Introduction to Using Precise Math Language

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Introduction to Using Precise Math Language
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What is Using Precise Math Language?

• Using precise language is a strategy to build a
  shared understanding of key mathematics terms and
  symbols.
• Students practice using new termsand familiar
  terms with new meaningscorrectly to convey ideas
  and concepts.

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Key Elements of Using Precise Math Language

• Students recognize that common words and phrases
  can have math-specific meanings.
• Students practice using new mathematical terms
  and symbols to
• Solve problems
• Explain ideas
• Collaborate with peers
• Give feedback

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How Does Using Precise Math Language Help
Students?

• Expands their mathematics vocabulary and builds
  capacity to define/learn new terms.
• Supports them in thinking more carefully about
  their ideas and their peers ideas.
• Enables them to clearly communicate and ask
  questions as they solve problems.
• Helps them refine their ideas and learn the
  importance of precision in language.

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Discussion Questions 1

• How do you let your students know when precise
  mathematical language is needed?
• How have you highlighted differences between the
  common definitions of words and the math-specific
  meanings?
• How has precise math language helped your
  students in their thinking aloud and solving of
  math problems?

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How Can I Support Student Use of Precise Math
Language?
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Use Evidence-Based Instructional Practices

• Provide clear explanations
• Use varied examples, materials, and models
• Provide ongoing formative assessment

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Differentiated Instruction

• Plan instruction that considers students'
  readiness, learning needs, and interests.
• Use a range of technology tools to
• engage learners at varying levels
• engage learners in multiple ways.
• offer students options for demonstrating
  understanding and mastery

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Teacher-Dependent Ways to Differentiate

• By Content
• Different levels of reading or resource
  materials, reading buddies, small group
  instruction, curriculum compacting, multi-level
  computer programs and Web Quests, audio
  materials, etc.
• By Product
• Activity choice boards, tiered activities,
  multi-level learning center tasks, similar
  readiness groups, choice in group work, varied
  journal prompts, mixed readiness groups with
  targeted roles for students, etc.
• By Process
• Tiered products, students choose mode of
  presentation to demonstrate learning, independent
  study, varied rubrics, mentorships,
  interest-based investigations

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Student-Dependent Ways to Differentiate

• By Readiness
• Options in content, topic, or theme, options in
  the tools needed for production, options in
  methods for engagement
• By Profile
• Consideration of gender, culture, learning
  styles, strengths, and weaknesses
• By Process
• Identification of background knowledge/gaps in
  learning, vary amount of direct instruction, and
  practice, pace of instruction, complexity of
  activities, and exploration of a topic

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Discussion Questions 2

• How does using precise math language support the
  CCSS Mathematical Practices and the UDL
  principles?
• How has technology helped you to differentiate
  instruction?

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Provide Clear Expectations Possible Strategies

• Highlight math terms to be used in the lesson.
• When supplying examples and non-examples of
  vocabulary words, vary unimportant aspects such
  as size, shape, and spatial orientation.
• Support students in shaping accurate class
  definitions with examples and illustrations for
  lesson-specific words.

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Use Varied Examples, Materials, and Models
Possible Strategies

• Introduce new vocabulary words through
  explanations, examples, and illustrations.
• Engage your class in discussing and defining
  terms use open-ended questions to guide their
  work.
• Have students update their personal mathematics
  glossaries with definitions and illustrations.

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Provide Ongoing Formative Assessment Possible
Strategies

• Observe small group discussions and activities to
  gain a sense of each students progress in
  defining and learning new terms.
• Ask students to paraphrase what you or other
  students have said.
• Regularly review students mathematics glossaries
  to assess their learning and needs.
• When a student uses a new vocabulary word
  correctly, point it out (for the benefit of the
  whole class, not just that student).

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Use Online and Offline Tools

• Manipulatives
• Interactive whiteboard
• Web-based applets
• Math drawing tools
• Calculators
• 3D design software
• Graphing and charting software

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Use Evidence-Based Strategies and Tools

• To launch the lesson
• During the learning task
• As you bring closure to the lesson

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Discussion Questions 3

• What challenges have your students faced when
  learning new math terms?
• Are there models or visual representations that
  you have found useful when introducing precise
  math language?
• What technology tools have you used to support
  formative assessment?

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Disclaimer

• Awarded through a cooperative agreement from the
  U.S. Department of education, Office of Special
  Education Programs (OSEP), Grant H327G090004-10,
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  experts in education, technology, differentiated
  instruction/UDL, and special education at the
  Center for Technology Implementation, operated by
  the American Institutes for Research (AIR) in
  collaboration with the Education Development
  Center, Inc. (EDC) and the Center for Applied
  Special Technology (CAST).
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