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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