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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.

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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  • We are concentrating on the School-wide literacy component, but have other components surrounding us. Forest Hills has adapted a school wide time for SSR/DEAR. Many grade leveled subjects already have common assessments. We valued consensus scoring on previous literacy initiatives, such as WAC.
  • Constructivist Approach, layer word meanings with common language and gently immerse.
  • Pass out Math Word Sections and review at this time………………….Compare to other Vocabulary Lists – GLCEs, KC4, whatever.
  • Share Procedures, activities and overhead binders at this time.
  • Share Procedures, activities and overhead binders at this time.
  • Share Procedures, activities and overhead binders at this time.
  • Share checking system I use for vocabulary – ten terms to two pages, check, then x then circle – DO NOT check w/o word wall (duplicates) I “do not teach math” on Fridays, but REALLY, I am teaching how to learn Math!
  • Share checking system I use for vocabulary – ten terms to two pages, check, then x then circle – DO NOT check w/o word wall (duplicates) I “do not teach math” on Fridays, but REALLY, I am teaching how to learn Math!
  • 1 (lowest) very uncertain about the term. Don’t understand what it means 2 I;m alittle uncertain about what the term means, but I have a general idea. 3 I understand the term and I’m not confused about any part of what it means 4 I understand even more than what has been taught about this term.
  • (Baumann & Kame’enui, pg. 16) “If the words used to define a target word are likely unknown to the students, then the word is too hard.” Words also have to have a use and capture the interest of the students. What makes a word grade level appropriate? If the student can understand the meaning of the words that define the vocabulary term, that term is an appropriate term. For instance, to use direct instruction with words that will immediately or shortly appear in student reading is more effective than simply directly instructing on those words (Baumann & Kame’enui, pg. 110 study from Stahl & Fairbanks, by Marzano). To compare the effect sizes (meta-analysis): “..instruction in general words…(from) high-frequency word lists had an average effect size of .30 on students’ comprehension of content. However, when the words taught to students are words they will encounter in the reading passages used in the study, the effect size was .97.” According to this information a word is three times as likely to be learned if followed with an appearance within context. Selecting their own words for vocabulary study takes a suspended state of judgment from the instructors’ point of view. Will the students choose appropriate words? Will the teacher be able to accurately evaluate if the words chosen are at level for his or her students? Student selection is supposed to be “powerful in vocabulary learning.” Haggard used interviews of secondary and previous students and reports that (Blachowicz, Fisher 2006, pg. 7-8) students reported peers influenced the learning of words. Other important factors were frequent words from reading and current words in the media that surrounded the students. Haggard further suggests that self-selection was a major factor in students learning generalized words. Her studies were based on reading class situations, not a mathematics classroom. “In all groups studied, the students consistently chose words at or above grade level…” (pg. 8)
  • (Baumann & Kame’enui, pg. 16) “If the words used to define a target word are likely unknown to the students, then the word is too hard.” Words also have to have a use and capture the interest of the students. What makes a word grade level appropriate? If the student can understand the meaning of the words that define the vocabulary term, that term is an appropriate term. For instance, to use direct instruction with words that will immediately or shortly appear in student reading is more effective than simply directly instructing on those words (Baumann & Kame’enui, pg. 110 study from Stahl & Fairbanks, by Marzano). To compare the effect sizes (meta-analysis): “..instruction in general words…(from) high-frequency word lists had an average effect size of .30 on students’ comprehension of content. However, when the words taught to students are words they will encounter in the reading passages used in the study, the effect size was .97.” According to this information a word is three times as likely to be learned if followed with an appearance within context. Selecting their own words for vocabulary study takes a suspended state of judgment from the instructors’ point of view. Will the students choose appropriate words? Will the teacher be able to accurately evaluate if the words chosen are at level for his or her students? Student selection is supposed to be “powerful in vocabulary learning.” Haggard used interviews of secondary and previous students and reports that (Blachowicz, Fisher 2006, pg. 7-8) students reported peers influenced the learning of words. Other important factors were frequent words from reading and current words in the media that surrounded the students. Haggard further suggests that self-selection was a major factor in students learning generalized words. Her studies were based on reading class situations, not a mathematics classroom. “In all groups studied, the students consistently chose words at or above grade level…” (pg. 8)
  • (Baumann & Kame’enui, pg. 16) “If the words used to define a target word are likely unknown to the students, then the word is too hard.” Words also have to have a use and capture the interest of the students. What makes a word grade level appropriate? If the student can understand the meaning of the words that define the vocabulary term, that term is an appropriate term. For instance, to use direct instruction with words that will immediately or shortly appear in student reading is more effective than simply directly instructing on those words (Baumann & Kame’enui, pg. 110 study from Stahl & Fairbanks, by Marzano). To compare the effect sizes (meta-analysis): “..instruction in general words…(from) high-frequency word lists had an average effect size of .30 on students’ comprehension of content. However, when the words taught to students are words they will encounter in the reading passages used in the study, the effect size was .97.” According to this information a word is three times as likely to be learned if followed with an appearance within context. Selecting their own words for vocabulary study takes a suspended state of judgment from the instructors’ point of view. Will the students choose appropriate words? Will the teacher be able to accurately evaluate if the words chosen are at level for his or her students? Student selection is supposed to be “powerful in vocabulary learning.” Haggard used interviews of secondary and previous students and reports that (Blachowicz, Fisher 2006, pg. 7-8) students reported peers influenced the learning of words. Other important factors were frequent words from reading and current words in the media that surrounded the students. Haggard further suggests that self-selection was a major factor in students learning generalized words. Her studies were based on reading class situations, not a mathematics classroom. “In all groups studied, the students consistently chose words at or above grade level…” (pg. 8)
  • My goal this year was to concentrate on Specialized, but there ARE SO MANY TECHNICAL words to teach just to teach my subject it seems.
  • My goal this year was to concentrate on Specialized, but there ARE SO MANY TECHNICAL words to teach just to teach my subject it seems.
  • My goal this year was to concentrate on Specialized, but there ARE SO MANY TECHNICAL words to teach just to teach my subject it seems.
  • My goal this year was to concentrate on Specialized, but there ARE SO MANY TECHNICAL words to teach just to teach my subject it seems.
  • Student Vocabularies are not as overwhelming as once thought. More recent studies show smaller numbers in student vocabularies. This means more to explicitly teach! THE MOST IMPORTANT thing is to establish a pattern…..the distributed practice is priceless!!! Pg 161, Blue Book, “…Nagy and Anderson (1984) asserted that ‘for every word a child learns, we estimate that there are an average of one to three additional related words that should also be understandable to the child.’”
  • Teacher is “going live” Try to keep all on same words
  • “I see you have positive & negative separate from zero, any reason?”
  • “ Do you have any other words that might fit with greater than & less than?”
  • “Equivalent is a good choice, but you also need a heading for this new sub category.”
  • 3 rd & 4 th grade are considered a “speed bump,” until 3 rd grade vocabulary words are already used in a student’s life/vocabulary. 3 rd /4 th content vocabulary now enjoys no previous exposure. Marzano, Page 69, FIGURE 4.4 Impact of Direct Vocabulary Instruction: Direct Vocabulary ES .32, Direct Vocabulary Instruction on Words related to content ES .97. “…will increase by 33 percentile points when voacbulary instruction focuses on specific words important to the content they are reading as opposed to words from high frequency lists.”
  • The precision of effective student use of vocabulary reveals mastery/misconceptions

Nctm 03 24 07 Nctm 03 24 07 Presentation Transcript

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