Responsive Teaching in Science and Mathematics

Amy D. Robertson, Rachel Scherr, David Hammer, Amy D. Robertson, Rachel Scherr, David Hammer

• Publisher: Routledge
• Year: 2015
• Print ISBN: 9781138916999
• eBook ISBN: 9781317423737
• Topic: Education
• Subtopic: Education General

Answering calls in recent reform documents to shape instruction in response to students' ideas while integrating key concepts and scientific and/or mathematical practices, this text presents the concept of responsive teaching, synthesizes existing research, and examines implications for both research and teaching. Case studies across the curriculum from elementary school through adult education illustrate the variety of forms this approach to instruction and learning can take, what is common among them, and how teachers and students experience it. The cases include intellectual products of students' work in responsive classrooms and address assessment methods and issues. Many of the cases are supplemented with online resources (http://www.studentsthinking.org/rtsm) including classroom video and extensive transcripts, providing readers with additional opportunities to immerse themselves in responsive classrooms and to see for themselves what these environments look and feel like.

1

What Is Responsive Teaching?

Amy D. Robertson, Leslie J. Atkins, Daniel M. Levin, and Jennifer Richards

This book is about responsive teaching in science and mathematics. Before we explore nuances in the nature of responsive teaching, challenge common assumptions in the literature, and connect responsive teaching to other, relevant constructs—as do many of the chapters in this book—we first offer a rough sketch of what it is and what it looks like in practice. Our goal in doing so is not to make distinct analytical points or to add to the literature by challenging notions of responsive teaching; it is to give examples of responsive teaching and to show how each one instantiates this kind of instruction—to illustrate the phenomenon, so to speak, and to establish shared meaning for responsive teaching before we explore it together in the rest of the book.

Although different researchers, teachers, and teacher educators conceptualize, measure, and enact responsive teaching in distinct ways,¹ there are certain themes that recur across conceptualizations and instantiations. In particular, the literature highlights that responsive teaching involves:

(a) Foregrounding the substance of students’ ideas. Responsive teaching involves attending to the meaning that students are making of their disciplinary experiences (Ball, 1993; Brodie, 2011; Carpenter, Fennema, Franke, Levi, & Empson, 2000; Coffey, Hammer, Levin, & Grant, 2011; Colestock & Linnenbringer, 2010; Duckworth, 2006; Gallas, 1995; Hammer, 1997; Hammer, Goldberg, & Fargason, 2012; Hammer & van Zee, 2006; Jacobs, Lamb, & Philipp, 2010; Lau, 2010; Levin, Hammer, Elby, & Coffey, 2012; Levin, 2008; Levin, Hammer, & Coffey, 2009; Pierson, 2008; Schifter, 2011; Sherin, Jacobs, & Philipp, 2011; Sherin & van Es, 2005, 2009; van Es & Sherin, 2008, 2010; Wallach & Even, 2005). It instantiates intellectual empathy, in that a primary aim of a teacher listening is to understand and be present to his or her students’ thinking, rather than to evaluate or correct it. Teachers go beyond attending to whether or not students are sharing their ideas; they try to understand what students are saying, from the student’s perspective.

(b) Recognizing the disciplinary connections within students’ ideas. Responsive teaching is disciplinary in that the teacher listens for nascent connections between students’ meanings and the discipline (Ball, 1993; Chazan & Ball, 1999; Gallas, 1995; Goldsmith & Seago, 2011; Hammer, 1997; Hammer et al., 2012; Hammer & van Zee, 2006; Hutchison & Hammer, 2010; Jacobs, Franke, Carpenter, Levi, & Battey, 2007; Jacobs et al., 2010; Levin et al., 2012; Russ, Coffey, Hammer, & Hutchison, 2009; Schifter, 2011; Sherin & van Es, 2005), including “disciplinary progenitors” (Harrer, Flood, & Wittmann, 2013) or “seeds of science” (Hammer & van Zee, 2006). These seeds may be, for example, the beginnings of canonical understanding, the instantiation of specific scientific practices, or the affective experiences that promote experiences of pleasure in doing science. They may include children’s puzzlement over a phenomenon, their citing evidence to support an idea, their efforts toward precision, their using mechanistic reasoning (or the beginnings of it) to support their predictions or explanations, or their devising an informal experiment or suggesting an explanation; they could be the first flickers of scientific concepts, such as a sense of air as material, of living organisms as needing energy, or of energy as needing a source. In responsive teaching, the teacher “consider[s] the [discipline] in relation to the [students] and the [students] in relation to the [discipline]”(Ball, 1993, p. 394).

