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Welcome

California Mathematics and Science Partnership (CaMSP)Year 2, Follow Up 3January 22, 2011

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Agenda: Making the Invisible Visible

• We will identify the language of explaining quadratic equations to teach this language effectively.

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Essential Questions

• How can we identify the language that we need to teach our students so that they can discuss quadratic equations?

• What are effective instructional strategies that help students learn this language?

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Step 1: Analyzing language use to identify the many features.

Step 2: Limiting the features to a manageable number.

Identifying Language to Teach

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Identifying the language features to teach entails language analysis of texts—oral and written

Written – written explanations, e.g., from the students’ textbooks and other resources

Oral – transcribed language use – usually of teachers and students

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Handout

Let’s analyze how others describe quadratic equations.

Student talk = outputOur talk to students = inputLanguage students read = input

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We will be doing a task shortly that requires you to use a handout.

Handout : The Language Needed to Explain Quadratic Equations

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You need a handout that looks like this one:

 

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Stand up! Hand up! Pair up!

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Steps

Read the handout on the language of quadratic equations. Take at least five minutes. Underline the language you might use to explain quadratic equations. Write down any additional language.

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Steps

Stand up when you are done and find a partner across the room.

Put your hand up, smile and establish eye contact with someone else who has finished reading the handout.

Do a high five. Partners interact for three minutes. They discuss the answers to several questions.

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Task—Answer these questions:

What language enables you to explain quadratic equations?

Would you use any of the language in the handout?

What additional language would you use?

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Would you use any additional vocabulary?

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What about prepositions?

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Would anyone use the word functions?

Would anyone say:• Functions are rules that describe the

relationship between two variables. They are commonly expressed as equations.

• Functions are often expressed as equations that include two variables, as in x+3=y.

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What about function table?

Did anyone say:• Function tables represent pairs of numbers

that follow a certain rule, or function.

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Function Table (cont.)

Did anyone say?A function table for x+3=y would include

a column of corresponding numbers for "x" and a column for "y" to reveal a numerical pattern.

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Would anyone give an example of a function table?

X y

1 8

2 10

3 12

4 14

y = 2x + 6

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Column

a line of numbers or words written under each other that goes down a page

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Row

a line of things or people next to each other

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In a row

One after another, consecutively

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Would anyone use unknown numbers or the word let?

Did anyone say:When you are looking for unknown

numbers, let a variable represent that numbers?

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What about the word represent?

1.Partners find a place to sit down. They decide who is Partner 1 and who is Partner 2.

2.Teacher describes the task. Partners will take turns explaining what a quadratic equation is.

3.In pairs, Partner 1 explains a quadratic equation as Partner 2 listens and completes the graphic organizer.

4.Teacher calls “time”.

5.Partners switch roles. Partner 2 explains what a quadratic equation is as Partner 1 listens and completes the graphic organizer.

Timed Pair Share

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TASK: What language enables you to explain quadratic equation?

First Partner: Explains quadratic equations. Second Partner: The partner completes the

graphic organizer, writing down the language his/her partner has used.

Both Partners: Discuss the language.

Next, partners switch roles.

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Take a minute to prepare.

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What language did you or your partner use to explain quadratic equations?

Reminder: Complete the graphic organizer.

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Identifying Language Features to Teach

STEP TWO: Narrowing the language features to a manageable number that you want students to learn.

Step 2: Narrowing the List of Features:Step 2: Narrowing the List of Features:Using the guiding questions below, determine what Using the guiding questions below, determine what manageable list of features you would choose to teach.manageable list of features you would choose to teach.

Guiding QuestionsGuiding Questions

• • Is the language feature unknown?Is the language feature unknown?

• • Will it improve students’ ability to explain patterns?Will it improve students’ ability to explain patterns?

• • Will it increase students’ understanding of math?Will it increase students’ understanding of math?

• • Will students use the feature in other math assignments?Will students use the feature in other math assignments?

• • Will knowledge of the feature help to improve students’Will knowledge of the feature help to improve students’knowledge of academic language and/or the language of knowledge of academic language and/or the language of math?math?

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Key Language Features

Task: Write 6 key features of language you would want to teach students before asking them to discuss or explain quadratic equations in partner activities.

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Perfect Practice in Conversation

Each time a teacher gets a student to practice

a language feature correctly, it helps the student learn the feature!

That’s right!

Adapted from David Howe 2006

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How Much Practice is Needed?

Number of correct repetitions in a row of a new word needed to “automatize” the word - NICHD

Type of Learner Number of Repetitions

Most Able 1 or 2

Average 4-14

Least Able 20+ (?)

(R. Lyon, 1997)

What techniques can we use to make sure students deliberately practice using specific language?

Does anyone suggest reading explanations aloud to students, explaining the language in it and discussing it?What about asking students to read it aloud afterwards?

Deliberate modeling and repetition – individual, group and choral

Reading Aloud: Tables, equations, algebraicexpressions

Mathematically Speaking

Discussions and Analyses – e.g., of student notes, textbook explanations, teacher summaries …especially with word banks and/or

sentence stems!

Here are just a few (see handout for other ideas):

Choral Repetition

Algebraic Expression

Word Phrase Operation

w + 4 A number plus 4. Addition

w – 4 A number minus 4.

Subtraction

4 x w or 4w 4 times a number Multiplication

w 4 or w/4 4 divided by a number

Division

Choral Repetition

Repetition

2x2 + 3x + 1 = 0

x2 + x = 2x + 3

(x+2)(x+3) = 5

x2 - 6x + 2 = 0

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Tips for Preparing Choral Response Activities

Make sure to elicit at least four-six sentences, phrases or words

Try to make sure all sentences, phrases or words are parallel in form

Choral Repetition for Answering Questions

Think--Think how you would respond.

Listen -- Listen to the directions or prompt

Wait--Keep from blurting out the answer. Give everyone time to think.

Respond--When given the signal say or write your response.

Why should we use choral repetition?

Why is language use important?

Kathryn Morgan Woodward, research associate Williams, T., Kirst, M., Haertel, E., et al. (2010). Gaining Ground in the Middle Grades: Why Some Schools Do Better. Mountain View, CA: EdSource.

http://www.edsource.org/middle-grades-summary.html

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Let’s look at the language in the released word problems on the California Standards Test in Mathematics.

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What makes these problems difficult for English learners?

• With your one or two partners, determine the answers to the released algebra items.

• List the language in the problem that could be difficult for English learners to understand. Decide how you could teach it to them.

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Debrief

• Share solutions.

• Discuss language that could cause English learners difficulties.

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What the Research Says

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Summary

• How can we identify the language students need to know to discuss patterns?

• What are effective instructional strategies we can use to help students use this language?

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Take a Break