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Toni Morrison's “Beloved” is a beautiful, poetic, and haunting work about love, motherhood and the lengths to which a mother will go to protect her children. The runaway slave woman Sethe kills one of her children (and attempts to kill the others) in order to save its life, and in doing so destroys the beautiful world she's tried so hard to create for the rest of her family. The baby's ghost haunts Sethe's world through the enigmatic character of Beloved, a character with at least three distinct possible interpretations. Is Beloved the ghost of the “already-crawling? baby,” or a simple runaway slave who just happens to call herself “Beloved,” or perhaps not even there at all? The novel is intentionally written to keep our interpretations vague, and each interpretation comes with its own commentary on the relationships in the novel. On the one hand, Beloved could be a real, physical girl, not related to the family, who ran away from an abusive slave owner and found... read more

I received this problem from a friend, who was having trouble while helping her nephew with it. It turned out to be quite a doozy, so I'm presenting it as today's Math Journey to show how the process we used last time works even with a gnarly, complicated problem. Solve using the Addition Method: 3x – 3y + 4z = – 15 3x + y – 3z = – 8 23x – y – 4z = 0 As we discussed last month, the basic idea behind solving a system of equations is to use one equation to solve another for a specific variable, and to do that enough times that you can eventually rewrite one of those equations with only one variable in it, and solve from there. The way I learned to do this is the “substitution” method, where you solve one equation for one variable, plug the expression in for that variable in a second equation, et cetera until you're down to one variable. The addition method works a little differently, but it's the same basic goal: eliminate enough of... read more

For the next few Ellen's Choices, unless I have a brilliant idea that must be discussed immediately, I'm going to start recapping the books I've read for my 2015 Reading Challenge.  The Challenge is an ambitious attempt to read one book a week for the entire year, selecting each book based on prompt items in a checklist.   Book 1: "A Book You Started But Never Finished"   For my first Reading Challenge book, I tackled "A book you started but never finished" - and boy, am I glad that I did! I've had Stormdancer by Jay Kristoff on my shelf for years, after I bought it and read the first few chapters, but got busy and lost interest. Turns out, this unassuming little book is an amazingly unique steampunk-dystopian-epic fantasy! The steampunk dystopia is thorough and riveting - I mean, c'mon, the sky is RED! And in amongst all the civil unrest, plots to overthrow society, and men clanking around in insectoid mechanical suits, there's... read more

Narrative Point of View, sometimes called Narrative Perspective, describes the position of the narrator in relation to the story. Commonly-used points of view include First Person, where the narrator is a main character in the story, describing the events using “I,” and Third Person, where the narrator is a separate entity describing the events of the story using “he” or “she”. Within Third Person there are two sub-categories dealing with how much information the narrator chooses to give. Third Person Omniscient places the narrator above the story, where they can provide narration of events that the main characters are unaware of. A good example of this is the Harry Potter series, where the books sometimes show scenes of the Malfoys, Snape, or Voldemort – things that Harry and his friends would have no way of knowing about. In contrast, Third Person Limited places the narrator inside the main character's head but not AS the main character – events are still described as “he... read more

Settle in, folks, today's a long one. In The Function Machine, we learned that functions can be depicted as curves graphed on a coordinate plane. In What Does the Function Look Like?, we learned how to tell the general shape of a function's graph based on characteristics of its equation, and vice versa. Today, we'll be focusing on linear equations (meaning any equation that graphs into a straight line). The defining characteristic of a linear equation is that the highest power of x in the equation is x to the first. This denotes that for every y value, there is exactly one corresponding x value. Of course, there is always exactly one corresponding y value for every x, but this is one of those “square is a rectangle; rectangle is not necessarily a square” moments. We know there's exactly one y for every x because we choose our x's independently and the y's are dependent on them. There can't be more than one y for any given x; you've only got one output... read more

So-called “Young Adult” fiction seems to have gotten a bad rap lately among parents of teenage students. It seems as though adults tend to view YA as somehow “lesser” to other works, particularly as compared to the classics students are assigned in high school. I suspect this is because “Young Adult” as we conceptualize it today is a relatively recent invention – most bookstores and libraries didn't even have a YA shelf until the mid-1990s. When we were teenagers, there was no “Young Adult” section at the bookstore – there was “Children's” and there was “the rest of the store,” usually organized by genre. So as teens, too old for the Children's section, we chose books from the rest of the store based on genre or author. I enjoyed sci-fi and fantasy, for example, so I found each next reading experience in the Sci-Fi/Fantasy aisle of the store, reading greats like Larry Niven, Neil Gaiman, and Isaac Asimov. Young Adult, though, is a completely different animal... read more

Back in the day, where you wanted to go to college dictated which standardized test you took. Colleges in the midwest generally required the ACT, while those on the coasts wanted the SAT. These days, the score conversions are commonplace enough that most colleges will accept either one. So how do you choose which one to take? Well, there are a few differences to keep in mind. Format Most of the differences between the tests are matters of format. The SAT is comprised of ten sections ranging from 12 to 35 minutes each. The sections alternate between reading comprehension, math, and writing, and the whole test begins with a 25-minute timed essay. One of the ten sections is an “experimental” section, which is not scored as part of your test and is a chance for the test-makers to try out new ideas on a group of students. The ACT, in contrast, is four 75-minute sections, one for each subject. The ACT does not include an essay, but it does include a “science” section... read more

