reading mathematics is different

Reading Mathematics is DifferentPresenter

Judy Spicer

Ohio Resource Center

September 30, 2009

- www.msteacher2.org

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!


• 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




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

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)


http://ohiorc.org/record/12736.aspx









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.


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


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.



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


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

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


Semantic Feature Analysis


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 ReadingFive-Step Format

1. Restate the problem (understand the problem)2. Analyze the problem (find needed data)3. Solution plan4. Find the answer5. 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.


http://ohiorc.org/search/results/default.aspx?searchInterface=advanced&txtNumber=&txtSearchText=&ddlSearchType=any&txtSearchText2=Roulette&txtSearchText3=&ddlField2=3&ddlField3=2&ddlSearchType2=phrase&ddlSearchType3=any&chkDiscMath=False&chkDiscReading=Fal


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


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



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.



http://ohiorc.org/search/results/default.aspx?searchInterface=advanced&txtNumber=&txtSearchText=&ddlSearchType=any&txtSearchText2=Roulette&txtSearchText3=&ddlField2=3&ddlField3=2&ddlSearchType2=phrase&ddlSearchType3=any&chkDiscMath=False&chkDiscReading=Fal


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

http://www.lexfiles.info/


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.


ResourcesIn the NSDL Wiki See MiddleSchoolPortal/Reading and Writing MathematicsSee MiddleSchoolPortal/Quantitative Literacy

Go to the Ohio Resource Center for high-quality, peer-reviewed lessons aligned to Ohio and national standards, andprofessional support materials.

Find all resources mentioned in this presentation at Resources for Reading Mathematics Webinar

http://wiki.nsdl.org/index.php/MiddleSchoolPortal/Reading_and_Writing_Mathematics

http://www.ohiorc.org/

http://ohiorc.org/bookmark/view_a_folder.aspx?uid=5823&folderID=21367

reading mathematics is different

Education

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