1 Reading and Math Vocabulary: Knowledge Counts! AMATYC Conference 2009 – Session S51 Amber Rust University of Maryland – College Park November 12 th -

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Reading and MathReading and MathVocabulary: Vocabulary:

Knowledge Counts!Knowledge Counts!

AMATYC Conference 2009 – Session S51AMATYC Conference 2009 – Session S51Amber RustAmber Rust

University of Maryland – College ParkUniversity of Maryland – College ParkNovember 12November 12thth - Thursday - Thursday

1:40 – 2:301:40 – 2:30

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Activity OneActivity One

Complete the Complete the tabletable for 2 of the words for 2 of the words given.given.

Work with others at your Work with others at your tabletable if you like. if you like. ConsiderConsider

What could be a student’s definition for the What could be a student’s definition for the word?word?

What definitions could students bring to class What definitions could students bring to class and want to apply to mathematics?and want to apply to mathematics?

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Why teach vocabulary? Why teach vocabulary? (Allen, 1999)(Allen, 1999)

There is research supporting the connection There is research supporting the connection between vocabulary development and success between vocabulary development and success in mathematics since 1944. in mathematics since 1944.

Vocabulary knowledge…Vocabulary knowledge… increases students’ reading comprehension.increases students’ reading comprehension. develops students’ knowledge of new concepts.develops students’ knowledge of new concepts. improves students’ range and precision in writing.improves students’ range and precision in writing. helps students communicate more effectively.helps students communicate more effectively. develops students’ deeper understanding of words develops students’ deeper understanding of words

and concepts.and concepts.

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Research on Vocabulary SaysResearch on Vocabulary Says Vocabulary knowledge plays a key role in Vocabulary knowledge plays a key role in

comprehension of text. comprehension of text. (Nagy & Scott, 2000)(Nagy & Scott, 2000)

Vocabulary knowledge increases when Vocabulary knowledge increases when students (students (not teachersnot teachers) make connections ) make connections between vocabulary terms. between vocabulary terms. (Blachowicz & (Blachowicz & Fisher, 2000)Fisher, 2000)

Vocabulary knowledge increases when Vocabulary knowledge increases when students use new vocabulary terms in students use new vocabulary terms in multiple ways (writing, talking, organizing, multiple ways (writing, talking, organizing, graphics, etc.) graphics, etc.) (Blachowicz & Fisher, 2000)(Blachowicz & Fisher, 2000)

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Teaching vocabulary well…Teaching vocabulary well…

enables students to make connections between enables students to make connections between their prior knowledge of a topic and the their prior knowledge of a topic and the vocabulary they encounter.vocabulary they encounter.

provides the students with strategies they can provides the students with strategies they can use in the future which provides students with use in the future which provides students with more control over their learning.more control over their learning.

enables students to move from a surface enables students to move from a surface understanding to a deeper understanding of understanding to a deeper understanding of concepts.concepts.

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Activity TwoActivity Two

Read the paragraph and circle vocabulary Read the paragraph and circle vocabulary words.words.

Work with others at your table if you like.Work with others at your table if you like. ConsiderConsider

What vocabulary words do students need to What vocabulary words do students need to understand in order to comprehend the understand in order to comprehend the paragraph?paragraph?

Which words could the students apply other Which words could the students apply other meanings to when first reading this meanings to when first reading this paragraph?paragraph?

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Activity TwoActivity Two

EveryEvery angleangle has a has a measuremeasure associatedassociated with it. If a with it. If a circlecircle is is divideddivided into 360 into 360 equalequal arcsarcs and two and two raysrays are drawn from the are drawn from the centercenter of the circle of the circle throughthrough two two successivesuccessive points of divisionpoints of division onon the circle, then that the circle, then that angle is said to angle is said to measure one measure one degreedegree..

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Math VocabularyMath Vocabulary(Rubenstein, 2007)(Rubenstein, 2007)

Some words are…Some words are… found only in math (e.g., denominator, found only in math (e.g., denominator,

hypotenuse, polynomial, histogram)hypotenuse, polynomial, histogram) shared with science or other disciplines (e.g., shared with science or other disciplines (e.g.,

divide, radical, power, experiment)divide, radical, power, experiment) shared with everyday language, sometimes shared with everyday language, sometimes

with different meanings, sometimes with with different meanings, sometimes with comparable meanings in mathematics comparable meanings in mathematics (fraction, similar, variable, median)(fraction, similar, variable, median)

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Math VocabularyMath Vocabulary(Rubenstein, 2007)(Rubenstein, 2007)

