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Reading MathematicsPaul E. Smith
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Agenda
The Unique Aspects of Reading Text
Comprehension Strategies
Vocabulary Strategies
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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
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Mathematics Text LiteracyUsually, 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 pageThe words in a mathematics text may not have the same meaning in another subject area textbookMathematics is the most difficult content area for most students to read.
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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
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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
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Reading Mathematics Require
Decoding and comprehending what is readPlanning for and monitoring the effectiveness of one’s readingAnalyzing and evaluating the content in light of one’s prior knowledge, experiences and schemataMaking inferences and generating conclusions based on the reader’s unique interpretation of what is read
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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
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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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“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….
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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
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Vocabulary Strategies
LINCS
Concept Mapping
Frayer Model
Math Dictionary
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LINCS Strategy Term LINCing Story LINCing Picture Essential Definition
Reminding Word
Reminding Word
Reminding Word
Reminding Word
List the Parts Indicate a Reminding word Note a LINCing Story Construct a LINCing Picture Self-test
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16What are Some Examples?
The Word >
What is it? What is it Like?
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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
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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
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Frayer Model
WORD
Definition (in own words) Characteristics
Examples in Life Non-Examples
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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
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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.”
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Problem Solving Graphic Organizers
KNWS
Four-Square
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K-N-W-S
KWhat facts do I KNOW from the information in the problem?
NWhich information do I NOT need?
WWHAT does the problem ask me to find?
SWhat STRATEGY / operation/tools will I use to solve the problem?
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K-N-W-S
KWhat facts do I KNOW from the information in the problem?
NWhich information do I NOT need?
WWHAT does the problem ask me to find?
SWhat 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 inches2
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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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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
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Strategies That Work - Harvey
Making Connections
Creating Mental Models
Drawing Inferences
Determining Importance
Questioning
Synthesizing
Monitoring Meaning
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Fix-Up Strategies - Tovani
Visualize
Use Print Conventions
Retell what You’ve Read
Reread
Look for Patterns
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Fix-Up Strategies - Tovani
Connection between text toSelfWorldText
Make a Prediction
Slow Down
Ask yourself questions
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Thinking Strategies
Thinking Aloud
Marking Text
Modeling
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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?
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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
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What Shapes do I know?
Where have I heard the word Quad used?
How Many sides does each shape
have?
H, B, F, G
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Where Have I seen these
numbers in Real Life?
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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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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