(c) Taking up and pursuing the substance of student thinking. Responsive teaching is responsive because it takes up and pursues the substance of student thinking (Ball, 1993; Carpenter, Fennema, Peterson, Chiang, & Loef, 1989; Colestock & Linnenbringer, 2010; Empson & Jacobs, 2008; Fennema et al., 1996; Fennema, Franke, Carpenter, & Carey, 1993; Gallas, 1995; Hammer, 1997; Hammer et al., 2012; Jacobs et al., 2010; Jacobs, Lamb, Philipp, & Shappelle, 2011; Lau, 2010; Levin et al., 2012; Lineback, 2014; Maskiewicz & Winters, 2012; Pierson, 2008; Russ et al., 2009; Schifter, 2011; Sherin & van Es, 2005). The short-term and, in some cases, long-term direction that the classroom activity takes emerges from the students themselves and from the connections that teachers and, in some cases, students make between students’ reasoning and the discipline. Teachers may, for example, invite students to assess one another’s ideas, draw connections between students’ ideas themselves, encourage students to design and conduct experiments to test their ideas, or plan entire units of inquiry that take up a student’s question.

This kind of teaching is grounded in an empirically and theoretically supported expectation that students’ intuitive thinking about science is productive and resourceful (diSessa, 1993; Hammer, 1996, 2000; Hammer, Elby, Scherr, & Redish, 2005; Hammer et al., 2012; Hammer & van Zee, 2006; May, Hammer, & Roy, 2006; Smith III, diSessa, & Roschelle, 1993):

… this approach presumes—in fact it builds from—a view that children are richly endowed with resources for understanding and learning about the physical world: Engage children in a generative activity, and there will be productive beginnings to discover and support.

(Hammer et al., 2012, p. 55)

Responsive teaching serves multiple instructional goals, such as fostering productive scientific discourse and argumentation, promoting participation in scientific practices, and enhancing students’ conceptual understanding. See Chapter 2 for more on the benefits of responsive teaching.

It may be tempting to interpret these three characteristics as a checklist of sorts—a set of actions that cultivate or constitute responsive teaching. We suspect, instead, that responsive teaching grows out of and is grounded in a stance toward students and their ideas rather than through any particular structure of activities, and we caution readers against viewing this list as prescriptive. Likewise, highlighting these three may suggest that they are distinct acts in a performance—e.g., that the teacher may follow a routine of first eliciting ideas, then seeking out connections, etc.—when they are far more integrated in practice, as the examples below show. Finally, it may be tempting to think that these three characteristics cover the space of “responsive teaching moves”—that is, that these and only these activities will be at play in a responsive classroom. In reality, teachers balance a range of instructional goals, and they select and foreground ideas and activities for a variety of reasons, not always because of their substance and connection to disciplinary ideas and practices (e.g., a teacher may foreground an idea offered by a student who has spoken up for the first time in order to encourage that student’s participation in class discussions).

In the remainder of this chapter, we will explore what responsive teaching looks like in detail. First, we will use seminal examples from the literature to illustrate what we mean above by (a), (b), and (c), and then we will offer several classroom examples of responsive teaching across the curriculum, from K–12 to university science instruction. We show that responsive teaching takes different forms in different contexts—that teachers can recognize a variety of disciplinary opportunities within their students’ thinking, from opportunities to distinguish between experimental variables (Ann), to opportunities to pursue mechanistic thinking (Jenny), to opportunities to clarify what is meant by specific scientific language (Leslie and Irene), to opportunities to capitalize on students’ intuitive notions of force (David). We show that teachers take these opportunities up in diverse ways, including planning experiments to test students’ ideas (Ann), proposing that students investigate a student-generated number group (Ball), allowing students’ emergent ideas to influence the direction of classroom inquiry (many), and designing homework (Leslie and Irene) or clicker questions (David) on the basis of student thinking. We encourage our readers to sample from our examples according to their own purposes; one certainly need not read all six to get a feel for what we mean by responsive teaching.

