1. The book I chose to study for this blog post is Jon
Scieszka and Lane Smith’s Math Curse. A
favorite childhood book of mine, the story begins with our protagonist starting
his day off in elementary mathematics in school. His math teacher Ms.
Fibonacci, stats innocently one day during her class that “You know, almost
everything in life can be considered a math problem”, on page 2 of the book
this begins his downward spiral into the curse of math. Upon the next morning
our young protagonist awakens to a series of problems that involve his ability
to be adequately prepared for school in time. The bus comes to pick him up at
8:00 am, but he has to brush his teeth, get dressed, and eat breakfast. A
sleepy, math baffled brain, begins to wander and ask itself confusing
questions, such as why he still has that ugly Christmas sweater from Uncle
Zeno. Our protagonist continues on to go into his kitchen and grab some cereal.
Surprise however, even cereal can be viewed as a math problem. He begins to
question how many quarts make up a pint, and how many flakes go into a bowl of
cereal. The protagonists thinks better of this than spending his entire morning
trying to find problems to figure this out, he heads to the school bus for
school.
As he
arrives on his school bus, it too becomes a math problem. At every stop the
same amount of kids get on, but he needs to know how to determine the bus driver’s
name. Further, he becomes preoccupied with the number of birthdays in his class
and trying to figure out why they closely resemble a row of buildings when
presented in a bar graph.
Once in
class an entirely new series of problems begins to present itself to our
protagonist. There are 24 kids in his class, and he begins to question how many
pairs of eyes there are in the class, along with tongues, and ears. Our young
hero also begins to wonder how many ways are possible to re-arrange the
structure of the room. You could use three rows, two rows, and so on. He is
about to drive himself crazy, but fortunately the lunch bell rings. In his
school they are serving pizza, which is cut into eight slices, and apple pie,
cut into six slices, for lunch. How many ways can he ask for two slices of
pizza? Further, which is better a half of a pizza or a half of a pie, he
wonders to himself. Fortunately they had not gotten to the fractions unit, so
our hero decides to take twelve carrot sticks, three at a time and eat them two
at a time.
Back in social
studies class, however, it too becomes a mathematical cascade of information. The
hero is faced with a geography problem to calculate how many M&M’s® it would require
to measure the length of the Mississippi river. He knows that 1cm=1M&M and
that 1km=1,000cm. But gets distracted wondering how many M&Ms one could eat
out of the amount it takes to measure the Mississippi river. English class
becomes a series of world problems. For example, does mail + box=mailbox? Or
does lipstick- stick = lip? Physical education becomes no easier as this class
becomes a series of sports problems dealing with comparisons of Babe Ruth’s
batting average and salary paid, to the average baseball player’s salary and
batting average in 1991. He hoped to relax in art class where they were allotted
time to do a connect the dot puzzle. Unfortunately for our hero, it is an
ancient Mayan numerals connect the dot puzzle.
Back in Ms.
Fibonacci’s class the students go over the ways they count. One simply counts
by one’s on each finger, adding up to 10. Another student counts by twos adding
up to ten, while Ms. Fibonacci recites the first few numbers of the Fibonacci
number sequence. Further, our hero wonders what aliens with only two fingers
count, or what aliens on the planet binary count to. Apparently it’s ‘1, 10’.
Following this our protagonist finds the class is having problem with
determining what portion of cupcakes each student will receive if there are 25
people and only 24 cupcakes. Our hero graciously states that he is allergic to
cupcakes, and therefore will not need one, reducing the number to equilibrium at
24=24.
Leaving
class the hero wants to buy his favorite candy bar to help him with his qualms.
Unfortunately, however, it is 10% of its usual sale price of $0.50. He gets
confused in calculating how much it will cost now, and even cites the quadratic
formula to calculate an answer. He pulls out of his pocket a $5 bill, $1 bill,
$0.25 and $0.01. He begins to ponder how many $1 are equal to a $5 bill and if
Thomas Jefferson is upset he is not on any of the commonly used bills of money.
