Teachers’ Developing Talk About
the Mathematical Practice of
Attending to Precision
Samuel Otten, Christopher Engledowl, & Vickie Spain
University of Missouri, USA
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
TERM
relation
TERM
XXX
XXX
relation
relation
TERM
TERM
XXX
XXX
XXX
XXX
XXX
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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
xy-plane
Official
Vocabulary
Unofficial
Vocabulary
Examples
Examples
factoring by grouping
MARF
coordinate plane
SYNONYMS
x-intercepts
zeros
roots
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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
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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.
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