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# Week 7: Intrinsically mathematical stories (February 27 - March 4)

Last week, we discussed intrinsically mathematical games: http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-6-say-say-oh-playmate-february-20-26/

What it means to be intrinsically mathematical? This is the heart of a major temptation of  elementary education!

Generic learing games, stories, movies or songs are much easier to produce than intrinsic ones. For example, it's easier to use Jeopardy or Trashcanball for every topic, rather than designing a game that is uniquely tied with this topic, like Tetris is tied with combinatorics and tilings: http://en.wikipedia.org/wiki/Tetromino

1. For a good summary and definitions of intrinsic games, read this current (2011) article by Kathleen Offenholley, using Dimension M and Ko's Journey as examples of generic and intrinsic game mechanics, much like the task last week. http://journals.tc-library.org/index.php/matheducation/article/download/716/446 We will ask Kathleen and other members of the Math Game Design group to comment on our examples at the end of this week. http://groups.google.com/group/mathgamedesign
2. Find an example of an episode of a story or a rhyme where mathematics is inserted in the "chocolate-covered brokkoli" manner. That is, the story elements, such as characters and events, are not closely tied with the math the story presents. Characters may be counting something, or solving a math puzzle, for example - which any characters can do.
3. Find an example of an episode where particular mathematics is intrinsically tied to the plot, is important for characters, and otherwise is central to how the story works. For example, the classic Hotel Infinity story is directly about the mathematics of intinity: http://scidiv.bellevuecollege.edu/math/infinitehotel.html On the other hand, Discworld novels by Terry Pratchett aren't all about mathematics, but they feature, for example, the fifth horseman named Kaos who uses a lot of infinity and complexity ideas in his dealings with the universe http://wiki.lspace.org/wiki/Kaos
4. (Bonus) Think of nursery rhymes and fairy tales. What math concepts do you see in them? For example, I can't help but view "Goldilocks" as a story about gradients.

You can think back to stories you read as kids, or head to a public library and ask for math stories. You can find an excellent list of math readers, both intrinsic and extrinsic, here: http://livingmath.net/ReaderLists/tabid/268/language/en-US/Default.aspx

# Discusión de la Tarea

• 1. One example of "chocolate covered broccolli" math would be the television show Lost. In the show, there is a series of numbers (4, 8, 15, 16, 23, 42) which constantly appear, and each one is assigned to one of the characters. To avoid setting off an alarm, the characters have to punch the numbers into a computer once every 108 minutes, 108 being the sum of all the numbers. While this series of numbers affects the characters, the math behind it takes a backseat to the significance of the assignment, rather than the assignment itself.

2. One movie where math is the central idea is The Number 23. This movie is heavily based on numerology, as the main character believes he is haunted by the number 23 in all of his actions. His paranoia drives him crazy, and the more he thinks about it, the more he sees the number everywhere, and looks for increasingly complex ways to derive the number 23 out of anything. This man bases his story off of his math and plays off the numbers.

Bonus:

I think of "There Was An Old Lady Who Swallowed A Fly" as a nursery rhyme involving math. Here's a bit of it:

There was an old lady who swallowed a fly
I don't know why she swallowed a fly - perhaps she'll die!
There was an old lady who swallowed a spider,
That wriggled and wiggled and tiggled inside her;
She swallowed the spider to catch the fly;
I don't know why she swallowed a fly - Perhaps she'll die!
There was an old lady who swallowed a bird;
How absurd to swallow a bird.
She swallowed the bird to catch the spider,
She swallowed the spider to catch the fly...

This could be perfect for a lesson on greater than or less than. Each verse, the old lady swallows something slightly bigger than the last animal, like Russian Nesting dolls. The children could compare the animals, using signs for less than or greater than, based on the song. Or, one could count how many animals the woman has swallowed by the end, keeping a running track. I think there's a lot of potential in just one nursery rhyme!
•

1. Matilda is a movie I use to watch all the time when I was little. Math is definietly not the main plot in this movie, but Matilda is very intelligent for her age. When asked to solve a math problem, she solves it in her head. The teacher jokingly says that soon the class wil be able to add to large numbers and Matilda answers the problem, again mentally. The teacher checks the problem and sees that Matilda is right. There are a few other time in the movie where Matilda uses her math abilities to solve problems, but this time she really floors the class and teacher.

2. One of my favorite movies is A Beautiful Mind, which is about a mathematician who is struggling with schizophrenia. John, the main charcater, is a brilliant prize winning man and works and studeis at MIT, Princeton, The US Department of Defense and others. His ability to mentally solve problems amazes many. Again I absolutely LOVE this movie and although math may not arguably be the main story in this movie it definietly plays an integral part.

3. A nursery Ryhme that I found is Five Little Ducks...

Five little ducks went out to play
Over the hill and far away
The mother duck said Quack, Quack come back

Four little ducks came running back
Four little ducks went out to play
Over the hill and far away
The mother duck said Quack, Quack come back

Three little ducks came running back
Three little ducks went out to play
Over the hill and far away
The mother duck said Quack, Quack come back

Two little ducks came running back
Two little ducks went out to play
Over the hill and far away
The mother duck said Quack, Quack come back

One little duck came running back
One little duck went out to play
Over the hill and far away
The mother duck said Quack,Quack come back

No little ducks came running back
Sad mother duck went out one day
Over the hill and far away
The daddy duck yelled QUACK, QUACK COME BACK!