Returning
home our hero is convinced he is becoming a math zombie. He begins to fret that
his will keep up an entire year as he grumbles this as an answer when his
sister snarls at him asking what is wrong. He continues to deal with the
problem of figuring out if one of his parents is speaking the truth or not at dinner
and more mathematical problems when he gets prepared for sleep. His dreams,
however, are no vacation. He is trapped in a chalk-board room full of
mathematical problems. In his hand he holds a piece of chalk and realizes that
if he breaks it in two he can create one ‘hole’ and jump out. He’s free from
his curse!
He awakens
the next morning with no mathematical concepts or problems running through his
head and gets ready for school without any problems. Everything goes well until
in science class Mr. Newton says “You know, you can think of pretty much anything
like a science experiment”.
2. With no overarching theme, the book Math Curse deals with a multitude of mathematical concepts.
The first
one we will examine is the linear function that occurs when our hero gets on
the bus. As stated in the example, when he gets on the bus five kids get on we
will assume that the base number of kids is 0. Following this, five more kids
get on at the next two stops. Even with little information, it can be
reasonably inferred that the function for this linear function is represented
by f(x) =y= 5(x).
The above equation shows that y is
the number of kids on the bus, ‘0’ is our y-intercept, and ‘x’ represents the
bus stop.
This function works properly assuming that there are no
negative stops occur and all the values of ‘x’ are above 0.
After each stop 5 kids get on the bus. Therefore every stop
adds five more kids to the bus until it reaches its full capacity. This is a
great example of a linear function.
The next
example we will look at is when our hero walks into class and begins to think
about all the ways to redefine the room he lives in. This is a proper example
of domain and range, as we assume that the room is a box. Given these
parameters, and as our protagonist stated, the lowest number of rows we can
have is 2. We also know there are 24 kids in his class, which is our highest
bound.
(Rows) Therefore our domain function is Interval Notation: [2, 24]
Set-Builder Notation {XeN I 2 < X < 24}
(Columns) Therefore our range function is Interval Notation: [24, 2]
Set-Builder
Notation {YeN I 24< Y < 2}
The book does a good job of displaying the domain and range
of the function because it allows for us to see that only natural numbers can
be used. This is because we cannot have a negative value for X or Y, nor can it
be an irrational or rational value. An interesting example of both domain and
range dealing with a real world issue of how many rows and columns of seats to
set up creates a nice answer for our domain and range.
3. I believe that it is important and effective way to teach
mathematics in literature because it makes the mathematics enjoyable. It does
so by providing an interesting array of photographs and an enticing storyline
to accompany the mathematical equation. It is proven in many psychological
studies that people tend to learn best when there is an image to accompany the
concept one is trying to learn. For example, the image of the bus may be able
to help someone remember the idea of a linear function when they get older.
I also
believe that using literature to represent mathematics is important because it
helps to create a tangible example for learning mathematics when one grows up.
I find, personally, the biggest problem when studying for a test dealing with
mathematics may be a lack of examples. In literature, however, there are a ton
of examples such as in Math Curse. This
is why it is important to use literature to help teach mathematics.
This is so intense and long. Good job on actually explaining the whole book, i got a really good understanding of it based on your explanation/synopsis. Also your equations mentioned above and set of notations are explained really well. Seems like you actually took a good amount of time doing this and really trying to bring out the math within.
ReplyDeleteAs you said, I also agree that, psychologically, presenting a concept with an image helps an individual retain any concept. Of course, you are right--this goes for mathematical concepts such as linear functions and domain and range. However, this can also help with remembering names, faces, and lists, etc.
ReplyDeleteI was also interested in your explanation of domain and range and set-builder/interval notation. You did a fantastic job at applying concepts learned in class to situations within the book. Your explanations are very clear and rather helpful.
scott,
ReplyDeletereally great job of explaining the plot of this story in detail. i think i love the most how you broke down some of the concepts in the text in a way that we would see them symbolically in our math class. i entirely agree that many people learn such concepts much better when they can attach an image to it. also, doesn't ms. fibonacci have the best name?
professor little