WHITE PAPER: BUILDING SUPPORT FOR SCHOLARLY PRACTICE IN MATHEMATICS METHODS

Transcription

1 WHITE PAPER: BUILDING SUPPORT FOR SCHOLARLY PRACTICE IN MATHEMATICS METHODS Signe E. Kastberg, Alyson E. Lischka, Andrew M. Tyminski, Wendy B. Sanchez This white paper represents the impressions and insights of Sanchez, Kastberg, Tyminski, and Lischka, principle investigators (PI), for the National Science Foundation conference grant Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods (Sanchez, Kastberg, Lischka, & Tyminski, 2015). The opinions included in this paper represent those of the PIs as of November 5, Insights for the first four sections of the paper were drawn from participants presentation slides, PIs observations during the conference, and debriefing meetings during October, Oral feedback from external evaluator, Denise Spangler, provided at the post-conference PI meeting on October 2, 2015 informed the final section of the paper. Historically, mathematics methods courses have been as diverse as the mathematics educators who teach them. This finding was drawn from a collection of reports exploring what is taught in mathematics methods courses (Harder & Talbot, 1997; Kastberg, Tyminski, & Sanchez, in press; Taylor & Ronau, 2006; Watanabe & Yarnevich, 1999). Lee and Mewborn (2009) called for scholarly inquiry to support scholarly practices of mathematics teacher educators (MTEs). To bring attention to and frame scholarly inquiry to inform scholarly practices in mathematics education, the PIs secured funding to host the SIP conference held September 30 through October 2, During the conference over fifty mathematics educators from universities across the United States met to work toward the following goals: a) Discuss important goals for methods based on theoretical orientations, the participants experiences, and the literature. b) Identify the nature of activities that might be useful in methods to meet important goals; c) Discuss the evolution of methods instructors practices within and across individuals; d) Discuss and suggest protocols for research and reporting practices that would make the literature more useful for building scholarly practices in methods; e) Discuss and establish a research agenda for improving and determining the impact and residue of methods courses; f) Form working/writing groups to progress the research agenda and an action plan for creating and disseminating the agenda. (Sanchez, et al., 2015, p. 9) Breakout sessions during the conference were structured to focus on subsets of the goals. The participants self-identified as aligned with one of three perspectives: cognitive, sociopolitical, or situative 1. In three of the four sessions, participants worked with colleagues who identified the same perspective. The work of the groups was informed by a compilation of abstracts submitted by participants describing a methods activity they used, posters designed by and describing an activity a subset of the participants used in methods courses, keynote presentations from Martin Simon (2015, October) representing the cognitive perspective, 1 Kazemi (2015, October) described the use of the term situative (Greeno, 2006) rather than situated as a perspective informing her work.

2 Support For Scholarly Practice 2 Rochelle Gutiérrez (2015, October) representing the socio-political perspective, and Elham Kazemi (2015, October) representing the situative perspective, and results from a stakeholder survey characterizing stakeholders views on the strengths and challenges in new teachers. The breakout sessions were structured to encourage awareness of intentionality in planning for methods courses and support for scholarly inquiry (Lee & Mewborn, 2009). Breakout session 1 focused on the identification of learning goals (goals) for mathematics methods courses. Breakout session 2 focused on development or identification of activities to address identified learning goals. Breakout session 3 focused on the identification of evidence that would be used to measure progress toward the learning goals. Following each of these breakout sessions, presentations summarizing the work of each group were shared and discussed. PIs facilitated discussion across groups. Breakout session 4 provided time for cross-perspective collaboration and the development of writing groups. Participants were asked to create author teams and submit potential titles for papers to be included in a monograph informed by the conference. Insights Gained: Looking Across Perspectives The keynote presentations set the tone for interactions in the breakout sessions. Each presentation described one of the perspectives and how it might be used in the design of methods courses and activities. Participants reactions to these presentations included a significant focus on the need or desire to draw from multiple perspectives in the design of methods courses and activities. While the conference schedule did include time for collaboration across perspectives in whole group discussions of breakout sessions, meals, and during the formation of writing groups, participants expressed a desire to have more cross-perspective conversations. These requests encouraged the PIs, in their post-conference reflections, to attend to ways perspectives might shape learning goals, activities, and selection of evidence. In the next three sections, we illustrate potential ways in which participants operational views of the perspectives seemed to result in differences in goals, activities, and evidence. Learning Goals To illustrate the way perspectives seemed to inform learning goals, activities, and evidence, we share an example of a learning goal drawn from each of the three groups and explore differences in associated activities and evidence identified. We describe the category of the learning goal as supporting PSTs attention to learners mathematics and context as an asset. In particular, we highlight differences in language and focus that illustrate what was foregrounded for participants aligned with a particular perspective. The situative group identified student thinking as an asset. Developing skills, knowledge and dispositions for building on student thinking using an asset mindset to meet students where they are (GOALS for pre-service mathematics methods courses, 2015, October). In a related goal, the cognitive group focused on PSTs knowledge. Develop PSTs ability to anticipate student responses based on prior analysis of student thinking. Requires PSTs to have knowledge of the mathematics concept (the discipline), task, and students prior knowledge (Cognitive Perspective, 2015, October).

