Reading Mathematics Is Different

Reading Mathematics is Different Presenter Judy Spicer Ohio Resource Center September 30, 2009

Judy Spicer
Mathematics Teacher (Since forever!)
Mathematics Content Specialist at
Eisenhower National Clearinghouse (ENC) (1997-2006)
Ohio Resource Center (ORC) (2006-present)
Reader beginning in the 4 th grade!
No, I am not a pilot!

People are born with innate number sense.
Mathematics is part of everyday life .
Mathematics is more then mastering formulas and procedures.
Mathematics involves communication .
As mathematics educators, we believe

“ Reading mathematics” means the ability to
make sense of everything that is on a page
whether the page is a worksheet, spreadsheet, overhead transparency, computer screen, or a page in a textbook or journal—in other words, any resource that students might use to learn and apply mathematics.
Teaching Reading in Mathematics , ASCD, 2002

Obstacles to Reading Math
Abstract concepts
Mathematical symbols
Word order
Mathematics textbooks
Literacy Strategies for Improving Mathematics Instruction , ASCD, 2005

Figure 1.1. Confusing Terms, Formats, and Symbols in Mathematics Literacy Strategies for Improving Mathematics Instruction , ASCD, 2005 Literacy Strategies for Improving Mathematics Instruction , ASCD, 2005

Rewards of Reading Mathematics
Motivating : The ability to read and understand the words and symbols makes mathematics accessible to students.
Empowering : Students are empowered because when reading they will engage with and make sense of mathematics.
Conducive to a student-centered learning : Students who are readers can be autonomous, self-directed learners.

Interactive Elements of Reading Reader Reading and Writing to Learn in Mathematics: Strategies to Improve Problem Solving (ORC#: 12736) Classroom Environment Unlocking the Mystery of Mathematics: Give Vocabulary Instruction a Chance (ORC#: 11864) Text Features Getting to Know Your Middle Grades Mathematics Textbook (ORC#: 9282) Teaching Reading in Mathematics , ASCD, 2002

Effective Literacy Instruction Provides
Multiple exposures to words and symbols through conversation, visual displays, readings, etc.
Authentic opportunities to use words and symbols in classrooms and to make appropriate connections for use in other contexts
Diverse texts , including literary and factual pieces, poetry, and visual materials, from which students draw words and phrases to study more carefully
Retrieved 9/21/09 http://www.adlit.org/strategy_library

Strategies for Reading
Before reading : preview, activate prior knowledge, evaluate reason for reading
While reading : check understanding by paraphrasing, seek contextual clues for unfamiliar words, integrate information with prior knowledge
After reading : summarize, evaluate ideas and understanding, look for a broader perspective
Retrieved 9/21/09 http://www.adlit.org/strategy_library

Vocabulary Learning Strategies
Provides authentic connections to previous knowledge
Places vocabulary words and symbols in a meaningful context
Makes vocabulary words and symbols visible
Examples: Concept maps, semantic feature analysis charts, word maps, and Venn diagrams allow students to learn word meanings and analyze structures.

Three-Column Entry Word It usually means … In mathematics it means … Symbol Math meaning … Other meanings … . (decimal point) separates units and tenths digits separates integer part (left) from fractional part (right) indicates end of sentence can mean to multiply when in different position relative to numbers

Venn Diagram for Prime
Prime
English Mathematics
Something that is first and special Mathematical Literacy , Heinemann, 2008 Something that is of first quality, prime meats or prime number Prime numbers are the first, most basic numbers and are special. Every number is prime or can be factored into primes See Sorting Polygons ORC# 1163 for a math vocabulary lesson linking geometry to probability and statistics.

