Using Writing and Vocabulary in Mathematics Classes to...

Using Writing and Vocabulary in Mathematics Classes to

Accelerate Learning for ELLs

Mary H. Russell Mathematics Consultant, NC Department of Public Instruction mrussell@dpi.state.nc.us

Welcome and Housekeeping Discussion/Interactive Format

Quick Polling

Co presenter addressing questions in the text chat area

Those participating via teleconference can email questions to: mrussell@dpi.state.nc.us

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Quick Poll

Today’s Goal Is To:

• Explore importance of vocabulary and writing in the learning of mathematics

• Provide vocabulary and writing strategies

• Share and discuss students’ work samples

• Allow for collaboration among teachers

Vocabulary and Writing, Why are They Important?

•  Mathematics language

• Word knowledge, oral expression

• Clarify thinking

“Student mastery of a word means they can decode,

pronounce, spell, define it, write a meaningful sentence with it, and recognize it in a

different contest.” (Calderon, 2007)

NCSCS: Collect, organize, analyze, and display data (including scatterplots) to solve problems

The scatterplot above shows the number of people at the swimming pool from 1:00 – 5:30. What conclusion can be made about the number of people at the pool during this time span? How can a manager use this information to staff the pool?

1.  What would a correct response contain?

2.  What vocabulary would prevent your students from being able to answer successfully?

Compare the students’ responses that follow.

1.  Which response is the most acceptable? Why?

2.  What role does vocabulary play in the clarity of each response?

3.  Which words appear to be the issue?

Student 1

Teacher: In reading this question, it says the scatterplot above shows the number of people in the swimming pool from 1:00 -5:30. What conclusion can be made about the number of people at the pool during this time span?

Student 1: Uh. That it decreased as time passed. As it got later a lot of people started to leave.

Teacher: Ok. How can a manager use this information to staff the pool?

Student: I think that they shouldn’t need that many staff, much staff because there is not that many people there. So they could use to use fewer people, fewer staff.

Teacher: Ok. Now looking at this graph, how many people were at the pool at 2:30?

Student: About 14 people.

Teacher: Ok. At what time were there about 9 people at the pool?

Student: Uh, about 30, 35.

Teacher: Ok. What does the data pair (5:30, 5) represent?

Student: Uh. 5:30 is the hour and 5 is the number of people that were there.

Teacher: Do you see anything else, you want to say about the graph?

Student: That it’s a line graph.

Teacher: Thank you, very much.

Student 2

Teacher: In reading this question, it says the scatterplot above shows the number of people in the swimming pool from 1:00 -5:30. What conculsion can be made about the number of people at the pool during this time span?

Student: Uh. More people go at 1 o’clock and at 6:30 more people go. It lowers down at 3:00. It’s going down.

Teacher: Anything else?

Student: No.

Teacher: How can the manager use this information to staff the pool?

Student: He needs like to open early because there’s a lots of people go early. And, uh, he needs to know what time he needs to close to and when people need to leave. And that there is more people coming at 1:00.

Teacher: How many people were at the pool at 2:30?

Student: About 14.

Teacher: At what time was there about nine people at the pool?

Student: At 4.

Teacher: Ok. What does the data pair (5:30, 5) present?

Student: Uh. The number of people at the pool.

Teacher: Ok. Anything else?

Student: No.

Student 3

Teacher: I’m going to ask you a few questions about this graph. , it says the scatterplot above shows the number of people in the swimming pool from 1:00 -5:30. What conclusion can be made about the number of people at the pool during this time span?

Student: Doing, the time span? Ummm. (wait) well it’s like at 1 to 5:30 people come to the pool. Then it was at well it’s at more people at the pool at 1:30. Then when it comes 5:30 people are leaving the pool or something. That’s what I think it might mean.

Teacher: Ok. How can a manager use this information to staff the pool?

Student: So he will know how many people are there. How many people to monitor. And how many people he has to watch over.

Teacher: Ok. How many people were at the pool at 2:30?

Student: Ummm. About 14.

Teacher: At what time was there about 9 people at the pool?

Student: Um. At, I would say about 4, or 4.5

Teacher: What does the data pair (5:30, 5) represent?

Student: How many people were at the pool at 5:30.

Teacher: Alright, thank you.

Quick Poll

Which student response demonstrates a lack of word

mastery? Why?

Words to Understanding

ELLs and At Risk Students

Manager

Conclusion

Staff

Time Span

Math terms

Scatterplot

Data points

Correlations

Axis

Meaning of data

Key Vocabulary Issues for ELLs

• Same Words Different Meaning

• Similar Meanings Different Precision

• Complete understanding

Why is vocabulary so challenging in mathematics?

• Signal Words (transitions and connectors)

• Cognates

• Symbols

• Homophones

• Polysemous

Teach words that are needed to:

• Understand a text

• Use in writing

• Answer a test question

• Enhance academic verbal repertoire

Signal Words

Topic Words Addition Sum, Increased by, More

than Subtraction Decreased by, Subtract,

Take away Multiplication Product, Doubled, Times as

much Division Per, Quotient, Contained in Equality Is, Will be, Results Inequality Greater than, Greater than

or equal to, Less than, Less than or equal to

Cognates English Spanish equality igualdad equation ecuación number número complement complementar decimal decimal factor factor base base fraction fracción irrational irracional negative negativo

False Cognates

Spanish English fábrica Fabric but means factory,

mill, plant lector Lecturer but means reader Popa Pop or pope but means a

stern of a ship

Calderon, 2007

Homophones General Mathematics Other

sum some pair pear whole hole Plane plain pi pie profit prophet

gnu/knew/new hail/hale rain/reign/rein rapped/rapt/wrapped Hugh/hew/hue seas/sees/seize their/there/they’re way/weigh/whey

