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1 Reading and Math Vocabulary: Knowledge Counts! AMATYC Conference 2009 – Session S51 Amber Rust University of Maryland – College Park November 12 th - Thursday 1:40 – 2:30

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2 Activity One Complete the table for 2 of the words given. Work with others at your table if you like. Consider What could be a student’s definition for the word? What could be a student’s definition for the word? What definitions could students bring to class and want to apply to mathematics? What definitions could students bring to class and want to apply to mathematics?

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3 Why teach vocabulary? (Allen, 1999) There is research supporting the connection between vocabulary development and success in mathematics since 1944. 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 and concepts. develops students’ deeper understanding of words and concepts.

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4 Research on Vocabulary Says Vocabulary knowledge plays a key role in comprehension of text. (Nagy & Scott, 2000) Vocabulary knowledge increases when students (not teachers) make connections between vocabulary terms. (Blachowicz & Fisher, 2000) Vocabulary knowledge increases when students use new vocabulary terms in multiple ways (writing, talking, organizing, graphics, etc.) (Blachowicz & Fisher, 2000)

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5 Teaching vocabulary well… enables students to make connections between their prior knowledge of a topic and the vocabulary they encounter. provides the students with strategies they can use in the future which provides students with more control over their learning. enables students to move from a surface understanding to a deeper understanding of concepts.

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6 Activity Two Read the paragraph and circle vocabulary words. Work with others at your table if you like. Consider What vocabulary words do students need to understand in order to comprehend the paragraph? What vocabulary words do students need to understand in order to comprehend the paragraph? Which words could the students apply other meanings to when first reading this paragraph? Which words could the students apply other meanings to when first reading this paragraph?

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7 Activity Two Every angle has a measure associated with it. If a circle is divided into 360 equal arcs and two rays are drawn from the center of the circle through two successive points of division on the circle, then that angle is said to measure one degree.

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8 Math Vocabulary (Rubenstein, 2007) Some words are… found only in math (e.g., denominator, hypotenuse, polynomial, histogram) found only in math (e.g., denominator, hypotenuse, polynomial, histogram) shared with science or other disciplines (e.g., divide, radical, power, experiment) shared with science or other disciplines (e.g., divide, radical, power, experiment) shared with everyday language, sometimes with different meanings, sometimes with comparable meanings in mathematics (fraction, similar, variable, median) shared with everyday language, sometimes with different meanings, sometimes with comparable meanings in mathematics (fraction, similar, variable, median)

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9 Math Vocabulary (Rubenstein, 2007) Some words… have multiple meanings in math (e.g., point, cube, range) have multiple meanings in math (e.g., point, cube, range) sound like other words (e.g., sum & some, plane & plain, intercept & intersect, complement & compliment, hundreds & hundredths, pie & pi) sound like other words (e.g., sum & some, plane & plain, intercept & intersect, complement & compliment, hundreds & hundredths, pie & pi) are learned in pairs that often confuse students (e.g., complement & supplement, combination & permutation, solve & simplify, at most & at least) are learned in pairs that often confuse students (e.g., complement & supplement, combination & permutation, solve & simplify, at most & at least)

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10 Verbal and Visual Word Association (Barton & Heidema, 2002) Vocabulary Term(s) Visual Representation Definition(s) Personal Association or a characteristic

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11 Ex: Verbal and Visual Word Association (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-axis y-axis f(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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12 Word Sort (Barton & Heidema, 2002; O’Connell & Croskey, 2008) Encourages students to notice and talk about the connection among words, meanings, and the concepts they represent. Two types: Open and Closed Sorts Open – students create the categories Open – students create the categories Closed – teacher provides the categories Closed – teacher provides the categories Suggestions say to provide approximately 20-25 words and 4-5 categories The given example in handout has 45 words and 7 categories. The given example in handout has 45 words and 7 categories.

