JOSÉ IS GREATER THAN XMACC IMPROVING READING ACHIEVEMENT

(MIRA) WEBINARMarch 31st, 2011

Warm Up Problem #1

Which is the best buy for sale on soda pop?

A.3 cans for $1.50B.4 cans for $1.60C.5 cans for $2.55

Warm Up Problem #2

Choose the algebraic expression for the phrase “Seven times a number X”

A.7 + XB.7xC.7/x

Warm Up Problem #3

Choose the algebraic equation for solving this.“Juan made $18 selling brownies for $3 each.

How many brownies did he sell?”A.18 = x + 3B.6 = xC.18 = 3x

Is reading in mathematics different from reading in other

content areas?

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YES!

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Reading in Math is Unique

• Use of Symbols• Unique knowledge and skills• Conceptual density• Terse writing style• Layout• Text above grade level• Increasingly long prose passages

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Prior Knowledge of Topics

Some of your students who have attended school in their native country may have been taught different methods for solving mathematical problems.

(In the chat box, please share some of your experiences with students who studied math in another country.)

Math PSSA Data (2009-10)Math Grade 8 Below Basic Basic Proficient Advanced

Migrant (fluent)

15% 9% 33% 42%

Migrant (non-fluent)

51% 14% 23% 12%

Math Grade 11

Migrant (fluent)

38% 33% 5% 14%

Migrant (non-fluent)

63% 21% 8% 9%

ELL (3-8 & 11)

33% 24% 29% 15%

Mathematics for ELLs• Provide opportunities for students to listen to other

students explain their strategies and mathematical thinking.

• Allow students to verbalize their mathematical thinking one-on-one to other students or to the teacher, rather than always in front of the large group.

• Model how students can invent and write their own story problems.

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Reading Accuracy Levels:Implications for Math Textbooks

• Independent – 95-100% accuracy• Instructional – 90-94% accuracy• Frustrational – 89% and below accuracy

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Selected Focus: Vocabulary

Student achievement can increase by 33 percentile points when vocabulary instruction focuses on specific words that are important to what students are learning.

--Stahl and Fairbanks, 1986

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Remember José?

• Age: 14 • Grade: 8• Country of Origin: Mexico• Home/Native Language: Spanish (rarely

uses English at home)• Time in US Schools: 5 years

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Remember José?• Time in Schools in Mexico: 1 year • Is Student Literate in Native Language? YES NO SOMEWHAT• ESL/Other Supplemental Services (describe service

type and frequency): José is pulled out for tutoring two times/week for

30 minutes. He also attends after-school homework help sessions 2-3 times/week.

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Remember José?Student’s WIDA English Proficiency Levels: (1 – Entering, 2 – Beginning, 3 – Developing, 4 – Expanding, 5 – Bridging)• LISTENING (1 2 3 4 5) SPEAKING (1 2 3 4 5) • READING (1 2 3 4 5) WRITING (1 2 3 4 5)Student’s Strongest Language Abilities: • LISTENING (4.6) SPEAKING (3.6) Weakest language abilities: • READING (2.6) WRITING (2.4)• Rate Student’s BICS (everyday English) and CALP (academic English) on a

1 – 5 Scale (1 = least proficient, 5 = most proficient) • BICS 1 2 3 4 5 CALP 1 2 3 4 5José’s PSSA Math level is “Basic” and his most recent Math grade was a C-.

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Setting the Stage – How Can We Help?

• José’s latest PSSA assessment indicates that he is performing at the “Basic” level. He is struggling with his content-area assignments and textbooks. The Fundamentals of Algebra course (where he earned a C-) has been a particular challenge for him.

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Setting the Stage – How Can We Help?

• You have been asked to provide José with supplemental instruction to help him catch up with his class work in math. He lacks self-confidence and is desperate to use the time he spends with you to complete his homework. You try to honor his requests, but you also have decided that you can best spend your time together by helping him with some problem-solving strategies as well as filling in some of his vocabulary and background knowledge gaps. It is a tall order, but José has a great deal of potential, and has been falling through the cracks in both reading and math for a number of years.

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José’s Homework Assignment#1 Some students held a car wash. They charged $3 to wash

each car. The students made a profit of $181 after they spent $11 on supplies for the car wash.

A. How many cars did they wash? Show all your work. Explain why you did each step.

B. What is the least number of cars the students must wash to have a profit of $330 after spending a total of $15 on supplies? Show all your work. Explain why you did each step.

