Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Reading Mathematics is Different Presenter Judy Spicer Ohio Resource Center  September 30, 2009
<ul><li>Judy Spicer </li></ul><ul><li>Mathematics Teacher (Since forever!)  </li></ul><ul><li>Mathematics Content Speciali...
<ul><li>People are born with  innate number sense. </li></ul><ul><li>Mathematics is part of  everyday life . </li></ul><ul...
<ul><li>“ Reading mathematics” means the ability to </li></ul><ul><li>make sense  of everything that is on a page </li></u...
Obstacles to Reading Math <ul><li>Abstract concepts </li></ul><ul><li>Mathematical symbols </li></ul><ul><li>Word order </...
Figure 1.1. Confusing Terms, Formats, and Symbols in Mathematics                                                          ...
Rewards of Reading Mathematics  <ul><li>Motivating : The ability to read and understand the words and symbols makes mathem...
Interactive Elements of Reading Reader Reading and Writing to Learn in Mathematics: Strategies to Improve Problem Solving ...
Effective Literacy Instruction Provides <ul><li>Multiple exposures  to words and symbols through conversation, visual disp...
Strategies for Reading  <ul><li>Before reading : preview, activate prior knowledge, evaluate reason for reading  </li></ul...
Vocabulary Learning Strategies  <ul><ul><li>Provides authentic connections to previous knowledge </li></ul></ul><ul><ul><l...
Three-Column Entry  Word It usually means … In mathematics it means … Symbol Math meaning … Other meanings … . (decimal po...
Venn Diagram for Prime <ul><ul><ul><ul><ul><li>Prime  </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>English  Mathe...
An equation is a mathematical statement that shows that two expressions are equal. Facts/Characteristics 3x – 2 = 4x + 7 (...
My definition: Perpendicular  to Forms a 90   angle Illustration: Example(s) of Use: AB    CD Related words and symbols:...
 
<ul><li>Category: Whole Numbers  </li></ul>Semantic Feature Analysis Teaching Reading in Mathematics , ASCD, 2002 Features...
Using Literacy Strategies <ul><li>Introduce one strategy at a time. </li></ul><ul><li>Model and explain the use of a strat...
Problem Solving and Reading <ul><li>Five-Step Format </li></ul><ul><ul><li>Restate the problem (understand the problem) </...
Retrieved 9/2/09 http://ritter.tea.state.tx.us/curriculum/biling/teares-sims-ms-mm-TOT.pdf
Problem Solving <ul><li>K-N-W-S  and  KWC  </li></ul><ul><ul><ul><li>What facts do I  KNOW ?  Which info do I  NOT  need? ...
Problem Solving <ul><li>SQRQCQ  </li></ul><ul><ul><li>Survey :  Read  the problem quickly for general understanding.  </li...
Communicating Math Beyond the Classroom <ul><li>Make &quot;explain a solution&quot; to someone at home part of homework as...
Reading for Understanding  <ul><li>Coordinate nonfiction reading, including textbook reading, with  experiential learning ...
Resources <ul><li>In the NSDL Wiki  </li></ul><ul><li>See  MiddleSchoolPortal/Reading and Writing Mathematics </li></ul><u...
Upcoming SlideShare
Loading in …5
×

Reading Mathematics Is Different

4,166 views

Published on

These slides are from a webinar on why reading mathematics is challenging for many students and what teachers can do. We will examine how mathematics symbols, vocabulary, and content presentation can create roadblocks to students’ mathematics understanding. Learn how to address students’ difficulties by approaching mathematics as a language and to use specific strategies to improve mathematics learning.

