It’s that time of year — I get to brag on my amazing students and mentees for their important research.
(I am going to focus on journal articles here, but if you want to see more about what we are finding on the National Science Foundation-sponsored project, my lab’s major current research project, Supporting Instructional Growth in Mathematics study (Project SIGMa), you can look here.)
For those of you not familiar with my lab, we study teachers’ sensemaking from an anthropological perspective. We blend a mix of methods to really dig into how teachers (mostly math teachers, mostly teaching in urban secondary schools) understand what they are up to, with an eye towards how different social arrangements and activities shape those meanings. This approach supports the development of ecologically valid models of teachers’ learning and, relatedly, context-sensitive designs for instructional improvement.
Looking at how teachers monitor student-led work
Nadav Ehrenfeld & Ilana Horn (2020). Initiation-entry-focus-exit and participation: a framework for understanding teacher groupwork monitoring routines. Educational Studies in Mathematics. 103, 251–272 https://doi.org/10.1007/s10649-020-09939-2
In this paper, we offer a framework for teacher monitoring routines—a consequential yet understudied aspect of instruction when teachers oversee students’ working together. Using a comparative case study design, we examine eight lessons of experienced secondary mathematics teachers, identifying common interactional routines that they take up with variation. We present a framework that illuminates the common moves teachers make while monitoring, including how they initiate conversations with students, their forms of conversational entry, the focus of their interactions, when and how they exit the interaction as well as the conversation’s overall participation pattern. We illustrate the framework through our focal cases, highlighting the instructional issues the different enactments engage. By breaking down the complex work of groupwork monitoring, this study informs both researchers and teachers in understanding the teachers’ role in supporting students’ collaborative mathematical sensemaking.
(Here is a blog post written by folks at Vosaic, the video-coding software that we used in this analysis.)
Considering Ethical Dimensions of Mathematics Teaching
Grace A. Chen, Samantha Marshall, & Ilana Seidel Horn (2020). “How do I choose?” Mathematics Teachers’ Sensemaking about Pedagogical Responsibility. Pedagogy, Culture & Society. https://doi.org/10.1080/14681366.2020.1735497
Teachers’ decisions are often undergirded by their sense of pedagogical responsibility: whom and what they feel beholden to. However, research on teacher sensemaking has rarely examined how teachers reason about their pedagogical responsibilities. The study analyzed an emotional conversation among urban mathematics teachers about what they teach mathematics for, given the many non-mathematical challenges they and their students face. The familiarity and simplicity of love and life skills narratives deployed to describe what it means to be a good teacher and to do good teaching may be comforting, but limit teachers’ engagement with other authentic forms of pedagogical reasoning about their pedagogical responsibility in complex sociopolitical contexts. The findings reveal the importance of opportunities to explore alternate possibilities ‘for what,’ especially within structured and supportive teacher collaborative group
(Here is a research outreach document that summarizes this work nicely.)
Taking Seriously the Meaningful Preparation of Black Women Teachers
Mariah D. Harmon and Ilana Seidel Horn (in press). Seeking Healing through Black Sisterhood: Examining the Affordances of a Counterspace for Black Women Pre-Service Teachers. AILACTE Journal.
Calls to increase diversity in the United States teacher workforce emphasize benefits to students without strategic consideration of minoritized teachers’ needs. In this ethnographic study, we investigate the affordances of a counterspace for Black women pre-service teachers in a predominantly white institution to support their development as educators. Using a grounded theory approach, we analyze fieldnotes from one meeting to understand how the counterspace offered participants a space to reconcile with contradictions experienced working in schools. The counterspace contributed to participants’ healing in three ways: (1) it made space for participants to interrogate their own experiences in U.S. schools; (2) it offered insider connections, a fundamental sense of belonging and legitimacy; and (3) it busted the myth of the monolith, by inviting the breadth of Black women’s stories and histories. These findings suggest that building community through shared identity markers can foster a rich environment for teacher development.
The Impact of Strong Teacher Collaboration on Teachers’ Advice-Seeking Networks
Ilana Horn, Brette Garner, I-Chien Chen, and Kenneth A. Frank. (2020, April). “Seeing Colleagues as Learning Resources: The Influence of Mathematics Teacher Meetings on Advice-Seeking Social Networks.” AERA Open 6(2): 2332858420914898.
Teacher collaboration is often assumed to support school’s ongoing improvement, but it is unclear how formal learning opportunities in teacher workgroups shape informal ones. In this mixed methods study, we examined 77 teacher collaborative meetings from 24 schools representing 116 teacher pairs. We coupled qualitative analysis of the learning opportunities in formal meetings with quantitative analysis of teachers’ advice-seeking ties in informal social networks. We found that teachers’ coparticipation in learning-rich, high-depth meetings strongly predicted the formation of new advice-seeking ties. What is more, these new informal ties were linked to growth in teachers’ expertise, pointing to added value of teachers’ participation in high-depth teacher collaboration.
