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Amy D. Robertson, Erika P. Eppard, Lisa M. Goodhew, Emily L. Maaske, Hannah C. Sabo,
Faith C. Stewart, David L. Tuell, and Scott T. Wenzinger
Seattle Pacific University
Learning Assistant (LA) Programs — with their three-pronged approach to preparation (“prep”), pedagogy, and practice — provide novice teachers opportunities to articulate theories of knowledge and philosophies of teaching that are grounded in the practice of teaching. Research on the effectiveness of LA Programs has tended to focus on the outcomes of these opportunities in terms of recruitment of K-12 teachers,1, 2 student and LA learning and attitudes,1, 3, 4 faculty take-up and/or use of reform-oriented teaching strategies,1, 3, 5-10 and LA teaching practice or views of teaching.11-15 Little has been done to understand the experience itself — what it looks or feels like to be an LA.
This article describes one adaptation of the University of Colorado-Boulder (CU) Learning Assistant model1 from the perspective of the LAs themselves. In particular, we describe the lived experiences of seven Seattle Pacific University (SPU) LA co-authors: Erika, Lisa, Emily, Hannah, Faith, David, and Scott. We write from their perspective: these LAs met together (with Amy, the LA Program Coordinator and LA course instructor) to define the content and organization of the article, and each took active editorial and authorship roles on multiple drafts. We use the first person plural — “we” — to refer to the experiences of the LA community (sometimes including Amy), and we use the third person “Amy” when referring to her alone. We answer the questions: what are the defining experiences of SPU introductory physics LAs a, from their perspective, and how does the SPU LA Program foster such experiences?
Most notably, we (SPU LAs) experience being heard and hearing others in authentic dialogue with peers. LA Prep and Pedagogy class sessions break the traditional cycle of triadic dialogue;16, 17 we speak to one another, rather than through Amy. We revoice one another’s thoughts, ask clarifying questions, and respectfully challenge one another’s thinking. We do so around the shared experience of teaching introductory physics and engaging with STEM education research. In addition, we learn to listen to and build on student ideas in our own teaching practice. In our interactions with students, we practice intellectual empathy, seeking to understand the meaning our students are making, from the students’ point of view. We learn to notice “seeds of science” in our students’ talk and action – the beginnings of scientific ideas, reasoning or practice. “Seeds” may include, for example, a student making a connection between a physics concept and their everyday experiences, trying to make sense of a phenomenon, proposing an experiment to test an idea, or sharing an idea that has glimmers of canonical thinking. We seek to build on these “seeds of science” by, for example, designing an experiment to test a student’s idea, noticing that two students’ thinking are in conflict and seeking to foster productive argumentation, or refining a “seed” of a canonical concept in collaboration with students.
In the remainder of this article, we will explore those elements of the SPU LA Program that we (LAs) see as fostering these transformative experiences of listening and being heard, elaborating on the experiences themselves as we go. Before we begin, we will contextualize our claims in general details about the SPU LA Program model.
Unlike in the CU-Boulder program, we are required to participate in Prep and Pedagogy courses every quarter that we are an LA (rather than only the first semester of our LA experience).
Our role as LAs is framed as that of an “expert learner”: we are recruited to be facilitators of discussion, not masters of content. LAs differ from TAs in our role in the classroom — we work with faculty to support student learning during class time — and in the regular pedagogical preparation that we receive.
We consider being heard in dialogue with our peers and learning to listen to and build on student ideas in our teaching practice as the transformative experiences that define our participation in the LA Program. In this section, we point to specific programmatic elements and culture that we feel foster these experiences: the LA-driven nature of the Prep and Pedagogy courses, the way that claims are framed in class discussions, the centrality of student ideas to the theories of knowledge we discuss, our search for “seeds of science” in student talk and action, the development of our curricular and pedagogical content knowledge, and the way that the LA Program frames the role of teaching. We flesh out each of these elements and their connection to our experiences of listening and being heard. We do not mean to suggest that these elements are independent of one another; rather, we believe they are entangled but distinctly important.
Our (LAs’) experiences, questions, and interests drive the content and discussions in our Prep and Pedagogy courses.
