1. 1 Reading Mathematics Paul E. Smith

2. 2 Agenda The Unique Aspects of Reading Text Comprehension Strategies Vocabulary Strategies

3. 3 Mathematics Text Literacy Mathematics textbooks have fewer words per page than social studies text, so you can read them more quickly. You need to use different reading skills when you read your math textbook than the skills you use to read textbooks in other classes

4. 4 Mathematics Text Literacy Usually, you can skim over or skip most worded passages in math textbooks because the diagram, graphs, number lines, and symbols contain the most important information on the page The words in a mathematics text may not have the same meaning in another subject area textbook Mathematics is the most difficult content area for most students to read.

5. 5 How is Reading Mathematics Different? Reading mathematics is not always from left to right Mathematics texts contains more concepts per word, per sentence, and per paragraph than other text Writers of mathematics texts generally write in a very terse or compact style

6. 6 How is Reading Mathematics Different? Mathematics also requires students to be proficient at decoding not only words but also numeric and nonnumeric symbols Many mathematics textbooks are written above the grade level for which they are intended

7. 7 Reading Mathematics Require Decoding and comprehending what is read Planning for and monitoring the effectiveness of one’s reading Analyzing and evaluating the content in light of one’s prior knowledge, experiences and schemata Making inferences and generating conclusions based on the reader’s unique interpretation of what is read

8. 8 Vocabulary Certain concepts in mathematics are embedded within other concepts to be defined and understood. Three categories of math words Words that have the same meaning in Mathematical English (ME) and Ordinary English (OE) Words that have meaning only in ME Words that have different meanings in ME and in OE

9. 9 Research conducted in the past ten years reveals that vocabulary knowledge is the single most important factor contributing to reading comprehension.

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11. 11 “Drill and practice methods, which involve multiple repetitions if the same type of information about a target word using only associative processing, did not appear to have reliable effects on comprehension” Debbie Miller – Words Words Words OK class write out the definition of “sum” 20 times….

12. 12 1. Students must encounter words in context more than once to learn them 2. Instruction in new words enhances learning those words in context 3. One of the best ways to learn a new word is to associate an image with it 4. Direct instruction on words that are critical to new content procedures the most powerful learning Classroom Instruction That Works - Marzano

13. 13 Vocabulary Strategies LINCS Concept Mapping Frayer Model Math Dictionary

14. 14 LINCS Strategy Term LINCing Story LINCing Picture Essential Definition Reminding Word L ist the Parts I ndicate a Reminding word N ote a LINCing Story C onstruct a LINCing Picture S elf-test

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16. 16 What are Some Examples? The Word > What is it? What is it Like?

17. 17 What are Some Examples? The Word > What is it? What is it Like? Polygon Mathematical Shape Closed Plane Figure Straight Sides Two- Dimensional Made of line segments Pentagon Hexagon Rhombus

18. 18 What are Some Examples? The Word > What is it? What is it Like? Even Classification of numbers Multiple of 2 skip count starting at 0 2 is only even number that is a prime Ones digit is 0,2,4,6,8 Includes 0 but not 1 12 58 474

19. 19 Frayer Model WORD Definition (in own words) Characteristics Examples in LifeNon-Examples

20. 20 Frayer Model Polygon Definition A mathematical shape that is a closed plane figure bounded by 3 or more lines segments. Characteristics  Closed  Plane Figure  More than 2 straight sides  2-Dimensional  Made of line segments Examples in Life  Pentagon  Hexagon  Square  Trapezoid Non-Examples  Circle  Cone  Arrow  Cylinder

21. 21 Informational Text “Once a student leaves high school, 90% of his reading will be informational reading. Only 10% of his reading will be for pleasure.”

22. 22 Problem Solving Graphic Organizers KNWS Four-Square

23. 23 K-N-W-S K What facts do I KNOW from the information in the problem? N Which information do I NOT need? W WHAT does the problem ask me to find? S What STRATEGY / operation/tools will I use to solve the problem?

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25. 25 K-N-W-S K What facts do I KNOW from the information in the problem? N Which information do I NOT need? W WHAT does the problem ask me to find? S What STRATEGY / operation/tools will I use to solve the problem? It is a parallelogram. The area of a parallelogram is Base X Height The base can also be at the top Height is up and down The base = 16 in. The height = 9 in. 10 in. is neither the base or the height, it is the length of a side Find the area of the parallelogram 16 X 9 = 144 inches 2

26. 26 What facts do I KNOW from the information in the problem? WHAT does the problem ask me to find? What STRATEGY/ operation/ tools will I use to solve the problem? Is the answer reasonable? Did I answer the question asked?

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28. 28 Is the answer reasonable? Did I answer the question asked? What STRATEGY/ operation/ tools will I use to solve the problem? WHAT does the problem ask me to find?What facts do I KNOW from the information in the problem? Jason has 8 plants Each plant needs ¼ cup of food Jason has bags containing 1 ½ cup of food Describe the approach to determine that he does not have enough plant food 8 X ¼ = 2 cups 2 cups is less than 1 1/2 I check for reasonableness of answer Or I could draw a picture

29. 29 Strategies That Work - Harvey Making Connections Creating Mental Models Drawing Inferences Determining Importance Questioning Synthesizing Monitoring Meaning

30. 30 Fix-Up Strategies - Tovani Visualize Use Print Conventions Retell what You’ve Read Reread Look for Patterns

31. 31 Fix-Up Strategies - Tovani Connection between text to Self World Text Make a Prediction Slow Down Ask yourself questions

32. 32 Thinking Strategies Thinking Aloud Marking Text Modeling

33. 33 Strategies Find Key Numbers and Words – Mark Text Make Connections Use Vocabulary Strategies Ask Questions – Think Aloud Draw Pictures, when possible Learn Problem Solving Strategies What is the Bottom Line Question Is my answer reasonable?

34. 34 What do I think this problem is about? What do I know about Circles? How do I find Circumference ? Back Wheel= 14 inches Front Wheel= 14 X 3 = 42 in

35. 35 What Shapes do I know? Where have I heard the word Quad used? How Many sides does each shape have? H, B, F, G

36. 36 Where Have I seen these numbers in Real Life?

37. 37 How many toys do I have in all? What is another Word for Probability? What is the Chance I will pull out a red toy?

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39. 39 References Barton, Mary Lee & Heidema, Clare. 2002. Teaching Reading in Mathematics. Colorado: MCREL Billmeyer, Rachel & Barton, Mary Lee. 2002. Teaching Reading in the Content Areas: If Not Me, Then Who? Alexandria: ASCD Harvey, Stephanie & Goudvis, Anne. 2000. Strategies That Work. Ontario: Stenhouse Publishers. Tovani, Cris. 2000. I Read It, But I Don’t Get It. Maine: Stenhouse Publishers