Math in The Simpsons

I'm not really sure what to write about for this week so I decided to write about something that I find interesting and that may be interesting to other students in our class and even perhaps interesting to junior high and high school students.

The Simpsons is a popular TV sitcom that is not necessarily directed for young children but is aimed at older children and adults, some may find the content humorous and entertaining while others may think the content isn't fit to be on TV and the common catch phrase from Bart Simpson, "Eat my shorts", is nothing more then teaching young children to be brazen and ignorant. Some others may also think of the cartoon within the show Itchy and Scratchy is nothing more then a form of violence that teaches children that is is ok for a mouse to shoot at a cats head with a cannon, place a cat in a blender and then serve him as a drink, pour spiders on his head that eat his flesh, or hang him by his intestines into a volcano of hot lava.

I do understand where the parents of young children would be concerned about these issues however The Simpsons is the longest running sitcom of all time. It has been running in prime time television for the last 20 years, they must be doing something right. In fact The Simpsons has a large reference to various academic subjects including mathematics. It contains over one hundred references to math that range from arithmetic to geometry to calculus. Many of these references are aimed to poke fun at innumeracy.

Al Jean is the current Executive Producer and Head Writer of The Simpsons and has been involved with The Simpsons since the show began in 1989. He graduated from Harvard University in 1981 with a Bachelor of Mathematics. Ken Keeler was a writer for The Simpsons from 1994-1998. He graduated from Harvard University in 1983 with a Bachelor of Applied Mathematics and later received his Ph.D in Mathematics in 1990 (also from Harvard). J. Stewart Burns graduated from Harvard University in 1992 with his Bachelor of Mathematics, and his Masters Degree from UC Berkeley in 1993, he began working on The Simpsons in 2002 after he got his start on another cartoon show, Futurama.

Other members of The Simpsons staff have a physics degree, Ph.D in inorganic chemistry, and Ph.D in computer science. These multiple areas of academics are represented directly in the show by Professor Frink, the local Springfield Scientist.

examples from the show:

Bart the Genius (1/14/1990)
Bart reads a math problem out loud, and then day dreams about it.
Bart: 7:30 am an express train travelling 60 miles per hour leaves Santa Fe bound for Phoenix,
Train conductor: Ticket please!
Bart: I don't have a ticket!
Train conductor: Come with me, boy.
[ Train conductor drags Bart off, numbers circle around Bart's head]
Train conductor: We've got a stowaway, sir.
Bart: I'll Pay! How much?
[the train engineer is Martin, shoveling numbers into the engine]
Martin: Twice the fare from Tucson from Flagstaff minus two-thirds of the fare from Albuquerque to El Paso! Ha ha ha ha!

Dead Putting Society (11/15/1990)
Lisa: And I'm studying for the math fair, If I win, I'll bring home a brand new protractor.
Homer: Too bad we don't live on a farm.

Dead Putting Society (11/15/1990)
Lisa, armed with a measuring tape, helps Bart play miniature golf.
Lisa: The basis of this game seems to be simple geometry. All you have to do is hit the ball...here.
[The ball is hit, gets bounced around, and goes into the hole.]
Bart: I can't believe it. You've actually found a practical use for geometry!

Springfield (12/16/1993)
[After putting on Henry Kissinger's glasses, found in a men's room toilet]
Homer: The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.
Man in stall: That's a right triangle, you idiot!
Homer: D'Oh!

This carries on throughout all 20 years that the show has been produced, and it covers many topics from the basics of mathematics, 2+2=4, in one show to talking about the Pythagorean Theorem and 3 dimensional space. The Simpsons is intended for a more mature audience and should not been shown to younger children without adult supervision. It contains many inside jokes and academic content that is directed at an older audience

(This information was written with the help of Simpsons Math http://www.mathsci.appstate.edu/~sjg/simpsonsmath/)

Problem Solving

In the past few classes we have been looking at problem solving, mainly for the purpose of our own problem solving session in class, but also to teach us how to use it in the classroom. I think problem solving in the primary/elementary years of school is very important.

When you ask students to solve problems in class it can be done in several different ways. The first way is that you can give specific details for a problem and students will have figure out the answer based on the information they are given. Another way is to give students open ended questions that have multiple answers, students are able to look at all different perspectives and possibilities. Some students will have their mind set on one answer and one answer only and not be able to broaden their perspective to look at the problem in a different way.

Getting students to work in pairs or groups is a good way to get students to look at the problem in another way. When students bounce ideas off each other they are likely to come up with their own solutions and solutions that neither student would have came up with on their own.

Grouping students is also a good way to get them to understand a new concept, I remember in school my teacher used to explain a new topic and give us a few example problems and then group us into pairs or groups of three so we could discuss the topic and explain it to each other, this method gave us a new view if we didn't understand it or explaining it to our group helped us remember it ourselves. Then we could work on problems together to make sure everyone got the concept.

Observation Day Math

Each Friday of this semester the students of Memorial University's Primary/Elementary Consecutive Program participate in observation days at various local schools. So far I have completed five of these observation days and have seen math being taught during four of them. I am shocked when classmates come back to class and tell us that they are yet to see any regular math happening in classrooms.

As a math major I am very pleased to see as much math happening in schools as possible, I get quite excited when I able to get involved in students' learning experiences. During the first observation day I was able to observe a class of grade 2 students who were learning about patterns. The teacher first explained to the students what the elements of a pattern were and then what the core of the pattern was. The teacher then modeled several patterns using connector blocks and asked the students to tell what the elements were and what the core was. Once the students had seen many examples of patterns the teacher then placed them into groups and gave each group different manipulatives to make their own patterns. Students were given connector blocks, colored wooden blocks, linking chains, etc... Once they had mastered the process of making patterns the teacher then made a request of what type of pattern she wanted each group to make. For example a pattern that contained 3 elements and had a core of size 4 repeated 5 times could be in general ABBCABBCABBCABBCABBC.