Prep and Pedagogy course content and discussions are driven by our (LAs’) experiences, interests, and questions. We are given significant agency over the direction the course takes. Sometimes this is implicit: Amy feels genuine excitement about the ideas that we share and takes these ideas up as the backbone of our class’ inquiry into teaching and learning. She seeks out resources from the STEM education research literature that respond to our experiences and questions. Sometimes this is more explicit: Amy often brainstorms a number of productive directions our conversation could take and invites us to choose among them. In practice, what often happens is that initial ideas and questions evolve into a central question that we (the community) pursue over an extended period of time, such as, “Is it ever okay to leave students with the wrong answer?,” “What is my own theory of learning?,” or, “How can we teach in a way that is both responsive to students and responsible to the discipline of physics?” This approach — including the careful, enthusiastic attention to emergent ideas, the connecting of our (LA) experiences to the discipline of STEM education research, and the invitation to us (LAs) to participate in decision-making about the direction of shared inquiry — derives from an emerging body of literature on responsive teaching.24-30
We experience the LA-driven nature of our course as influential in promoting dialogue and listening practices in the following ways:
It communicates acceptance of our ideas. That our ideas drive the content and direction of the Prep and Pedagogy course communicates to us that our ideas are seen as productive and sensible — that Amy (and eventually we, as a community) expect these ideas to “get us somewhere,”31 even if that somewhere is simply a better understanding of ourselves and others. This acceptance and positive regard32 for our ideas fosters a safe environment in which we can share our ideas and challenge the ideas of our peers; in such an environment, we see challenges as opportunities to clarify and understand, rather than as threats.
It inspires enthusiasm for peers’ ideas. Our pursuit of our own thoughts — being challenged to think deeply about what we mean — and having Amy do so with such enthusiasm encourages us to value, get excited about, and pursue one another’s thoughts.
It focuses our attention on the substance of ideas. Amy gets most excited about the substance of our ideas33 (what we mean, where these ideas come from, and how the ideas interact with one another and education research literature); it is not merely participation that Amy values, it is the content of our participation that she notices and attends to. This brings ideas to the fore and makes them the subject of our class’ inquiry. With ideas on display, we can see their diversity and depth, and we can try on different ideas to see what it would feel like to embody these ideas in practice. Engaging with ideas in this way fosters authentic dialogue between ideas.
It cultivates a sense of community. Our experiences of having our ideas accepted, having others get excited about our ideas, and having our ideas act as a voice in the content and direction of shared inquiry support and sustain a sense of community among us. Being cared for in community — in particular, being cared for intellectually, such that our ideas are nurtured and enjoyed — further supports and sustains the acceptance, enthusiasm, and attention to the substance of ideas that foster community in the first place.34
It inspires attention to the substance of students’ ideas. Our experience of discussions that are driven by our ideas inspires us to have discussions with students driven by their experiences, ideas, and excitement. We find that we become passionate about teaching and learning — something few of us were interested in initially — through having our voices heard and our ideas taken up. Thus, we wonder whether students who were not originally interested in physics will become passionate about the subject through the experience of having their own voices drive the discussion.
It acts as a model for attending to ideas. Prep and Pedagogy course discussions provide us with examples for enriching dialogue and community-building that we then try to emulate. We practice listening to our peers and valuing their ideas in Prep and Pedagogy class sessions — appreciating the complexity and diversity of ideas that emerge — and this carries over into our teaching practice, focusing our attention on students’ complex, diverse ideas.
Claims are framed as ideas to discuss and try on.
Claims made by articles, expert visitors, and peers are framed as ideas to discuss and try on, rather than as voices of authority about teaching and learning. We are encouraged to think critically about how these theories and approaches may build upon our experiences and what we already think. A primary goal of the Pedagogy course is for us to articulate our own theories of learning and philosophies of teaching and to develop a shared, community language with which to express what we think and experience. This framing supports us in (1) participating in substantive dialogue with one another and in (2) listening to and building on our students’ ideas by:
Fostering a sense of openness toward ideas that are different than our own. Framing claims from articles, expert visitors, and peers as ideas to discuss and try on distributes the authority for assessment: ideas are weighed against our experiences and open to challenge, no matter the source. This both lowers any artificial barriers between our ideas and those presented in the articles we read — every contribution is worth considering — and reduces the risk of considering others’ ideas — we are not asked to agree or adapt unless this agreement or adaptation is authentic. This framing promotes openness to ideas that are different than our own.
Further, the openness that is modeled in Prep and Pedagogy class discussions promotes a stance of openness toward students’ ideas. It is this kind of openness that supports us in shifting our attention away from our ideas — and ultimately away from leading students down a pre-determined path toward pre-determined content objectives — toward students’ ideas and the natural course that these ideas take.