An equation is a mathematical statement that shows that two expressions are equal. Facts/Characteristics 3x – 2 = 4x + 7 (linear equation) ab = ba (an identity) F = 1.8C + 32 (a formula) 5 + 6 = 11 (a number statement) P = 2l + 2w (a formula) x = 3 (statement of value) Non-examples Frayer Model 2x + 3y (expression) 3 (number) perimeter (word) x < y (inequality) = 4.2 (has no left side) Equation -always has exactly one equal sign - the left side is equivalent to the right side - some equations have 0, 1, 2 or more solutions - some equations contain just numbers - some equations are algebraic models of relationships with corresponding graphical and numerical models (e.g., tables) Examples Definition Retrieved 9/24/09 http://oame.on.ca/main/files/thinklit/FrayerModel.pdf

My definition: Perpendicular to Forms a 90  angle Illustration: Example(s) of Use: AB  CD Related words and symbols: Symbol :  Modified Frayer Model two legs of triangle form a right angle & are perpendicular

Category: Whole Numbers
Semantic Feature Analysis Teaching Reading in Mathematics , ASCD, 2002 Features/ Properties prime perfect deficient abundant square triangular Terms 2 x x 3 x x x 4 x x 5 x x 6 x x 7 x x

Using Literacy Strategies
Introduce one strategy at a time.
Model and explain the use of a strategy in an activity that lets students see how and why to use it.
Let students apply it several times while you observe what they are doing and where they may need help.
Practice a strategy as a whole class before asking students to use it independently.

Problem Solving and Reading
Five-Step Format
Restate the problem (understand the problem)
Analyze the problem (find needed data)
Solution plan
Find the answer
Check. Is the answer reasonable?
See Adapting Literacy Strategies to Improve Student Performance on Constructed-Response Items ORC #11602
See Roulette Problem Solving activity p. 7 ORC #11861 to give students a chance to collaborate and communicate while problem solving.

Retrieved 9/2/09 http://ritter.tea.state.tx.us/curriculum/biling/teares-sims-ms-mm-TOT.pdf

Problem Solving
K-N-W-S and KWC
What facts do I KNOW ? Which info do I NOT need? WHAT does the problem ask me to find? What STRATEGY /operation/tools can I use to solve the problem?
What do I KNOW ? What do I WANT to find out? Are there special CONDITIONS that I have to look out for?
See Adapting Literacy Strategies to Improve Student Performance on Constructed-Response Items ORC #11602

Problem Solving
SQRQCQ
Survey : Read the problem quickly for general understanding.
Question : Ask what information the problem requires.
Read : Reread the problem for information needed to find a solution.
Question : Ask what operations, in what order, should be performed.
Compute : Do the computation/construct a solution.
Question : Ask if the solution process seems correct and the answer reasonable. Requires rereading the problem again.

See Roulette Problem Solving activity in ORC #11861 to give students a chance to collaborate and communicate while problem solving.

Communicating Math Beyond the Classroom
Make "explain a solution" to someone at home part of homework assignments.
Assign a "Word Sleuth Team" to research the word origins of a chapter's vocabulary. Be sure to check out The Lex Files http://www.lexfiles.info/
Encourage students to find and report real world uses of mathematics
Mathematical Literacy, Heinemann, 2008

Reading for Understanding
Coordinate nonfiction reading, including textbook reading, with experiential learning activities .
Use prereading or text preview strategies to orient students to the text.
Model the use of literacy strategies with think-alouds, explicit strategy lessons, and guided instruction.
Teach vocabulary with attention to helping students learn word and symbol meanings and relationships.
Provide graphic organizers for note taking and synthesis of important information. Use writing frames, T-charts, and column notes to guide students through texts.

Resources
In the NSDL Wiki
See MiddleSchoolPortal/Reading and Writing Mathematics
See MiddleSchoolPortal/Quantitative Literacy
Go to the Ohio Resource Center for high-quality, peer-
reviewed lessons aligned to Ohio and national standards, and
professional support materials.
Find all resources mentioned in this presentation at
Resources for Reading Mathematics Webinar

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Reading Mathematics Is Different

by The Ohio State University, College of Education and Human Ecology

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