tips and techniques I can give to help you find your writing style. By far one of the most useful techniques in my own experience has been working with what I call “Finding your ‘however’.” The name comes from my sister, who always used to incorporate the word ‘however’ into practically every sentence in her paper, even when it didn’t make sense. It was just a quirk of the way her brain liked to formulate thoughts, so it ended up in her rough drafts a lot because it was in her head while trying to sort out what she wanted to say. I had a similar experience, but in my case it was not ‘however’ but ‘I believe that’. I used to start every sentence in an opinion essay with “I believe that,” since that’s how my brain formulated thoughts. In an opinion piece, though, the idea that these statements are your beliefs is implied – you don’t need to keep telling the reader that. It was hard for me to remember that I could just state my opinions as fact and with confidence, and the reader would understand implicitly.

We all have these little quirks in the way we write, and they’re different for each person. It’s a natural reflection of the way our brains process information. Usually these quirks end up detracting from the strength of the overall paper, throwing the difference between spoken and written English into stark contrast and sounding stilted or affected when read. Catching yourself in the process of falling into a quirk is difficult, though, so my strategy is simply to recognize and acknowledge your little ‘however’. In my case, I recognize the fact that I like to start every sentence with “I believe that,” and that this quirk will need to be dealt with before my paper can be considered finished.

But here’s the key – ignore it when writing your rough draft. It’s easiest to get the information out on paper if you’re not worrying about editing, so just get it all out and don’t censor yourself. On your first round of editing, after you have a completed draft, go through methodically and remove all of those little ‘howevers.’ In my case, when it’s time to edit I start by going through and cutting out every single instance of “I believe that,” adjusting sentences where necessary.

And don’t worry – if you work in this way long enough, your brain will eventually figure out that you don’t need those quirks and you’ll find they stop making their way into your paper in the first place. I hardly ever start sentences with “I believe that” anymore, but I still make a first pass through the paper and check for them anyway. In fact, far from being a detrimental quirk, my little ‘however’ has become a tool that I use to help me generate content. When I’m having trouble articulating a point, I’ll say it to myself starting with “I believe that” – and then simply write the rest of the sentence without those first three words. Find your ‘however’ and keep on top of it, and you’ll be well on your way to writing a great essay.

Literature Spotlight: Psychological Punishment

Crime and Punishment by Fyodor Dostoyevsky is a novel about guilt, morality and emotion. Throughout the novel many characters espouse the idea of reason and willpower over emotion – that if you have sufficient mental faculties you can prevent emotion from getting in the way of your actions and behave truly rationally. The student Raskolnikov believes this with all his heart when he sets out to murder a pawnbroker for the good of the community. This concept is quickly proved to be fundamentally flawed, however, as his inner guilt throws him into emotional turmoil and his brain attempts to protect him from the ugly truth of his actions. Raskolnikov displays several textbook examples of psychological defense mechanisms throughout the course of the novel, proving that even the most thorough reasoning and intellect cannot prevent the emotional and psychological response to a crisis.

Psychological “defense mechanisms” are the brain’s way of protecting itself from full awareness of unpleasant thoughts or behaviors. In Raskolnikov’s case, they are his brain’s way of protecting him from the full reality of what he has done, and the guilt associated with that reality. Some are more primitive, living in the subconscious and relying on emotion, and some are more complex and rely on conscious thought. Raskolnikov displays many of them over the course of the novel, as his brain attempts to come to terms with what he has done. Here are just a few examples.

A relatively primitive defense mechanism, Dissociation involves losing track of time; the narrative of life becoming disjointed. It allows the person to disconnect from reality for a while, seeking psychological shelter by escaping to a different sense of time. At one point in the novel, Raskolnikov gets confused about whether he has been to the police station yet. He states, “Bah! I am mixing it up; that was then. I looked at my sock then, too, but now…” (P. 192) An action that he associates with guilt (looking at the sock) causes his brain to try to escape to a different time, a time before he had interacted with the police. Dissociation appears in many places in the novel, with Raskolnikov frequently getting mixed up with regard to who was present during a certain time, whether he had said something or just thought it, and even with regard to his dreams and their relationship to reality.