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Strategies used by good readersThere considerable research documenting the strategies that

good readers use. These strategies include:1. Asking questions2. Making predictions3. Testing predictions4. Summarizing5. Monitoring understanding and deploying fix-it strategies as

needed.From Reading in the Disciplines

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Solving Math Equations…Problem Solving Steps:• Understand the Question– Number words– Function words (more than, less than, equal to)– Language structures (How old is…? What is the

difference…?)• Find the Needed Information (circle, underline, color)• Choose a Plan (draw a picture, make a chart, find the pattern)• Solve the Problem• Check the answer

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Tutoring Lesson Plan for Math Story Problems

Student InformationTutoring Lesson Purposes

Lesson Plan: BeforeDuringAfter

Reflection

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Let Us Begin with the Car Wash Story Problem (Parts A & B)

BEFORE: Features of Text

• Tutor reviews features of text

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BEFORE: Background Knowledge

• Background knowledge – Tutor leads discussion– What do you think José already knows about

earning money at a car wash?– What background knowledge do you think José

needs to learn to solve this problem?

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BEFORE: Vocabulary

• Vocabulary–Words from problem scenario–Number words– Function words–Direction words

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BEFORE: Language Structures

• Tutor reviews language structures found in the story problem that are confusing or that are important to solving the problem.

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BEFORE: Make Predictions

Tutor asks José• What ideas do you already have about this

story problem and how we might solve it?• What kinds of math do you think we will use?

Adding, multiplying?• What information should we look for in this

problem?

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DURING: Find Needed Information

• Tutor helps José to underline the needed information in the story problem.

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DURING: Choose a Plan to Solve the Problem

• Tutor helps José to draw a picture about the problem.

• Tutor helps José to write an equation to solve the problem.

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DURING: Solve the Problem

• Tutor watches while José solves the equations and helps as needed.

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DURING: Check the Answer

• Tutor reminds José to check the answer and shows how to do it as needed.

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DURING: Explain the Work

• Tutor helps José to write in his own words the steps he used to solve the problem.

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AFTER: Summarize

• Tutor talks briefly with José to summarize what was easy or hard about solving the problem.

• Tutor helps José identify one strategy that can be used in the future to solve a problem, and the tutor writes this down.

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AFTER: Vocabulary Review

• Tutor reviews the vocabulary words taught in the beginning of the lesson. [profit, supplies, the least number, explain]

• Tutor makes sure José has a written copy of these words to keep.

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AFTER: Homework Assignment

• Tutor helps José complete the BEFORE and some of the DURING steps of the other math story problems.

• José may be able to complete the problems on his own after he has had help starting each problem.

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Next the Bake Sale Story Problem #2 on the Homework (yum…)

BEFORE: Features of Text

• Tutor reviews features of textIs there anything you need to review with

José about the features of text?

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BEFORE: Background Knowledge• Background knowledge – Tutor leads

discussion–What do you think José already knows

about a bake sale?–What background knowledge do you think

José needs to learn to solve this problem?

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BEFORE: Vocabulary

• Vocabulary–Words from problem scenario–Number words– Function words–Direction words

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BEFORE: Language Structures

• Tutor reviews language structures found in the story problem that are confusing or that are important to solving the problem.

What language structures will you review with José?

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BEFORE: Make Predictions

How will José answer?• What ideas do you already have about this

story problem and how we might solve it?• What kinds of math do you think we will use?

Adding, multiplying?• What information should we look for in this

problem?

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DURING: Find Needed Information

What information will José underline in order to solve the story problem?

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DURING: Choose a Plan to Solve the Problem

• José can draw a picture about the problem.

• José can make a chart or write an equation to solve the problem.

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Cupcake Picture

$8 spent + $12 earned

= $2 x number of cupcakes sold

Cupcake ChartCupcakes Sold Money Earned

1 $22 $43 $65 $1010 $20

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Cupcake Equations

A. 12 = 2xB. 8 + 12 = 2xC. 8 + 12 = x

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REFLECTION

• Write (in the chat box) what you learned as a tutor that will help you the next time you work with José or another student.

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How Comfortable Are You?

In the chat box, let us know how comfortable you feel helping a student with math assignments that require knowledge beyond basic arithmetic.

A = Not at all comfortable........E = Very comfortable

If You Can’t---Who Can?

A hat that you wear frequently has “Advocate” written on it. If you have a student like José who is struggling in math—and you do not feel comfortable tutoring him—what are some strategies you might use to obtain the help he needs?

(Share your ideas in the chat box…)

Next Steps• You will be receiving a Survey Monkey link

with follow-up questions.• We will be sending you a link to the webinar

archive.Thanks for participating in our MIRA

webinars and for all you do to support migrant students in PA…

And now for one last story problem!

Advanced Math Story Problem -Your Worst Nightmare!

José is on a train headed north at 30 mph, and you are on a train headed south at 40 mph. The trains left their respective stations 30 minutes ago, and started 100 miles apart.

What grade is José in?