Methods for Studying Teachers’ Collaborative Learning
Ilana Horn & Nicole A. Bannister (2020, February). Interactionist Perspectives on Mathematics Teachers’ Collaborative Learning. International Commission of Mathematics Instruction Study Conference. Lisbon, Portugal. (Link to paper)
Interactionist analyses of teachers’ professional conversations respond to open questions about collaborative mathematics teacher learning in ways that are proximal and relevant to their lived experiences and everyday work. Drawing on situative theories of learning, we analyze partitioned conversational records for evidence of learning. Key findings from our prior studies point to four design considerations for interventions that seek to leverage the potential of mathematics teacher collaboration: (1) deeper collaboration is relatively novel and rare for teachers; (2) development of a shared vision for teaching is essential and deliberate work; (3) adequate representations of teaching are necessary for supporting intersubjectivity about core instructional ideas; and (4) frames are an important site for reconceptualization of key ideas about teaching. Examples from our current projects show the application and broader utility of these findings for interventions that use collaboration to support mathematics teacher learning.
A STRANGE NEW WORLD: PRE-PRINTS
For the first time, I have also been experimenting with pre-prints. Grace Chen and I received support from the Gates Mindset Scholars network, where we were introduced to this practice. Then, last spring, Katherine Schneeberger McGugan and I embarked on an interview study of experienced secondary mathematics teachers’ transitions to virtual instruction during the pandemic. Because of the timeliness of our findings, we felt compelled to share on a quicker timeline than the usual publication process permits. Finally, Grace and I collaborated with sociologist Jessica Calarco on an analysis of inequalities produced through elementary and middle school math homework, which also seemed urgent, since currently all school is homework.
A Literature Review Synthesizing on How Students Get Marginalized in Mathematics Classrooms
Grace A. Chen & Ilana Seidel Horn (2020, August). Mechanisms of Marginalization in Mathematics Classrooms: A Call to Critical Bifocality. DOI: 10.31219/osf.io/nv6kd
In light of decades of research seeking to document and transform extensive injustices in mathematics education in the United States, we examine how different conceptualizations of which students are marginalized and by what processes they are marginalized in order to contribute to a more thorough, nuanced understanding of marginalization in mathematics education. To do so, we review literature theorizing marginalization across social identity categories and synthesize the disciplinary traditions they draw on and the mechanisms of marginalization they articulate. Findings from this review highlight the normality of marginalization in mathematics education, the material and ideological means of marginalization, and the interlacing of individual and structural sources of marginalization. As a result, we argue for critical bifocality in attending simultaneously to the processes of marginalization that occur in individual mathematics classrooms alongside the systemic structures that organize marginalization in society more broadly.
How Experienced Secondary Urban Mathematics Teachers Transitioned to Virtual Teaching
Ilana Seidel Horn & Katherine Schneeberger McGugan (2020, June). Adaptive expertise in mathematics teaching during a crisis: How highly-committed secondary U.S. mathematics teachers adjusted their instruction in the COVID-19 pandemic. DOI: 10.13140/RG.2.2.13720.83200
The global COVID-19 pandemic disrupted education across the world, requiring a quick re-organization of instruction on a large scale. In this study, we examine how highly-committed secondary mathematics teachers in the U.S. responded as they shifted their instruction online. Building off a four-year research practice partnership, we interviewed 11 secondary mathematics teachers whom we conceptualize as adaptive experts –– experienced teachers who responded flexibly and with an openness to learning –– about their pivot to online instruction. Conducting semi-structured interviews during school closures, we found that, while the teachers maintained commitments to ambitious and equitable teaching, new dilemmas arose around time management, centering student thinking, and building and maintaining relationships. By documenting how highly-reflective educators responded to this crisis, we highlight issues for others to anticipate in times of educational disruption, as well as contribute to the field’s understanding of adaptive expertise in mathematics teaching.
Jessica Calarco, Ilana Horn, and Grace A. Chen (2020, August). “You Need to Be More Responsible”: How Math Homework Operates as a Status-Reinforcing Process in School. DOI: 10.31235/osf.io/xf96q
Practices like ability grouping, tracking, and standardized testing operate as status-reinforcing processes—amplifying then naturalizing unequal student outcomes. Using a longitudinal, ethnographic study following students from elementary to middle school, we examine whether math homework can operate similarly. Because of inequalities in families’ resources for supporting homework, higher-SES students’ homework was more consistently complete and correct than lower-SES students’ homework. Teachers acknowledged these unequal homework production contexts. Yet, official policies treated homework as an individual endeavor, leading teachers to interpret and respond to homework in status-reinforcing ways. Students with consistently correct and complete homework were seen as responsible, capable, and motivated and rewarded with praise and opportunities. Other students were seen as irresponsible, incapable, and unmotivated; they were punished and docked points. These practices were status-enhancing for higher-SES students and status-degrading for lower-SES students. We discuss implications for homework policies, parent involvement, and interpretations of inequalities in school.
Finally, I would be remiss if I did not shout out a new book by my former advisee, Elizabeth Self, and my colleague, Barb Stengel: Toward Anti-Oppressive Teaching: Designing and Using Simulated Encounters. They wrote about the incredible work they have led on the SHIFT Project, which has transformed Peabody’s teacher preparation program.