Displacement is when a person redirects their thoughts or actions away from the actual source of their problem, sometimes referred to as “taking it out on someone else.” It allows the person to vent their frustrations when they cannot take them out on the actual source. Raskolnikov is angry at Luzhin and lashes out at him almost from the very beginning, and his anger isn’t necessarily warranted to the extent that he experiences it. Getting mad at Luzhin is a way for his brain to release the feelings of anger and guilt that he feels towards himself without hurting someone he cares about.

Acting Out
Acting Out is when a person performs extreme behaviors in an attempt to express thoughts or feelings that they can’t comfortably acknowledge. The classic example of acting out is a child throwing a temper tantrum. Raskolnikov acts out for much of the middle part of the novel; the most noteworthy example is when he runs into Zametov at a cafe and makes a speech explaining exactly how he committed the murder, under the guise of conjecture. He makes this speech in a creepy whisper, standing too close to Zametov, and tops it off with a strange laugh, so that Zametov is convinced he is a madman. This allows him the freedom to get the confession off his chest in a safe way, a way where he knows nobody will actually believe him. He continues to act out for the next few chapters, saying and doing things that offend and incense others and lend credence to their belief that he is delirious.

Rationalization involves providing a seemingly-plausible alternate explanation for why something is happening, an explanation that sounds more reasonable or is easier to deal with than the real one. Raskolnikov blames his guilty conscience and crazy dreams and thoughts on a physical illness. “ ‘It is because I am very ill,’ he decided grimly at last, ‘I have been worrying and fretting myself, and I don’t know what I am doing…I shall get well and I shall not worry…’ “ (P. 169) Blaming his guilty feelings on an illness allows him to distance himself from the reality of the situation, and also ties in to his belief that he can control his emotions – he comes up with a seemingly-logical reason for his emotional actions in order to devalue them.

Intellectualization is the blaming of every emotional reaction on some kind of intellectual reason, finding an explanation for unwanted emotions that ignores the obvious source of them. While waiting in the police station Raskolnikov begins to get nervous, but intellectualizes the problem by saying “It’s a pity there’s no air here…it’s stifling…It makes one’s head dizzier than ever…and one’s mind too…” (P. 148)

The use of intellectualization ties in particularly strongly to the overall theme of reason over emotion and highlights the importance of these defense mechanisms to the text. Using textbook examples of defense mechanisms shows just how little control Raskolnikov really has over his own psychology. When setting out to commit the murder Raskolnikov is convinced he can get away with it, specifically because he will use his reason and not allow emotion to get in the way. Raskolnikov believes that the reason most crimes are badly concealed and easily detected “lay not so much in the material impossibility of concealing the crime, as in the criminal himself. Almost every criminal is subject to a failure of will and reasoning power by a childish and phenomenal heedlessness, at the very instant when prudence and caution are most essential.” (P. 112) Raskolnikov believes this “failure of will” is an avoidable circumstance, and further believes that he will not suffer the failure himself, because in his mind his actions are “not a crime.” His entire reasoning process relies on the idea that murdering the pawnbroker is not actually a crime, and that consciously remembering this fact will be enough to keep him sane and safe after the act is committed.

Right from the beginning, however, he runs into problems. His plan does not go as smoothly as he had anticipated, with one problem after another piling up and straining his nerves, culminating in the pawnbroker’s sister coming in at the wrong time and Raskolnikov being forced to murder her as well. No matter how thoroughly he had rationalized the murder of the pawnbroker, he did not anticipate the sister and so he has no justification for her death. This unjustified murder pokes holes in Raskolnikov’s carefully thought out reasoning process, and his own brain begins to betray him. Raskolnikov reacts psychologically to the murders, even as he endeavors to explain his actions rationally. By showing us these psychological defense mechanisms, Dostoyevsky argues that even the most well-reasoned justification is no match for the emotional turmoil that follows a crime. Raskolnikov’s guilt is his punishment, and all the defense mechanisms in existence cannot protect him from it.