3 Support For Scholarly Practice 3 The socio-political group identified awareness of knowledge of context as a goal. Become aware of and draw on knowledge of context in which PSTs work, including families, communities (Socio-political persepctive, 2015, October). This example illustrates attention to students as a common goal. Likely all participants valued and set as a learning goal, attending to student knowledge and thinking, yet the perspectives of the groups may have informed what was emphasized in these goal statements. The participants in the situative group reached beyond knowledge to target PSTs skills and dispositions. The sociopolitical group emphasized the need to support PSTs to attend to and draw upon the contexts that affect their work as teachers. This example does not suggest that these goals are at odds, but rather that emphasis or what is foregrounded and backgrounded in MTEs methods class could vary quite significantly, a finding also identified by Taylor and Ronau (2006) in their methods syllabi study. Continued dialogue across perspectives, as called for by participants, could enable MTEs to move towards a series of common goals for methods instruction. What is not clear is what might be lost in such a negotiation. Activities Exploration of activities designed to support PSTs development in the direction of these identified learning goals further illustrates how perspectives inform activities in methods courses. Drawing on the aligned goal of attention to learners mathematics and context as an asset, each group described an activity. For the situative group, bringing methods into schools (Swartz et al., 2015, October-a) had the potential of immediately addressing their identified goal of Developing skills, knowledge and dispositions for building on student thinking using an asset mindset to meet students where they are (GOALS for pre-service mathematics methods courses, 2015, October). The situative perspective includes an activity system to support the development of an interrelated set of skills, knowledge, and dispositions. Drawing from this idea the subgroup s methods activity was described as a series of engagements in the context of school. In contrast, the cognitive group described a particular activity that focused on providing opportunities for PSTs to build their knowledge of mathematics and of children s mathematics. The activity begins with discussions of PSTs own mathematics involved in a particular task and learners responses to the task. This activity would include learners work samples, video of learners doing the task, and presentations given by learners as mechanisms to support the development of awareness that children s mathematics was quite different from their own mathematics. For the socio-political group, activities that seemed to align with their learning goal: Knowledge of context in which they (PSTs) work, including families, communities (Socio-political persepctive, 2015, October). They summarized such activity as: Learner analysis (community walk; observation vs. inference; learn about school; learn about students interviews, observations, interests, family background, languages; connect this to planning; reflect on enactment) (Socio-political: Experiences & impacts, 2015, October) These activity designs further highlighted the ways in which differences in perspectives inform activity design. This is not to say that overlap does not exist, but rather that activities are specifically informed by perspectives. This discussion points to the significant challenge a single MTE would face in coordinating multiple perspectives and implementing activities in methods designed to meet the broad learning goal of attention to learners mathematics and context as an

