negotiating a vision of high-quality mathematics teaching in the context of professional development...

Negotiating a Vision of High-Quality Mathematics Teaching in the Context of

Professional Development

Paul Cobb Melissa Gresalfi Vanderbilt University Indiana University

Purpose

• How teachers become motivated to improve their classroom practices

• Conflict in visions of high-quality mathematics instruction:– The school contexts in which the teachers worked– Professional development

Background: US Educational Policy

• No Child Left Behind Policy (NCLB)– Standards for mathematics learning• 50-80 standards per grade common

– Assessments at the end of each school year to test whether students are achieving these standards• Primarily procedural skills at expense of conceptual

understanding– Yearly student achievement goals in mathematics

for each school


• Most schools clueless about how to respond productively to high-stakes accountability

• School leaders respond by attempting to regulate instruction:– Teach directly to the test– Classroom management• Teaching viewed as a routine activity


• National Council of Teachers of Mathematics’ (NCTM) Principles and Standards for School Mathematics– Build on students’ current reasoning to achieve a

mathematical agenda that focuses on central mathematical ideas


• Teacher adjusts instruction to the students– Ongoing assessment of students’ reasoning

• Teaching becomes non-routine – A complex and demanding activity


• Deep understanding of mathematics– Mathematical knowledge for teaching

• Knowledge of how students’ reasoning develops in particular mathematical domains– Anticipate range of solutions

• Know-in-action how to achieve a mathematical agenda by building on students’ (diverse) solutions

National Policies as Discourses

• NCLB and NCTM constitute alternative policy Discourses– Discourse of high-stakes accountability• Increase student performance in mathematics

– Discourse of instructional reform• Improve quality of mathematics teachers’ instructional

practices(Confrey et al., 2000)

National Policies as Discourses

• Discourses are sociohistorical coordinations of people, objects (props), ways of talking, acting, interacting, thinking, valuing, and (sometimes) writing and reading that allow for the display and recognition of socially significant identities(Gee, 1997)

Overview of the Collaboration

• First two years of a five-year collaboration with 12 middle-school mathematics teachers

• Selected because resisted implementing reform mathematics curriculum

• Focused on statistical data analysis


• Over the course of the collaboration changes in:– Understanding of statistical data analysis– How teachers planned and conducted lessons• Students’ reasoning• Students’ interests - engagement

(Dean, 2005; Visnovska, 2009)


• Demanding nature of envisioned instructional practices: Critical that came to view effort involved as worthwhile– Coming to identify with this vision of high-quality

instruction made the teachers’ subsequent reorganization of their classroom practices possible


• The reform movement challenges most ways that the majority of teachers have come to view themselves and their role in the teaching and learning process. Hence, viewing the transformation from a skills-oriented to an inquiry-oriented teacher as a journey involving personal identity development is quite appropriate (Stein, Silver, and Smith, 1998)

Overview of the Presentation

• Theoretical constructs– Identities for teaching

• History of the teacher learning group• Data and method of analysis• Results of the analysis– The identities that the teachers were developing

Identities for Teaching

• Draw on two treatments of identity to accounting for the teachers’ developing motivation to improve their classrooms practices– Gee (2001)– Cobb, Gresalfi, & Hodge (2009)

Recognition and Identity

• How a person is recognized in a particular context is central to identity development– Recognized as acting in a particular way • Teaching extraneous topics

– Recognized being a particular type of person • An incompetent mathematics teacher

(Sfard, 2008)

Recognition and Identity

• How recognized is relative to the norms, values, and practices of a specific context

• An interactive accomplishment rather a set of inherent characteristics of the person

Institutional and Affinity Identity

• Gee distinguishes four different bases for acts of recognition, two of which are directly relevant to our purposes – Institutional identity – Affinity identity

Institutional Identity

• Recognized as being a certain kind of person based on the ways that a particular positional role is defined and legitimized by authorities within an institution– Mathematics teacher or principal

Affinity Identity

• Recognized as being a certain kind of person based on the ways in which she participates in a particular group – Teacher learning group

Institutional and Affinity Identity

• Same instructional practices might be (and were) recognized differently:– by school leaders– by members of the teacher learning group

• Central issues– How the teachers negotiated this tension– The identities for teaching that they were

developing

Normative Identity for Teaching

• The set of obligations that a teacher would have to fulfill to be recognized as a competent mathematics teacher in a particular setting – Normative institutional identity– Normative affiliation identity