Instantiating the practices of academic debate in the scientific community. When we take up the framing we describe, we effectively treat papers and expert visitors as our peers, a form of self-initiation into the discipline of STEM education research. Discussions take on the norms of dialogue in the scientific community: we discuss and assess the ideas of our expert “peers,” test these ideas in our own teaching practice, and report back to our LA community about their experiences. We often frame our Pedagogy and Prep class activity as coming to consensus and/or understanding existing perspectives, further instantiating norms of disciplinary discussion.
Providing ideas to ‘try on’ in practice. As we say above, this framing reduces the risk of considering and/or trying on the “ways of being” proposed by the articles we read: we are not asked to agree or to permanently adapt our practice; we are asked to test these perspectives in our teaching and to report back on our experiences. We regularly modify our practice to try on an idea. In many cases, prolonged exposure to an idea shapes our practice in a more permanent way. For example, a major focus of our Prep and Pedagogy courses has been noticing and building on the “seeds of science”30 in student talk and action. Articles we read and videos we watched — such as the “Sean numbers” episode (see http://deepblue.lib.umich.edu/handle/2027.42/65013) from Ball’s “With an Eye on the Mathematical Horizon”25 — provided us (LAs) with a model for attending to the nascent science in student thinking.
Developing shared language for describing our teaching experiences. As we come to consensus around and/or seek to understand existing perspectives in STEM education research, we develop a shared language for describing teaching and learning (often an adaptation of language from the articles we read). Doing so enhances the dialogue of our community and affects our teaching practice as we take up ideas and lenses from educational research. It supports us in articulating our own teaching values and in instantiating practices consistent with these values.
We (LAs) see valuing student ideas as central to theories of learning.
Throughout the first quarter of the year, we (LAs) engage with and try on different theories of knowledge/learning — constructivism,35, 36 misconceptions and pieces,37, 38 and participation and acquisition metaphors for learning.39 We articulate our own developing theories of knowledge/learning, and we are challenged to try on those theories that resonate less with us, to see what it “feels like” to see learning through these lenses. There is often quite a bit of diversity and disagreement among us (LAs) about theories of knowledge/learning. However, in listening to one another, we realize that what all of these theories (and many of our own personal theories) have in common is the central role of students’ ideas to their learning, engagement, and agency. This recognition fosters the transformative experiences of listening and being heard by:
Providing generative content for dialogue. Theories of knowledge/learning is content that is personal and generative — it is engaging, central to the task/experience of being an LA, and connected to our experiences as students. Paired with the LA-driven nature of the course – that our ideas are central, on display, and the subject of our community inquiry — as well as the framing of claims from articles as ideas to discuss and try on, this content fosters rich dialogue.
Providing student-centric theories to try on. We have the experience of realizing that teaching that is consistent with theories of knowledge/learning must start from the same place – the student. As we attempt to implement these theories in our own practice (as a form of testing them), we focus on trying to listen to and build on students’ experiences and ideas. These experiences flesh out and reinforce the theories themselves; we buy into teaching as listening and responding to student thinking and consider successful interactions in terms of how well we understood what students were thinking.
Reinforcing the importance of student thinking to our personal teaching values. We (LAs) are encouraged not only to articulate our own theories of knowledge; we are also asked to make explicit the values that drive our interactions: why do we want to teach? What do we consider to be important goals for learning? What do we strive for in our interactions with students? Conversations around theories of knowledge bring to the fore that we (all of us) value student thinking. We do so for different reasons: some of us value student thinking because it helps us to figure out how to lead students to the correct answer; others of us value student thinking as an expression of care;32, 34, 40, 41 and still others of us value student thinking for its intrinsic sophistication and sensibility.
Recognizing that we value student thinking, we seek to put these theories of knowledge/learning into practice. Doing so not only promotes intellectual buy in to the theories, as above; the success of these interactions — and the pleasure that we experience as we engage with the thoughtful ideas of our students — also reinforces and sustains the experience of valuing student thinking, which further encourages careful attention to student ideas.
We (LAs) look for “seeds of science” in student talk and actions.