4 Support For Scholarly Practice 4 asset. Kazemi s (2015, October) focus on of the need to build a network of colleagues at institutions seems particularly significant in efforts to draw from and address a broad range of learning goals associated with multiple perspectives. Additional discussion of the desire and need of MTEs to address learning goals raised by the socio-political group focused on empowering MTEs to find their own ways to do this. Gutiérrez described the need to support MTEs by identifying or describing pitfalls and bumps in the road MTEs experience in their efforts to enact various activities drawing from a particular perspective. Experience, Impact, and Residue Breakout 3 focused on the types of experience, impact, and residue various activities might support. PIs post-conference discussions raised concerns about these terms and their meanings for participants. The sub-group within the situative group focused on bringing methods into school (Swartz, et al., 2015, October-a) identified PSTs reflections as potential evidence of impact of their series of methods activities on PSTs learning and pedagogical skill (Swartz et al., 2015, October-b). For the cognitive group, evidence of impact of their activity to support PSTs abilities to anticipate learners thinking would lie in their abilities to anticipate children s thinking in a different task in the same domain (Cognitive Breakout 3 assessing impact and residue, 2015, October). The socio-political group focused on experiences PSTs might have as a result of various activities. Group reports suggest that impact is measured by gaining insight into shifts in PSTs behaviors that can be inferred to align with growth in the direction of the learning goals. The situative group s effort to operationalize these constructs may suggest that the terms were useful to subgroups within the group and aligned with tenets held by those embracing this perspective. All groups attended to the idea that designing opportunities to collect evidence of PSTs experiences and development toward associated learning goals would be important to gain insight into the productivity of the activities. Experience, impact, and residue were phenomenon associated with the process of development that might have meaning for the PIs and only a subset of the participants. Understanding how and whether these terms are useful to MTEs within particular perspective is an open question. Conclusion of Insights and Questions Perhaps the most significant insight from the conference was MTEs discussion of the use of perspectives in identifying learning goals and align activities. MTEs worked to align goals and activities making significant strides toward the development of intentional practice, or activities whose purpose is clear and that have a learning goal in mind. Further exploration of the desire of MTEs to work across perspectives and hypotheses about how this can be accomplished are needed. Participants working within a perspective are adept at building activities that align with learning goals informed by a single perspective. Still unknown is how MTEs might design activities that align with learning goals from multiple perspectives. Two goals for the conference seemed difficult to address given the time frame: setting a research agenda for exploring teaching and learning in mathematics methods and describing the design of research reports of use to MTEs as they build scholarly practice. PIs anticipate that the proposed monograph will result in papers that serve as models for the types of reports MTEs can use to build their scholarly practice (Lee & Mewborn, 2009). In addition, the conference

5 Support For Scholarly Practice 5 organizers will use this white paper, heavily focused on the notion of how perspectives are used in the identification of learning goals and design of activities, along with papers submitted for the monograph to posit a research agenda informed by these discussions. Preliminary Evaluation Discussion among the PIs and with the external evaluator produced three areas for further discussion: impact of the socio-political group and presentations on the community of mathematics teacher educators, tensions and opportunities involved in thinking across perspectives and activities, and positive impact of asking mathematics teacher educators to be explicit about their perspectives, goals, activities, and impacts. Gutiérrez s initial remarks provided a language and motivation for the discussion for the perspective, goals, and activities during the conference discussions. The inclusion of the sociopolitical perspective provoked discussion of and attention to opportunities for PSTs to build relationships with mathematics, question the position of the discipline, and attend to resources of learners, family, and community in mathematics education. These discussions provoked awareness that MTEs might not be serving the needs of PSTs well when goals identified by the socio-political group were left unattended. Yet, some MTEs expressed concern about their preparation for facilitating discussions of these issues with PSTs. MTEs discussed the need for professional resources to accompany descriptions of activities such as Gutiérrez s In my shoes (2015, October). To support PSTs to build insights and practices that counter oppressive talk and structures in K-12 schools (Gutiérrez, 2013), In my shoes, is an activity that draws from teacher leader s experiences. PSTs have opportunities to practice what they would say and do if they were in the teacher leader s shoes. To productively engage PSTs in this activity, MTEs need to realistically anticipate PSTs actions and insights during such conversations. Resources are needed to support MTEs in their desire to move the field forward in efforts to address the needs of all PSTs and all learners. While the inclusion of the socio-political perspective seemed to inform MTEs aligning with the situative and cognitive groups, the impacts of the presentations of the cognitive and situative group were not as visible. These insights further emphasize the need to know whether and how multiple perspectives might inform MTE s scholarly practices. The tension between working within a group and needing time to discuss ideas with other groups was noted by Spangler and the PIs. This tension further highlighted the need for researchers to attend to whether and how multiple perspectives inform MTEs practices. Two sorts of reports may inform the work of mathematics teacher educators. The first type includes explorations of implications, design accommodations, and resulting experiences and impacts when one activity such as anticipating student thinking is implemented from each of the three perspectives. A second type of report includes explorations of how MTEs drawing from different perspectives might support the development of PSTs attention to learners mathematics and context as an asset as described above. Finally, participants identified the value of being explicit about their work and practices as an outcome of the conference. This impression suggests that the mathematics teacher education must continue efforts to build research that can be used as the basis for course and program design as well as MTE s practices. In addition, the definition of research must expand to include material that has the power to inform and move MTEs. Research that has been

