Proceedings+ Thirty0Seventh+Annual+Meeting of+the+North+American+Chapter%of+the+International+Group+for+the% Psychology+ of+ Mathematics+ Education
Critical(Responses(to(Enduring(Challenges(in(Mathematics(Education
Editors:+ Tonya+Gau+Bartell+ Kristen+N.+Bieda+ Ralph+T.+Putnam,++ Kenneth+Bradfield+ Higinio+Dominguez+
East%Lansing,%MI% November%558,%2015%
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Proceedings+of+the+Thirty1Seventh+Annual+ Meeting+of+the+North+American+Chapter!of+the+ International+Group+for+the!
Psychology+of+Mathematics+Education+!
+ Critical(Responses(to(Enduring(Challenges(in( Mathematics(Education! East!Lansing,!Michigan,!USA! November!598,!2015! !
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Editors+ Tonya!Gau!Bartell! Kristen!N.!Bieda! Ralph!T.!Putnam! Kenneth!Bradfield! Higinio!Dominguez!
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Proceedings!of!the!37 !Annual!Meeting!of!PME9NA! !
ii!
Citation+ Bartell, T. G., Bieda, K. N., Putnam, R. T., Bradfield, K., & Dominguez, H. (Eds.). (2015). Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. East Lansing, MI: Michigan State University.
ISBN+ 978-0-692-54039-8
Articles published in the Proceedings are copyrighted by the authors. Permission to reproduce an article or portions from an article must be obtained from the author.
Bartell,!T.!G.,!Bieda,!K.!N.,!Putnam,!R.!T.,!Bradfield,!K.,!&!Dominguez,!H.!(Eds.).!(2015).!Proceedings+of+the+37th+ annual+meeting+of+the+North+American+Chapter+of+the+International+Group+for+the+Psychology+of+Mathematics+ Education.!East!Lansing,!MI:!Michigan!State!University.!
Curriculm!and!Related!Factors:!Poster!Presentations!
117!!
CONTRASTING MATHEMATICAL PLOTS: A STUDY OF “IDENTICAL” MATHEMATICS LESSONS Aaron Brakoniecki Boston University
[email protected]
Elyssa Miller Boston University
[email protected]
Andrew Richman Boston University
[email protected]
Leslie Dietiker Boston University
[email protected]
Keywords: Curriculum; Curriculum Analysis, Instructional Activities and Practice, High School Education Efforts to analyze the enactment of curricular materials have largely used tasks as their unit of curricular analysis (e.g., Henningsen & Stein, 1997). While the quality of tasks is clearly central to student learning, this level of analysis ignores the role that the sequencing of tasks plays in the way that students experience the lesson. Examining the sequence of tasks enables the examiner to see how the posing and resolution of questions over time shapes the experience of the learner. Interpreting a math lesson as a story (Dietiker, 2013) allows for this type of analysis. This poster uses Author’s mathematical story framework to address the research question: When enacted lessons based on the same written materials are interpreted as mathematical stories, what are the variations in how the content unfolds and how do these variations potentially impact students’ mathematical experiences? For this study, student mathematical experiences can include emotional responses to the story, opportunities for continued investigations, the closure of explorations, engagement with new content, etc. As part of a larger, ongoing study, this poster presents contrasting case studies of two different enactments of content that are based on the same textbook lesson. Two teachers were recorded teaching a lesson on using substitution to solve systems of linear equations from the same curriculum materials (blinded here, as an author of the materials is also an author on this proposal). These were veteran teachers with three or more years of experience teaching with the selected textbook and were chosen to represent a range of geographic and demographic sites. The recorded videos and interviews with the teachers were analyzed by the research team for the mathematical plot of the lesson (Dietiker, 2013). The questions found in these enactments, though often similar in form, emerged in different orders and are addressed in different ways. This poster presents an analysis that helps us understand and describe how the unfolding of content may result in different mathematical experiences for the students. Note: An author of this poster receives research funding from College Preparatory Mathematics (CPM), which is developing products related to research described in this poster. This author also receives book royalties from CPM for the textbooks used in the study. The terms of this arrangement have been reviewed and approved by Boston University in accordance with its conflict of interest policies. References Dietiker, L. (2013). Mathematics texts as narrative: Rethinking curriculum. For the Learning of Mathematics, 33(3), 14–19. Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549.
Bartell,!T.!G.,!Bieda,!K.!N.,!Putnam,!R.!T.,!Bradfield,!K.,!&!Dominguez,!H.!(Eds.).!(2015).!Proceedings+of+the+37th+ annual+meeting+of+the+North+American+Chapter+of+the+International+Group+for+the+Psychology+of+Mathematics+ Education.!East!Lansing,!MI:!Michigan!State!University.!