Published in: Education, Technology

Reading Mathematics Is Different

  1. 1. Reading Mathematics is Different Presenter Judy Spicer Ohio Resource Center September 30, 2009
  2. 2. <ul><li>Judy Spicer </li></ul><ul><li>Mathematics Teacher (Since forever!) </li></ul><ul><li>Mathematics Content Specialist at </li></ul><ul><ul><li>Eisenhower National Clearinghouse (ENC) (1997-2006) </li></ul></ul><ul><ul><li>Ohio Resource Center (ORC) (2006-present) </li></ul></ul><ul><li>Reader beginning in the 4 th grade! </li></ul>No, I am not a pilot!
  3. 3. <ul><li>People are born with innate number sense. </li></ul><ul><li>Mathematics is part of everyday life . </li></ul><ul><li>Mathematics is more then mastering formulas and procedures. </li></ul><ul><li>Mathematics involves communication . </li></ul>As mathematics educators, we believe
  4. 4. <ul><li>“ Reading mathematics” means the ability to </li></ul><ul><li>make sense of everything that is on a page </li></ul><ul><li>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. </li></ul><ul><li> Teaching Reading in Mathematics , ASCD, 2002 </li></ul>
  5. 5. Obstacles to Reading Math <ul><li>Abstract concepts </li></ul><ul><li>Mathematical symbols </li></ul><ul><li>Word order </li></ul><ul><li>Mathematics textbooks </li></ul><ul><ul><ul><li>Literacy Strategies for Improving Mathematics Instruction , ASCD, 2005 </li></ul></ul></ul>
  6. 6. 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
  7. 7. Rewards of Reading Mathematics <ul><li>Motivating : The ability to read and understand the words and symbols makes mathematics accessible to students. </li></ul><ul><li>Empowering : Students are empowered because when reading they will engage with and make sense of mathematics. </li></ul><ul><li>Conducive to a student-centered learning : Students who are readers can be autonomous, self-directed learners. </li></ul>
  8. 8. 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
  9. 9. Effective Literacy Instruction Provides <ul><li>Multiple exposures to words and symbols through conversation, visual displays, readings, etc. </li></ul><ul><li>Authentic opportunities to use words and symbols in classrooms and to make appropriate connections for use in other contexts </li></ul><ul><li>Diverse texts , including literary and factual pieces, poetry, and visual materials, from which students draw words and phrases to study more carefully </li></ul><ul><li>Retrieved 9/21/09 http://www.adlit.org/strategy_library </li></ul>
  10. 10. Strategies for Reading <ul><li>Before reading : preview, activate prior knowledge, evaluate reason for reading </li></ul><ul><li>While reading : check understanding by paraphrasing, seek contextual clues for unfamiliar words, integrate information with prior knowledge </li></ul><ul><li>After reading : summarize, evaluate ideas and understanding, look for a broader perspective </li></ul><ul><li> Retrieved 9/21/09 http://www.adlit.org/strategy_library </li></ul>Literacy Strategies for Improving Mathematics Instruction , ASCD, 2005
  11. 11. Vocabulary Learning Strategies <ul><ul><li>Provides authentic connections to previous knowledge </li></ul></ul><ul><ul><li>Places vocabulary words and symbols in a meaningful context </li></ul></ul><ul><li>Makes vocabulary words and symbols visible </li></ul><ul><li>Examples: Concept maps, semantic feature analysis charts, word maps, and Venn diagrams allow students to learn word meanings and analyze structures. </li></ul>
  12. 12. 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
  13. 13. Venn Diagram for Prime <ul><ul><ul><ul><ul><li>Prime </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>English Mathematics </li></ul></ul></ul></ul></ul>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.
  14. 14. 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
  15. 15. 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
  16. 17. <ul><li>Category: Whole Numbers </li></ul>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
