1. Mathematical Literacy: Reading and Writing Count in Mathematics Learning Julie Learned University of Michigan January 28, 2010

2. Learning Goals Define mathematical literacy Design instruction for translating across multiple forms of representation in mathematics Analyze mathematical texts and identify the reading demands students will encounter Use a variety of teaching tools to support students’ reading Design instruction for communicating mathematical understanding in writing

3. Agenda Mathematical Literacy Multiple Representations in Mathematics Mathematical Text Analysis Teaching Tools for Reading Comprehension Communicating Mathematical Understanding in Writing Teaching Tools for Writing

4. What is mathematical literacy? Review the following images and answer these questions: Is this mathematical literacy? Is the person engaged in an act of mathematical literacy?

5. Reading math textbook

9. World-famous mathematician, Qiu Chengtong, lecturing

11. What counts as mathematical literacy? Consider the images of people engaged in mathematical thinking, writing, reading, speaking, and problem solving Jot down your own definition of mathematical literacy

12. What’s unique about mathematics? Knowledge is certified by means of a deductive proof. Mathematicians make claims of absolute certainty. Words, terms, symbols, and diagrams have precise, shared meanings. Mathematicians navigate multiple symbol systems. Mathematical knowledge builds on and does not discard what came before. Mathematical research and literature is stable and reliable. The knowledge system must be free of logical contradiction. Adapted from mathematician, Dr. Hyman Bass, 2006

13. Mathematical Literacy Navigate across multiple symbol systems Read and make meaning with mathematical texts Understand and manipulate mathematical concepts to create mathematical arguments Communicate mathematical understanding Make sense and evaluations of “real-world” mathematics Engage in a way of knowing and seeing the world, a way of problem solving that goes beyond just doing the math

14. Multiple Representations in Mathematics - What’s the connection?

15. Navigating Multiple Representations Exercise 1 Reading Mathematical Texts Read each of the “texts.” List specific knowledge you put to use to understand what you read. List ways of reading and ways of knowing you use in order to understand.

16. Navigating Multiple Representations Exercise 2 Role Play Role play with a partner. Teach your partner how to make sense of the particular way in which each text represents a linear function. Include explanations of how you read each text. Articulate what you did as a reader to make meaning.

17. Navigating Multiple Representations Debriefing Exercises 1 and 2

18. Analyzing Mathematical Texts Complex word problems Examine the nature of the text Predict the relationship between text and reader Analyze and plan for relationships across texts

19. Text Analysis Homework 8: To Kearny by Equation Answer relevant text analysis questions with a partner Note Homework 8 is two pages Create a chart with your table that lists what you learned from the analysis (e.g., key text features, reading demands, challenging vocabulary, what students need to know before reading)

20. Text Analysis Debriefing Homework 8 Long text with a lot of mathematical information and multiple questions Lots of extraneous information Vocabulary: emigrants, ferries, Fort Laramie, Papan brothers, profit, expense Necessary knowledge: variables, substitution, manipulating equations, knowledge of Overland Trail, ability to connect math to “real-life” problems Multiple representations: words, equations, picture

21. Now what? Given the reading demands of the text, what do we do about it? Many ways to support students’ reading Choose based on what you know about the students, the text, and the context. Read aloud, underlining, pair and share reading, graphic organizer

22. Teaching Tool: Reading Mathematical Word Problems What is the word problem asking; what is the main question? List any words or concepts you do not understand. Get an explanation or definition. List all of the relevant, important information for this question. Answer the question using the relevant information. Show all of your thinking. You may use words, numbers, symbols, pictures, graphs, charts, and tables. Justify the mathematical approach you took to solve this problem. Write down any questions or confusion you still have about the problem.

23. Reading Mathematical Word Problems Homework 8 Use the graphic organizer to read and answer Question 1 or 2 in Homework 8. Assume you have a family unit of 14. Assume your group’s four family units have 52 people in total. When finished, debrief with a partner: in what ways might this support mathematical knowledge building and literacy?

24. Communicating Mathematical Understanding in Writing Deepens understanding Requires technical vocabulary Requires knowledge about how to structure mathematical arguments Requires opportunities to practice writing about mathematics

25. Teaching Tools for Writing 1. Best work reflections 2. Frayer model of concept development 3. Building vocabulary: word walls, word cards, word sort 4. Summarizing mathematics texts with GIST

26. Best Work Reflection How do you demonstrate your learning in this work? What academic strengths do you display in this work? How did you improve your skills and learning by completing this work? What learning from this work will you remember most at this time next year? How will you take your strengths from this work and apply them to other projects in or out of school?

27. Frayer Model of Concept Development Definition in your own words Characteristics ExamplesNon-examples Concept Adapted from Frayer, Federick, & Klausmeier, 1969

28. Frayer Model of Concept Development Example Definition in your own words A simple closed curve made up of three or more line segments Characteristics Closed; simple (curve does not intersect itself) 2 dimensional; 3 or more line segments Examples Square Triangle Rectangle Trapezoid Hexagon Non-examples Circle Cone Ray Pyramid Polygon

29. Building Vocabulary: Word Wall Organized collection of words displayed in large letters on wall Post vocabulary with precise, simple definitions Effectiveness depends on incorporating word wall into daily instruction

30. Building Vocabulary: Word Card Dictionary/Textbook Definition A three-sided polygon Everyday Definition The shape of a yield sign Diagram, Picture, or Illustration What the word is NOT Circle, rectangle, square Adapted from the Michigan Department of Education, Writing Across the Curriculum, 2009

31. Building Vocabulary: Word Sort I learned this in elementary I ’ ve heard this word I haven ’ t learned this yet Sum Multiplication Subtraction Dividend Divisor Equation Expression Solution Algebra Function Linear equation Quadratic equation Adapted from the Michigan Department of Education, Writing Across the Curriculum, 2009

32. Summarizing Mathematics Texts with GIST (Generating Interactions Between Schemata and Text) Read a portion of text, and write down important ideas and phrases. Using important ideas, write a summary in 15 words or less. Continue portion by portion for longer pieces of text. Write a short summary for the entire selection. Adapted from the Michigan Department of Education, Writing Across the Curriculum, 2009

33. Learning Goals Revisited Define mathematical literacy Design instruction for translating across multiple forms of representation in mathematics Analyze mathematical texts and identify the reading demands students will encounter Use a variety of teaching tools to support students’ reading Design instruction for communicating mathematical understanding in writing

34. Questions? Thank you! Julie Learned Jlearned@umich.edu