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Analyzing sets of students’ written work on mathematical tasks has been identified as a worthwhile professional development activity (Ball and Cohen 1999; Smith 2001).  In this work session, we will explore how collections of student work can support mathematics education research by serving as stable indicators of classroom practice (Borko et al. 2003; Clare and Aschbacher 2001; Matsumura, Garnier, Pascal, and Valdes 2002). In comparison to classroom observations, student work is less expensive and less invasive to obtain, is harder to manipulate in ways that please researchers, and encapsulates longer periods of instruction in a classroom (Clare and Ashbacher 2001). Collections of student work serve as indicators of the conditions of learning, reflecting the norms and instructional practices impacting students’ mathematical thinking as they produced the work.

We will engage participants in considering what aspects of instruction are captured in classroom sets of students’ written work, with respect to the mathematical content and the normative mathematical practices. For example, what might we say about a teacher’s classroom instruction if: a) students solved the task in multiple ways even though the directions did not specifically request multiple strategies; b) most students did not complete the cognitively challenging parts of the task; or c) all students provide explanations similar in wording or all student work samples look ‘template.’ Samples of students’ written work can indicate a teacher’s expectations for what ‘counts’ as an written explanation or whether the teacher’s instructional practice maintained or diminished opportunities for cognitively challenging work (i.e., all the student work looks exactly the same), or simply eliminated the demands as students engaged in solving the task. The ways in which students carry out the work of solving mathematical tasks can provide important insights into the extent to which norms that reflect the Standards for Mathematical Practice (CCSS, 2011) are enacted in the classroom on a regular basis. In addition, analyses of student work can provide insight into the important mathematical understandings, or residue, evident from an episode of instruction.

The goal of this session is to engage participants in considering how student work can serve as a reflection on instruction and provide a valuable tool for use in research and in professional learning activities with mathematics teachers. We will introduce participants to a set of rubrics for analyzing collections of student work and describe our research in using the rubrics to: 1) assess instructional quality in mathematics at the district level; 2) evaluate the effectiveness of a professional development initiative; and 3) assess the implementation of a conceptually-based algebra curriculum. This set of rubrics is part of a validated measure developed to assess the quality of instruction in mathematics classrooms, through analysis of instructional tasks, task implementation, and students’ mathematical learning evident in their written work. Participants will engage in analyzing blinded student work packets, and thus gain experience in considering the ways in which student work can reveal the conditions of learning in a mathematics classroom and the ways in which these rubrics can be used in professional development and research.

Central Questions:

1. What information can a set of student work provide about the quality of mathematics classroom instruction?
2. In what ways can assessing instructional quality using student work help researchers understand how teachers make use of intellectual resources (e.g., professional development, curriculum)?
3. How might the analysis of student work using these rubrics be integrated into professional development work with teachers?
4. What questions about classroom teaching still remain unanswered after analyzing a student work packet, and what analytical tools might support answering those questions?

Organization of the Session:

• The session will  open with participants analyzing specific samples of students’ work and considering what the work indicates about the quality of instruction and students’ learning (10 min);
• We will describe the development and conceptual basis of a set of rubrics for analyzing students’ work (10 min);
• Participants will engage in using the rubrics to rate sets of students’ work (20 min);
• Participants will discuss the experience of rating the student work in light of the focus questions (20 min);
• Each presenter will describe how we have used student work as a research tool to assess teachers’ instructional practices 1) following a professional development initiative; and 2) to assess curriculum implementation (20 min);
• The session will close by asking participants to generate ideas for using student work and the rubrics in teacher education, professional development, and professional development research, with remaining time for questions (10 min).

This session is important because it illustrates the ways in which mathematics education researchers and teacher educators can use a tool for assessing teachers’ instructional practices to supplement or replace classroom observations, when classroom observations are not possible due to constraints in time, resources, or district permission. Collections of students work and the rubrics are valuable for research on the effectiveness of professional development initiatives, curriculum implementation projects, and assessment systems that intend to evaluate instructional quality. They are also valuable for use in professional learning, to have teams of teachers rate student work and consider what the ratings indicate about instruction and students’ opportunities for learning.

References

Ball, D.L., & Cohen, D.K. (1999). Developing practice, developing practitioners: Towards a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey-Bass.

Borko, H., Stecher, B., Alonzo, A., Moncure, S., & McClam, S. (2003). Artifact packages for measuring instructional practice: A pilot study (CSE Tech. Rep. No. 615). Los Angeles: University of California, National Center for Research on Evaluation, Standards, and Student Testing (CRESST).

Clare, L., & Aschbacher, P. (2001). Exploring the technical quality of using assignments and student work as indicators of classroom practice. Educational Assessment, 7(1), 39-59.

Matsumura, L. C., Garnier, H., Pascal, J., & Valdés, R. (2002). Measuring instructional quality in accountability systems: Classroom assignments and student achievement. Educational Assessment, 8(3), 207-229.

Smith, M.S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: NCTM.