What are your 5 outside the box tips that help make your tutoring lessons fun? 1. Have a sense of humor about learning. I like to use humor in my tutoring, to keep students engaged and interested in the material. I've found that it's easy to zone out during a lesson, and the classes I've retained the most information from myself have been ones where the teacher employed humor. In a writing class, a teacher explained the importance of context to spelling with the quip “You need to remember which witch is which, or you'll suddenly have a lady with a black hat appear in your paper.” My high-school calculus teacher helped us remember the SOH-CAH-TOA trig function sequence by telling us a long joke about a native american who stubbed his toe and was advised by the village elder to “Soak-a-toe-a.” And later on, in a materials science class in college, our professor explained the molecular physics properties of a certain material with a joke about coal trying to... read more

Since it's Thanksgiving week, let's think about pie for a second. No, not mathematical pi, just actual real edible pies. For Thanksgiving I'm in charge of making dessert, so I'll be bringing two pies, one pumpkin and one apple. Let's say that I sliced the apple pie into 12 pieces, and the pumpkin pie, since it held together better, into 18. Fast forward to the end of the evening. My pies were a big hit, and I have almost none left. In fact, all I have is three pieces of apple and four pieces of pumpkin. I want to combine the remaining slices into a single pie pan, so that they take up less space in the fridge. How do I figure out if my remaining pie will fit in one pan? Well, let's start by writing down the remaining amounts of pie in the form of fractions. Remember, one of the definitions of a fraction is parts of a whole, so let's apply that definition to figure out our starting fractions. The apple pie was cut into 12 pieces, and we have three... read more

War of the Worlds, by H.G. Wells, is classic science fiction. Written in 1924, it depicts the catastrophic and totally unexpected near-extinction of humanity by aliens from Mars. One of the main themes running through War of the Worlds is the idea that mankind's assumptions about their world, the universe and the nature of life are constantly being challenged. The main reason the martians' landing is so catastrophic to humankind is because the humans, by and large, have been lulled into a false sense of security. They believe they are capable of overcoming anything, that they are the most powerful beings in the universe, and as such are completely unprepared for the martians' attack. Humans at the beginning of H.G. Wells's novel are portrayed as very self-satisfied. Even when confronted with the landing of the first martian cylinder, humanity is quick to dismiss the event as a mere curiosity. The story on the eve of the first day was “dead men from Mars,” (P. 14)... read more

Ragtime, by E.L. Doctorow, is a story about the American dream. Set in New York during the “period of Ragtime” between the turn of the 20th century and the beginning of World War I, Ragtime tells the story of three different families struggling to find their place in this new America. Doctorow makes use of an unusual writing style in Ragtime. He eschews the use of quotation marks and line breaks during dialogue, making the visual appearance of the novel one of long, blocky paragraphs. In addition, Doctorow writes the novel in third person from the perspective of not one but all of the main characters, allowing us to see the innermost thoughts and feelings of everyone in the story in turn. The characters have various degrees of name specificity, ranging from simply “Mother” and “Father” to “Sarah” (nobody knows her last name) to “Coalhouse Walker Jr.” All of these stylistic decisions come together to make a surprisingly fluid novel where actions speak much louder than... read more

Well, the new school year has started, and that means SAT test dates are fast approaching. In fact, the first one is this coming weekend. To anyone taking the SAT on Saturday, good luck! Remember to get a good night's sleep on Friday! If you are thinking about applying to college in the next few years, it might be time to schedule an SAT date! Remember, you can retake the test as many times as you need to, so don't be afraid to schedule an early date. Also, remember that the big SAT Redesign will be kicking into effect in the Spring of 2016, so if you are in the class of 2016 you may want to start your testing early, to make sure you have time to retake the current style of test and not have to relearn everything for a completely new test the following year. This semester's SAT test dates and registration deadlines are as follows: October 11th – Registration ends September 12th November 8th – Registration ends October 9th December... read more

Computerized spell-check can be a handy time-saver when writing papers, and many students swear by it. However amazing it may be, though, spell-check is still just a computer program, and as such should not be considered a substitute for proofreading with human eyes. As evidence, here are three common mistakes that spell-check won't catch. Proper Nouns Spell-check uses a dictionary to compare the words you type to existing words. Proper nouns, like names of people or places, usually won't be in the computer's dictionary, and so the spell-check will flag them as misspelled. This means that when you proofread, you'll have to ignore the wavy underline under those names. But this can also backfire – what if you happened to misspell that name? The computer will underline it same as before, but your brain is already prepared to ignore underlining on that name so you run the risk of not catching it yourself. This is one reason I advocate actually printing out a hard... read more

We recently passed the 30th anniversary of "the 2 Sigma Problem," which is the problem of achieving the effectiveness of personalized, one-on-one instruction at a large scale. As a tutor, how do you help multiple students at the same time while retaining the benefits of personalized tutoring? To me, one of the major benefits of personalized tutoring is that the tutor has the space, time, and flexibility to respond to the student's needs. If I am tutoring a student in math, we can spend as many sessions as we need on a given topic to make sure the student understands it thoroughly. I can also try a lot of different methods to explain a topic, since not everyone learns the same way. If a spatial or visual learner is having trouble with division, I might bring in a bag of M&Ms and show them physically the process of dividing up a pile into smaller piles. If a student is having trouble understanding probability, I might bring in a set of polyhedral dice... read more

Suppose I place you at one end of a long, empty room. Your task is to get to the door at the other end of the room. Simple, right? But what if I told you that this simple task is actually mathematically impossible? Think about it – in order to traverse the whole room, you first have to get to the halfway point, right? You'll have to travel one-half of the way there. And before you can get to that halfway point, you have to travel one-quarter of the way there (halfway to the halfway point). And before you can get to the one-quarter point, you have to travel one-eighth of the way there (halfway to the quarter-way point). Since you have to go half of each distance before you can go the full distance, you'll never actually get anywhere. The task requires an infinite number of steps, and you can never complete an infinite number of steps since there will always be another one. Furthermore, in order to even start your journey you would need to travel a specific distance, and... read more