At Dublin School (NH), precalculus is a rite of passage. While the teacher contends there is no information in the course that is new to students who have completed algebra II and trigonometry, the way the course is structured creates a tectonic shift for most students. They have to learn to think like mathematicians. The method, based on Exeter’s Harkness approach, groups students to solve problems in their own ways. For students who have succeeded in math courses in the past by following instructions outlined by teachers or books, the approach is disorienting, and they spend a good deal of the first term adjusting to the method. Most troublesome for these students is the implicit idea that there is no one right answer to a problem. Another is that their peers could be their teachers or that no one will spell out for them how to resolve their confusion. Many students protest, complain to the dean or to their parents, ask to drop the course when they earn Cs on tests, and feel they can never succeed. But as they persevere, students are gradually inducted into a new way of thinking about math; they come to see themselves as the authority. Students leave the course thinking in new ways, about mathematics and about themselves as learners.
Learning is about knowledge and skills, but it is also inextricably tied to our perceptions of ourselves. As we face cognitive challenges, we also face challenges to our identity. When we can’t quickly resolve these challenges, we are unmoored and drift in a “liquid space.” This is the place of liminality. It can be a place of danger or an adventure; it can drown or nourish learning.
The Threshold Concept Framework
Learning thresholds are often the points at which students experience difficulty and are often troublesome as they require a letting go of customary ways of seeing things, of prior familiar views. This entails an uncomfortable ontological shift as, in many respects, we are what we know.This quote is from a text written by Ray Land and Jan H.F. Meyer, professors of higher education at the University of Durham, England, who first articulated the threshold concept framework in 2002 at a conference on teaching and learning at the university level. Land and Meyer recognized that truly transformative learning requires a shift in identity. Deep learning is not only a matter of acquiring information but of altering identity; facing cognitive challenges that require a student to deconstruct and reconstruct their identity involves a journey through a liminal state.
Land and Meyer further recognized that certain key ideas mark thresholds in students’ development. These ideas tend to be core ideas in each academic discipline, and learning them is akin to passing through a portal: The student crosses a threshold into a new realm of understanding. Usually these ideas are complex and dissonant, and they constitute “troublesome knowledge.” Students may feel stuck, or frustrated by these new ideas; they must struggle to use them. This period of struggle is essential to transformative learning.
Liminality is a space between stages of secure knowledge when students feel insecure, inadequate, challenged to the depths of their being. They can tell that their old habits and identity structures cannot encompass the knowledge or understanding needed to make the next step, but they aren’t sure how to open up to the troublesome perspectives. It is a deeply uncomfortable state, and especially so in adolescence, a time when there are challenges to identity in other aspects as well.
As educators, we tacitly understand liminality as part of the learning process. And yet we probably leave it up to our students to deal with the discomfort of liminality on their own or gloss over it. Often teachers encourage students to minimize their uncertainty and confusion, exhorting them to show grit, to push through this stage to a resolution. Students respond emotionally and may not see the difficulty underlying their insecurity. As students face liminal concepts, teachers may see heightened anxiety in the classroom, feelings of being stupid or tuning out or giving up, or a flurry of surface industriousness. Students may seek ever more precise directions to ensure success. Having language to name their experience allows teachers to validate this stage in learning. Understanding the centrality of the liminal state can help teachers slow down, allow students to be in different places in the learning process, and recognize that they are grappling with challenges to their identity. In this way, the threshold concepts framework extends the growth mindset from a shift in attitude about learning to one that recognizes the student’s whole identity is involved in meeting major cognitive challenges. Understanding the affective experience that threshold concepts can precipitate makes us more effective educators.
Applying this framework to work with high school students reveals the need to coach students in dealing with uncertainty. Teachers must not only challenge students with troublesome knowledge, but also attend to and validate the struggle such knowledge creates, and help students develop the habits of mind to deal with challenges to their identities. Anxiety, uncertainty, and confusion in the struggle to learn is an important phase that should not be rushed, but welcomed. Students must dwell in the discomfort and find their own routes to a next stage of understanding. As teachers, we need to affirm the feelings students experience, create time and exercises for them to make sense of their experience, encourage persistence, and reward them for the process of learning. We also need to help students see their progress and voice the changes they are undergoing. When we legitimize and value their struggles and walk with them through these passages, we are helping students undergo transformation.
Crossing the Threshold
Dublin School first encountered the threshold concept framework when Brad Bates, head of school, met Hari Stephen Kumar, then director of instructional and curricular design services at Amherst College, at the Aspen Ideas Institute in the summer of 2016. Fascinated by the potential application of this approach, Bates invited Kumar to faculty meetings at the opening of our school year in August. Kumar presented key aspects of the framework and their implications for instructional design, and many of them resonated immediately and reinforced best teaching practices Dublin faculty were already using.One of Dublin’s core community practices is our daily morning meeting where anyone in the school can make an announcement, perform or present, or raise issues for discussion and consideration. Bates has made it a practice to inform students about many aspects of school administration—the agenda for an upcoming board meeting, construction plans, or faculty development topics in faculty professional development. Bates introduced the threshold concept framework and the idea of liminal states to our students as part of an announcement sharing ways the faculty were preparing for the new academic year; there was an astonished moment of silence, followed by a surge of interest.
Over the past year and a half, Dublin faculty have discussed the language and ideas of the threshold concept framework and sought ways to use it in our practice. We have looked for threshold concepts in our own courses, and worked on ways we can focus on these key points in our curricula. The threshold concept framework has brought insight to all aspects of the Dublin experience—academic, athletic, and residential—and it helps us understand the ways Dublin succeeds in transforming students. It gives us opportunities to create transformational experiences for more of our students and to support them until they arrive at that sense of exhilaration and excitement that comes from finally “getting it.” Simply put, it helps us nurture our students’ growth.
