Nctm 03 24 07

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Presented at the NCTM in Atlanta, GA, 3/24/07. Presented an example of Marzano, Fisher & Murray research theories practised on 7th mathematics students through intentional vocabulary study.

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Nctm 03 24 07

  1. 1. Vocabulary in the Mathematics Classroom Can words help my students learn math ?
  2. 2. Main Sources for Math Vocab. <ul><li>Doug Fisher and Nancy Frey </li></ul><ul><li>Miki Murray </li></ul><ul><li>Robert Marzano </li></ul>
  3. 4. Improving Adolescent Literacy <ul><li>Vocab. as school wide component of literacy </li></ul><ul><li>“ Five Pronged Approach” </li></ul><ul><ul><li>Wide Reading </li></ul></ul><ul><ul><li>Read Alouds </li></ul></ul><ul><ul><li>Content Vocabulary Instruction </li></ul></ul><ul><ul><li>Academic Word Study </li></ul></ul><ul><ul><li>Words of the Week </li></ul></ul><ul><li>Suggests identifying key words within content </li></ul><ul><ul><ul><ul><ul><li>Doug Fisher/Nancy Frey </li></ul></ul></ul></ul></ul>
  4. 5. Teaching Mathematics Vocabulary in Context: Windows, Doors and Secret Passages <ul><li>Based on CMP program, but adaptable to any </li></ul><ul><li>Clean and Clear Program for Word Collection </li></ul><ul><li>“ Seven Characteristics for Robust Vocabulary Development” </li></ul><ul><ul><li>Immerse Students in Words </li></ul></ul><ul><ul><li>Personalize Word Learning </li></ul></ul><ul><ul><li>Use Multiple Sources of Information </li></ul></ul><ul><ul><li>Help Students Control Their Learning </li></ul></ul><ul><ul><li>Help Students Develop Independent Strategies </li></ul></ul><ul><ul><li>Assist Students in Using Words in Meaningful Ways </li></ul></ul><ul><ul><ul><ul><ul><li>Miki Murray </li></ul></ul></ul></ul></ul>
  5. 6. Building Background Knowledge <ul><li>Vocabulary = Background Knowledge </li></ul><ul><li>Identifies nearly 8,000 words by level & grade </li></ul><ul><li>Six Steps, Eight Characteristics, very detailed </li></ul><ul><ul><li>Teacher gives description, example of term </li></ul></ul><ul><ul><li>Students rephrase description in own words </li></ul></ul><ul><ul><li>Nonlinguistic Representation required </li></ul></ul><ul><ul><li>Activities for new Terms </li></ul></ul><ul><ul><li>Students Discuss Terms with Each Other </li></ul></ul><ul><ul><li>Play with the Terms </li></ul></ul><ul><ul><ul><ul><ul><li>Robert J. Marzano </li></ul></ul></ul></ul></ul>
  6. 7. Vocabulary Student Pages
  7. 8. Vocabulary Student Pages <ul><li>Some teachers give the words to define </li></ul><ul><li>Five entries per side make each page 10 terms, easy to count </li></ul><ul><li>Give space for additions, corrections, etc. </li></ul>
  8. 9. Vocabulary Student Pages <ul><ul><li>Student’s personal Word Wall helps them organize words alphabetically as they add them </li></ul></ul><ul><ul><li>Numbers next to words are where the word can be located in their vocabulary pages </li></ul></ul>
  9. 10. Math Class Word Walls
  10. 11. Dictionary Definitions <ul><li>mean adj </li></ul><ul><li>1: (statistics) approximating the statistical norm or average or expected value; &quot;the average income in New England is below that of the nation&quot;; &quot;of average height for his age&quot;; &quot;the mean annual rainfall&quot; [syn: average, mean] </li></ul><ul><li>2: characterized by malice; &quot;a hateful thing to do&quot;; &quot;in a mean mood&quot; [syn: hateful] </li></ul><ul><li>3: having or showing an ignoble lack of honor or morality; &quot;that liberal obedience without which your army would be a base rabble&quot;- Edmund Burke; &quot;taking a mean advantage&quot;; &quot;chok'd with ambition of the meaner sort&quot;- Shakespeare; &quot;something essentially vulgar and mean spirited in politics&quot; [syn: base, mean spirited] </li></ul><ul><li>4: (slang) excellent; &quot;famous for a mean backhand&quot; </li></ul><ul><li>5: marked by poverty befitting a beggar; &quot;a beggarly existence in the slums&quot;; &quot;a mean hut&quot; [syn: beggarly] </li></ul><ul><li>6: used of persons or behavior; characterized by or indicative of lack of generosity; &quot;a mean person&quot;; &quot;he left a miserly tip&quot; [syn: mingy, miserly, tight] </li></ul><ul><li>7: used of sums of money; so small in amount as to deserve contempt [syn: beggarly] n : an average of n numbers computed by adding some function of the numbers and dividing by some function of n [syn: mean value] </li></ul><ul><li>v 1: mean or intend to express or convey; &quot;You never understand what I mean!