We will have more to share in the new year… Patricia Buenrostro and Nadav Ehrenfeld have a paper about a teacher’s reasoning about productive struggle, a key construct in a lot of mathematics reform … Samantha Marshall’s recently defended dissertation, Responsive, Locally-Relevant Coaching: Supporting STEM Teachers’ Learning of Justice-Oriented Pedagogies, should be yielding some publications … and our team, led by myself and Brette Garner, is developing a book describing our theory of teacher learning.
About 5 years ago, I wrote a blog post calling out the problematics of Teach Like a Champion (TLAC). It gained a bit of traction, started some conversations about why this very controlling pedagogy was becoming so popular in schools that served primarily Black and brown children.
After this past summer of 2020, with the murders of George Floyd, Breana Taylor, Amaud Arbery and so many others, the Black Lives Matter movement became re-centered on the conversation about anti-Black racism in the U.S. and its all too frequent lethal consequences.
In June, I participated in #Strike4BlackLives, led by physicist Chanda Prescod-Weinstein, re-upping that post along with a more explicit call to name the dominating and controlling TLAC approach as a tool for anti-Blackness. I encouraged people who agreed with my perspective to let their opinions be known on public forums like Amazon or Goodreads, since the book’s popularity continues unabated.
Subsequently, education journalist Jennifer Berkshire and historian Jack Schneider did a story on their Have You Heard podcast about TLAC and its racism problem. Interestingly, I learned from listening to the episode that TLAC’s emphasis on controlling Black children’s bodies has eerie resonances with Reconstruction-era teaching approaches for formerly enslaved children, with a lot of anti-Black notions of “correcting” their amoral character.
So here we are in September. I am participating on Tuesday, September 8 in the Scholar Strike for Racial Justice, a mass action of higher education professionals protesting racist policing, state violence against communities of color, mass incarceration and other manifestations of racism.
I encourage you to follow #SCHOLARSTRIKE on Facebook, Instagram, and Twitter, and to engage with the teach-in occurring on the Scholar Strike YouTube channel.
My contribution to the teach-in is available here. I will also be holding a Twitter #SlowChat using the #EndCarceralPedagogy hashtag on Tuesday, September 8, posting questions every hour from 8 AM to 4 PM Central time. Please join me if you are able to .
Humor serves many functions in my life. Noticing the absurd. Playing with unexpected associations and enjoying the surprise. Sharing inside jokes with friends. Resisting, venting, and gaining temporary relief about abuses of power by belittling them with laughter.
I am obviously not unique in this. Humor is a crucial part of being human in a complex (and often ridiculous) world.
But humor –– especially in certain forms –– is not always welcome in school. What does this mean for students’ expressions of their humanity? Think about the well known class clown archetype. Some educators use this label with derision, assuming students step into this role for negative reasons, like avoiding work or garnering attention that distracts from lessons, making the teacher’s job harder.
The essential role of humor for many people’s ways of being in the world is thus in tension with many ways of “doing school” that require deference to the teacher’s authority. This leads to dilemmas for those of us who want to build inclusive and humanizing classrooms. We get many messages from administrators, teacher educators, and other colleagues that a good class is an orderly class, one where the teacher leads and students follow, not one where spontaneous outbursts might be embraced and incorporated, where laughter might be happening in small groups, or where a class clown can have a legitimate place in learning –– even be an important member of the community.
Personally, I knew early on I was going to struggle to navigate my own predilections with these common images of “good teaching.” During my student teaching, I accompanied a group of seventh graders on a field trip to the courthouse to observe a trial. Our guide welcomed us to the courthouse and looked at the docket to see what case we would be viewing.
“Oh, good. It’s a nice, clean trial,” she said.
“Dang!” said one student, leading me to snicker audibly.
Some nearby students turned to me in surprise: Wasn’t I supposed to scold him for his lack of decorum? Perhaps I was. But as a human, I loved his reaction for its honesty. In fact, much of my joy as an educator comes from engaging students’ clear eyed honesty, which extends to their disappointment about a “nice, clean trial.” I realized then that I would need to develop a way to enforce behavioral norms (many of which I myself find challenging to adhere to) and my genuine appreciation for his rascally reaction.
Let me be clear. I am not suggesting an “anything goes” approach to humor in schools. Educators resist humor for many reasons. Humor can be subversive. Humor can be exclusionary. And, obviously, humor can be mean. But shouldn’t we have a way of inviting some humor into our math classrooms? Can we pick and choose with a little more care?
Seeking a framework for humor in math classrooms
Recently, I have been working with my colleague, Dr. Nicole Joseph, and an undergraduate research assistant, Yasmin Aguillon, to look at humor in math classrooms.
Dr. J and I are working on this together for a few reasons. We share a commitment to welcoming students’ full humanity into the math classroom and seek to help teachers understand what that entails. In one of her recent articles, she and her colleagues heard from Black girls that they wanted math classes to be a place to be their full selves, including the silly and “goofy” (an adjective one of the participants used). We also share that our ways of being in the world do not require us to put our own silliness in a box when we are doing work. We can sing, tell jokes, code switch –– play –– while we are working on things we deeply care about. This, in our lived experience, is not at odds with deep and rigorous work. In fact, bringing our authentic selves to our work only enhances its depth and rigor.