Our shared priority of valuing student thinking problematized the question of how to build on this thinking in the classroom. Influenced by our interest in fostering student agency and voice, our community began to think in terms of pursuing “seeds of science” in what students were saying and doing. We read a number of case studies of teachers who attended and responded to the “seeds of science” (or mathematics) in their students’ thinking [including Refs. 25, 26, 42], which supported us in articulating (in a preliminary way) the types of “seeds” we might notice. We began to keep teaching journals about the “seeds” we saw in our own interactions with students, supporting us in refining our original list. And we watched video of ourselves and others listening to and building on “seeds” in student talk and action to support us in putting this into practice.
Our final scheme included “seeds of scientific practice,” “seeds of scientific reasoning,” “seeds of the canon,” “seeds of connection,” and “seeds of disciplinary affect.” “Seeds of scientific practice” echo what practicing scientists do and include, for example, instances in which students are giving reasons that they disagree with one another, formulating hypotheses, testing their ideas, and noticing patterns. “Seeds of scientific reasoning” are productive beginnings of mechanistic reasoning, instances in which students’ reasoning is reasonable, mechanistic, causal, or sensible. “Seeds of the canon” are ideas that may be productive for getting the canonical answer, including ideas that are correct in certain contexts but not properly applied in a given instance, or ideas that are not fully developed but may be the beginnings of canonical answers. “Seeds of connection” are instances in which students draw on their everyday experiences to make sense of classroom physics. And “seeds of disciplinary affect” are affective experiences that mirror those experienced by practicing scientists, or that sustain and promote participation in science, such as empathizing with an object of study, expressing pleasure in figuring things out, or persisting through frustration toward figuring something out.c
Intentionally noticing and building on the “seeds of science” in student thinking is itself one of the transformative experiences that defines our participation in the SPU LA Program. To illustrate what this looks like in practice, we share two excerpts from our weekly teaching reflections. The first is Erika’s reflection on her interaction with students as they worked through the Electric Field and Flux Tutorial:
Towards the end of class, I was just listening in on the students' conversation about the last page [of the Electric Field and Flux Tutorial]. At the top of the page, the tutorial asks the students to "sketch vectors A [area] and E [electric field] such that the electric flux is" positive, negative, and zero. The paragraph above spells out how to draw the vectors so that the electric flux is positive and so that it is negative. The students all did this "correctly." It was when they got to the zero part that they all paused and didn't know exactly what to do. After a long pause, one student said, "Hey, this looks like the same thing we drew for the work tutorial!" This was most definitely a seed of scientific practice and let me tell you, I was excited!! It was awesome that they made that connection. I continued to listen to their conversation and as a table group they put together that for the electric flux to be zero, the A and E vectors must be perpendicular. Then, I asked them, "Why do you think that is so?" One student chimed in that it depends on the angle between the vectors, while another student added that if the equation for electric flux is similar to work then it should be Electric Flux = E*A*cos(angle). Another student explained that the cosine of 90 degrees is zero thus, making the electric flux zero.
Here, Erika notices that students are connecting the relationship between the electric field and area vectors (in the flux equation) to that between the force and displacement vectors (in the equation for work). She not only sees what they are doing; she celebrates it and becomes curious as to how they are making sense of these relationships, treating her students’ ideas as an object of inquiry. The second reflection, written by Hannah, is derived from interactions around the same Tutorial:
The class was working on the Electric Field and Flux tutorial. During the second section of the tutorial, it attempts to build the idea that the ratio F/qtest is a constant, and this constant is the electric field, such that F = qE. While I was working with a table, one of the students asked if "E" was like "little g," meaning the gravitational constant on Earth/a specific planet. At first I was confused by what she was trying to say, but then I realized what she meant. Fgrav = g*m1 and Felec = E*qtest. So the configuration of the electric field is a constant, in the sense that it is not dependent on the test charge, like g is not dependent on the mass. She was able to see similarities between the two that I had not realized. I really liked this interaction because she taught me something. She saw similarities that I had missed. I was also really proud to see how her thinking had been developed and refined over the course of the year. This interaction was really special to me.
Like Erika, Hannah expresses her excitement and curiosity about a connection that her students are making. When she was confused about what her student was saying, she sought to understand what she meant, remaining open and empathetic. In this quote, Hannah expresses her sense that learning from a student is a hallmark of great teaching; she has done something right as a teacher when she learns something new from a student — she was not ill prepared or uninformed.