• Collective or communal notions with respect to which teachers are recognized as effective or nor by others in these two settings

Personal Identity for Teaching

• Extent to which a teacher identifies with the obligations for effective teaching established in a particular setting– Three cases to consider


• Sees little value in what counts as effective teaching established a particular setting but attempts to comply with others' expectations – Attempts to fulfill obligations-to-others


• Comes to identify with what counts as competent teaching in a particular context and thus becomes motivated to develop instructional practices of this type – Obligations-to-others become obligations-to-

oneself


• Identification viewed as a process whereby communal activities “in which one has been acting according to the directions of others becomes a world that one uses to understand and organize aspects of one’s self and at least some of one’s own feelings and thoughts”(Holland et al., 1998)


• Oppose what counts as competent teaching in a particular setting by developing contrary instructional practices– Obligations-for-others but not oneself

Normative and Personal Identity

• What matters are:– The ways that that a teacher's instructional practice

are interpreted, named, and reified with respect to the standards for good teaching established in a particular context (normative identity)

– The ways in which the teacher responds to these acts of recognition (personal identity)

Illustration

• Classroom in which:– Instructional focuses on central mathematical

ideas– Noise level is relatively high as students work

together– Students move around the room on their own

initiative to get materials, to talk to other students, etc.

Illustration

• The teacher might apologize for her students’ behavior, and might be or anxious and embarrassed when the principal or another school leader observes her teaching – Developing a personal identity as an incompetent

teacher

Illustration

• The teacher might challenge how she is recognized by school leaders – Developing a personal identity as a renegade

reform teacher

Normative and Personal Identity

• How recognized in a particular setting shapes but does not determine the personal identity that a teacher is developing in that setting– Social structure – normative identity– Agency – personal identity

Summary: Analytical Constructs

Institutional IdentityAffinity Identity

Normative Institutional Identity Normative Affinity Identity

Personal Identity

Background: The Teacher Learning Group

• 12 middle-school mathematics teachers– Students 12-14 years old

• Taught in 5 different schools– 60% minority student population

• US state with a high stakes accountability program


• First summer: 2 days• First school year: 3 days• Second summer: 3 days• Second school year: 6 days• Third summer: 3 days


• A design experiment– Our overall goal was to improve our initial design

for supporting the teachers’ learning• Tested and revised conjectures about:– The process of the teachers’ learning– The means of supporting that learning


• We designed the types of activities in which the teachers engaged– Our overall goals for the teachers’ learning– Analysis of prior sessions– Teachers’ expressed needs


• Planned for future sessions by analyzing:– Video-recordings of prior sessions– Products the teachers’ created in those sessions

• Ongoing revision of our conjectures


• Primary focus: Statistical data analysis– Teachers engaged in instructional activities that

had been designed, tested, and revised during a prior research project• Classroom design experiments conducted with middle-

grade students

Goals During First Two Years

• Support the development of the teachers’ statistical reasoning– Worked through data analysis tasks as learners– Launch + computer tools + whole class discussion


• Support the teachers in supporting the development of their students’ statistical reasoning– Used statistics activities in their classrooms– Analyzed their students’ work in the next session


• Support the development of a genuine learning community

• Instructional practices initial highly privatized– Became deprivatized after 18 months– Accounts of their classroom instruction became

topics of conversation


• Video-recordings of other classrooms– Statistics design experiment– TIMSS video-study

• Activities in which their school settings became an explicit focus– Summer 3: Activity in which they clarified aspects

of the school settings that they wanted to work to change

Summary: Goals During First Two Years

• Increasingly sophisticated forms of statistical reasoning

• Increasingly effective practices for supporting the development of their students’ statistical reasoning

• A genuine learning community

Data Collection

• Video-recordings of all professional development sessions– 90 hours

• Audio-recordings when worked in groups• Interviews conducted with principals of 4 of 5

of the teachers’ schools

Analysis: Normative Identity

• The normative institutional identity for mathematics teaching as perceived and described by the teachers– Perceptions of school leaders’ expectations that were

constituted as legitimate in the group– Triangulated with principal interviews

• The normative affinity identity for mathematics teaching constituted in the teacher group– Emerging expectations to which the teachers held each

other accountable during discussions of and reflections on teaching


• Identified and coded exchanges that focused on: – What it means to be a teacher– What counts as good teaching– The standards to which they were held

accountable in their teaching


• Determined whether discussing:– Aspects of the institutional settings in which they

worked– The practices of the teacher group


• 156 exchanges– 53 related to the school setting– 52 related to the teacher learning group– 51 were not classified