Dr. Nicole Joseph and me, clowning with math at the Escher Museum
To build our framework, we draw on several sources. First, we have looked at research on humor in social life, especially classrooms. Second, we have looked at classroom level data from my recent research project where students are clowning around. Finally, we conducted a completely unscientific #MTBoS #iteachmath twitter poll on whether math teachers felt humor had a place in the classroom.
We are working on a fuller discussion of humor in math class, but for the purposes of this blog post, I want to suggest the following:
The playful –– and even the subversive –– aspects of humor belong in math class, not only because they allow students to more fully be themselves, but because they embody important mathematical habits of mind and allow entrée for students’ broader identities. At the same time, we recognize that inviting humor may require teachers to develop new forms of teaching and cultural competence.
Playful and subversive humor belongs in math class
If you think about the pleasurable aha! of mathematics, you might notice its similarity to the pleasurable moment of getting a joke. The common experience is that of insight.
Mathematics has its share of jokers. Aside from famous people like Lewis Carroll who enjoyed playing with logic, we have mathematical entities that upend the order of things. Infinity and zero subversively violate our expectations of how operations and functions work: what do you mean we can’t divide by zero? why do functions change when we imagine taking them to infinity? The whole field of topology essentially invites us to imagine that objects as made of rubber, making a coffee mug “the same” as a donut. These delights of insight and absurdity tickle any good rascal.
When we invite humor into math class, we also change the emotional tenor of what we are doing. Humor positively effects learning by releasing tension. When we laugh, we are at often more at ease. Humor has even been shown to improve students’ performance on tests. Maybe laughing sessions can improve study sessions. Humor can build rapport, either with individual students or with a classroom community. I know a teacher who strategically looks for something to laugh at with each of his classes, so that they can have a shared inside joke.
Humor also invites students’ broader identities into their learning. Who we are is fundamental to how we make sense of the world; when we have to leave part of our selves at the door in order to be seen as “acceptable,” we abandon crucial sensemaking resources. Although laughing at my student’s response to the “nice, clean” court case may have not followed a proper teacher script, it appreciated him for the twelve year old boy that he was and his understandable wish for a meatier, dirtier case. In sanitizing the world for children, often in the name of protection, we omit important details. By the time they are twelve, they have often started to question who is actually protected through adult judgments of “appropriateness.” This kind of questioning signals curiosity and intelligence.
Why wouldn’t we welcome such attitudes in school?
Teachers may need new forms of teaching competence to productively support humor in class
Indeed, in our completely unscientific twitter poll of 741 people on the Internet, 94% of respondents agreed with our idea that humor belongs in math class. Among the 31 respondents who elaborated on their reasoning, we found that most people (64.5%) referred to math humor, like math puns and math jokes. The next most mentioned form of humor were intentional mistakes (12.9%), a pedagogical strategy where teachers present an incorrect solution and humorously play at not understanding to prompt student explanations. Most of the remaining responses referred to negative forms of humor such as sarcasm (9.7%), put downs (6.5%), or teasing (3.2%).
What is interesting about these responses, as limited as they might be because of the nature of the poll, is that the positive examples of humor are teacher-centered; that is, they are controlled by the teachers’ choices about curriculum and pedagogy. The negative examples signal adverse relationships, whether from students to the teacher, teacher to students, or among students themselves. But, in the examples offered, we do not see examples of how students themselves can be a positive source of classroom humor.
We suspect this is because student-derived humor is trickier teaching terrain. (Or it may be due to the limitations of our completely unscientific Twitter poll.)
Building off of the first interpretation, we acknowledge that there are many shades of gray when we laugh with students. How do we navigate the ideas of “appropriate” that can vary so much within a classroom, let alone a broader school community?
Once we open the door to students’ humor, how do we ensure that positive humor does not cross over into the exclusionary humor that can lead to hurt feelings and negative social dynamics?
How do we feel if students are laughing at us? Or even if we are not the target, how do we feel if they are sharing a joke that, for reasons of generational, linguistic, or cultural differences, we don’t get? What would it mean for us, as teachers, if we are on the outside of the humor?
We suspect that productively managing humor requires a unique form of teaching competence. As the outsider example suggests, this also includes forms of cultural competence.
We are just starting to figure out how to name and describe what these teaching competencies might look like, using the classroom data examples. From our initial look, we think humor competence for teaching involves a form of self-knowledge –– knowing yourself, being comfortable with your own identities, having the humility to laugh at yourself. But it also involves relational skills of reading students’ reactions, developing rapport to invite open communication, and having strategies for repairing relationships when lines get crossed or feelings hurt.
We would love to hear more about how you use humor in math class to make it a more humanizing space. Math class could use a few more laughs.