Five little ducks came running back!

This nursery rhyme incorporates counting down. The ducks each time decrease by one illustrating subtraction to young kids.

•

1. My first example would be the movie Good Will Hunting. The main character Will is gifted in mathematics and is considered a genius. He can solve any problem that comes his way but the main plot of the movie is that he struggles with his own personal life and needs help finding direction. He is forced to go to therapy and to study math or be sent to jail. The movie is heavily surrounded by Will’s work with math and one of his professors trying to get him to take advantage of his skills.

2. My example for intrinsic mathematics is the story of The Tower of Hanoi. The story says that in a temple in Benares there are 3 diamond needles where God placed 64 discs of pure gold on one of the needles. The largest plate is on the bottom and get smaller as it works its way up to the final disk on top. The priests in the temple must transfer all the discs to another needle without a larger disk being on top of a smaller disk. Not only is it a fun story but an interesting math problem for kids to work on!

3. One nursery rhyme that come to mind right away is One, Two, Buckle My Shoe.

One, two,

Buckle my shoe;

Three, four,

Knock at the door;

Five, six,

Pick up sticks;

Seven, eight,

Lay them straight:

Nine, ten,

A big fat hen;

Eleven, twelve,

Dig and delve;

Thirteen, fourteen,

Maids a-courting;

Fifteen, sixteen,

Maids in the kitchen;

Seventeen, eighteen,

Maids a-waiting

Nineteen, twenty,

My plate's empty

I always loved this as a little kid because it was a ton of fun. It is a great way for young children to learn to count and remember their numbers by singing!

• 1. Here's an example of a rhyme where mathematics has been snuck in. We have 4 and 20 blackbirds which I'm guessing equals 24 blackbirds, and the king counting his money:

Sing a Song of Sixpence

Sing a song of sixpence a pocket full of rye,
Four and twenty blackbirds baked in a pie.
When the pie was opened the birds began to sing,
Oh wasn't that a dainty dish to set before the king?
The king was in his counting house counting out his money,
The queen was in the parlour eating bread and honey
The maid was in the garden hanging out the clothes,
When down came a blackbird and pecked off her nose!

2. The first movie that comes to mind where the plot is tied in with math would be "Wargames" starring Mathew Broderick.  His charactor, David Lightman has to find a way to program the right formula into the military's central computer data base in order to prevent World War III from occurring. By punching in the right numbers he convinces the computer that it is impossible for anyone to win a nuclear holicost.

•

I think a good example is PI film.

Pi features several references to mathematics and mathematical theories. For instance, Max finds the golden spiral occurring everywhere, including the stock market. Max's belief that diverse systems embodying highly nonlinear dynamics share a unifying pattern bears much similarity to results in chaos theory, which provides machinery for describing certain phenomena of nonlinear systems, which might be thought of as patterns.

• 1. The children’s book Phantom Tollbooth by Norton Juster is a great example of math being inserted as part of the plot.  The main character, Milo, travels to a land called the Kingdom of Wisdom where he travels to the lands of Dictionopolis and Digitopolis.  In this story, everyone lived in harmony until the rulers disagreed with the princesses' decision that letters and numbers were equally important.  In Digitopolis, their first stop is the mine where numbers are dug out and precious stones are thrown away. Another example is that they eat subtraction stew, which only makes the diner hungrier. There is a  Mathemagician who erases the mine with his magic pencil eraser, he and Milo discuss the concept of Infinity. Milo proves to the Mathemagician that he must allow them to rescue the princesses (Princess Rhyme and Princess Reason).  It’s a great book that really makes math (and words) fun. I love this book as much as an adult as I did as a child.  It's full of really clever puns and concepts.

2. I think an example of this would be the book (and TV show) Numb3rs. This TV crime drama (premiered January 2005) follows the adventures of a pair of brothers, one a mathematics professor and the other an FBI agent, as they combine forces to solve mysteries. The least sensible aspect of it is that this one person, Charlie, knows everything about math and is amazingly fast at applying his knowledge to solve problems.  An example of how math is an integral part of the plot can be seen in Episode 1. The main character Charlie invents an algorithm for determining the likely location of the residence and workplace of a criminal by analyzing the crime patterns.

3. (Bonus)

I immediately thought of the jump rope rhymes children like to play such as “Cinderella dressed in yellow went upstairs to kiss her fellow. Made a mistake and kissed a snake. How many doctors will it take? 1-2-3, etc.   Counting is clearly the goal here.

The rhyme about St. Ives also comes to mind for its (potential) addition and/or multiplication and logic question at the end:  As I was going to St. Ives, I met a man with seven wives.  Every wife had 7 sacks, and every sack had seven cats.  Every cat had 7 kits.  Kits, cats, sacks, and wives, how many were going to St. Ives?

The fairy tale Little Red Riding Hood could be used to teach several math concepts: Measures (Not far (from); far; very far; the shortest road; the longest road; a long time; a small wooden box for butter; long arms; long legs; big ears; big eyes; big teeth; another village); number/quantity (Still more; more than three days); direction (to go through the wood; down); sequence (The first house of the village); and geometrical placement (above/over, under the blanket, on the chest, beside/ next to).