What Does It Mean to Study Teachers’ Learning from a Sociocultural Perspective?

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.

dancing pigeons

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.

Why Meaningful Math Learning Matters

What Meaningfulness Means

Learning and schooling are not the same thing. There are children who are great learners but terrible students. These young people are full of ideas and questions, but they have not managed to connect their innate curiosity with their experiences in school. There are many possible reasons for this. Children may find school to be a hard place to inhabit, due to invisible expectations that leave them feeling alienated. Sometimes, school curriculum just seems irrelevant: their personal questions about the world do not find inroads in the work they are asked to do.
Although many parenting books extol children’s natural curiosity and emphasize its importance in their learning and development, schooling too often emphasizes compliance over curiosity. Thus, it is not surprising that children who are great learners and weak students have their antithesis: children who are great students but who are less invested in learning and sense making. Make no mistake: these students hit every mark of good organization, compliance, diligence, and timely work production, but they do not seek deep engagement with ideas. Given the freedom to develop a question or explore an idea, they balk and ask for more explicit directions. I have heard teachers refer to these children as “teacher-dependent.”
Too often, meaningfulness falls through this gap between learning and schooling. There is a fundamental contradiction at play: meaningfulness arises from and connects to children’s curiosity, yet “curious children” is not entirely synonymous with “successful students.” Meaningfulness comes about when students develop an appreciation for mathematical ideas. Rich and meaningful learning happens when students draw on prior knowledge and experiences to make sense of ideas and explore problems, invoke their own strategies, get to ask “what if…?”  In short, meaningful learning happens when students’ activity connects to their own curiosity. To make meaningfulness central to math teaching, then, teachers need to narrow the gap between being curious and being a good student.

___________________________________________________

Meaningfulness: When students connect their own curiosity and experience to ideas, thereby developing an interest in and appreciation for mathematical content.
___________________________________________________

Why Meaningfulness Matters

Every math teacher, at one one time or another, has been asked the question, “When are we going to use this?” While this question often gets cast as students’ resistance to learning, it can be productively reinterpreted as a plea for meaningfulness. When the hidden curriculum of math class –– the messages that are inadvertently relayed through classroom organization and activity –– consistently communicates that meaning does not matter, we end up with hordes of students who no longer reason when they are doing math. They instead focus on rituals, such as following the worked example, and cues, such as applying the last learned procedure to the current problem.
As researcher Sheila Tobias explained in her classic exploration of math anxiety, a lack of meaning exacerbates many students’ negative experiences learning mathematics. When math class emphasizes rituals and cues that rely on memorization over sense making, students’ own interpretations become worthless.

For instance, they memorize multiplication facts, and, in a search for meaning, they decide that multiplication makes things bigger. Then, they learn how to multiply numbers between 0 and 1. Their prior understanding of multiplication no longer works, so they might settle on the idea that mulitiplication intensifies numbers since it makes these fractional quantities even smaller. Finally, when they learn how to multiply negative numbers, all their ideas about multiplication become meaningless, leaving them completely at sea in their sense making. The inability to make meaning out of procedures leaves students grasping and anxious, as the procedures seem ever more arbitrary.
In contrast, when classrooms are geared toward supporting mathematical sense making, they reap multiple motivational benefits. First, students’ sense of ownership over their learning increases. Students see that multiplication can be thought of as repeated addition, the dimensions of a rectangle as related to its area, or the inverse of division. When they learn new types of multiplication, the procedures have a conceptual basis to expand on. Relatedly, their learning is more durable. Because they understand the meaning behind the mathematics they are learning, they are more likely to connect it to their own experiences. This, in turn, provides openings for their curiosity and questions. Beyond giving students opportunities for sense making, meaningful mathematics classrooms provide students chances to identify and explore their own problems. Indeed, in a systematic comparison of teacher-guided and student-driven problem solving, educational researchers Tesha Sengupta-Irving and Noel Enyedy found that the ownership, relevance, and opportunities to engage curiosity in student-driven problem solving supported stronger outcomes in student affect and engagement.[1]

The challenge, then, for teachers is how to help students engage in meaningful mathematical learning within the structures of schooling. I would love to hear your ideas about how to achieve this.


[1] Tesha Sengupta-Irving & Noel Enyedy (2014): Why Engaging in Mathematical Practices May Explain Stronger Outcomes in Affect and Engagement: Comparing Student-Driven With Highly Guided Inquiry, Journal of the Learning Sciences, DOI: 10.1080/10508406.2014.928214

How Does School Culture Reflect Middle Class Culture?

Class is rarely talked about in the United States; nowhere is there a more intense silence about the reality of class differences than in educational settings.

bell hooks

One of the things teachers often hear in the course of teacher education is that school culture typically reflects middle class culture. For teachers who grew up middle class, this statement can be perplexing. It’s like trying to alert fishes to the unique presence of water: they are so immersed in it that alternatives cannot be fully imagined.

Yet class shapes everything from interactional styles to the kinds of competencies valued in the home. In her famous ethnography of class and American childhoods, Annette Lareau characterized working class and poor families as tending to promote natural growth in children. These parents tend to let children determine their leisure activities. When they interject authority, they tend to do so with directives.

lareau cover

In contrast, middle-class families tended to practice a form of parenting Lareau calls concerted cultivation. These parents tended to equate good parenting with deliberate development of their children’s talents, especially through organized leisure activities. They also used fewer directives, instead reasoning with their children when seeking to change their behavior.

(There are other contrasts between these approaches to parenting, as summarized in this table.)