This post was written as a part of The Virtual Conference on Humanizing Mathematics (#VConHM on Twitter)
Note: This post was written by my two doctoral students, Lara Jasien and Nadav Ehrenfeld, as part of the Virtual Conference on Mathematical Flavors. This essay responds to the prompt “How do teachers move the needle on what their kids think about the doing of math?” It is also part of a strand inside that conference, inspired by an essay by Tim Gowers,“Two Cultures in Mathematics.“
Before we begin responding to Gowers’ essay, we’d like to share a little bit about what draws us to this conversation. As budding researchers of mathematics teaching and learning, we spend our days watching teachers go about their daily routines with their students. We look for the ways teachers support their students to engage in meaningful learning and position them as capable, curious thinkers. Our work is fundamentally concerned with the ways classroom culture shapes what it means to teach, learn, and do mathematics. Gowers’ essay provides us with an interesting new lens on the role of culture in mathematics. We want to share (what we think is) a problem-of-practice worth considering and then point to an often overlooked teaching move that we recently saw a teacher use in ways that counteracted this problem-of-practice.
As educators and learners of mathematics, our experiences usually involve engaging students in correctly solving mathematical problems that are predetermined, handed down to us over generations through textbooks and pacing guides (with slight variations). This means that students have few opportunities to engage in a core element of mathematics — finding and articulating problems that are interesting to solve. We think this is intimately connected to a missing aspect of mathematics culture in typical math education: the mathematical aesthetic. Mathematicians’ aesthetic tastes and values lead them to pursue some problems, solution strategies, and forms of proof write-ups over others. When mathematicians’ inquiry is driven by their aesthetics, they engage in exploration, noticing, wondering, and problem-posing.
The mathematical aesthetic is the mechanism by which mathematicians distinguish between what they experience as meaningful, interesting mathematics and trivial, boring mathematics. In his essay, The Two Cultures of Mathematics, W.T. Gowers identified two groups of mathematicians who find each other’s work equally distasteful (with a little dramatic flare): problem solving mathematicians and theoretical mathematicians. Typically, school instruction exposes students to problems that fit both cultures of mathematics: Some school mathematics is done for mathematics sake, some is done for the purpose of real life or pseudo real life (word problems) problem solving. Yet, when do students have the opportunity to develop aesthetic preferences for different ways of engaging with and thinking about mathematics?
In our work, we have seen classrooms with cultures that support students in posing questions to their peers — questions like, I wonder if there is a reason for that? or What’s your hunch?. In these classrooms, we see students begin to be interested in and passionate about mathematics. In our minds, when students develop such passionate tastes about meaningful mathematics, we are on a good track for empowering our students for success.
The questions we just mentioned are actually questions we recently overheard a teacher asking her students as her last statement before exiting small group conversations. We consider her enthusiastic questions to be a form of modelling mathematical aesthetics, prompting students to be curious, explore, wonder, and use their intuition. While ideally the classroom culture would eventually lead to students asking themselves and each other these kinds of aesthetic questions, we know that our own authentic intellectual curiosity as educators does not go unnoticed by our students. Importantly, this teacher did not ask these questions and then hang around and wait for student answers. She left the students with juicy questions that they could investigate together.
As teachers, we rarely get feedback on how our exit moves from small group conversations affect their conversation or the classroom culture. Of course, some exit strategies –– such as telling students the answer or funneling them towards it –– will clearly lead to cultures where students see mathematics as a discipline of quick-and-correct answer finding. This view of mathematics can preclude opportunities for students to develop as autonomous doers and thinkers of mathematics. Fortunately, options for productive exit strategies and modelling of intellectual interests are many. These options also present new decision-making challenges to teachers as what happens when we exit the conversation becomes far less predictable. Our students do not need to have the same mathematical tastes as we do, but we do want them to feel empowered and intellectually curious in our classrooms. By foregrounding noticing, wondering, and problem-posing as authentic mathematical practices, we can support students in developing their own mathematical aesthetic. Of course, doing so requires us to model genuine intellectual curiosity, make room for uncertainty and ambiguity in our tasks (groupworthy!), create access to multiple resources for pursuing mathematical questions (Google is acceptable!), and scaffold for conversation rather than bottom-lines (exit moves!). Leaving students with a juicy, natural question is a start.
One of the great things about coming up in this profession is seeing all the great work my students (current and former) produce. As you may note, their work varies yet addresses some central themes. I hope you will read any papers that sound interesting.
Without further ado, here are some of the highlights from 2017:
Though test-based accountability policies seek to redress educational inequities, their underlying theories of action treat inequality as a technical problem rather than a political one: data point educators toward ameliorative actions without forcing them to confront systemic inequities that contribute to achievement disparities. To highlight the problematic nature of this tension, the purpose of this paper is to identify key problems with the techno-rational logic of accountability policies and reflect on the ways in which they influence teachers’ data-use practices.
This paper illustrates the data use practices of a workgroup of sixth-grade math educators. Their meeting represents a “best case” of commonplace practice: during a full-day professional development session, they used data from a standardized district benchmark assessment with support from an expert instructional leader. This sociolinguistic analysis examines episodes of data reasoning to understand the links between the educators’ interpretations and instructional decisions.
This paper identifies three primary issues with test-based accountability policies: reducing complex constructs to quantitative variables, valuing remediation over instructional improvement, and enacting faith in instrument validity. At the same time, possibilities for equitable instruction were foreclosed, as teachers analyzed data in ways that gave little consideration of students’ cultural identities or funds of knowledge.
