READING IN MATHReading and reasoning in the Math classroom

GATES OF OPPORTUNITY:

Foreign Languages

EnglishSocial StudiesMath

Science

“Reading don’t Fix No Chevy’s”

CYCLES OF READING GROWTH

CYCLES OF READING FAILURE

TIME SPENT READING

THE SPECIAL CASE OF READING IN MATH When teachers think aloud about math

“texts” they provide a model for:1. Mathematical thinking/reasoning2. Reading comprehension3. “Close readings”

When teachers ask students to put math knowledge into writing they:

1. Practice encoding mathematical ideas

LITERACY FOR MATH/MATH FOR LITERACY

Working smarter, not harder at teaching math.

TODAY’S AGENDA=YOUR TOP TWO VOCABULARY

Teaching words in 3-D

COMPREHENSION1. Think-alouds to demonstrate your

meaning-making and reasoning process2. Using writing to check for and deepen

understanding

WHAT MAKES MATH TEXTS DIFFICULT?What do you need to know in order to

answer this 8th grade TCAP question:

About how many miles are equivalent to 55 kilometers (1kilometer is about 0.621 miles)

A. 341.550 milesB. 88.567 milesC. 55.621 milesD. 34.155 miles

ACCURACY MATTERS About how many miles are ________to 55

kilometers (1kilometer is about 0.621 miles)

About how _____miles are equivalent to 55 kilometers (1kilometer is about 0.621 miles)

MATH TEXT DEMANDS Density of ideas…requires close reading Multiple meaning words…requires deep (not

surface) word knowledge Comprehension of pictures and abstract

symbols…not just words.

PRINCIPLES FOR STUDENTS READING MATH TEXTBOOKS

BY TIM DONOHUE, SMOKY HILL HIGH SCHOOL Speed kills. This is not a magazine. Read/reread with a pencil and paper in hand for notes. There are never enough commas. Insert your own

pause to help you slow down. Draw and label diagrams as you go. Think about

related problems and procedures as you read. You can’t just read, you have to “do it” as you go. Magic sometimes happens between the lines. Follow the instructions (“Review the proof…”) The figures and tables are important The same number has different faces (1/4, .25) Mathematical writing has an idiosyncratic structure

that when mastered will aid in constructing meaning.

FROM ANOTHER MATH TEACHER…

Slow down!! The flow of a math book is not like the flow of a novel.

Every word counts. Math books are usually not repetitive, so there is little chance of picking up missed information from reading on. Writers of math textbooks believe that extra words get in the way of clarity.

Do not skim diagrams or other kinds of illustrative material. They hold as much meaning as printed words.

Words and symbols of math have very specific meanings.

Students are made aware that mathematics textbooks follow this expository pattern: statement, example, and explanation/summary.

Understand each sentence before you go on. Reread as many times as necessary.

COMPREHENSION IS A MEANING-MAKING, MESSAGE-GETTING PROCESS

Reading is an interaction

A TALE OF THREE COACHES…

COMPREHENSION IS A MEANING-MAKING, MESSAGE-GETTING PROCESS

META-COGNITIVE STRATEGIES: MAKING THE INVISIBLE VISIBLE If you asked the average proficient reader

what she does when reading, she might simply say, “I read.” But upon further investigation she would find that she unconsciously processes and problem-solves as she reads, almost like a reflect. We teach our brains to adjust to the different demands of various types of texts, which helps us read an income tax form just as successfully as we read a novel. We may not enjoy both text equally, but we can read each effectively and strategically.”-From The Right To Literacy in Secondary Schools

OUR FOCUS: THE ACTIVITY What do you do to make meaning out of a

difficult passage? Watch yourself as a reader

How Ask yourself – what do I know? How do I know

it? What am I doing to fix what I don’t know? Why

cognitive apprenticeship Model complex invisible skills

HOW DO I KNOW WHAT I KNOW? WHAT AM I DOING TO UNDERSTAND?

“Batsmen & Bowlers” The Batsmen were merciless against the

Bowlers. The Bowlers placed their men in slips and covers. But to no avail. The Batsmen hit one four after another along with an occasional six. Not once did their balls hit their stumps or get caught.