&quot; &quot;what do his words intend?&quot; [syn: intend] </li></ul><ul><li>2: have as a logical consequence; &quot;The water shortage means that we have to stop taking long showers&quot; [syn: entail, imply] </li></ul><ul><li>3: denote or connote; &quot;`maison' means `house' in French&quot;; &quot;An example sentence would show what this word means&quot; [syn: intend, signify, stand for] </li></ul><ul><li>4: have in mind as a purpose; &quot;I mean no harm&quot;; &quot;I only meant to help you&quot;; &quot;She didn't think to harm me&quot;; &quot;We thought to return early that night&quot; [syn: intend, think] </li></ul><ul><li>5: have a specified degree of importance; &quot;My ex-husband means nothing to me&quot;; &quot;Happiness means everything&quot; </li></ul><ul><li>6: &quot;I'm thinking of good food when I talk about France&quot;; &quot;Yes, I meant you when I complained about people who gossip!&quot; [syn: think of, have in mind] </li></ul><ul><li>7: destine or designate for a certain purpose; &quot;These flowers were meant for you&quot; Source: Webster's Revised Unabridged Dictionary (1913) </li></ul>
  11. 12. Dictionary Definitions <ul><li>mean adj </li></ul><ul><li>1: (statistics) approximating the statistical norm or average or expected value; &quot;the average income in New England is below that of the nation&quot;; &quot;of average height for his age&quot;; &quot;the mean annual rainfall&quot; [syn: average, mean] </li></ul><ul><li>2: characterized by malice; &quot;a hateful thing to do&quot;; &quot;in a mean mood&quot; [syn: hateful] </li></ul><ul><li>3: having or showing an ignoble lack of honor or morality; &quot;that liberal obedience without which your army would be a base rabble&quot;- Edmund Burke; &quot;taking a mean advantage&quot;; &quot;chok'd with ambition of the meaner sort&quot;- Shakespeare; &quot;something essentially vulgar and meanspirited in politics&quot; [syn: base, meanspirited] </li></ul><ul><li>4: (slang) excellent; &quot;famous for a mean backhand&quot; </li></ul><ul><li>5: marked by poverty befitting a beggar; &quot;a beggarly existence in the slums&quot;; &quot;a mean hut&quot; [syn: beggarly] </li></ul><ul><li>6: used of persons or behavior; characterized by or indicative of lack of generosity; &quot;a mean person&quot;; &quot;he left a miserly tip&quot; [syn: mingy, miserly, tight] </li></ul><ul><li>7: used of sums of money; so small in amount as to deserve contempt [syn: beggarly] n : an average of n numbers computed by adding some function of the numbers and dividing by some function of n [syn: mean value] </li></ul><ul><li>v 1: mean or intend to express or convey; &quot;You never understand what I mean!&quot; &quot;what do his words intend?&quot; [syn: intend] </li></ul><ul><li>2: have as a logical consequence; &quot;The water shortage means that we have to stop taking long showers&quot; [syn: entail, imply] </li></ul><ul><li>3: denote or connote; &quot;`maison' means `house' in French&quot;; &quot;An example sentence would show what this word means&quot; [syn: intend, signify, stand for] </li></ul><ul><li>4: have in mind as a purpose; &quot;I mean no harm&quot;; &quot;I only meant to help you&quot;; &quot;She didn't think to harm me&quot;; &quot;We thought to return early that night&quot; [syn: intend, think] </li></ul><ul><li>5: have a specified degree of importance; &quot;My ex-husband means nothing to me&quot;; &quot;Happiness means everything&quot; </li></ul><ul><li>6: &quot;I'm thinking of good food when I talk about France&quot;; &quot;Yes, I meant you when I complained about people who gossip!&quot; [syn: think of, have in mind] </li></ul><ul><li>7: destine or designate for a certain purpose; &quot;These flowers were meant for you&quot; Source: Webster's Revised Unabridged Dictionary (1913) </li></ul>
