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Explore the benefits of connecting mathematics and literature at the NCTM National Conference. Learn about reading mathematically, books about mathematics, and mathematical tools for analyzing text. Discover how literacy for mathematics can enhance student interest and understanding in both subjects.
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Connecting Math and Literature NCTM National Conference April 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.
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
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
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
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 son 1/5 to his second son 1/6 to his third son 1/10 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?
The Phantom Tollbooth by Juster Norton Concepts Infinity, 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?
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 Compass Dial 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
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 poetry Old 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
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 havesolved 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 CBC http://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
