Reading Mathematics is DifferentPresenter
Judy Spicer
Ohio Resource Center
September 30, 2009
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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 4th grade!
No, I am not a pilot!
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• 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
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“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
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Obstacles to Reading Math
• Abstract concepts
• Mathematical symbols
• Word order
• Mathematics textbooks
Literacy Strategies for Improving Mathematics Instruction, ASCD, 2005
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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
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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.
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Interactive Elements of Reading
ReaderReading and Writing to Learn in Mathematics: Strategies to Improve Problem Solving (ORC#: 12736)
Classroom EnvironmentUnlocking the Mystery of Mathematics: Give Vocabulary Instruction a Chance (ORC#: 11864)
Text FeaturesGetting to Know Your Middle Grades Mathematics Textbook (ORC#: 9282)
Teaching Reading in Mathematics, ASCD, 2002
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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
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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
Literacy Strategies for Improving Mathematics Instruction, ASCD, 2005
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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.
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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
Three-Column Entry
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Venn Diagram for PrimePrime
English Mathematics
Something that is firstand 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.
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An equation is a mathematical statementthat 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
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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
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Category: Whole Numbers
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
Teaching Reading in Mathematics, ASCD, 2002
Semantic Feature Analysis
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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.
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Problem Solving and ReadingFive-Step Format
1. Restate the problem (understand the problem)
2. Analyze the problem (find needed data)
3. Solution plan
4. Find the answer
5. 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.
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Retrieved 9/2/09 http://ritter.tea.state.tx.us/curriculum/biling/teares-sims-ms-mm-TOT.pdf
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Problem SolvingK-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
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Problem SolvingSQRQCQ
– 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.
Literacy Strategies for Improving Mathematics Instruction, ASCD, 2005
Literacy Strategies for Improving Mathematics Instruction, ASCD, 2005
- www.msteacher2.org
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
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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.
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ResourcesIn 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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