Some words…Some words… have multiple meanings in math (e.g., point, have multiple meanings in math (e.g., point,

cube, range)cube, range) sound like other words (e.g., sum & some, sound like other words (e.g., sum & some,

plane & plain, intercept & intersect, plane & plain, intercept & intersect, complement & compliment, hundreds & complement & compliment, hundreds & hundredths, pie & pi)hundredths, pie & pi)

are learned in pairs that often confuse are learned in pairs that often confuse students (e.g., complement & supplement, students (e.g., complement & supplement, combination & permutation, solve & simplify, combination & permutation, solve & simplify, at most & at least)at most & at least)

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Verbal and Visual Word AssociationVerbal and Visual Word Association(Barton & Heidema, 2002)(Barton & Heidema, 2002)

Vocabulary Term(s) Visual Representation

Definition(s)Personal Association or a characteristic

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Ex: Verbal and Visual Word AssociationEx: Verbal and Visual Word Association(Barton & Heidema, 2002)(Barton & Heidema, 2002)

Root, Zero, Factor, Solution, x-intercept

Each word can represent the answer to the function y=f(x) where f(a)=0 and a is a root, zero, factor, solution, and x-intercept

-Point (a,0) is the x-intercept of the graph of y=f(x)

-number a is a zero of the function f -number a is a solution of f(x)=0 -(x-a) is a factor of polynomial f(x) -Root is the function on the TI for this

x= -2 x= 3

x-ax

is

y-axisf(x)

Just find the answer to the function and that will be the zero. If I graph it, the zeros are where the function crosses the x-axis.

Special Note: this is just for real solutions and I can have 0, 1, or 2 of them.

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Word SortWord Sort

(Barton & Heidema, 2002; O’Connell & Croskey, 2008)(Barton & Heidema, 2002; O’Connell & Croskey, 2008)

Encourages students to notice and talk about Encourages students to notice and talk about the connection among words, meanings, and the the connection among words, meanings, and the concepts they represent.concepts they represent.

Two types: Open and Closed SortsTwo types: Open and Closed Sorts Open – students create the categoriesOpen – students create the categories Closed – teacher provides the categoriesClosed – teacher provides the categories

Suggestions say to provide approximately 20-25 Suggestions say to provide approximately 20-25 words and 4-5 categorieswords and 4-5 categories The given example in handout has 45 words and 7 The given example in handout has 45 words and 7

categories.categories.

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Tic-Tac-Toe Vocabulary Tic-Tac-Toe Vocabulary (Developed by Dr. Karen Moroz, Concordia University in St. Paul, MN)(Developed by Dr. Karen Moroz, Concordia University in St. Paul, MN)

Chose nine vocabulary words/concepts.Chose nine vocabulary words/concepts.

In any order, place in a tic-tac-toe format.In any order, place in a tic-tac-toe format.

Students are to write a sentence connecting Students are to write a sentence connecting the three words in each row, column, and the three words in each row, column, and diagonal for a total of 8 sentences.diagonal for a total of 8 sentences.

This connects vocabulary words with This connects vocabulary words with concepts.concepts.

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Gesturing Gesturing (aka Motor Imaging)(aka Motor Imaging)

Vocabulary knowledge increases when students create Vocabulary knowledge increases when students create their own images and actions to represent word their own images and actions to represent word meanings. meanings. (Blachowicz & Fisher, 2000)(Blachowicz & Fisher, 2000)

Uses non-verbal, physical movement to help Uses non-verbal, physical movement to help emphasize and clarify vocabulary wordsemphasize and clarify vocabulary words Includes facial expressions, movement or placement Includes facial expressions, movement or placement

of body, and combinationsof body, and combinations

Helps students form images in their minds when Helps students form images in their minds when hear vocabulary words (vocabulary becomes visual)hear vocabulary words (vocabulary becomes visual)

Caution: Second language students may have Caution: Second language students may have different interpretations for some gestures!different interpretations for some gestures!

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Activity ThreeActivity Three

Choose any two words and create a Choose any two words and create a gesture that represents the mathematics.gesture that represents the mathematics.

Work with others at your table if you like.Work with others at your table if you like.

Consider:Consider: What gesture would represent the word and What gesture would represent the word and

be informative?be informative? Does the gesture enhance understanding?Does the gesture enhance understanding?

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Semantic Feature AnalysisSemantic Feature Analysis(Barton & Heidema, 2002; Mower, 2003)(Barton & Heidema, 2002; Mower, 2003)

Helps students to distinguish a word’s Helps students to distinguish a word’s meaning by comparing its features to other meaning by comparing its features to other related terms.related terms.

It can become a visual learning tool.It can become a visual learning tool.

