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Teachers’ Developing Talk About the Mathematical Practice of Attending to Precision

Teachers’ Developing Talk About the Mathematical Practice of Attending to Precision. Samuel Otten , Christopher Engledowl, & Vickie Spain University of Missouri, USA. Rationale.

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Teachers’ Developing Talk About the Mathematical Practice of Attending to Precision

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  1. Teachers’ Developing Talk Aboutthe Mathematical Practice ofAttending to Precision Samuel Otten, Christopher Engledowl, & Vickie Spain University of Missouri, USA

  2. Rationale • Mathematical practices, such as reasoning, problem solving, and attending to precision, are important for students to experience but difficult for teachers to enact successfully. • The Common Core (2010) Standards for Mathematical Practice explicitly include attending to precision (SMP6). • Precision of computations and measurement • Precision of communication and language (Koestler et al., 2013) • In order to support teachers in enacting SMP6, we need to understand how they interpret this mathematical practice.

  3. Research Question • How do middle and high school mathematics teachers talk about the mathematical practice of attending to precision? • Initially – based on the Common Core paragraph description • Over time – based on extended experiences with the SMPs

  4. Project Overview • Participants: Eight mathematics teachers (grades 5-12) • Five Summer Study Sessions centered around the Standards for Mathematical Practice from Common Core (15 hours) • Data Sources • Audio/Video recordings • Teacher written work • Focus on Attending to Precision (SMP6) • Session 1 – brainstorm, discussion based on Common Core paragraph • Session 3 – reading, task, transcript, and related discussions

  5. Analysis • Sociocultural/Sociolinguistic perspective (Lave & Wenger, 1991; Halliday & Matthiessen, 2003) • Lexical chains and thematic mappings (Herbel-Eisenmann & Otten, 2011; Lemke, 1990)

  6. Analysis relation TERM TERM relation relation TERM TERM

  7. Preliminary Results

  8. Initial Discourse about SMP6 • Precision as appropriate rounding within a problem context • Emilee: Knowing when to round versus when to truncate. Like, if you need 8.24 gallons of paint, what’s an acceptable answer for that? Nine’s a great answer but what about 8 gallons and one quart? And that could get into the discussion. • Teachers provided other examples • $13.647 • 3 and a half people • Negative kittens

  9. Initial Discourse about SMP6 • Precision as correct use of vocabulary / mathematical language Unofficial Vocabulary Official Vocabulary Examples Examples factoring by grouping MARF coordinate plane xy-plane SYNONYMS x-intercepts zeros roots

  10. Initial Discourse about SMP6 • Precision as correct use of the equal sign (=) 2x – 5 = 13 2x = 18 = x = 9 2x + 5 7 2(8) = 16 + 5 = 21 ÷ 7 = 3

  11. Later Discourse about SMP6 • Vocabulary comes up again with regard to precise communication, but it is connected to precision in reasoning. • E.g., carefully formulated argument • Precision with symbols are discussed with regard to possible misinterpretations. • E.g., 2a in the denominator of the quadratic formula • Using parentheses to clarify expressions

  12. Later Discourse about SMP6 • With regard to number/estimation, precision as an awareness of exactness vs. inexactness • E.g., 1/3 vs. 0.33 • “If you round in step one, and then you round in step two, and round in step three, each time you’ve gotten further and further and further…” • Dilemma about how to push students toward precision without turning them off. Which students should be pushed and when?

  13. Discussion • Initial talk focused on student errors and a desire for more correctness (as opposed to precision, per se). • The distinction between precision and correctness may be important to make explicit as we support teachers in enacting SMP6. • Initial talk did involve both rounding/measurement and language, but these became more nuanced and comprehensive in later discussions. • Discussions of classroom examples where SMP6 occurred seemed helpful in promoting new ideas in the teacher’s discourse.

  14. Acknowledgments • Thank you for coming • Funding provided by the University of Missouri System Research Board and the MU Research Council • We appreciate the participation of the teachers and students who made this study possible www.MathEdPodcast.com

  15. References Halliday, M., & Matthiessen, C. M. (2003). An introduction to functional grammar. New York, NY: Oxford University Press. Herbel-Eisenmann, B. A., & Otten, S. (2011). Mapping mathematics in classroom discourse. Journal for Research in Mathematics Education, 42, 451-485. Koestler, C., Felton, M. D., Bieda, K. N., & Otten, S. (2013). Connecting the NCTM Process Standards and the CCSSM Practices. Reston, VA: National Council of Teachers of Mathematics. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, England: Cambridge University Press. Lemke, J. L. (1990). Talking science: Language, learning, and values. Norwood, NJ: Greenwood Publishing. National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Author.

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