Success In AlgebraSeptember 5, 2013

Leitchfield, KY

Facilitated by the P12 Math and Science Outreach Unit of PIMSER, UKFunding provided by Council on Post Secondary Ed

Gathering• Chart #1

–What SIA activities I’ve done already this year…

• Chart #2–Now that I know my classes, these are

my concerns…

Vocabulary

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Why Teach Vocabulary

• Learning is fundamentally and profoundly dependent on vocabulary knowledge.

• Vocabulary knowledge is highly correlated with overall reading achievement.

• Vocabulary knowledge affects a student’s ability to participate fully in both social and academic activities.

Access Center, Improving Outcomes for All Students K-8

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Why Teach Vocabulary

• Significant disparities exist in word knowledge among students.

• Vocabulary deficiencies are a primary cause of academic failure in Grades 3–12.

vocabulary: reading O2: breathing

Access Center, Improving Outcomes for All Students K-8

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The Matthew Effect (Stanovich, 1986)

Children who fail at early reading, begin todislike reading.

They read less than their peers who are stronger

readers.

Their limited vocabularies

interfere with their

comprehension.

Their limitedcomprehensioncontributes to reading failure.

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Vocabulary Acquisition• At age 5-6 children typically have 2,500-5,000

words in their oral vocabulary.• 3,000 words per year are added during their

early school years.• 25-50% of annual vocabulary growth is

incidental.• Typical vocabulary lessons focus on 10-20

words per week.

(average 8 words/day)

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Why Students Struggle With Vocabulary

Meaningful Differences (Hart & Risley, 1995)

 

Words

Heard

per Hour

Words Heard in a 100-Hour

Week

Words Heard in a 5,200

Hour Year

Words Heard in 4

Years

Welfare 616 62,000 3 million 13 million

Working Class 1,251 125,000 6 million 26

million

Professional 2,153 215,000 11 million 45

million

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Generate interest in new words

Relate new words to children’s personal experiences

Help children make connections and attach meanings to new words and concepts that go beyond a label or definition

Vocabulary Development

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Vocabulary Research• Researchers have named vocabulary

knowledge as the most important factor in reading comprehension. (White, Sowell, & Yanagihara, 1989)

• Effective vocabulary instruction requires active and positive student participation. (Carr & Wixson,

1986) • Personal engagement with a new word can

lead to deep processing of meaning. (Dole, Sloan & Trathen, 1995)

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National Reading Panel Report, 2000

• Vocabulary instruction leads to gains in comprehension, but the methods must be appropriate to the age and ability of the reader.

• Vocabulary should be taught both directly and indirectly.

• Teaching vocabulary before reading has significant effects on vocabulary development.

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National Reading Panel Report, 2000

• Repetition and multiple exposures to vocabulary items are important.

• Learning in rich contexts, incidental learning, and the use of computer technology all enhance the acquisition of vocabulary.

• Direct instruction should include task restructuring and should engage the student.

• Dependence on a single vocabulary instruction method will not result in optimal learning.

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National Reading Panel Report, 2000• Repetition and multiple exposures to vocabulary items

are important.• Learning in rich contexts, incidental learning, and the

use of computer technology all enhance the acquisition of vocabulary.

• Direct instruction should include task restructuring and should engage the student.

• Dependence on a single vocabulary instruction method will not result in optimal learning.

© EDC, 2012

Reading Math Texts vs. Fiction

FICTIONDorothy lived in the midst of the great Kansas prairies, with Uncle Henry, who was a farmer, and Aunt Em, who was the farmer's wife. Their house was small, for the lumber to build it had to be carried by wagon many miles.

Baum, L. F. p.1-----------------------------------------------MATH TEXT

Based on the pattern, how could you figure out the number of small squares in any figure number? Write an equation to find the number of squares in Figure n.

What differences do you notice?14

© EDC, 2012

Conceptual Density of Mathematics Text

“One reason students struggle with reading mathematics is the sheer number of concepts packed into the text. According to Schell, math text presents more concepts per word, sentence, and paragraph than any other content-area text.”

Source: Barton, M. and Heidema, C. (2002) p.14

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© EDC, 2012

What’s different about reading math texts?

• Not just left to right -- need to read in different directions

• Not just words – also tables, graphs diagrams, and symbols

• The process of decoding symbols is different from decoding words. Symbols are like “sight words.”

• One challenge is that different symbols are used to describe the same process.– Multiplication *, x, (), ●

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Multiple exposures to a word shape word meaning for the

student.

6-10 Exposures (Marzano)

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Multiple Exposures • Extensive reading/wide variety of texts• Discussion in the classroom• Discussions at home• Explicit vocabulary instruction in the

classroom

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Word Recognition The cognitive level of a student is a factor in the number of exposures required for word recognition.

120-129………………..…….... 20110-119……………..……….....3090-109………………………......3589- 80……………………………4079- 70……………………….…..4569- 60……………………..…….55

Dr. Bonnie Armbruster University of IllinoisUrbana-Champaign

20Beck, McKeown, and Kucan, 2002

Levels of LanguageSelecting

Words

Tier 1High

Frequency Words

Tier 2

Vocabulary

Tier 3

SpecializedVocabulary

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Tier 1 Language• Most commonly used words that should be

learned by sight.• Once the core of the basic sight words has been

committed to memory, children generally go on to master phonics rules and generalizations more easily and efficiently.

• Sight Word Lists:– Dolch List– Fry List

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Tier 2 Language

• Sophisticated words (e.g., absurd, commotion, reluctant)

• Frequently occurring words across a variety of domains• Building rich representations and connections with

words in a variety of ways• High frequency for mature language users

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Tier 3 Language

• Specialized Vocabulary• Examples: evaporation, asymmetrical,

peninsula• Specialized words typically associated with

a content area or topic

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Guidelines for Selecting Tier 3 Words

• Teach terms that are central to the unit or theme of study

• Teach terms that address key concepts or ideas• Teach terms that will be used repeatedly throughout

the term, semester, or year

Less is More

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Guidelines for Selecting Tier 3 Words

AVOID Choosing Words:• Just because they are highlighted • Just because they appear in a list at the end of the chapter• With little utility once the student has passed the test• You cannot define• In large quantities • Which students will rarely encounter again

Levels of Language

Selecting WordsTier I

High Frequency

Words

Tier II

Vocabulary

Tier III

SpecializedVocabulary

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1. Teacher provides description, explanation, or example of new term.

2. Students restate explanation of the term in their own words.

3. Students create nonlinguistic representation of term.

4. Students periodically do activities that help them add to their knowledge of vocabulary terms.

5. Periodically, students are asked to discuss terms with one another.

6. Periodically, students are involved in games that allow them to play with the terms.

Math Practice Standards1. Make sense of problems and persevere in solving

them2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

Lunch

Telephone

Revisit Fractional Workers

Effective Discussion

Closing

• Homework –Vocabulary Homework Menu