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Middle grade teachers’ thinking of algebraic reasoning in relation to their classrooms
David Glassmeyer, Belinda Edwards
To cite this version:
David Glassmeyer, Belinda Edwards. Middle grade teachers’ thinking of algebraic reasoning in relation to their classrooms. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague, Czech Republic. pp.488-489. �hal-01286967�
498 CERME9 (2015) – TWG03
Middle grade teachers’ thinking of algebraic reasoning in relation to their classrooms
David Glassmeyer and Belinda Edwards
Kennesaw State University, Kennesaw, USA, [email protected]
The purpose of this study was to investigate United States mathematics teachers’ thinking about algebraic reason- ing within the context of their middle school classrooms.
After collecting document and observation data from 19 teachers in a two-week summer professional devel- opment workshop, we analysed how teachers defined algebraic reasoning in their classroom and their de- scription of algebraic reasoning tasks for their students.
Our findings detail the ways teachers initially described algebraic reasoning in the context of their classroom and the changes in thinking teachers reported during and after the workshop.
Keywords: Algebraic reasoning, professional development, teacher thinking.
AIMS AND RESEARCH QUESTION
Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathemat- ics (Kaput, 2008), yet little is known about how K-12 mathematics teachers think about algebraic reason- ing in the context of their classroom (Blanton & Kaput, 2005; Ellis, 2011). In this project, we aimed to address
this research need by examining how algebraic rea- soning was considered by middle school in-service mathematics teachers who taught grades 6, 7, or 8 in the United States. Our research question was: how do teachers develop their understanding of algebraic reasoning in the context of their classroom through a two-week professional development session? This question focused our efforts on characterizing how teachers communicated their understanding of alge- braic reasoning throughout the professional develop- ment and during the following months, after teachers returned to their classrooms. We use Blanton and Kaput’s (2005) definition of algebraic reasoning as
“a process in which students generalize mathemat- ical ideas from a set of particular instances, estab- lish those generalizations through the discourse of argumentation, and express them in increasingly formal and age-appropriate ways” (p. 413). We use these authors’ depiction of algebraic reasoning as a framework for this study.
METHODS
The participants of this study were 19 middle school teachers from the Southern United States engaged in
Code Reflection 1 Reflections 2–5 Reflection 6
Single Solution 11 (58%) 0 (0%) 0 (0%)
Single Solution Strategy 6 (32%) 0 (0%) 0 (0%)
Single Representation 2 (11%) 0 (0%) 0 (0%)
Multiple Solutions 1 (5%) 4 (21%) 1 (5%)
Multiple Solution Strategies 5 (26%) 17 (89%) 6 (32%)
Multiple Representations 3 (16%) 8 (42%) 3 (16%)
Procedural knowledge 12 (63%) 3 (16%) 0 (0%)
Conceptual knowledge 10 (53%) 14 (74%) 11 (58%)
Expressing Generalization 2 (11%) 13 (68%) 5 (26%)
Functional Thinking 1 (5%) 7 (37%) 0 (0%)
Table 1: Counts of how many teachers (n=19) made statements coded using our coding dictionary before (reflection 1), during (reflections 2–5) and after (reflection 6) the professional development
Middle grade teachers’ thinking of algebraic reasoning in relation to their classrooms (David Glassmeyer and Belinda Edwards)
499 a two-week professional development session and a
follow-up meeting two months later. We conducted observations and collected documents from teachers during and after a two-week professional develop- ment session. Data consisted of teachers’ daily re- flections prompting teachers to reveal their thinking about algebraic reasoning and researcher notes about teacher work on various activities and conversations during the professional development sessions. We used content analysis to analyze teachers’ reflections and our observation notes by creating and refining our codes based on existing literature.
FINDINGS
As summarized in Table 1, we found that teachers’
initial thinking about algebraic reasoning includ- ed procedural tasks with a single solution, solution strategy, or representation. At the end of the two-week professional development, teachers described alge- braic reasoning as requiring conceptual knowledge and multiple solutions, solution strategies, or rep- resentations. Some teachers also associated aspects of generalization and functional thinking as part of algebraic reasoning. Two months after the profes- sional development, teachers still described algebraic reasoning as tasks requiring conceptual knowledge rather than procedural skills, and included multiple solutions or solutions strategies. Teachers did not continue to associate generalization or functional thinking as part of algebraic reasoning.
These findings may help other teacher educators an- ticipate teacher thinking when working to develop algebraic reasoning in professional development settings and identifies more work with teachers’ al- gebraic reasoning is needed to support teachers’ use of generalization and functional thinking in their classrooms.
REFERENCES
Blanton, M., & Kaput, J., (2005). Characterizing a classroom practice that promotes algebraic thinking. Journal for Research in Mathematics Education, 36(5), 412–446.
Ellis, A. B. (2011). Generalizing – Promoting actions: how class- room collaborations can support students’ mathematical generalizations. Journal for Research in Mathematics Education, 42(4), 308–345.
Kaput, J. (2008). What is Algebra? What is algebraic thinking? In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the ear- ly grades (pp. 5–17). New York: Lawrence Erlbaum/NCTM.