  12. 13. Multiple Resources for Descriptions <ul><li>People are the first resource: </li></ul><ul><ul><li>Draw from students what they already know </li></ul></ul><ul><ul><li>‘Think Aloud’ and selectively add what you know </li></ul></ul><ul><li>If the context is good use it </li></ul><ul><li>Finally go to a dictionary for a more formal definition </li></ul><ul><li>Model rephrasing the formal to a description </li></ul>
  13. 14. Multiple Resources for Descriptions <ul><li>Online Dictionaries </li></ul><ul><li>Kid-friendly Math Dictionaries </li></ul><ul><li>Cheap online ordering of used books </li></ul>
  14. 15. How Much Work is Vocab. Friday? <ul><li>Students bring five new words, before defining </li></ul><ul><li>Students are responsible for definitions before Monday </li></ul><ul><li>Students maintain numbering system between word wall & terms </li></ul><ul><li>Teacher dedicates one day, 20+/- minutes </li></ul><ul><li>Teacher looks ahead to meaningful words upcoming in unit </li></ul><ul><li>Teacher walks through selection of current words and helps to form a description </li></ul><ul><li>Keep Word Wall current </li></ul>
  15. 16. How Much Work is the Notebook? <ul><li>Students maintain word wall & number terms </li></ul><ul><li>Students are responsible for collection & definitions on own </li></ul><ul><li>Student ‘grades’ demonstrate ‘Good Faith Effort,’ or lack of effort. </li></ul><ul><li>Teacher looks for the number of words and counts pages </li></ul><ul><li>Teacher grades for completeness, not correctness </li></ul><ul><li>Teacher responds to discussions/ assessments asks to see related definitions </li></ul>
  16. 17. Assessing Vocabulary Knowledge <ul><li>Levels of Understanding </li></ul><ul><ul><li>I am very uncertain about the term. I don’t understand what it means. </li></ul></ul><ul><ul><li>I’m a little uncertain about what the term means, but I have a general idea. </li></ul></ul><ul><ul><li>I understand the term and I’m not confused about any part of what it means. </li></ul></ul><ul><ul><li>I understand even more than what has been taught about this term. </li></ul></ul><ul><li>Student OR Teacher selection of Terms </li></ul><ul><li>Can include “extra” information </li></ul>
  17. 18. What is acceptable understanding? <ul><li>Assessments dictate depth of required knowledge </li></ul><ul><li>Exposure to words/concepts can be checked periodically </li></ul><ul><li>Scaffolding: It is okay to have partial understanding of a word, for awhile </li></ul>
  18. 19. What is acceptable understanding? <ul><li>Assessments dictate depth of required knowledge </li></ul><ul><ul><li>Formative Assessments can be places to “check” important definitions </li></ul></ul><ul><ul><li>Repeated errors mean the definition needs to be teacher directed / re-teach time </li></ul></ul>
  19. 20. What is acceptable understanding? <ul><li>Exposure to words/concepts can be checked periodically </li></ul><ul><ul><li>End / start of unit: </li></ul></ul>S. Koning
  20. 21. Which Words to Teach? <ul><li>Fisher suggests agreeing on words </li></ul><ul><li>Murray provides a list of what she used within a typical year in 7 th /8 th grade </li></ul><ul><li>Marzano provides us with a leveled list by content (contains proper nouns) </li></ul><ul><li>Compare with the important words in your text and instruction – any you would add? </li></ul><ul><li>Dialogue with the grade above/below </li></ul>
  21. 22. Miki Murray
  22. 23. Robert J. Marzano
  23. 24. Types of Words: <ul><li>Generalized/Tier One </li></ul><ul><ul><li>Common words </li></ul></ul><ul><li>Specialized/Tier Two </li></ul><ul><ul><li>High Frequency </li></ul></ul><ul><ul><li>Across many subjects </li></ul></ul><ul><li>Technical/Tier Three </li></ul><ul><ul><li>Unique to one content area </li></ul></ul>
  24. 25. Types of Words: <ul><li>Generalized/Tier One </li></ul><ul><ul><li>Common words </li></ul></ul><ul><li>Specialized/Tier Two </li></ul><ul><ul><li>High Frequency </li></ul></ul><ul><ul><li>Across many subjects </li></ul></ul><ul><li>most researchers report this is the category to teach to achieve greatest impact </li></ul><ul><li>Technical/Tier Three </li></ul><ul><ul><li>Unique to one content area </li></ul></ul>
