Connecting Math and Literature

NCTM National ConferenceApril 18, 2015

Pendred Noyce, MD

Where to get a handout

http://www.tumblehomelearning.com/nctm2015

A peripatetic approach

Why try to connect mathematics and literature?

What is reading mathematically? Books about mathematics. Books partially about mathematics. Books for which you can sneak in

some mathematics. Mathematical tools for looking at

text.

Stage, Asturias, Cheuk, Daro & Hampton, Science, April 2013

What is different about reading mathematically?

Words have different meanings, e.g. difference, common, rational, value.

Reading is not always linear, left to right and top to bottom.

Graphics require close attention. There is less room for intuition and

assumptions. Re-reading is critical.

Literacy for Mathematics

Mathematics as Language

Reading Writing Graphical

representation Discourse

English –Spanish mathematics dictionary from COMAP

Why connect mathematics and literacy?

Literacy for citizenship in today’s world needs to include numeracy.

There are many gateways to student interest. Affective connection to a field is vital. Stories can help.

Applying mathematical thinking to a piece of literature can open new perspectives.

Preschool and elementary

Make sense of problems Develop and use models Look for and make use of structure Look for and express regularity in

repeated reasoning. Obtain, evaluate, and communicate

information

From www.share2learn.com

Upper elementary/middle school

Build a strong base of knowledge through content-rich texts.

Ask questions and define problems Obtain, evaluate and communicate

information Obtain, synthesize, and report

information

Stories about mathematics

29 camels

Beremiz, leading his old camel, comes upon a caravanserai where four young men are arguing bitterly. Their father has just died, leaving behind 29 camels, His will leaves:

½ the camels to his first son1/5 to his second son1/6 to his third son1/10 to his youngest son.

The sons are arguing about how to divide the camels. They don’t want to butcher any? How does Beremiz solve the problem?

Novels partly about mathematics

The Phantom Tollbooth by Juster Norton

ConceptsInfinity, paradox, subtraction, fractional parts and averages, order of operations, platonic solids

Possible activities- Create the net of a dodecahedron and other platonic solids- Create a portrait of the “average” student in a group—height, letters in the last name, age in months, etc.- Solve the problem on page 186 (The Humbug cries out

“17!”)- What would happen if, in Subtraction Soup, Milo and his

friends ate negative numbers?

Subtraction Soup

Lost in Lexicon by Pendred Noyce

Concepts– Geometry, measurement, pi, Cartesian plane– Slope, transformations in the plane– 1729, propositional logic, number system,

infinity– Sexism in math and math anxiety

Possible activities– Deduce the approximate value of pi through

measurement. How did Archimedes estimate pi?

– Analyze the logical arguments in the chapter “Irrationality.”

– 1729 can be expressed as the sum of two cube numbers in two different ways. What are they?

The Algebraic CompassDial in two points. The compass points to the

slope between them.All villages in Lexicon have a number name

(ordered pair) as well as a word name.Slope is defined as “the number of leagues

you go north divided by the number of leagues you go east” to move from one point to another.

Explore the slope between towns. Is the slope the same in both directions?

Construct an algebraic compass, translating degrees to slope. www.lostinlexicon.com

Novels not about mathematics

Mathematizing Roll of Thunder

How big is 400 acres? (One acre = 43,560 sq. ft.) If the Logan land is ¼ mile long, how wide is it? How much cotton could grow on 400 acres?

What is a mortgage? How about property tax? Discuss percentage.

Suppose you boycott a store and have to pay 7% to get your food elsewhere. Based on what a typical family spends on groceries, how much more will you have to pay?

Mathematizing The Giver

In The Giver, any couple may raise children, but only some girls are given the adult role of Birthmother. Each Birthmother bears three children before she retires.

What percentage of girls will need to be Birthmothers for the population to remain steady?

What percentage of girls seem to become birth mothers in Jonas’ age group? Model what will happen to the population if this trend continues.

Population Growth #2

Two societies decide they want to control their population growth. In society A, each couple is allowed to have two children. In society B, each couple is allowed to keep having children until they have their first boy.

Which society will end up with more children? Which will end up with a greater proportion of boys?

Math Poetry?

from: Fermat's Last Theorem Poetry Challenge,

A Limerick by Ted Munger With an integer greater than 2 It's something one simply can't do. If this margin were fat, I'd show you all that, But it's not, so the proof is on you!

More math poetryOld Euclid drew a circle On a sand beach long ago He bounded and enclosed it With angles thus and so His set of solemn greybeards Talked and argued much Of arc and of circumference Diameter and such. A silent child stood by them From morning until noon Because they drew such charming Round pictures of the moon. -Vachel Lindsay

High school and beyond

Build a strong base of knowledge through content-rich texts.

Reason abstractly and quantitatively Construct viable arguments and

critique reasoning of others Demonstrate independence in

reading complex texts and in writing and speaking about them

Books about mathematicians and their

work

Books about mathematics

. . . and statistics

A story and some puzzles

Four Resources

www.InsideMathematics.org

Problems of the Month A problem that you can solve in less than a day

is usually similar to one that you have solved before.

Party Time Level A

Cindy had a party. She invited two guests. Her guests each invited 4 more guests, and each of those guests invited 3 more guests.

How many guests came to Cindy’s party? Explain how you found out.

Party Time Level C

Mia, Jake, Carol, Ford, Barbara and Jeff all go to a costume party. Figure out which costume each guest wore and in what order the guests arrived at the party.

The person that arrived fourth wore a bathing suit.Barbara was the last to arrive.Jake and Mia arrived and stayed together.The first person was dressed as a French maid.Superman arrived right before Barbara.The Potato Heads stayed together at the party.Ford was a Surfer Dude.The Vampire arrived after Superman.The French Maid was not Carol.

Party Time Level E

A man and his wife invite 5 other couples to a dinner party. As the guests arrive for appetizers before dinner, they shake hands. Not everybody shakes hands, and of course nobody shakes hands with his or her spouse. As they sit down to dinner, the host asks every other person, including his own wife, “How many hands did you shake?” To his surprise, he learns that each person shook a different number of hands.

How many hands did the host’s wife shake?

Other Resources

Mathical awards from MSRI and CBChttp

://mathicalbooks.org/portfolio/prize-winners/

Mathematical Fiction: Searchable lists and reviews.

http://Kasmana.people.cofc.edu/MATHFICT

For finding the math in middle school literature: https://www.chatham.edu/pti/curriculum/units/2009/LoAlbo.pdf