Test-based accountability policies do not compel educators to use data to address the deeper issues of equity, thereby inadvertently reinforcing biased systems and positioning students from marginalized backgrounds at an educational disadvantage.
Good news to share: another research grant has been funded by the National Science Foundation. Yay!
This is what we pitched to the NSF:
This study addresses the need to develop processes for adequate and timely feedback to inform mathematics teachers’ instructional improvement goals. In this study, we propose using design-based implementation research to develop and investigate a process for documenting mathematics teachers’ instruction in a way that is close to classroom practice and contributes to teachers’ ongoing pedagogical sense making. The practical contribution will be a framework for formative feedback for mathematics teachers’ learning in and from practice. The intellectual contribution will be a theory of mathematics teachers’ learning, as they move from typical to more ambitious forms of teaching in the context of urban secondary schools. Both the practical and theoretical products can inform the design of professional development and boost other instructional improvement efforts.
In a recent Spencer study, my team and I investigated how teachers used standardized test data to inform their instruction. (That team was Mollie Appelgate, Jason Brasel, Brette Garner, Britnie Kane, and Jonee Wilson.)
Part of the theory of accountability policies like No Child Left Behind is that students fail to learn because teachers do not always know what they know. By providing teachers with better information, teachers can adjust instruction and reach more students. There are a few ways we saw that theory break down. First, the standardized test data did not always come back to teachers in a timely fashion. It doesn’t really help teachers adjust instruction when the information arrives in September about students they taught last May. Second, the standardized test data took a lot of translation to apply to what teachers did in their classroom. Most of the time, teachers used data to identify frequently challenging topics and simply re-taught them. So students got basically the same instruction again, instead of instruction that had been modified to address central misunderstandings. We called this “more of the same,” which is not synonymous with better instruction. Finally, there were a lot of issues of alignment. Part of how schools and districts addressed the first problem on this list was by giving interim assessments –– basically mini versions of year end tests. Often, the instruments were designed in-house and thus not psychometrically validated, so they may have not always measured what they purported to measure. Other times, districts bought off-the-shelf interim assessments whose items had been developed in the traditional (and more expensive) manner. However, these tests seldom aligned to the curriculum. You can read the synopsis here.
Accountability theory’s central idea –– giving teachers feedback –– seemed important. We saw where that version broke down, so we wanted to figure out a way to give feedback that was closer to what happens in the classroom and doesn’t require so much translation to improve instruction. Data-informed action is a good idea, we just wanted to think about better kinds of data. We plan to use a dual video coaching system — yet to be developed — to help teachers make sharper interpretations of what is happening in their classrooms.
Why did we partner MfA LA? When I reviewed the literature on teachers’ professional learning, they seemed to be hitting all the marks of what we know to be effective professional development. They focus on content knowledge; organize their work around materials that can be used in the classroom; focus on specific instructional practices; they have a coherent and multifaceted professional development program; and they garner the support of teacher communities. Despite hitting all of these marks, the program knows it can do more to support teachers.
This is where I, as a researcher, get to make conjectures. I looked at the professional development literature and compared it to what we know about teacher learning. MfA may hit all the marks in the PD literature, but when we look at what we know about learning, we can start to see some gaps.
|*Conjecture 1||Professional learning activities need to address teachers’ existing concepts about and practices for teaching.
|Conjecture 2||Professional learning activities need to align with teachers’ personal goals for their learning.
|Conjecture 3||Professional learning activities need to draw on knowledge of accomplished teaching.
|*Conjecture 4||Professional learning activities need to respond to issues that come up in teachers’ ongoing instruction
|*Conjecture 5||Professional learning activities need to provide adequate and timely feedback on teachers’ attempts to improve their instructional practice to support their ongoing efforts.
|Conjecture 6||Professional learning activities should provide teachers with a community of like-minded colleagues to learn with and garner support from as they work through the challenges inevitable in transformative learning.
|*Conjecture 7||Professional learning activities should provide teachers with rich images of their own classroom teaching.
The conjectures with * are the ones we will use to design our two camera coaching method.
We need to work out the details (that’s the research!) but teacher’s instruction will be recorded with two cameras, one to capture their perspective on significant teaching moments and a second to capture an entire class session. The first self-archiving, point-of-view camera will be mounted on the teacher’s head. When the teacher decides that a moment of classroom discourse illustrates work toward her learning goal, she will press a button on a remote worn around her wrist that will archive video of that interaction, starting 30 seconds prior to her noticing the event. (As weird as it sounds, it has been used successfully by Elizabeth Dyer and Miriam Sherin!) The act of archiving encodes the moment as significant and worthy of reflection. For example, if a teacher’s learning goal is to incorporate the CCSSM practice of justification into her classroom discourse, she will archive moments that she thinks illustrate her efforts to get students to justify their reasoning. Simultaneously, a second tablet-based camera would record the entire class session using Swivl®. Swivl® is a capture app installed in the tablet. It works with a robot tripod and tracks the teacher as she moves around the room, allowing for a teacher-centered recording of the whole class session. Extending the prior example, the tablet-based recording will allow project team members to review the class session to identify moments where the teacher might support students’ justifying their reasoning but did not do so. The second recording also captures the overall lesson, capturing some of the lesson tone and classroom dynamics that are a critical context for the archived interactions. Through a discussion and comparison of what the teachers capture and what the project team notices, teachers will receive feedback on their work toward their learning goals. We will design this coaching system to address the starred conjectures in the table
I will keep you posted!
