We examine the case of a lesson planning session within the context of professional development for dialogic instruction, and the lesson enacted following this session, which was intended to provide opportunities to 11th and 12th grade algebra students to explore polynomial functions in terms of their roots and linear factors. Our goal was, through the close analysis of the planning and enactment of the lesson, to gain deeper understanding of how the two participants were framing mathematical learning and how such different frames may explain the disparity between the planned lesson and its outcome. The analysis and discussion point to the complexities of supporting teachers in transitioning from a “doing” frame to an “exploring” frame.
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All names, except Munter’s, are pseudonyms.
In this case, conceptual distinctions such as Skemp’s (1976) “instrumental” vs. “relational” understanding or Lithner’s (2008) “creative” vs. “imitative” reasoning are also relevant. However, we chose to employ Smith and Stein’s (1998) mathematical tasks lens because it more directly relates to an expectation for Ms. Q’s practice at the time—implementing a more conceptually oriented curriculum.
An “Algebra 2” course in the USA is a second, year-long algebra course that typically follows a first algebra course and a geometry course and focuses largely on expanding work with functions to polynomial, rational, radical, and possibly trigonometric functions.
For more information on Accountable Talk, see http://ifl.pitt.edu/index.php/educator_resources/accountable_talk.
In her “teacher-leader” role, Ms. Q’s teaching load was reduced to allow time for her to provide direct instructional support to other teachers (e.g., co-teaching, observing, and other instructional “coaching” activities).
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Transcript conventions used in the examples were adapted from those developed by Gail Jefferson (see Atkinson & Heritage, 1984/2006):
[X.Y] Turns at talk numbered for excerpt X and turn Y
((text)) Descriptions of actions or paraphrases
(text) Transcriber uncertainty
Text Emphatic talk
te::ext Elongated speech
(Zs) Pauses in speech, where Z is the duration of the pause in seconds
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Heyd-Metzuyanim, E., Munter, C. & Greeno, J. Conflicting frames: a case of misalignment between professional development efforts and a teacher’s practice in a high school mathematics classroom. Educ Stud Math 97, 21–37 (2018). https://doi.org/10.1007/s10649-017-9777-0
- Professional development
- High school algebra
- Lesson planning
- Secondary school teaching
- Dialogic instruction