Strategic Responsiveness: Building on Student Thinking Through Instructional Design

• In Event: Responding to Student Thinking in Secondary Mathematics Classrooms: Studying and Supporting Teaching Practice

Abstract

Objectives and Perspectives

Responding to student thinking has typically been conceptualized as teaching practice enacted in the moment of instruction (Robertson, Scherr, & Hammer, 2015; Sherin, Jacobs, & Philipp, 2011). This paper puts forth a complementary perspective, highlighting the way teachers respond to student thinking in designing future instruction, creating content storylines that build on and develop student thinking over multiple lessons.

Researchers have noted the importance of preparing for teaching by planning and anticipation (Clark & Peterson, 2001; John, 2006). In reform-oriented mathematics teaching, these practices focus on student thinking (Drake & Sherin, 2008; Santagata & Angelici, 2010; Stein, Engle, Smith, & Hughes, 2008). This paper conceptualizes the process of preparing for teaching as instructional design in which teachers negotiate goals, curriculum or materials, and context.

Methods and Data

Case study methodology is used to examine the planning of one teacher, Rachel, who frequently exhibited in-the-moment responsiveness (Authors, 2016). Ten of Rachel’s Algebra II/Trigonometry lessons were videotaped using the point-of-view observation methodology (Sherin, Russ, & Colestock, 2011). Rachel wore a camera and tagged moments that would influence her efforts to improve her teaching. She was interviewed about each of the moments directly after each lesson, unpacking her sense-making and implications for future teaching.

Arcs of concept development across multiple lessons, content storylines (Roth, 2009), were the primary episode of analysis, including lesson and interview video to examine teaching and teacher thinking. Each content storyline that showed evidence of instructional design was examined in terms of the storyline’s goals (i.e., learning goals), and the instructional design decisions around those goals. Finally, confirming and disconfirming evidence of responding to student thinking was identified in each storyline.

Results

Rachel exhibited frequent responsiveness to student thinking in her instructional design through content storylines, complementing her in-the-moment responsiveness. In these storylines, the design of mathematical tasks (e.g., the representation, sequencing) were significant leverage points by which she attempted to build on student thinking. These tasks represented the co-development of Rachel’s understanding of student thinking and learning goals throughout a storyline. For example, in a storyline centered on finding multiple solutions for equations with trigonometric functions, Rachel first realizes the challenge of finding solutions not outputted by inverse trigonometric functions when interacting with a student. They consider how symmetry in graphs may be useful to find the additional solutions. Over time, her learning goals develop to include graphical symmetry approaches as students also resonate with this approach, leading her to design tasks to motivate students to use this approach specifically.

Scholarly Significance

This case highlights the important role that instructional design, often completed outside of in-the-moment teaching, plays in responding to student thinking. Rachel demonstrates how teachers can be responsive to student thinking in service of learning goals rather than dictated solely by the student ideas surfaced. The long-term nature of learning goals, typically spanning multiple lessons in reform-oriented contexts, may lend themselves to this responsiveness in planning rather than in-the-moment decisions.

Author

• Elizabeth B. Dyer, WestEd