I have had the great pleasure of spending the last several days at the Minnesota State Fair.
My colleague Melissa Gresalfi and I got a National Science Foundation grant to study a very special exhibit there called Math On-A-Stick. We have an awesome team of graduate students helping us with the research. They are Lara Heiberger, Panchompoo Fai Wisittanawat, Kate Chapman, and Amanda Bell.
On the left is a tile station. The tiles are half black, half colored, and children can make all kinds of patterns with them. The center image comes from the pentagon station. I could spend all day there myself. I made that creation. On the right are tessalating lizards and turtles.
Today, Christopher was the Visiting Mathematician. He built a giant pattern machine that children could play with. It is made up of little “pattern machines,” and the buttons pop up and down, making a satisfying clicking noise.
Melissa and I are interested in studying two things about children’s encounters with the exhibit. First, we are interested in the design, investigating how the various activities support mathematical interactions between children, the exhibit, the mathematics educators, parents –– and each other. Second, we are interested in children’s engagement. We want to examine how the children engage with different parts of the exhibit, looking for relationships among children’s ideas about mathematics, reported experiences in math class, and the exhibit design.
Our primary data come from recordings the kids make while they are playing. We outfit them with GoPro cameras so we can see how they interact with the exhibit, recording their interactions, their general gaze, and the time they spend at the various stations.
This is supplemented by entry and exit surveys, brief interviews, and stationary recordings of the stations (e.g. a camera positioned at the Pentagons so we can see how a cross section of children play with that station and compare that to the activity of our focal children). We weren’t sure how kids would feel about us approaching them and asking them to wear the cameras on their heads. It turns out that they love it. They are really happy to share, as are the amazing volunteers, who have been very agreeable to getting captured in the video footage as the children play.
Our research findings will help us identify more ways to make mathematics play a part of instruction. Already, many children are telling us that Math On-A-Stick math is different than what they do in school –– even kids who are inventing and problem solving in impressive and novel ways. We are looking forward to analyzing the hundreds of hours of data we collect and sharing what we learn with all of you.
I try to be a plain-talking academic when I engage in the public realm of social media. Sometimes, despite my best efforts, I find myself wanting to use academic jargon. My goal in writing this blog is to have conversations with both educators and researchers, so I think it is okay to have “turns” of conversation that lean a little more on my research voice than my educator voice.
Sociocultural is jargon word that I have wanted to invoke from time to time when talking to my practitioner friends. In particular, the research I do uses sociocultural learning theories as a way of describing both how students and teachers learn.
But what does that mean? In order to understand, you need a little history on how we have come to think about learning the way we do.
In the late 19th and early 20th centuries, U.S. research on learning was dominated by behaviorism. Seeking a rigorous empirical basis for a study of behavior, researchers like E.L. Thorndike and B.F. Skinner sought to explain how learning happened by documenting what they could see empirically.
Out of this theory, we have ideas like operant conditioning, where actions are shaped by stimulus and responses in the environment to ultimately change behavior. Skinner famously made little operant conditioning chambers called “Skinner boxes” that successfully “taught” pigeons to dance. Through the boxes, food was dispensed in response to the pigeon’s movements. If he turned his head to the left –– the stimulus –– he would get a food pellet –– the response. The next time, he had to turn his head a little further to get his food. Eventually, through operant conditioning, the pigeon learned to turn in a full circle –– to “dance” –– to get food.
Behaviorism explained some forms of learning, but it couldn’t explain everything. In the 1950s, the cognitive revolution began. Researchers like Jerome Bruner began to critique behaviorism, noting that a sole focus on behavior precluded a study of how people created meaning, a central question in understanding why people do what they do. Researchers realized they could do empirical studies that included a theory of the mind. Using methods like case studies and talk aloud protocols, investigators could examine how people made sense of their activities in the world.
Cognitive science, as it came to be called, led to important insights like schema theory and conceptions. A schema is a general system for understanding how knowledge is represented and how it is used.
Researchers can look for evidence of different schemata (the plural of schema). Like the behaviorists, they observed what people did to understanding learning. However, they augmented this by asking people to explain their thinking through interviews and surveys.
To give an example of a schema, let’s take the word “dog.” When I say “dog” what do you imagine?
You probably think of four-legged animals that bark, are furry, have tails. But how do you know that these are all dogs?
How do you know that these are not?
This is the question that underlies the idea of schemata.
The examination of schemata started to point to the importance of culture. Schemata are closely related to prototypes. So, for example, when I say the word “furniture” what do you think of?
Linguists have found that when you say the word “furniture” to Americans, they think the best examples are chair and sofa.
When you say the word “möbel” to Germans, however, they think the best examples are bed and table. Our schemata and our prototypes –– the building blocks of concepts in the world –– are culturally specific.