As part of our discussions, Dublin faculty identified key themes and ideas that students seem to grapple with that may constitute threshold concepts in their courses. Some examples include: historical texts carry bias, contain arguments masked as fact, and omit opposing voices or perspectives; most people in most places have had a fundamentally religious world view; identifying and valuing characters who represent another; recognizing the struggles and challenges of immigrant culture; that multiple solutions in math are valid.
These examples all point to the adolescent developmental task of understanding the self. They emphasize the difficulty of letting go of assumptions and previous knowledge as a central task of learning in a liminal space. At Dublin, we note that challenges exist on different levels, and what may create a full liminal experience for some students may not for others. However, it is clear from these examples that our students encounter threshold concepts in all disciplines and at all levels. Real learning cannot occur without encountering threshold concepts, and students cannot advance without facing the need to shift their assumed positions. They must bring unconscious assumptions to consciousness in order to make room for bigger understandings.
Pedagogy to Foster Transformation
Struggling to learn and perform well is an experience fraught with emotion. When feeling stuck in a liminal space, students use either fight or flight strategies. Some students fight back against the challenging ideas and redouble their more limited identities. For example, the parents of one student at Dublin recently noted their son was becoming more conservative as he felt forced to deal with others’ positions in class. Other students may seek to discredit the sources of the challenge, even their teachers, or to drop a class. Still others may pretend to understand material they have not actually learned, even in the face of poor grades.Anger, denial, despair, helplessness, and anxiety are emotions that can lead to negative outcomes or can become catalysts. Many teachers may not realize their students are undergoing such intense emotional reactions to their courses, or that such insecurity may underlie outward expressions of intransigence or disengagement.
Later in the year, Dublin teachers shared several strategies they used to help students deal with threshold concepts and liminality. Above all, they noted that patience was important and effective. They noticed that spiraling curriculum, revisiting key ideas and material from new vantage points, was often effective. Returning to complex and troublesome material allowed students to encounter it from different angles and with the benefit of confidence gained from another exercise. Being silly, playing games, and building community to develop trust among the group was another important method. Modeling discomfort was another important strategy, as well as welcoming mistakes, exploring them without blame, and helping students grow through them. Allowing students to grade themselves on certain tasks and assessing process over content was also key.
The most exciting teaching occurs when students are grappling with different perspectives, building realizations, and widening their outlooks, as opposed to doing well on tests and quizzes. For Dublin teachers, the threshold framework’s emphasis on deep and complex learning—as opposed to a system of utter clarity to relieve students of stress—resonated as important and valuable. This idea underlines the trust needed between students and their learning environment, which independent school teachers know is the bedrock in which all true growth is rooted. Magnifying the role of that fundamental trust in transformative learning is significant for our teachers; it allows them to take group discussions beyond safe parameters, to push students to reconsider their perspectives, and to allow a group to create and enter new intellectual territory. Recognizing the intricate emotional dynamics our teachers manage, like conductors of orchestras, speaks to the most significant work they do. Dublin teachers feel empowered by a model that values the trust they build in their classrooms and the power of the learning that results.
Moving Beyond Boundaries
The residential experience always involves interaction with people from different places, religious backgrounds, and socioeconomic groups. Conflicts when a roommate from another culture is upset by a casual comment or joke might confront a student with the full force of another culture’s moral system. Indeed at Dublin we hope such experiences will occur. Or when students just can’t do what they are asked in athletics, and are being pushed past their limits, they may feel the full force of a crisis in identity. Self-exposure in the arts can induce experiences of liminality for some; public speaking can for others. Climbing Mt. Monadnock on Mountain Day puts some of our students into a liminal and anxious space every year.When we help and support students in tackling the mountain, and they summit and get safely home, their sense of their options in the world has undergone a profound shift, perhaps in proportion to the discomfort they experienced, and this experience opens up a sense of new possibilities. In the past year, we’ve noticed that all areas of boarding school life can involve emotional thresholds. Identifying certain experiences as possible thresholds helps teachers, coaches, and dorm parents focus on the need to provide time, to coach students through the experience of difficulty, and to pay attention to the affective demands of the learning underway.
The threshold concept framework has helped Dublin expand our awareness of the process of transformational learning, and holds promise as we further explore the ideas, problems, and situations that confront students. It has helped our teachers deal with the variety and unpredictability of student responses and focus on enjoying the learning journey. This model makes space for engaged aliveness, which creates voracious learners far beyond high school.
In some ways, all of adolescence is a liminal space, and teenagers are particularly prone to re-examining their identities in relation to new knowledge. This makes the secondary level a particularly important time to understand the stress and emotion that can accompany liminal experiences, and their potential to induce transformation. If we can be intentional and sensitive to students’ experience of liminality, we can support the deep transformation education aims to create.
bell hooks encourages us to “move beyond boundaries, to transgress” as a way to achieve “education as the practice of freedom.” Without inspiring or inciting students to move past their boundaries, we may help instill knowledge, but we will not effect transformation. Independent schools, with the opportunity to provide threshold experiences in all areas of school life, have the precious and extraordinary opportunity to induce truly transformative learning if we embrace the struggles our students experience and pay close attention to the work transformation requires of their hearts and minds. ▪
Read More
“Threshold Concepts: Undergraduate Teaching, Postgraduate Training, Professional Development and School Education” by Michael T. Flanagan
Threshold Concepts in Practice by Ray Land, Jan H.J. Meyer, and Michael T. Flanagan
Threshold Concepts Within the Disciplines by Ray Land, Jan H.J. Meyer, and Jan Smith