Lareau’s point is not that one style is better than the other, but instead to point out that school often assumes middle class parenting, leaving poor and working class families with less of an institutional fit. In fact, as somebody who was raised in this manner, I personally see many strengths that come out of the accomplishment of natural growth. Children have more opportunities to develop autonomy and engage in more social problem solving than children whose leisure activities are organized and led by adults.

How do these middle class assumptions play out in school? Classrooms are crowded places, and teachers frequently need to direct children’s attention and activities. Many teachers tend toward the middle class style of suggesting a transition (“Would you like to join us on the rug?”) rather than directing it (“Please come to the rug now”). If you are used to the latter, the former can be understandably ambiguous and confusing.

What is more, middle class children, through their greater experience with formally organized leisure activities, usually come to school with tacit understandings about how to participate. They have more experience responding to the authority of a non-kin adult with whom they will likely form a superficial and transitory relationship. In contrast, if your early socialization has been primarily with family, taking directions from a stranger may seem like a strange and maybe not entirely wise endeavor.

There are also subject-specific ways that social class makes school more or less a fit with children. Valerie Walkerdine has documented the ways class can interact with mathematics education in particular. She points to the quantitative fictions common to math class, describing, for example, an elementary number game requiring the “purchase” of various items for 1 to 10 pence and then making change. The working class children she observed, whose lives were much more consequentially tied to actual prices of things, found the premise of the game absurd. As I often tell my pre-service teachers, which of your students knows where to find the best price on a gallon of milk, and which simply look to make sure it’s organic? How does that change your job in making sure the cost in your word problem is realistic?

To feel comfortable participating in classrooms, children need to have a reason to be there. They need to see a connection to their lives and experience a sense of belonging. Social class differences are sometimes the source of cultural barriers to feeling like you belong in school, that school is a place that matters, that things make sense. Teachers need to be thoughtful in how they bridge these differences with their students.

How do teachers teach responsively?

The idea of responsiveness is one of the biggest challenges of equity-geared teaching approaches.

Responsiveness, by definition, means that lessons cannot entirely be planned without considering the students. What is more, since the students’ input and ideas are actively sought out, it increases the uncertainty of how a lesson will unfold.

This weekend, I have been reading a book by Adam Lefstein and Julia Snell called Better than Best Practice. Like me, these scholars spend a lot of time thinking about good teaching, although their study is in literacy classrooms in the UK, while I spend my time thinking about US mathematics classrooms.

Nonetheless, the premise of their book resonates with me. As the title suggests, they argue against “best practice” language that seeks to “prove” the efficacy of exact teacher moves or curricula. Like me, they are interested in the kind of teaching that seeks out, engages, and responds to students’ ideas.

Lefstein and Snell refer to this as professional teaching, arguing that involves sensitivity, interpretation, judgment and a flexible repertoire of methods. I found this to be a useful framework.

lefstein and snell coverBy sensitivity, the authors refer to teachers’ attentiveness and openness to critical moments in the flow of a class. Did a student raise an important issue? Did another student speak up for the first time? Does a conflict seem to be brewing? Classroom dynamics involve numerous people, all with their own feelings and thoughts and challenges, and a teacher must thoughtfully navigate these while moving lessons in a productive direction.

Once teachers are alert to a critical moment, they must then figure out its significance –– what Lefstein and Snell call interpretation. Was a student’s objection to a teacher’s premise simply an attempt to derail a lesson, or is there an important question that needs to be aired?

What will the broader message to the student and the class be if the teacher pursues the question? What if she shuts it down?

In the latter set of questions, sensitivity and interpretation work together as the teacher figures out which part of her repertoire to engage. By repertoire, the authors refer to a teacher’s flexibility and depth in calling upon a range of possible actions and success in implementing them.

Together, these resources come together to constitute judgments about teaching. Teachers make hundreds of decisions a day, and the demand only increases when they seek out student input.

I like this framework because it positions the teacher not as just “doing” things in the class, but actively responding to and making decisions about students. It also broadens the object of professional learning beyond the usual activities or specific teaching moves to increased sensitivity to student and classroom dynamics and their relation to ongoing judgments.

Asking The Right Question

John Dewey . . . asked a class, “What would you find if you dug a hole in the earth?” Getting no response, he repeated the question; again he obtained nothing but silence. The teacher chided Dr. Dewey, “You’re asking the wrong question.” Turning to the class, she asked, “What is the state of the center of the earth?” The class replied in unison, “Igneous fusion.” (Bloom, Engelhart, Furst, Hill, & Krathwohl, 1956, p. 29)

Did the class know about the center of the earth? The point of this little parable, of course, is not really. Being able to correctly recite the words ‘igneous fusion’ on cue does not make evident that these words had meaning to the students.

Meaning. An ultimate goal of learning, to enrich our lives with meaning.

From this perspective, Dewey’s question was the right one. It connected school learning to meaning in the world.

How do we do that in math class, the place with the most deep-seated rituals of recitation and mindless calculation? How do we move from what English mathematician and philosopher Alfred North Whitehead called ‘inert ideas’ — those which have been received and not utilized or tested or ‘thrown into fresh combinations’?

I am about to go teach a class of pre-service teachers to engage this very set of issues. We are looking in math class at the nature of the tasks being used through the lens of Margaret Smith and Mary Kay Stein’s work on this topic.

I already anticipate some of the arguments that will come up about the richness of particular tasks. Over the years of using this framework with both new and experienced teachers, I can boil the issues down to these questions:

1. What kind of thinking will students do as they engage in this activity?

2. Is there sufficient ambiguity that they can approach it in different ways or re-think familiar ideas in new ways?

I would love to hear from others about your ways of judging good mathematical tasks, as well as your favorite resources for finding them.