HOW DO I KNOW WHAT I KNOW? WHAT AM I DOING TO UNDERSTAND?

MAKING MEANING FROM SYMBOLS

READING IS THINKING… Predict Connect Infer Visualize Question Summarize

We all do this all the time, but need to be reminded/guided to do it (“think”) while we read.

READING STRATEGIES IN MATH LOOK LIKE… (see handout)

USING YOUR SAMPLE TEST ITEMS Working with your tables, select a question

and use a post-it to note what you might “think aloud” as you read this problem to your students. What strategy are you using? What can you tell them about how you make

sense of the words and symbols?

NOTE: any strategy could be used with any question, but some are more likely to be helpful than others

WHAT DOES READING COMPREHENSION INSTRUCTION LOOK LIKE? Math classes nation-wide are often reading-

instruction-free in an “ASSIGN-ASSESS” cycle.

When students do not understand what they read we often say…

“read it again”“think about it”“draw it”“try again”

Toward a scientific view of reading comprehension as an active meaning-

making processWe ASSIGN and ASSESS without teaching

because reading comprehension is:ComplexInvisibleObvious to us as expert readers

HOW DO WE TEACH STRATEGIES? MODEL – PROMPT - GUIDE Gradual release of responsibility= I do, We

do, You do.

Show me Help me Watch me!

MAKING THE INVISIBLE VISIBLEANNOTATION: Choose a set of symbols to “code”

the text.Examples: Operation words and context words People, places, dates Vocab and unfamiliar words Subjects and actions (who and what) Greek and Latin roots you recognize Direction words

STOP AND JOT: keep track of your thoughts, key words, translations in the margins

LITERACY FOR MATH/MATH FOR LITERACY Read-aloud/think-aloud demonstrates your

thought process Models and gradually releases responsibility

for comprehension

STEP 2:

Writing about math…

INTEGRATING WRITING… Allows students to process information

linguistically Put “mathematical” thoughts or their own

thoughts into words Reinforces vocabulary in a different mode

(reading/writing) Reading and writing are reciprocal (practice

encoding is as good as practice decoding)

RAFT: TEACHER SETS RAFT, STUDENTS WRITE ACCORDINGLY Role: Audience: Format: Topic:

RAFT EXAMPLES: Create a personal ad atoms advertising who

they would want to make ionic or covalent bonds with.

You are placing a want add for a missing angle in your equilateral triangle. What does the angle need to be like?

RAFT EXAMPLES FOR MATH

MATH JOURNAL Math stories Combine pictures and words Tell step-by-step directions as a narrative Write letters to yourself, a younger sibling, a

pen-pal, the teacher explaining what you know or a procedure you’ve learned

ONE-MINUTE PAPERS/60 SECOND ELEVATOR SPEECH

Index card or scrap of paper, or email Limited space of the card forces students to focus Lowers levels of writing anxiety Summarize, question, reiterate, support or counter

a thesis or argument, or to apply new information to new circumstances

Gives students practice putting their mathematical knowledge into words

WAIT!

What about phonics and fluency in middle and high school???

phenomenologyph-enomenolog-yphen-o-men-ol-o-gyphenomen-ology

Word Study from pre-K-graduate school…

INTEGRATING WORD STUDY WITHOUT “STOPPING EVERYTHING” As you come to words, make a habit of visually

showing the roots, prefixes and suffixes.

Put meaningful root words on the word wall and add them to the vocabulary you practice and quiz

Think aloud about how you approach long, complex words – show them how your scientist brain handles science words.

Teach the “chunks” and how to “chunk a word” as part of your vocabulary instruction.

WAIT!

What about phonics and fluency in middle and high school???

phenomenologyph-enomenolog-yphen-o-men-ol-o-gyphenomen-ology

Word Study from pre-K-graduate school…

INTEGRATING WORD STUDY WITHOUT “STOPPING EVERYTHING” As you come to words, make a habit of visually

showing the roots, prefixes and suffixes.

Put meaningful root words on the word wall and add them to the vocabulary you practice and quiz

Think aloud about how you approach long, complex words – show them how your scientist brain handles science words.

Teach the “chunks” and how to “chunk a word” as part of your vocabulary instruction.