The second observation day I was in a grade 1 classroom where the teacher let me get involved in her math lesson. I stood in front of the class and held up paper plates with colored stickers on them, the plates had 1-10 stickers on them. Some plates had all one color and some plates and two different colored stickers on them. Each student had their own cards with the numbers 1-10 on them and had to count the stickers and then hold up the number that represented how many stickers were on the plate. This was nice because it familiarized students with the numbers 1-10 and also started them on addition. For example a plate with 6 blue dots and 2 red dots had a total of 8 dots.

The third class I observed was a special education class, this class I did not see any math since Fridays are "games day" for the students. These students are only in this class for one or two periods a day and usually need more help with language arts activities. However I did get to see some very interesting games that were educational for the students, there was a game that focused on phonics, a game that focused on sentence formation, picture bingo, and of course one of my favorites, Scattergories.

The fourth week of observation I was in a class of grade 6 students. This was a great experience for me. First thing in the morning the teacher gave me the guide to the math book and asked if I would correct a few questions that the students were supposed to have done previously and then teach the next section. I was thrilled about this :) He gave me sufficient time to get my thoughts together and understand what I was supposed to be teaching them, then while the students were in music class I was able to test out the SMART board for the very first time and see how it worked. Once the students returned I started correcting the questions and then taught them how to compare very large numbers (in the millions). As I was conducting the lesson the teacher wrote down comments about my lesson, and during lunch he gave me a sheet full of wonderful feedback. I thought this was a great idea, it let me know what I was doing right, what I should keep doing, and what I need to improve on.

Last Friday was the fifth week of observation and I was in a grade 3 classroom, this was a bit of a difficult day for me. The regular teacher was out sick and I was observing a substitute, this was nice because I got to see what it was like to be a substitute walking into a classroom and having to pick up where someone else left off. However the students do tend to give substitutes a bit of a harder time, they push the limits to see what they can do without getting in trouble. The math lesson was supposed to be on estimating and rounding off numbers to the nearest 10, but I don't think it was a very successful lesson. This seemed to be a new topic for students and they were very confused as too why certain numbers round down and not up. This was not explained to them very well because the substitute hadn't realized it was totally new to them. I think If I was in his shoes I would have noticed the students were having difficulty and went back and explained how rounding works in a different way so more students would understand better.

Overall I have seen quite a bit of math during my observation days and quite pleased with the results, When I become a teacher I would hope that I would be able to not only conduct a math lesson but bring a little bit of math into the other subjects as well, like in language arts you can read books that have some math in them, or even in the younger grades you can count how many days you have been in school since the start of the year.

What is mathematics?

I was one of those students in school who always ask "why?". Sometimes I didn't get an answer as to why things were they way they were, sometimes I did get the answer and even sometimes I got a delayed answer that may have just had to wait a class or two. My experiences growing up were good and I was really interested in math, so when I got older and went to university I decided to find out "why" for myself. After four years of a math degree I still can't give you an exact definition of what math is because math is complex and many people look at math in different ways.

Throughout elementary school students were expected to learn how to add and subtract, and multiply and divide using a given algorithm to find an answer and then they were tested with pencil and paper on how well they had mastered this procedure. The same is true for junior high and high school. Math wasn't made to be fun, it was taught as one subject that was separated from all other subjects. Students mostly thought that math was memorizing formulas and then solving problems with these formulas to get one particular answer. Chances are if you were a student who solved a problem in a different way then was expected, you may have gotten it marked wrong. But the truth is that math is not a subject that should be separated from everything else and it's not just having a formula and answering a question to produce an answer, in fact there are many branches of math such as geometry, patterns, counting, sequencing, algebra, graphing, etc.. Some of these involve formulas and some don't, and if they do involve formulas then there may be more then one way to solve the problem. Many students would try to memorize what they were doing and not fully understand it, therefore they would get very confused and end up not liking math.

In his talk "What Kind of Thing is a Number?", Reuben Hersh states "Mathematics is neither physical or mental. It's part of culture, it's part of history, it's like law, like religion, like money, like all those very real things which are real only as part of collective human consciousness". I think this is a good way to describe math, it is not internal or external, it is both, it's a concept that people follow, and it's involved in your everyday life whether you realize it or not. He later states "A good math teacher starts with examples. He first asks the question and then gives the answer, instead of giving the answer without mentioning what the question was." As a teacher I hope to give my students the ability to understand what it is they are doing and let them think for themselves, I would like to per mote cooperative learning and let the students discuss among themselves why things are they way they are, and make meaning of the answers they are producing. I will at first give them a question and give them time to think about it before talking about the question as a whole and then showing them the solution.

During class we read the book "Math Curse" by Jon Scieszka and Lane Smith. I highly enjoyed this book, I usually get excited when I see books directed at younger children about math. The main reason for this is because I don't remember reading anything like this when I was young and I think it is a great way to get young students involved and interested in learning math. Math is a universal concept that is involved in everyday life and this is represented in the book when Mrs Fibonacci tells the class "You know, you can think of almost everything as a math problem..." This book has one student in a whirl-wind of thoughts about math and she thinks about EVERYTHING as a math problem.

These are my thoughts and views on what math could be but there is still alot to learn and knowledge to be gained in the coming years of my career.