Analysis: Personal Identity

• The personal identities the teachers were developing concern the extent to which they identified with vision of high-quality teaching that was normative in the two settings– Consented or resisted expectations for high-

quality teaching in the two settings

Analysis: Personal Identity

• When individual teachers consented, focused on their valuations of their obligations:– Complying – obligations-to-others• Arbitrary, frustrating, constraining, debilitating

– Identifying – obligations-to-oneself• Reasonable, enabling

Findings: Normative Institutional Identity

• Covering state standards• Attending to generic features of instruction• Teaching as a solo activity

Covering State Standards

• Recurrent themes:– Ensure that students performed well on the state

test– Only teach state standards


• T1: One good example, we were doing [a statistics activity] yesterday, my principal came in [and] she saw me at the overhead and the room was kind of dark and the kids were talking about batteries. And she is looking at me like, “End of Grades Test and you are talking about batteries?" And she left the room and didn’t say nothing.(Year 1, February)


• R1: When your principals come into your classrooms, what do you think they are looking for?

• T3: When my principal comes into my classroom, he wants to see an objective written in the corner of the board saying what specific piece of the end-of-grade test I am working on that day.

• R2: Do you mean the Standard Course of Study [state mathematics objectives]?

• T3: Yes, Standard Course of Study, but that is really for the EOG test. He wants to be able to walk into my classroom and tell in 10 seconds, what part of the test I am teaching. (Year 2, June)


• Principal interviews:– All 4 mentioned the importance of students

performing well on state tests– 2 explained that this focus was expected by the

administrators to whom they were accountable

Attending to Generic Features of Instruction

• Recurrent theme:– Classroom management rather than aspects of

teaching that were specifically mathematical or that related to student learning


• T5: They are trying to require us to observe others during our planning period. We just got the results of what we are looking at... [W]e looked at the lack of discipline of the kids, well that is what we, I guess by nature, have focused on instead of content, we looked at how someone handles the classroom first, and then we starting to break down the walls.

• T6: Well that is how we have been evaluated for so long.• T7: Exactly,• T5: Yeah.• Other teachers: Yeah.

(Year 2, October)


• Principal interviews– All 4 said they evaluated the quality of instruction

by focusing on whether the classroom was under control, how many students raised their hands, etc.

Teaching as a Solo Activity

• Complained repeatedly that they did not have time talk with or work with others– Times allotted for joint work were frequently

appropriated by other tasks authorized by school leaders

• The implicit message was that being an effective teacher did not involve collaborating with others


• T2: I think that one of the important things is that we mentor new teachers. But of course, there is no real time to do that.

• R3: It is so important to find colleagues to discuss math content with. It’s just such a resource—and it’s important to find time to have these discussions.

• T2: You know, that’s what our study groups were supposed to be about. Each middle school was supposed to meet six times a year and talk about what was working with the [reform mathematics curriculum] and what wasn’t working. This was


• all supposed to be structured by [the district math coordinator’s] grant. But nothing ever really happened…and of course with the winter a couple of the meetings were cancelled because of the weather.

• Teachers discuss when study group will next meet.• T4: You know, I think it’s a great idea about meeting

together, but I don’t have a lot of time to do it, and I don’t feel compensated enough for the time I put into it. I am spending so much time already on lesson plans, etc. (Year 1, September)


• Principal interviews:• All 4 valued teacher collaboration – interdisciplinary

grade-level teams rather than discipline-specific teams• Consistent with focus on classroom management

Findings: Normative Affinity Identity

• Instructional goals – central mathematical ideas

• Students’ as capable of learning• Teacher collaboration

Instructional Goals: Central Mathematical Ideas

• Issue of what goals for mathematics instruction should be was a repeated topic of discussion– Teachers frequently disagreed– Supporting both students’ reasoning about central

mathematical ideas and their mastery of facts and procedures


• T5: The harsh reality is, if our schools can structure our course offerings that would expose kids to having to think, to take the pressure of having to cover for a test, to create a course that allows risk taking and room for error and room for debate on why they think their answer is valid. Then our thinking would definitely improve, but unfortunately the people who need to hear this [i.e., school leaders] are not here. The reality of a course may never ever be created.