By the early 1990s, this increasing recognition of the importance of language, culture, and context shifted our ideas about learning yet again. Language and culture were not just the setting for development and thinking –– some kind of external variable to be controlled for –– they were, in fact, fundamental components of these mental processes. This insight meant that, to explain some learning phenomena, researchers needed to do more than describe mental structures.
This required another broadening of research methods. Using linguistics, anthropology, and sociology, learning researchers wanted to account for how concepts stretched beyond individual minds and into the world. Deeply influenced by Soviet psychologist, Lev Vygotsky, researchers working in this sociocultural tradition examined learning as it happened in interactions in the world, requiring new units of analysis. That is, instead of studying individuals as they learned, researchers sought ways to study individuals in context.
My own research takes up these sociocultural insights to re-think how we study teacher learning. Let me paint a bit of a picture for you about the intellectual traditions that shape my work.
First, when I entered my doctoral program at UC Berkeley in the mid-1990s, debates between cognitive and sociocultural perspectives on learning were quite active in my courses and in research groups. Although most arguments centered on questions of student learning, there was a growing interest in what was often called “out-of-school learning.” Influenced by anthropological researchers like Jean Lave, a small group of scholars studied workplace learning, a particularly pressing topic in our modern information economy, where workers must constantly adapt to a rapidly changing world.
Meanwhile, in educational policy studies, there was a growing recognition that research on school organization, curriculum, and teacher professional development had overlooked a central question: How do teachers’ learn? Since almost all school improvement efforts want to improve instructional quality –– through curricular reform, changes in scheduling or assessment techniques –– they all depend on what happens inside of classrooms. And that, of course, depends on what happens with teachers.
For this reason, educational policy scholars like Judith Warren Little and Mike Knapp were recognizing that teachers’ learning is an underanalyzed component of any efforts at school change or instructional improvement. Yet it was not central to policy designs –– let alone to analyses of their effectiveness.
The moment was ripe for somebody to connect these ideas. My work starts with the policy-based observation that designs for instructional change must consider teacher learning. I then use methods and insights from sociocultural theories of learning to examine how teachers’ learning happens in the school as a workplace. As the sociocultural theorists suggest, what teachers know and learn is not solely a product of what is in their individual heads.
Concepts for teaching draw on culturally specific practices and language in the world. For instance, in the U.S., we often start grouping children by ability levels at a very young age. The concept of a “high ability 6 year old” makes sense for American teachers in a way that it would not to teachers in countries that do not track in the elementary years. There are consequences to that concept having social meaning, as educators make decisions about their schools and classrooms and parents advocate for certain experiences.
By using sociocultural perspectives to explain teachers’ learning, my research is culturally specific and theoretically specific. Although the details of what I find about U.S. teachers may not generalize to other countries, it is my hope that my descriptions of teachers’ learning can be more generalizable.
One great privilege of the work I do are the many opportunities I get to share the things I care about with different groups of people. If you do it enough, you get a chance to clarify your own ideas, learn from others, and notice connections.
This past weekend, I had the honor to give a keynote talk at the Carnegie Math Pathways Forum. If you don’t know about their work, it is worth checking out. Briefly, their work addresses the enormous blockage in the math pipeline as students transition from secondary to post-secondary. A staggering number of students get placed in developmental math classes, and often, these courses become a holding bin students cannot get out of. The Carnegie folks have worked primarily with community college instructors to re-think developmental math curricularly and pedagogically. It’s fascinating and important work.
My talk was about the relationship between structure and agency, how both contribute to inequalities in mathematics education. When we are teaching in a classroom, it is easy to see problems of inequality as they look locally: high enrollments in developmental math, over-representation of students coming from poverty and students of color, a sense of student apathy. To make progress, however, instructors can learn by linking the local to broader social processes: the maldistribution of qualified math teachers, STEM classrooms that are hostile environments to minoritized students, a K-12 curriculum that often reflects the institution of schooling more than what it means to do meaningful mathematics. I argued that if we frame these problems through what we see locally, we give ourselves, as teachers, less leverage to make progress on them. I shared two key concepts for linking these social processes to what we see in our classrooms: social risk and status. I have written about both of these (click the links if you are curious), but briefly, social risk refers to the threats people feel are posed to their status in a community while status describes the perception of students’ academic capability and social desirability. Both of these ideas link the social process explanations for inequality to what teachers see in their classrooms locally.
Teachers can then work to design classrooms that reduce social risk by, in part, attending to status dynamics. In other words, to connect structure and agency, we need ways to think across scale and look at the social origins of problems too often narrated as individual issues. Instead of, for example, blaming students for being apathetic about mathematics learning, we need to recognize what their history has likely been in our current system and accept their apparent apathy as a reasonable response. Our task shifts from finger pointing (“My students just aren’t motivated!“) to having the productive challenge of honoring their experience while trying to change their ideas about math and learning.
In the end, then, structure can help us change agency in two ways. First, by recognizing that it is there, along with the social processes it holds in place, we can arrive at more productive framings of the problems we face locally. Second, we can leverage the structural designs in our classroom to invite students’ agency.
I have written about designing structures to promote agency before. If you don’t feel like reading that (I realize it’s summer!), maybe watch this video instead. It is quite a joy.
And don’t we all need more of that right now?