I wrote a book about a highly effective differentiation strategy for mathematics classrooms called complex instruction. Complex instruction is a research-based approach to teaching that treats the classroom like a social system. Using this idea, it helps teachers engineer the environment to make for rich learning opportunities for as many students as possible through collaborative student work.
I spend enough time in classrooms to be a realist about the various challenges teachers face day to day. I know that collaborative learning may be a far leap for some. Nonetheless, if there is one idea that would benefit any classroom learning environment, it is that of student status. In this post, I explain status and how it plays out in mathematics classrooms.
By the time students are in secondary school, children enter their mathematics classes with strong ideas about who they and their peers are as mathematics learners. They can tell you who is smart and who is not. They base these judgments on earlier school achievement, as well as on categories such as race, class, popularity, and gender. These assessments play out in the classroom. Some students’ contributions are sought out and heard, whereas others’ contributions are ignored. This imbalance obstructs productive mathematical conversations because an argument’s valuation comes from who is speaking and not what is being said.
Productive mathematical conversations are ones in which arguments are weighed on the basis of the mathematical validity of what is being said, not on who is speaking.
Judgments about who is smart based on prior achievement or social categories violate a fundamental principle of equity and are consequential: learning is not the same as achievement. Confounding this problem, American schools tend to be organized in ways that obscure distinctions between learning and achievement. In fact, they are often built around the idea that differences in student achievement are the natural consequence of differences in ability. The logic of tracking, particularly in the early grades, rests on notions of identifiable differences in ability that require different approaches in teaching.
In reality, tracking often only reinforces achievement differences by giving high-achieving students better teaching and more enriched learning environments. An important principle of equitable teaching is that achievement gaps often reflect opportunity gaps. We typically think of opportunity gaps as existing across schools, with schools serving upper middle-class populations having greater resources than schools serving poor students. Although this tragically remains the case in the United States, the resource differences within schools are often overlooked. Two students in the same school placed in different tracks—on the basis of their prior achievement—typically have radically different learning opportunities through the quality of their teachers, the time spent engaged in academic activities, and the rigor of the curriculum. Once you are behind, getting ahead is hard.
Status is not just a concern for low-achieving students: all students in the United States need the opportunity to learn mathematics more deeply.
The belief in ability as the root of different levels of achievement is so entrenched in the organization of curriculum and schooling that many people have a hard time imagining another model. Other conceptualizations are possible, however. Japanese education attributes differences in achievement to students’ different levels of effort instead of differences in ability. Classrooms are organized to see student differences as a resource for teaching, instead of viewing them as an obstacle to be accommodated. Tracking does not occur in the early grades.
Considering students’ robust views on who is smart along with schooling practices such as tracking, which naturalize differences, it is no wonder that most students’ mathematical self-concepts seem immutable by the time they arrive in secondary classrooms. Everything around them fixes their sense of their ability, be it low, high, or average.
If learning is not the same as achievement, and if achievement gaps often reflect opportunity gaps, what do we make of students’ prior achievement when they enter our classrooms? Who are the students who have succeeded in mathematics before entering our classrooms? How about those who have not? Disentangling achievement and ability may sound reasonable, but we need a new model for thinking about students we teach. Elizabeth Cohen’s work on complex instruction frames these issues around status, a concept that clarifies the conflation of achievement and ability. Status gives teachers room to analyze this problem and respond through their instruction.
In this context, we will use the following definition of status:
Status is the perception of students’ academic capability and social desirability.
The word perception is key to this definition. Perception drives the wedge between social realities and perhaps yet unrealized possibilities of what students can do mathematically. Perception involves our expectations of what people have to offer.
Where do these status perceptions come from? Typically, the perception of academic capability often comes from students’ earlier academic performance. It might come from their academic track, with honors students having higher status than that of regular students. Status judgments about ability might also draw on stereotypes based on class, race, ethnicity, language, or gender.
The perception of social desirability arises from students’ experiences with peers. For instance, students often see attractive peers as desirable friends—or perhaps just undesirable enemies. Likewise, whatever drives popularity in local teen culture will show up in the classroom as status. The team captain, the talented artist, or the cut-up rebel—whomever students clamor to befriend or win the approval of—will have higher social status.
Status plays out in classroom interactions. Students with high status have their ideas heard, have their questions answered, and are endowed with the social latitude to dominate a discussion. On the other side, students with low status often have their ideas ignored, have their questions disregarded, and often fall into patterns of nonparticipation or, worse, marginalization.
Recognizing the relationship between status and speaking rights highlights an important way for educators to uncover these issues in their classrooms. Status manifests through participation patterns. Who speaks, who stays silent, who is excluded, and who dominates class discussions are all indicators of status. Individually, this concept influences students’ learning. If some students’ ideas are continually ignored, their questions will go unanswered and their confusions will remain unaired. Over time, this system may reinforce negative ideas they have about themselves as mathematics learners, because they may conclude that their ideas are not valuable. Conversely, students whose ideas are consistently heard and worked with will have greater opportunities to engage and sort through them. Socially, if students’ dominance becomes unregulated, they may develop an overblown sense of their value in the social and intellectual world of the classroom. Thus, status-driven interactions not only influence learning but also reinforce existing status hierarchies.
Skeptics might protest linking participation and status. “Some students are just shy,” someone might say. That is true. Likewise, students learning English often go through a silent period or may be self-conscious of their accents. Our goal with reluctant speakers is to design ways for them to comfortably participate more than they are perhaps naturally inclined to do. Strategies such as small-group talk first or individual think time may help build the confidence of shy or nervous speakers. The emphasis on participation in classroom discussions comes from several research studies showing that such involvement is essential to developing conceptual understanding and academic language.
Socially, status plays out in participation patterns. Individually, status influences students’ mathematical self-concepts, or their ideas about what kind of math learners they are. As mathematics educators, we have all encountered students who claim that they are not “good at mathematics” before they even give a new idea a chance. Intuitively, we know that students’ mathematical self-concept influences their motivation and effort in mathematical learning. If students know they are not good at mathematics, why should they push past their confusion when problems become difficult? If students know they are smart, why should they bother to explain their thinking, let alone pay attention to a classmate’s? Students’ self-concept is deeply tied to their attitudes about learning mathematics, in and out of our classrooms. Societal biases predispose students to think of themselves and their peers as more or less competent in mathematics, playing into students’ choices to engage, persist, and take risks in the classroom.
Text adapted from my book, Strength in Numbers. As always, I invite your respectful and curious questions and comments.