• T1: But why can’t we do that with anything we teach now?• T10: Yes, I think…• T5: It would in essence mean that state department of public

instruction would have to sit down with people and rethink and reword how they suggest, create an equilibrium for not instruction but for curriculum, there is a difference.


• T1: I can think of so many things that I am supposed to teach now, or have taught in the last few of weeks, and if I could use the strategy of actually sitting down and talking with my students, getting to understand what they feel about the topic, what they really understood about it and gone on from there and they probably would have learned a whole lot more than standing up and saying, today we are going to do this, da,da,da,da,da….

• T5: Oh, yeah.• T1: And I am about making changes within the system. I am not

happy with the way the system is now. So I can see doing this with any lesson, I would have to teach to make a difference. (Year 2, October)


• Summer 3 - 9 teachers present– 3 (including T1): Convinced important to focus on

central mathematical ideas– 4: Mathematical ideas should be central but

occasionally made contrary comments– 2 (including T5): Continued to struggle with this

issue• Questioned feasibility of focusing on mathematical

ideas


• Types of activities:– Completed statistical activities as learners and

then focused on supporting students’ development of similar understandings

– Designed and then conducted individual interviews with their students

Students’ as Capable of Learning

• Initially characterized students as:– Having ability or not– Being motivated or not• Inherent characteristics of students• Students’ social backgrounds

• Deficit language about students was gradually displaced by talk about why students thought or performed in particular ways


• T7: I think that is the hardest part [in accomplish mathematical goals with my students] right now, T5. And with mine I was very, very frustrated, except with one class, I was very frustrated, because they just did not want to think. They wanted me to tell them what they were supposed to be coming up with and do it.

• T1: Because they are so used to it. • T7: Yes.• T1: They expect us to do it.


• T7: And if I can get them to think…• R4: But they are not born that way, right?• T1: No.• T7: No.• R4: They have learned it.• T7: Yeah, they have learned it.• T1: They have learned it. • T7: Yeah, my third grader [son] is not like that.

(Year 2, October)


• Types of activities:• Discussions of the reasons for students’

understandings or misunderstandings– Failure to learn did not necessarily indicate a lack

of mathematical ability

Teacher Collaboration

• View of collaboration evolved over the two years

• Began to emphasize the value of collaboration when:– Preparing to teach, particularly when anticipating

how to respond to student contributions• Emerged as an important aspect of being an

effective teacher


• Types of activities– Co-planning a lesson and then observing one of

the group teach the lesson– TIMSS Video Study• US and Japanese 8th grade geometry lessons

– Japanese lesson study


• T3: I like very much the idea of us planning together, it gives us more time to strategize, plan minute by minute, think of key driving questions, have more discussion.

• R4: That would have been helpful to do more?• T3: Yes, in that way it’s kind of scripted for us, it takes a

level off us… I can make notes about whether something worked or not. It didn’t feel like I cut the launch short because it felt to me like comments were on target. But clearly, that’s not what’s going on often…


• T7: It was so helpful to have someone else teaching my kids for a time; I could watch them, and concentrate on what they were doing.

• T9: Yes, that’s so helpful.• T7: Like when T6 came in and taught, I could watch my

kids, it was much easier. It almost takes having someone else in there to give you feedback.(Year 2, November)

Summary

• Normative institutional identity– Covering state standards– Attending to generic features of instruction– Teaching as a solo activity

• Normative affinity identity– Instructional goals – central mathematics ideas– Students’ as capable of learning– Teacher collaboration

Findings: Personal Identity

• Extent to which the teachers were developing a sense of affiliation with the normative identities constituted in their schools and in the teacher group – Little variation among the teachers

Complying with and Resisting the Normative Institutional Identity

• Repeatedly critiqued many of their school leaders' expectations– Obligations-for-others rather than “obligations-for-

oneself• Few instances in which a teacher spoke of

explicitly disregarding school leaders’ expectations

Complying with and Resisting the Normative Institutional Identity

• Could legitimately exercise considerable agency in the institutional settings of the their schools– Developed strategies for challenging and

attempting to change principals' expectations about high-quality mathematics teaching

• Resistance and compliance


• Stated explicitly that school leaders’ expectations for instruction were incompatible with supporting students’ understanding of mathematical ideas

• Attempted to comply• Frustrated that doing so interfered with their

ability to address instructional goals that they believed to be valuable


• Saw value in the expectation that they manage their classrooms effectively

• However, high-quality mathematics teaching involves much more than this– A complex and demanding activity rather than

routine activity


• T2: You know, if our principals don’t buy into [the reform mathematics curriculum] and see a need for it, it’s going to be hard to get the other teachers motivated to teach in this way. I don’t know if the principals are really behind it—they have tunnel vision.