  25. 26. Types of Words: <ul><li>Generalized/Tier One </li></ul><ul><ul><li>Common words </li></ul></ul><ul><li>Specialized/Tier Two </li></ul><ul><ul><li>High Frequency </li></ul></ul><ul><ul><li>Across many subjects </li></ul></ul><ul><li>In order to do that, you need a system wide vocabulary effort in place </li></ul><ul><li>Technical/Tier Three </li></ul><ul><ul><li>Unique to one content area </li></ul></ul>
  26. 27. Types of Words: <ul><li>Generalized/Tier One </li></ul><ul><ul><li>Common words </li></ul></ul><ul><li>Specialized/Tier Two </li></ul><ul><ul><li>High Frequency </li></ul></ul><ul><ul><li>Across many subjects </li></ul></ul><ul><li>Technical/Tier Three </li></ul><ul><ul><li>Unique to one content area </li></ul></ul><ul><li>Teaching in just your content will likely consist of these words </li></ul>
  27. 28. Parts of Words: <ul><li>Related words are often spelled similarly </li></ul><ul><ul><li>Spelling matters once study has progressed to word meaning relationships </li></ul></ul><ul><li>Prefixes are important </li></ul><ul><ul><li>easy to identify, powerful </li></ul></ul><ul><ul><ul><li>Small number make up 20-50% of select word lists </li></ul></ul></ul><ul><ul><ul><ul><li>Un- </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Re- </li></ul></ul></ul></ul><ul><ul><ul><ul><li>In- </li></ul></ul></ul></ul>
  28. 29. Benefits of Direct Vocab. Instruction <ul><li>It’s Generative! For every word learned, students may understand up to three other words </li></ul><ul><li>The lowest readers have the most to gain </li></ul><ul><li>Distributed Practice </li></ul><ul><li>Strategies modeled apply elsewhere </li></ul><ul><li>Vocabulary is key to academic success </li></ul>
  29. 30. Vocabulary Self-collection Strategy <ul><li>Brain compatible component, choice is a strong motivation for adolescents </li></ul><ul><li>Addresses both LEP and SPED students, allowing them to self-level for individual instruction </li></ul><ul><li>Entire class reviews on GL words together </li></ul><ul><li>Fosters ownership </li></ul><ul><ul><ul><ul><ul><li>Haggard </li></ul></ul></ul></ul></ul>
  30. 31. Strategies for Learning Vocab.
  31. 32. Strategies for Learning Vocab. <ul><li>Analogies </li></ul><ul><li>Wordsmithing </li></ul><ul><li>Name That Category </li></ul><ul><li>Paraphrase </li></ul><ul><li>Knowledge Ratings </li></ul><ul><li>Feature Analysis </li></ul><ul><li>Semantic Word Map </li></ul><ul><li>Concept Circles </li></ul><ul><li>Frayer Model </li></ul>
  32. 33. Semantic Maps Semantic Map “ I see you have positive & negative at a different level than zero, any reason?”
  33. 34. Semantic Maps Semantic Map “ Do you have any other words that might fit with greater than & less than?”
  34. 35. Semantic Maps Semantic Map “ Equivalent is a good choice, but you also need a heading for this new sub category.”
  35. 36. Trivia Type Definitions
  36. 37. <ul><li>Create first slide with all definitions </li></ul><ul><li>Delete a definition as you insert each duplicate slide </li></ul><ul><li>Create trivia slide shows at logical intervals – end of units, as review after vacations or before assessments </li></ul>Trivia Type Definitions
  37. 38. Interesting Facts <ul><li>Before middle grades, children can read many fewer words than they comprehend through listening </li></ul><ul><li>After middle grades, vocabulary knowledge expands as a function of reading itself; more words are learned from reading than from the listening to spoken language </li></ul><ul><li>Pre-teaching vocabulary can triple the effect size, teach it before they encounter it. </li></ul>
  38. 39. <ul><ul><li>Vocabulary is connected to concepts, the concepts have specific vocabulary, and student thinking becomes public </li></ul></ul><ul><ul><li>Teachers can respond to errors immediately addressing misconceptions </li></ul></ul><ul><ul><li>Attending to concept development can affect comprehension </li></ul></ul>
  39. 40. Your Challenge: <ul><li>If you started this next year, what would be the first five words you teach? </li></ul><ul><li>Select two strategies that would work for your class </li></ul><ul><li>Discuss with colleagues, across GL, which words are essential by which grade </li></ul><ul><ul><li>Look at curriculum </li></ul></ul><ul><ul><li>Look at your text </li></ul></ul>
  40. 41. Research Sources on Amazon.com:

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