Teachers’ Developing Talk About

the Mathematical Practice ofAttending to Precision

Samuel Otten, Christopher Engledowl, & Vickie SpainUniversity of Missouri, USA

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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.

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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

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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

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Analysis

Sociocultural/Sociolinguistic perspective (Lave & Wenger, 1991; Halliday & Matthiessen, 2003)

Lexical chains and thematic mappings (Herbel-Eisenmann & Otten, 2011; Lemke, 1990)

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Analysis

TOPIC 1

TOPIC 2

TOPIC 3

XXX

XXX

XXX

XXX

XXX

XXX

XXX XXX

TERM TERM

TERM TERM

relation relation

relation

Preliminary Results

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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

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Initial Discourse about SMP6

Precision as correct use of vocabulary / mathematical language

Unofficial Vocabulary

Official Vocabulary

rootszerosx-intercepts

MARFfactoring by

grouping

xy-plane

coordinate plane

Examples

Examples

SYNONYMS

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Initial Discourse about SMP6

Precision as correct use of the equal sign (=)

2x – 5 = 13

2x = 18 = x = 9

2(8) = 16 + 5 = 21 ÷ 7 = 3

2x + 57

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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

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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?

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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.

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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

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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.