1. Introduction to Using Precise Math Language

2. 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 terms—and familiar terms with new meanings—correctly to convey ideas and concepts.

3. 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

4. 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.

5. 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?

6. How Can I Support Student Use of Precise Math Language?

7. Use Evidence-Based Instructional Practices
Provide clear explanations
Use varied examples, materials, and models
Provide ongoing formative assessment

8. 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

9. 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

10. 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

11. 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?

12. 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.

13. 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.

14. Provide Ongoing Formative Assessment: Possible Strategies
Observe small group discussions and activities to gain a sense of each student’s 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).

15. Use Online and Offline Tools
Manipulatives
Interactive whiteboard
Web-based applets
Math drawing tools
Calculators
3D design software
Graphing and charting software

16. Use Evidence-Based Strategies and Tools
To launch the lesson
During the learning task
As you bring closure to the lesson

17. 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?

18. Disclaimer
Awarded through a cooperative agreement from the U.S. Department of education, Office of Special Education Programs (OSEP), Grant #H327G , PowerUp What Works was developed by a team of 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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