• T7: I know. My principal just looks at the surface appearance of things, like the work displayed in the classroom. They talk a good game. But you know, there are many teachers who talk a good game but don’t do squat.


• T2: Well basically, principals are not instructional leaders; they don’t really know what we’re doing. Their focus is on doing things like ordering the janitors and dealing with issues of discipline with students.

• Complying rather than overtly resisting


• Resisted the school leaders’ view of mathematics teaching as an independent activity– Strategized to get common planning time

Identifying with and Complying with the Normative Affinity Identity

• When strategized to change aspects of the school settings, aimed for alignment with the vision of high-quality teaching emerging in the group – Normative affinity identity

• Attempted to change institutional expectations and resources rather than redirect the professional development sessions – Becoming obligations-for-oneself


• Supporting students’ understanding of mathematical ideas as well as their learning of facts and procedures

• Strong evidence was becoming an obligation-for-oneself for all the teachers– 19 exchanges– 6 classified as complying– 13 classified as identifying

Students as Capable of Learning

• Understanding why students thought or performed in particular ways

• Strong evidence was becoming an obligation-for-oneself for all the teachers


• Task - determine seven numbers whose average is1.39

• One student had divided 1.39 by seven


• T1: I am trying to understand what she was thinking to make her even do it. And they should have the opportunity to explain it to me and get me to understand.

• T7: So if you could have put 19 cents on each bag and said, ok, find the average. Then maybe she would have seen…

• T1: That was what I was trying to get to, but yeah


• T7: Then maybe she would have seen, oh! The total is 1.39.

• T1: Exactly, but she didn’t have the opportunity to at least look at it for what it was worth, and maybe make some adjustments after she realized she was totaling wrong.


• All the teachers appeared to view their collaboration as valuable

• Strong evidence was becoming an obligation-for-oneself

Teacher Collaboration• T3: I have another generalization—I think that working with

specialists and colleagues is a really positive thing. In those situations, planning time does not include the traditional idea of making photocopies. Instead it’s time to sit down and have professional conversations. We need to get out of the box that planning is making photocopies, and to having these type of conversations.

• T7: If everyone plans together at the same time, it would be less stressful.

• T6: I guess that’s true, but also doing that involves using your time more wisely.

• R3: So is it isolation?• T2: We are very isolated!

Summary

• Normative institutional identity– Complying and resisting

• Normative affinity identity– Identifying and complying

Summary

• We guided the development of a normative vision of high-quality instruction– No guarantee that we would succeed, or that

teachers would identify rather than merely comply• Claim: The analysis explains how a group of

teachers became motivated to improve their instructional practices in a not particularly hospitable institutional setting

Theory

• Integrated two treatments of identity:• Gee (2001) stressed that different bases for

recognition are interrelated but did not discuss the nature of these interrelations

• Normative institutional and affinity identities can be in conflict – Conflicts of this type do not appear to be unusual

Practice

• Previous work has demonstrated the importance of understanding the identities that teachers are developing– Reconceptualize what is involved in learning to

teach effectively• Previous work has not examined the process

by which teachers resolve conflicts between different visions of high-quality teaching

Practice

• The teachers came to view the institutional settings in which they worked differently– By the end of the two years, they saw themselves

as having greater expertise than their principals – The institutional vision of high-quality instruction

increasingly came to lack legitimacy

Practice

• Significant: The teachers' identification with the normative affinity identity made possible the subsequent improvements in their instructional practices – Conjecture that this might be the case more

generally

Practice

• Successful professional development supports teachers in:– Reconceptualizing what it means to teach

mathematics – Coming to view the effort required to reorganize

their classroom practices as worthwhile

Practice

• Clarifying the challenges in professional development

• Understanding why particular designs for supporting teachers' learning are effective or not requires documenting:– The normative identities constituted in the various

contexts in which teachers participate – The extent to which teachers identify with those

identities

negotiating a vision of high-quality mathematics teaching in the context of professional development...

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