The experience of intentionally searching for and seeking to build on the “seeds of science” in student talk and action are further influential in promoting dialogue within our community and in transforming our practice in the following ways:
It necessitates the (inherently dialogic) negotiation of shared language for building on student thinking. The process of developing a language around “seeds of science” — including the choice of which “seeds” to include in our list — was one of intense negotiation. The process was distinctly disciplinary: it began as a problem to solve — how can we put into practice our shared vision for valuing students’ ideas? It evolved into consideration of various perspectives from the literature and was fleshed out by our (LAs’) teaching experiences and collaborative viewing of video cases. Because different members of our community resonated more or less with particular perspectives, discussion often involved putting multiple ideas on the board for consideration, seeking to understand each one, and seeking to come to consensus through respectful debate.
It fosters appreciation for the sophistication and diversity of student thinking. The process of articulating which “seeds” were a part of our scheme highlighted additional foci of attention and assessment for us to try on. Doing so provided additional lenses through which to view and value student thinking and action, which fostered an appreciation for the sophistication and diversity of student thinking. In fact, looking for “seeds” often involved seeking to understand where a student was coming from, on his or her own terms, which supported us in framing ideas as grounded in students’ sense-making about their experiences. This further supported and sustained our appreciation for the complexity and sophistication of student thinking.
It promotes a sense of trust in the direction that emerges from student inquiry. In searching for “seeds,” we frame student thought and action as the beginnings of scientific ideas and practice. With experience, we find ourselves trusting that following students’ ideas will take us somewhere productive. This constitutes a significant shift away from our original perception that pursuing the natural course of student ideas is scary or is a loss of control. It also constitutes a significant shift away from listening for the familiar answer or attending to where to take the ideas, toward listening with a stance of openness toward what students are saying and doing.
We (LAs) develop curricular knowledge and pedagogical content knowledge.
Each week, in addition to going over relevant content with SPU introductory physics course instructors, we meet to develop knowledge of the Tutorials curriculum — what are the strategies it employs and what are the conceptual difficulties it seeks to address? For example, we infer that the Tutorials often employ an elicit, confront, resolve strategy to address common student difficulties.43 (This process of developing LAs’ curricular knowledge is described in detail in a forthcoming paper.44) We also seek to develop pedagogical content knowledge22, 23 including what are the productive ideas students may come to class with, and how might we elicit and build on these ideas? For example, we anticipate that students may have experiences in swimming pools or underwater diving that they can draw on in learning about pressure in a liquid. The process of developing this knowledge — and the knowledge itself — fosters our transformative experiences of listening and being heard by:
Providing generative content for dialogue. Like theories of knowledge/learning, the Tutorials curriculum is generative, personal content for us — we have had the experience of learning from the Tutorials as students, and we support courses in which Tutorials is the primary curriculum. Further, the process of figuring out what are the strategies implicit to the curriculum, the theoretical commitments underpinning the curriculum, and the student ideas that the curriculum is designed to address is intimately tied to our Pedagogy course discussions. Paired with the LA-driven nature of the Prep course and the framing of curricular strategies and sequence as ideas to try on, this content has fostered rich dialogue in our community.
Focusing on the connection between “big ideas” in physics and student ideas. Understanding what the curriculum deems important and anticipating student ideas about particular topics provides us with a framework for connecting students’ ideas to the discipline; it contextualizes our focus on building on student thinking. At the same time, knowing the “big picture” — what are the big ideas that the curriculum is seeking to develop and how do those ideas connect to past and future learning — mitigates a strict focus on the answers to specific Tutorials questions, giving us the freedom to shift our focus toward student thinking. Knowledge of the curriculum more broadly — its strategies and theoretical commitments — paired with knowledge of specific Tutorials, supports us in adapting the curriculum to each student, deviating from the details of particular sections or questions when appropriate.
Teaching is framed as a process of learning and discovery.
The SPU LA Program frames teaching as a process of learning and discovery. Amy and our introductory physics course instructors encourage us to use the classroom as a laboratory for learning about teaching and learning, and they celebrate opportunities for us to learn from our peers and students. Our primary role is to support learning (our own and that of our students), and the program does not expect us to be master teachers nor masters of content. This framing of teaching fosters dialogue within the community and affects our listening to our students by:
Alleviating our concern about “having the right answer.” Many of us become comfortable — in fact, embrace — not knowing the right answer. Framing our role as co-learners and making it clear to students that we do not necessarily have the right answer means that we can participate as facilitators of discussion and learning rather than a repository of knowledge against which students check their answers. In this process, we often learn more about the content or see it through the eyes of students as we foster dialogue amongst them and come to a table consensus. This sense of comfort in “not knowing” is connected to our conviction that students have productive ideas and that as a community we can put these ideas together in a way that makes sense.