6 Support For Scholarly Practice 6 identified as being valuable in teacher education, but has yet to be broadly accepted in mathematics education, such as narrative (Clandinin & Connelly, 2000) and self-study (Pinnegar & Hamilton, 2009), may have the power to serve the role of professional development called for by MTEs while retaining the notion that contexts matter and experiences have many unique qualities. References Clandinin, D. J., & Connelly, F. M. (2000). Narrative inquiry. SanFrancisco, CA: Jossey Bass. Cognitive Breakout 3 assessing impact and residue. (2015, October). Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods. Atlanta, GA. Cognitive Perspective. (2015, October). Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods. Atlanta, GA. GOALS for pre-service mathematics methods courses. (2015, October). Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods. Atlanta, GA. Gutiérrez, R. (2013). Why (urban) mathematics teachers need political knowledge. Journal of Urban Mathematics Education, 6(2), Gutiérrez, R. (2015, October). Political conocimiento for teaching mathematics: Why & how?. Paper presented at the Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods, Atlanta, GA. Harder, V., & Talbot, L. (1997). How are mathematics methods courses taught? Paper presented at the Annual Meeting of Association of Mathematics Teacher Educators, Washington, DC. Kastberg, S., Tyminski, A., & Sanchez, W. (in press). Reframing research on methods courses to inform mathematics teacher educators practice. The Mathematics Educator. Kazemi, E. (2015, October). Learning to teach elementary mathematics. Paper presented at the Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods, Atlanta, GA. Lee, H., & Mewborn, D. (2009). Mathematics teacher educators engaging in scholarly practices and inquiry. In D. Mewborn & H. Lee (Eds.), Scholarly practices and inquiry in the preparation of mathematics teachers. In M. Strutchens (Series Ed.) (pp. 1-6). San Diego, CA: Association of Mathematics Teacher Educators. Pinnegar, S., & Hamilton, M. L. (2009). Self-Study of practice as a genre of qualitative research. New York: Springer. Sanchez, W., Kastberg, S., Lischka, A., & Tyminski, A. (2015). Scholarly inquiry and practices (SIP) conference for mathematics education methods. Atlanta, GA: National Science Foundation. Simon, M. (2015, October). Challenges in mathematics teacher education from a (mostly) constructivist perspective Paper presented at the Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods, Atlanta, GA. Socio-political persepctive. (2015, October). Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods. Atlanta, GA. Socio-political: Experiences & impacts. (2015, October). Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods. Atlanta, GA. Swartz, B., Rumsey, C., Woods, D., Kazemi, E., Virmani, R., Taylor, M.,... Box, T. (2015, October-a) Breakout group: bringing methods into schools meaningfully. Scholarly

7 Support For Scholarly Practice 7 Inquiry and Practices (SIP) Conference for Mathematics Education Methods. Atlanta, GA. Swartz, B., Rumsey, C., Woods, D., Kazemi, E., Virmani, R., Taylor, M.,... Box, T. (2015, October-b) Breakout group: bringing methods into schools meaningfully: Impact & residue. Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods. Atlanta, GA. Taylor, M., & Ronau, R. (2006). Syllabus study: A structured look at mathematics methods courses. AMTE Connections, 16(1), Watanabe, T., & Yarnevich, M. (1999). What really should be taught in the elementary methods course? Paper presented at the Annual meeting of the Association of Mathematics Teacher Educators, Chicago, IL.