integrating mathematics and english€¦ · math and english? mathematicians today have paid too...
TRANSCRIPT
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Integrating Mathematics
and
English
Monique Hodziewich, Saddle Mountain Unified School District
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Math and English?
Mathematicians today have paid too much attention to their beloved specialties and not enough to good writing, good exposition, incisive judgment, and the overall health of the discipline.
Steven Krantz, from "See no evil, hear no evil, speak no evil" in Notices of the American
Mathematical Society, vol. 45, no. 9, October 1998.
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A little background:
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Common Core
• Mathematical Practices: Construct viable
arguments and critique the reasoning of
others
English Language Arts and Literacy in
Science and Technical Subjects
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Reading Comprehension
6-8.RST.2: Determine the central ideas or
conclusions of a text; provide an accurate summary
of the text distinct from prior knowledge or ideas
6-8.RST.1: Cite specific textual evidence to support
analysis of science and technical texts.
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Reading Mathematics
• Dense- can’t just skim
• Every word and symbol matters
• Words used in regular English are often
either more precise or have different
meanings entirely (prime, power, function,
radical)
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Helping Students Read
Talk to kids:
How do you read?
oNewspapers
oMagazines
oFiction
oNon-fiction
otexts
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Environment
• Supportive
• Be a role model
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Reader
• Prior knowledge
• Metacognition
• Attitude
• Aloud and with others
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Resources
• Newspapers
• Non-Fiction books
• Journals
• Government Websites
• Magazines
Side note: Availability of Fiction
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Using Media
Find examples of:
• A number greater than a million
• A number between zero and one
• A decimal, fraction or negative number
• Central tendency
• Graph
• Margin of error
• Prediction based on a math model
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Context: Make it meaningful
“The value of (Gates’) stock … reached an
incredible $81.4 billion. To put that in
perspective: That’s 209,357,326 14-ounce
tins of Beluga caviar or 513 Boeing 747s,
or nearly the gross domestic product of
Israel. In other words, it’s a lot more
money than most people can fathom.”
-- USA Today
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Thrill of a trill ...
Say you had the chance to blow about $2
trillion. You could:
• Buy 26,317,520 Jaguar XK8 convertibles –
- nearly three for everyone in Michigan.
• Pay off credit card debt for EVERYONE in
the United States -- four times!
• Give $7,272 to each of the 275 million
people in the United States.
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Reading Media Critically
• Not always explicit or correct
• Misleading
• Survey sampling misrepresentations
• Causality vs. Association
• Average vs. mean, median, mode
www.mathmistakes.com
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Writing
• Clear
• Concise
• Appropriate use of vocabulary
• Short or long
• Daily or occasional
• Cognitive or affective
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Benefits
• Saves time because they need less
instruction
• Promotes higher order thinking
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Writing
• Strengthens understanding
• Gives teacher a window into student thinking
• Increases retention
• Develops reasoning
• Shows growth
• Helps quiet students
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Writing
• Starting with thought
• Recalling words to express it
• Organizing logically
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Good Writing
• Well-organized
• Concise
• Clear
• Correct use of language and symbols
• Demonstrates logical reasoning
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Writing
• Focus on providing worthwhile tasks
• Once students are comfortable, stress
clarity
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Journaling
• Think time-write time
• 5-minute timer
• 2-3 times a week
• Teacher participates
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Journaling
• Start small
• Content, process, affective
• Use good verbs: explain, describe,
compare, summarize
• Relate to lesson
• Be flexible
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Tips
• Patience
• Start with affective
• Encouraging and regular feedback
• Grading not necessary, comments are
• Show samples
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R.A.F.T.
• Role, Audience, Format, Topic
• Higher on Bloom’s Taxonomy
• Standard or Creative
• Not just regurgitation
writingfix.com
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Formal Sample
Role: lawyer
Audience: enemy
Format: news story
Topic: probability
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Creative Sample
Role: zero
Audience: whole numbers
Format: campaign speech
Topic: the importance of zero
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Role
• Grant writer
• Business manager
• Economist
• Designer
• Teacher
• Casino owner
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Audience
• Governor of the state
• IRS
• Conference of mathematicians
• His/her boss
• student
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Format
• Magazine commentary article
• Classified ad
• How-to manual
• Resume
• Song
• 10-minute speech
• Book or film review
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Topic
• Mean, median, mode
• Estimation
• Mixed numbers
• Measurement
• Mental ways to calculate percents
• Laws of exponents
• Importance of functions
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Other Writing Assignments
• Write instructions
• Error analysis
• Open response
• Comparison of methods
• Word problems
• Proofs
• Arguments
• Math analogies
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Creative Writing • Poem
• Riddle
• Story for a line graph
• Imaginative stories: What would it be like
to be a square?
• Fairy tales
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Longer Assignments
• Pre-writing
• Drafting
• Revising
• Peer and self editing
• Sharing
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Longer Assignments
• Math autobiography
• Biography of a mathematician
• Research and report on an area of math
(functions, Pascal’s Triangle, the history of
zero)
• Report on an application of mathematics
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Vocabulary
6-8.RST.4: Craft and Structure
Determine the meaning of symbols, key
terms, and other domain-specific words
and phrases as they are used in a specific
scientific or technical context relevant to
grades 6-8 texts and topics
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Teaching Vocabulary
• Introduce concepts, then language
• Learn in context, make connections
• Compare and contrast English and math
use
• Teach prefixes and root words
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What Students Can Do • Write the definition in their own words as
well as with the formal definition
• Use the vocabulary in sentences
• Prefix and root word charts
• Student-constructed glossaries or
alphabet books
• Word sorting
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Frayer Model
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Semantic Feature Analysis (matrix showing how terms are
alike or different)
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Vocabulary
• Graphic organizer
• Visual Word Wall
• 3-column guess
• Magic Square (words & definitions
have numbers assigned)
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Symbol Story
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Other thoughts….
• Starting small
• Team approach
• Resources
• Brainstorming
• Other
Pure mathematics is, in its way, the poetry of
logical ideas.
Albert Einstein
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Questions?????
Comments?????