Ellen’s Choice: Tangent to the Classics

School’s almost out for the summer, and to me, summertime is a perfect excuse to try learning and growing in new, fun ways. When I tutor students over the summer, I make a concerted effort to inject some fun into our work, so that it doesn’t feel like homework. We read fun or unusual books, or we put a twist on a project. Write a creative, narrative response to a work instead of an analytical essay, or go on a little “field trip” to find learning in unexpected places. I’ve recently devised a new fun “field trip” type activity, and I’d like to share it today.

But first, some background. I participate in a monthly “Bring Your Own Book” club, where each month we are given a topic and we each choose a book that relates to the topic to read and bring in. We always end up with a really interesting mix of genres and types of stories, all revolving around a theme (such as “books with animals as main characters” or “books that have inspired music”). Since I tutor high school English, I tend to gravitate towards the classics, and I’ve brought in such books as Watership Down and Ragtime in previous meetings.

Last month, our theme was “alcoholic writers,” and after a quick search for a list of popular writers who were alcoholic, I settled on F. Scott Fitzgerald. My initial idea was to reread The Great Gatsby, a classic I hadn’t read since high school but remembered enjoying. I headed to the library and quickly found the F’s, then found about half a shelf of F. Scott Fitzgerald. Reaching for Gatsby, my eye was suddenly drawn to the book snuggled up next to it on the shelf, a volume slightly larger than Gatsby and also by Fitzgerald. I picked it up and looked at the blurb on the back, flipped through a few pages, and took it home with me instead of Gatsby. That book was “The Crack-Up,” an anthology of essays, letters, and notebook jottings from Fitzgerald’s life. It turned out to be a much more interesting and exciting experience than simply rereading an old classic.

Fitzgerald wrote essays about living in New York during the jazz age at a time when the jazz age was scarcely even over – an essay from 1931 had the same sort of wistful tone we’d expect from a period piece written today. But by far my favorite part of the collection was “the notebooks,” a sequence of random jottings, bits and pieces, collected into categories that started with each letter of the alphabet. “C” was for “Conversations and Things Overheard,” “D” was for “Descriptions,” “E” was for “Epigrams and Wisecracks.” It struck me as an intriguing glimpse into the inner workings of an author plying his craft, and my experience as a dancer and choreographer made this behind-the-scenes look into his process resonate with me even more strongly. I know the feeling of having an inspiration strike you and feeling that “I must write this down right now or I’ll forget it!” urge. Many of the little bits and pieces had Fitzgerald’s distinctive gorgeous wording, and I could almost see the reason behind putting each piece into his notebook. Lots of them were examples of “that’s a perfect way to describe this,” or just “I like that turn of phrase.” Some of my favorites were the ones completely devoid of context, such as:

Impersonating 46 presidents at once.

I absolutely loved this collection, and the experience gave me a great idea for a new “field trip” activity. I call this one “Tangent to the Classics.” The rules are simple:

  1. Head over to your nearest library and use the catalog to search for a classic novel you enjoy. It can be anything, really, so long as you enjoyed reading it.

  2. Jot down the call number and head into the stacks as if you were going to check it out.

  3. When you find the classic you searched for, don’t pick it up. Take a look at the books sitting to its immediate left and right. Read the blurbs on the back, flip through a few pages in the front, and choose one of those two books to check out.

  4. Take it home and read it. If it’s by the same author as your classic, think about how this book changes your conception of the author and his work. If it’s by a different author, think about why it was located right next to the classic. Libraries have an organizational structure that generally puts similar books near each other. Why is this book tangent to the one you searched for?

Try this one out and let me know how it goes! I’d love to see your experiences in the comments. What are your reactions to reading a book that was tangent to a classic?