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13 Tic-Tac-Toe Vocabulary (Developed by Dr. Karen Moroz, Concordia University in St. Paul, MN) Chose nine vocabulary words/concepts. In any order, place in a tic-tac-toe format. Students are to write a sentence connecting the three words in each row, column, and diagonal for a total of 8 sentences. This connects vocabulary words with concepts.

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14 Gesturing (aka Motor Imaging) Gesturing (aka Motor Imaging) Vocabulary knowledge increases when students create their own images and actions to represent word meanings. (Blachowicz & Fisher, 2000) Uses non-verbal, physical movement to help emphasize and clarify vocabulary words Includes facial expressions, movement or placement of body, and combinations Includes facial expressions, movement or placement of body, and combinations Helps students form images in their minds when hear vocabulary words (vocabulary becomes visual) Caution: Second language students may have different interpretations for some gestures!

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15 Activity Three Choose any two words and create a gesture that represents the mathematics. Work with others at your table if you like. Consider: What gesture would represent the word and be informative? What gesture would represent the word and be informative? Does the gesture enhance understanding? Does the gesture enhance understanding?

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16 Semantic Feature Analysis (Barton & Heidema, 2002; Mower, 2003) Semantic Feature Analysis (Barton & Heidema, 2002; Mower, 2003) Helps students to distinguish a word’s meaning by comparing its features to other related terms. It can become a visual learning tool. Students must reason and communicate the similarities and differences. Two examples are given in handout.

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17 Semantic Word Maps (another name could be Concept Maps) This strategy uses graphics to give a visual representation of the relationships between concepts and words. Students pull on prior knowledge. Students can consider the hierarchy of key words and concepts. Students can design study guides.

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18 10 questions to ask when implementing vocabulary strategies (Allen, 1999) 1. Which words are most important to understanding the text? 2. How much prior knowledge will students have about this word or its related concept? 3. Is the word encountered frequently? 4. Does the word have multiple meanings? 5. Is the concept significant and does it therefore require pre-teaching 6. Which words can be figured out from the context?

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19 10 questions to ask when implementing vocabulary strategies ( Allen, 1999) 7. Are there words that could be grouped together to enhance understanding a concept? 8. What strategies could I employ to help students integrate the concept (and related words) into their lives? 9. How can I make repeated exposures to the word/concept productive and enjoyable? 10. How can I help students use the word/concept in meaningful ways in multiple context?

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20 What you can do (Allen, 1999) Repeat words in varied contexts (lecture, activities, homework, directions, handouts, assessments, reading, writing, etc.) Describe words Support words with visuals Connect words to students’ lives Extend words with anecdotes (stories!) Make associations Give definitions

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21 What you can do continued… Compare and contrast Chart characteristics Rephrase sentences Analyze the structure Provide tactile examples Give examples of correct and incorrect usage Question (have discussions – Key to helping students make connections!!) Discussion can move students from surface understandings to deeper comprehension Discussion can move students from surface understandings to deeper comprehension

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22 Vocabulary Strategies Objectives Activities and assignments for learning vocabulary should not be divorced from the concepts. (; Vacca & Vacca, 2002) Creating a glossary and memorization does not help students learn. (Allen, 1999) Creating a glossary and memorization does not help students learn. (Allen, 1999) To be a valuable learning experience for students, vocabulary strategies should enhance and support the teaching of mathematics.

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23 Ideas for finding more info Use the NCTM website (join NCTM!) Don’t restrict yourself to college or even high school level strategies. Elementary school strategies can be modified if needed. Don’t restrict yourself to just looking for ideas within mathematics only. Search literacy websites Key words: literacy, content area reading strategies, content area writing strategies, content area literacy strategies, vocabulary strategies Key words: literacy, content area reading strategies, content area writing strategies, content area literacy strategies, vocabulary strategies

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24 Thanks for attending! Please contact me with any questions. University of Maryland: arust@umd.edu arust@umd.edu OR College of Southern Maryland: amberr@csmd.edu amberr@csmd.edu

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