Clarifying the Characteristics of Responsive Teaching: Seminal Examples From the Literature

The “Sean numbers” example from Ball’s “With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics” (Ball, 1993) and the unit on electrostatics described in Hammer’s “Discovery Learning and Discovery Teaching” (Hammer, 1997) are two seminal, first-hand accounts of responsive teaching. In this section, we look to Ball and Hammer to clarify the three characteristics of responsive teaching articulated in the introduction: foregrounding the substance of students’ disciplinary ideas, recognizing the disciplinary connections within students’ ideas, and taking up or pursuing the substance of students’ ideas.

Responsive Teaching in Elementary Mathematics: Excerpts From Ball (1993)²

In “With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics,” Ball describes an example from her third-grade classroom in which students discuss what it means for a number to be even or odd. Sean, a student in the class, presents his idea that six is both odd and even, because it is made up of three (odd) groups of two (even).³ Mei and Ofala disagree with Sean. Mei argues that if six is both odd and even, so is ten, and Sean agrees with her—according to his definition, ten is both odd and even. Mei objects on the grounds that if

you keep on going on like that, … maybe we’ll end up with all numbers are odd and even! Then it won’t make sense that all numbers should be odd and even, because if all numbers were odd and even, we wouldn’t be even having this discussion!

(p. 386)

Ofala also objects to Sean’s idea, on the basis of her sense of what makes a number even or odd: “even numbers have two in them, … and also odd numbers have two in them—except they have one left” (pg. 386), as in her drawing, replicated in Figure 1.1 below.

FIGURE 1.1 Ofala’s sense of what makes five odd: it has two groups of two and one left over.

Despite Mei’s, Ofala’s, and another student’s—Riba’s—protests, Ball tells us that Sean “persisted with this idea that some numbers could be both even and odd” (p. 386). She describes the dilemma she faced in deciding whether or not to encourage Sean and his classmates to explore patterns with “Sean numbers” as they also searched for patterns with even and odd numbers. On the one hand, she worried that doing so would confuse students, since the idea of “Sean numbers” is “nonstandard knowledge” and may therefore “interfere with the required ‘conventional’ understandings of even and odd numbers” (p. 387). On the other hand, exploring these numbers “ha[d] the potential to enhance what kids [were] thinking about ‘definition’ and its role, nature, and purpose in mathematical activity and discourse” and to “prepare the children for subsequent encounters with primes, multiples, and squares” (p. 387). Ultimately, Ball chose to “legitimize” the pursuit of “Sean numbers.”

Foregrounding the Substance of Students’ Ideas

Throughout this example, Ball foregrounds the substance of Sean’s, Mei’s, and Ofala’s mathematical ideas. In her writing, she describes each idea in detail; in the transcript, she attends to what Sean is saying by asking him whether Mei’s paraphrase of his idea is accurate, asking him, “Is that what you are saying, Sean?” (p. 386). In doing so, she maintains a stance of curiosity and openness toward what Sean means; she does not evaluate his idea against a predetermined instructional goal but instead seeks to make sense of his thinking. In the transcript that accompanies the online video of this discussion, she asks similar questions of other students, such as, “What are you trying to say?” (p. 4), “So, are you saying all numbers are odd then?” (p. 3), and “Why would that work?” (p. 4).

In addition, the students’ attention to the ideas of their peers—and to the embedded mathematics within these ideas—reinforces our sense that Ball consistently attends to and highlights students’ mathematical thinking. For example, after Sean presents his sense that six is both even and odd, Mei first revoices his idea—“I think I know what he is saying … I think what he’s s...

Table of contents

• Cover
• Title
• Copyright
• Contents
• List of figures
• List of boxes
• List of tables
• Preface
• 1 What Is Responsive Teaching?
• 2 A Review of the Research on Responsive Teaching in Science and Mathematics
• 3 Examining the Products of Responsive Inquiry
• 4 Understanding Responsive Teaching and Curriculum From the Students’ Perspective
• 5 Navigating the Challenges of Teaching Responsively: An Insider’s Perspective
• 6 What Teachers Notice When They Notice Student Thinking: Teacher-Identified Purposes for Attending to Students’ Mathematical Thinking
• 7 The Role Subject Matter Plays in Prospective Teachers’ Responsive Teaching Practices in Elementary Math and Science
• 8 Attending to Students’ Epistemic Affect
• 9 Attention to Student Framing in Responsive Teaching
• 10 Methods to Assess Teacher Responsiveness In Situ
• 11 Documenting Variability Within Teacher Attention and Responsiveness to the Substance of Student Thinking
• Epilogue
• List of Contributors
• Author Index
• Subject Index