Fostering a sense of excitement about learning from students. Hannah’s quote above speaks to the excitement that we experience when we frame our teaching as discovering what students think. One manifestation of being comfortable not knowing the right answer is that we can take pleasure in learning from our students.
Fostering collaborative teaching. When “knowing the right answer” is not a status symbol, and when “not knowing the right answer” is accepted and embraced, we can teach collaboratively, drawing on one another as resources in the classroom and fostering in-the-moment dialogue about student thinking.
Promoting students’ sharing of their ideas. Experiencing us (LAs) as co-learners — and understanding our intermediate role between that of instructor and peer — encourages students to entrust us with their ideas. The open sharing that is fostered by this trust is critical to developing and sustaining our practices of listening to and building on student thinking.
In the spirit of listening and being heard, this newsletter article shares the lived experiences of Seattle Pacific University Learning Assistants, adding to existing accounts of the effectiveness of LA Programs by describing what it is like to be an LA in one adaptation of the CU-Boulder LA model. We report that we (SPU LAs) are transformed by our experiences of (1) being heard and hearing others in authentic dialogue with peers and (2) learning to listen to and build on student ideas in our own teaching practice. We consider these to be the defining experiences of our participation in the LA Program, and we feel that these experiences foster an openness and enthusiasm toward ideas in our lives outside the classroom. Others who wish to provide similar experiences to their LAs — or to their students more broadly — may draw on the elements of our program that we perceive as fostering these transformative experiences.
Amy D. Robertson is a Research Assistant Professor of Physics at Seattle Pacific University. She has coordinated the Seattle Pacific University Learning Assistant Program since 2011 and teaches the Pedagogy and Prep courses for the introductory physics LAs.
Erika P. Eppard, Lisa M. Goodhew, Emily L. Maaske, Hannah C. Sabo, Faith C. Stewart, David L. Tuell, and Scott T. Wenzinger were introductory physics LAs at SPU during the 2013-2014 academic year. They span a variety of majors and interests including: physics with an interest in becoming a physics teacher, physics with an interest in pursuing a graduate degree in physics or physics education research, and physiology with an interest in pursuing a medical degree.
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41. N. Noddings, The Challenge to Care in Schools: An Alternative Approach to Education, 2nd ed. (Teachers College Press, New York, NY, 2005).
42. R. S. Russ, J. E. Coffey, D. Hammer and P. Hutchison, Science Education 93 (5), 875-891 (2009).
43. L. C. McDermott, American Journal of Physics 59 (4), 301-315 (1991).
44. A. D. Robertson, K. E. Gray, C. E. Lovegren, K. Rininger and S. T. Wenzinger, Physical Review Special Topics - Physics Education Research (in preparation).
45. E. Knuth and D. Peressini, Mathematics Teaching in the Middle School 6 (5), 320-325 (2001)
46. K. Brodie, Teaching and Teacher Education 27, 174-186 (2011)
47. L. Jaber, Tufts University, 2014
48. S. Michaels, Human Development 48, 136-145 (2005).
a Seattle Pacific University’s Learning Assistant Program staffs our introductory physics courses, our content courses for pre-service elementary education majors, and several of our non-majors physics courses (e.g., Physics of Sound or Nature of Science). This newsletter represents the perspectives of those LAs who staff our introductory physics courses; we will use “introductory physics LAs” and “LAs” interchangeably from this point forward.
b For example, this year, we read only two articles that presented questioning strategies: Knuth and Peressini’s “Unpacking the Nature of Discourse in Mathematics Classrooms” 45 and Brodie’s “Working with learners’ mathematical thinking: Towards a language of description for changing pedagogy”.46 The remainder of the year, we focused on theories of learning (e.g., Ref. 35-39), case studies of responsive teaching (e.g., Ref. 25 & 26), epistemic affect (e.g., Ref. 47), and culturally responsive teaching (e.g., Ref. 48).
c In articulating this scheme, we were influenced by several articles we read [e.g., Ref. 25, 26, 42, 47], by conversations with researchers who study responsive teaching, and by videos we watched [including videos from the Mathematics Teaching and Learning to Teach website, the Responsive Teaching in Science website, and the Video Resource for LA Development website].