Students must reason and communicate Students must reason and communicate the similarities and differences.the similarities and differences.

Two examples are given in handout.Two examples are given in handout.

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Semantic Word Maps Semantic Word Maps (another name could be Concept Maps)(another name could be Concept Maps)

This strategy uses graphics to give a This strategy uses graphics to give a visual representation of the relationships visual representation of the relationships between concepts and words.between concepts and words.

Students pull on prior knowledge.Students pull on prior knowledge.

Students can consider the hierarchy of key Students can consider the hierarchy of key words and concepts.words and concepts.

Students can design study guides.Students can design study guides.

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10 questions to ask when 10 questions to ask when implementing vocabulary strategiesimplementing vocabulary strategies

(Allen, 1999)(Allen, 1999)

1.1. Which words are most important to Which words are most important to understanding the text?understanding the text?

2.2. How much prior knowledge will students have How much prior knowledge will students have about this word or its related concept?about this word or its related concept?

3.3. Is the word encountered frequently?Is the word encountered frequently?4.4. Does the word have multiple meanings?Does the word have multiple meanings?5.5. Is the concept significant and does it therefore Is the concept significant and does it therefore

require pre-teachingrequire pre-teaching6.6. Which words can be figured out from the Which words can be figured out from the

context?context?

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10 questions to ask when 10 questions to ask when implementing vocabulary strategiesimplementing vocabulary strategies

((Allen, 1999)Allen, 1999)

7.7. Are there words that could be grouped Are there words that could be grouped together to enhance understanding a concept?together to enhance understanding a concept?

8.8. What strategies could I employ to help What strategies could I employ to help students integrate the concept (and related students integrate the concept (and related words) into their lives?words) into their lives?

9.9. How can I make repeated exposures to the How can I make repeated exposures to the word/concept productive and enjoyable?word/concept productive and enjoyable?

10.10. How can I help students use the word/concept How can I help students use the word/concept in meaningful ways in multiple context?in meaningful ways in multiple context?

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What you can doWhat you can do (Allen, 1999)(Allen, 1999)

Repeat words in varied contexts (lecture, Repeat words in varied contexts (lecture, activities, homework, directions, handouts, activities, homework, directions, handouts, assessments, reading, writing, etc.) assessments, reading, writing, etc.)

Describe wordsDescribe words Support words with visualsSupport words with visuals Connect words to students’ livesConnect words to students’ lives Extend words with anecdotes (stories!)Extend words with anecdotes (stories!) Make associationsMake associations Give definitionsGive definitions

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What you can do continued…What you can do continued…

Compare and contrastCompare and contrast Chart characteristicsChart characteristics Rephrase sentencesRephrase sentences Analyze the structureAnalyze the structure Provide tactile examplesProvide tactile examples Give examples of correct and incorrect usageGive examples of correct and incorrect usage Question (Question (have discussions – Key to helping have discussions – Key to helping

students make connections!!)students make connections!!) Discussion can move students from surface Discussion can move students from surface

understandings to deeper comprehensionunderstandings to deeper comprehension

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Vocabulary Strategies ObjectivesVocabulary Strategies Objectives

Activities and assignments for learning Activities and assignments for learning vocabulary should vocabulary should notnot be divorced from be divorced from the concepts. the concepts. (; Vacca & Vacca, 2002)(; Vacca & Vacca, 2002)

Creating a glossary and memorization does Creating a glossary and memorization does notnot help students learn. help students learn. (Allen, 1999)(Allen, 1999)

To be a valuable learning experience for To be a valuable learning experience for students, vocabulary strategies should students, vocabulary strategies should enhance and support the teaching of enhance and support the teaching of mathematics.mathematics.

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Ideas for finding more infoIdeas for finding more info

Use the NCTM website (join NCTM!)Use the NCTM website (join NCTM!) Don’t restrict yourself to college or even high Don’t restrict yourself to college or even high

school level strategies. Elementary school school level strategies. Elementary school strategies can be modified if needed.strategies can be modified if needed.

Don’t restrict yourself to just looking for ideas Don’t restrict yourself to just looking for ideas within mathematics only.within mathematics only.

Search literacy websitesSearch literacy websites Key words: literacy, content area reading strategies, Key words: literacy, content area reading strategies,

content area writing strategies, content area literacy content area writing strategies, content area literacy strategies, vocabulary strategies strategies, vocabulary strategies

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Thanks for attending!Thanks for attending!

Please contact me with any questions.Please contact me with any questions.

University of Maryland: University of Maryland: [email protected]@umd.edu

ORORCollege of Southern Maryland: College of Southern Maryland: [email protected]@csmd.edu