  17. 18. Using Literacy Strategies <ul><li>Introduce one strategy at a time. </li></ul><ul><li>Model and explain the use of a strategy in an activity that lets students see how and why to use it. </li></ul><ul><li>Let students apply it several times while you observe what they are doing and where they may need help. </li></ul><ul><li>Practice a strategy as a whole class before asking students to use it independently.  </li></ul>
  18. 19. Problem Solving and Reading <ul><li>Five-Step Format </li></ul><ul><ul><li>Restate the problem (understand the problem) </li></ul></ul><ul><ul><li>Analyze the problem (find needed data) </li></ul></ul><ul><ul><li>Solution plan </li></ul></ul><ul><ul><li>Find the answer </li></ul></ul><ul><ul><li>Check. Is the answer reasonable? </li></ul></ul><ul><li>See Adapting Literacy Strategies to Improve Student Performance on Constructed-Response Items ORC #11602 </li></ul><ul><li>See Roulette Problem Solving activity p. 7 ORC #11861 to give students a chance to collaborate and communicate while problem solving. </li></ul>
  19. 20. Retrieved 9/2/09 http://ritter.tea.state.tx.us/curriculum/biling/teares-sims-ms-mm-TOT.pdf
  20. 21. Problem Solving <ul><li>K-N-W-S and KWC </li></ul><ul><ul><ul><li>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? </li></ul></ul></ul><ul><ul><ul><li>What do I KNOW ? What do I WANT to find out? Are there special CONDITIONS that I have to look out for? </li></ul></ul></ul><ul><li>See Adapting Literacy Strategies to Improve Student Performance on Constructed-Response Items ORC #11602 </li></ul>
  21. 22. Problem Solving <ul><li>SQRQCQ </li></ul><ul><ul><li>Survey : Read the problem quickly for general understanding. </li></ul></ul><ul><ul><li>Question : Ask what information the problem requires. </li></ul></ul><ul><ul><li>Read : Reread the problem for information needed to find a solution. </li></ul></ul><ul><ul><li>Question : Ask what operations, in what order, should be performed. </li></ul></ul><ul><ul><li>Compute : Do the computation/construct a solution. </li></ul></ul><ul><ul><li>Question : Ask if the solution process seems correct and the answer reasonable. Requires rereading the problem again. </li></ul></ul><ul><li> </li></ul><ul><li>See Roulette Problem Solving activity in ORC #11861 to give students a chance to collaborate and communicate while problem solving. </li></ul><ul><li>Literacy Strategies for Improving Mathematics Instruction , ASCD, 2005 </li></ul><ul><li>Literacy Strategies for Improving Mathematics Instruction , ASCD, 2005 </li></ul>
  22. 23. Communicating Math Beyond the Classroom <ul><li>Make &quot;explain a solution&quot; to someone at home part of homework assignments. </li></ul><ul><li>Assign a &quot;Word Sleuth Team&quot; to research the word origins of a chapter's vocabulary. Be sure to check out The Lex Files http://www.lexfiles.info/ </li></ul><ul><li>Encourage students to find and report real world uses of mathematics </li></ul>Mathematical Literacy, Heinemann, 2008
  23. 24. Reading for Understanding <ul><li>Coordinate nonfiction reading, including textbook reading, with experiential learning activities . </li></ul><ul><li>Use prereading or text preview strategies to orient students to the text. </li></ul><ul><li>Model the use of literacy strategies with think-alouds, explicit strategy lessons, and guided instruction. </li></ul><ul><li>Teach vocabulary with attention to helping students learn word and symbol meanings and relationships. </li></ul><ul><li>Provide graphic organizers for note taking and synthesis of important information. Use writing frames, T-charts, and column notes to guide students through texts. </li></ul>
  24. 25. Resources <ul><li>In the NSDL Wiki </li></ul><ul><li>See MiddleSchoolPortal/Reading and Writing Mathematics </li></ul><ul><li>See MiddleSchoolPortal/Quantitative Literacy </li></ul><ul><li>Go to the Ohio Resource Center for high-quality, peer- </li></ul><ul><li>reviewed lessons aligned to Ohio and national standards, and </li></ul><ul><li>professional support materials. </li></ul><ul><li>Find all resources mentioned in this presentation at </li></ul><ul><li>Resources for Reading Mathematics Webinar </li></ul>

×