Polysemous Words Meanings

table 1.  a piece of furniture 2.  a tool for organizing

information in rows and columns

up 1.  from a lower to higher position

2.  cut up into pieces

pace 1.  a step made in walking 2.  a rate of speed at which

a person or animal walks or run

golden 1.  having the color of gold 2.  very favorable and

advantageous

Symbols Symbol Meaning

Right angle ≠ Is not equal to √

Square root ÷ Divide ± Plus or minus ⁄ Divide < Less than > Greater than ≤ Less than or equal to ≥ Greater than or equal to

Example of Cultural Differences

American German 3,895 3.895 45.69 45,69 twenty-one einundzwanz

Babylon.com

Tier 1 Tier 2 Tier 3 Most Difficult

Targeted for instruction Subject specific words—usually highlighted in text

Basic words Polysemous words across academic content areas

Polysemous and false cognates

Simple idioms ( make up your mind, sit up)

Words with instructional potential and less common idioms, phrases that take on a meaning of their own (stimulus package)

Connectors (so, if, then, however, finally)

Words in which students already have conceptual understanding (so, at, however, within, if

Cognates Cognates Many are cognates

Method of Selecting Vocabulary

Calderón, 2007)

Vocabulary Strategies

1.  Graphic Organizers

2.  Identify and Classify Vocabulary

3.  Games •  Vocabulary w/words and pictures •  Role play •  Guessing game

4.  Grouping •  Identify, highlight, and define

5.  Teach Vocabulary Before, During and After •  Use vocabulary indicators •  Word wall

Staff

Definition (in own words)

Facts/Characteristics

Examples Nonexamples

Staff

Definition (in own words)

Facts/Characteristics

Examples Nonexamples

Someone who works at the pool

stick cane baton pole

lifeguard

cashier

pool cleaner

Must do what is asked

Has specific assignment

Is paid for assignment

Vocabulary Indicators 1.  Teacher says word and student repeats 3 times

2.  Provide word in context from the text

3.  Provides dictionary or technical definition

4.  Provide definition in student friendly terms

5.  Prove example(s) of word use, including multiple meanings when necessary

6.  Point out helpful structures: prefix, suffix, cognate, tense, compound word, spelling, polysemy, pronunciation

7.  Engage 100% of the students in the production of the word

Calderón, 2007

Vocabulary References

Calderón, M. (2007). Teaching reading to english language learners. CA: Corwin Press.

Ellis, M.W. and Malloy, C. E. eds (2008). Mathematics for every student: responding to diversity, grades 6-8. VA: The National Council of Teachers of Mathematics, Inc.

Nash, R. (1997). NTC’s dictionary of spanish cognates: thematically organized. New York: McGraw.

Quick Poll

Why write?

“Exposure to the written word and basic reading skills helps

students develop a larger vocabulary.” (Calderon, 2007)

Advantages for Students •  Helps student raise questions about new ideas

•  Allows chance for reflection on what is known

•  Allow students to construct mathematics for themselves

•  Helps student keep thoughts organized

•  Helps address issue of “math anxiety”

Writing Types to Use in Mathematics

•  Journals •  Freewriting •  Learning Logs •  Note to Teacher •  Mathographies •  Formal Writing •  Expository

As teachers of mathematics, we sometimes forget that the words and phrases that are familiar to us are foreign to our students. Students need to master this language if they are to read, understand, and discuss mathematical ideas.

- Thompson & Rubenstein

Student 1

1.  What does the data pair (5:30, 5) represent?

Student response: That less people swim at later times of the day.

Student 2

Student response: 1 I can conclude that more people swim in earlier times of the day, and that less people swim in later times of the day. 2 She could use this information so that she can know how many staff to hire for certain jobs.

1What conclusion can be made about the number of people at the pool from 1:00-5:30? 2How can a manager use this information to staff the pool?

Quick Poll

Helpful-tips(n.d.).Source jeanoram.com

1.  Purpose

2.  Start Slow

3.  Affective, Open-Ended

4.  Word Limits

5.  Math Concepts

Writing Prompts

1.  I’m having problems with…

2.  Number 3 was the most difficult problem

because…..

3.  When solving word problems I feel…

Sample Mathematics Concept Prompts

1.  Explain how to subtract integers. 2.  Explain how can proportional reasoning

be used to find missing values in a problem.

Expository Writing and Word Problems

•  Revelation of Conceptions and misconceptions

•  Exploration of many multiple methods and solutions

•  Authors of own ideas •  Experience creative side of mathematics

Expository Writing and Word Problems

•  Writing activities promote mathematical inquiry

•  Encourages focus on thinking

•  Students use own language

•  Words are tools for thinking

Graphic Organizers for Writing

References Calderon, M. (2007). Teaching reading to english language learners, grades 6-12: a framework for improving achievement in the content areas. CA: Corwin Press.

Colorin colorado! Retreived on January 13 from http://www.colorincolorado.org/educators/content/vocabulary.

Free graphic organizers. Retreived on January 13 from http://freeology.com/graphicorgs/page6.php.

Helpful-tips(n.d.).Retrieved on January from jeanoram.com.

References cont… Online translation. Retrieved on January 13 from http://translation.babylon.com/.

Nash, R. Ph.D (1997). NTC”s dictionary of spanish cognates: thematically organized. New York, McGraw.

Prado, M. (1993). NTC’s dictionary of spanish false cognates. Chicago: NTC.

McIver, M. and Urquhart, V. (2005) Teaching writing in the content areas. VA: Association for Supervision and Curriculum Development.