In June 2012 I taught my last class. After 45 years of teaching algebra, calculus, geometry, trigonometry, multivariable calculus, and more, I retired. Not that I didn't enjoy what I was doing, I did. I loved the liveliness and humor of my students, the intellectual give and take in the classroom and with colleagues, the challenge of solving knotty math problems, and the many opportunities to engage with new ideas. I even enjoyed the challenge of writing tests; grading them is another thing entirely. I was fortunate to work in schools that respected their faculties and allowed teachers wide latitude in their teaching style and curriculum choice. But, if I wanted to have time to do other things —to read, travel, write, etc.; if I wanted to read the newspaper at 9 a.m. instead of 9 p.m. — I had to get out from under the strict daily schedule imposed by school life. So, with a few tinges of regret, I set aside my whiteboard markers, my calculator, and my gradebook, and stopped teaching.
My newly acquired leisure has given me the opportunity to think about how teaching and learning have changed since I first stepped into a classroom in 1967. And there have been many changes. One could talk at length about the monumental influence of technology, the widespread impact of standardized testing at all levels of public education, the constant pressure so many parents and their children feel that students must earn top grades, and the related strain of the college admission process. As we all know, these changes have dramatically altered the face of elementary and secondary education in both positive and negative ways. As significant as these changes are, though, I want to discuss another advancement that has the potential to significantly improve the way we teach and students learn far more significantly. I am referring to the startling idea that learning is a shared responsibility between students and their teachers, that classrooms are meeting places in which teachers and students learn together, that the learning process is far more interesting and effective when students assume a greater role for their own learning.
When I started teaching, the nearly universal belief was that secondary education was a process by which a teacher transfers her knowledge of the subject matter to her students. In my subject, mathematics, the instructor knew how to solve a quadratic equation, while the students did not, so it was the teacher's job to show them how it was done. We all remember the days when teachers introduced a new topic with an (often lengthy) explanation, followed by several examples, after which students did a few problems on their own, then were assigned 15 or 20 homework problems nearly identical to the examples. While teachers usually taught new material via lecture, they sometimes used group work as well as students working at the board. However the class was organized, though, the ethos of the classroom was that knowledge must pass from teacher to student.
This conception of education had prevailed forever, and it worked pretty well as long as students bought into the plan, were obedient enough to listen closely and take notes in class, and do the practice required. But there were many learners for whom this method was not effective. Some were students who couldn't sit still and be attentive for most of a class period; others couldn't abide the passive role of being talked to for 50 minutes daily; and still others, with more creative minds, who had their own ideas about how to solve a problem that differed from "the right way" that the instructor taught. I distinctly remember one young man, a student of mine in an Algebra II class nearly 20 years ago, who caused no end of trouble in that class, talking to other students, not paying attention, making wisecracks. I realized too late that he was very bright and was simply bored in that class, that he couldn't stand being talked at so much of the time. Because I did not create an opening in that class for his, and other students’, valuable input, much less learning took place than might otherwise have been the case.
Fortunately, this model of education, what some refer to as the "empty vessel approach," is gradually being replaced, at least in more progressive schools around the country, by methods that encourage students to become more responsible for their own learning. More and more class sessions are starting to look like this: students are assigned homework as they always have been, although probably fewer and more distinct problems rather than exercises that are clones of each other, which the students do individually or in groups; in class, several students present their work to the entire group, discussing how and why they did what they did or explaining why they were not able to understand a topic or solve a certain problem; other members of the class will suggest different methods for solving a problem or attempt to explain the difficult concept. Most (perhaps all) of the class consists of students explaining mathematics (or whatever the subject is) to their fellow students, answering each other's questions, and talking about the "how" and "why," as opposed to correct versus incorrect. The class may or may not use a textbook, often preferring problems sets developed by the teacher, but, either way, each student is expected to keep thorough, accurate notes of her work and of the class discussions.
All the while, the instructor is standing or sitting off to the side, watching the progress of the class, offering suggestions here and there, asking leading questions, mentioning unnoticed connections, or saying nothing at all. In this model of education, the teacher's role is quite different, but no less crucial than the old formulation. The teacher is no longer "explainer-in-chief," the source of understanding, the imparter of knowledge. Instead, the teacher is now the facilitator of learning, the person charged with creating an environment conducive to learning. There are, of course, still tests to write, troubled students to counsel, papers to mark, and grades to determine, but the student – teacher relationship is different, more collegial, less autocratic. I remember a student from one of my first years of teaching who, after receiving a poor grade on a test, shouted out in class, "This is so unfair. Why do we always have to do things your way? Why can't it be like English class where everyone is right?" This young man was more insightful than either of us realized. There was too much emphasis on "here's how you . . .," on getting the right answer, and not enough talk about process. That student was correct, too, in that the discussion-based nature of most English classes, depending as it does on the contributions from all, is more enjoyable, builds student confidence, and leads to more learning.
While the benefits from this model of teaching and learning are many, it poses distinct challenges to teachers and students used to a more traditional classroom. In this collaborative learning model, student responsibility goes well beyond simply repeating what has been shown in class. First, students often have to figure out what to do based on their own reading of a text or by using inductive reasoning to generalize a problem-solving method based on a number of examples. This is hard stuff, especially when one is just starting out, but doable so long as the instructor knows how to tailor the material to the ability levels of her students. Another hurdle students have to face is clearly explaining their thinking to their peers and answer "how" and "why" questions; the correct answer alone is no longer sufficient. This isn't always easy, but many educators believe that a clear explanation is an accurate measure of understanding. Teachers, as I have mentioned, have the task of judging which material students can and should learn on their own, the best order in which it should be tackled, and the right pace for the class. Another challenge, one more difficult than we believe, is for the teacher to remain on the sidelines as her students struggle through a tough concept or problem. These issues, while challenging initially, become easier with experience.
I have seen firsthand how exciting and effective collaborative learning is. For 10 years or so near the end of my time teaching, I taught a multivariable calculus course with a version of this method. Each class began with several students putting homework problems on the board, explaining their work to the class, and fielding any questions. Then, the student assigned the "section of the day" from the textbook explained the new material, did some examples, answered questions, and assigned several homework problems. I sat in the back, chiming in only when absolutely necessary, which wasn't that often. One worry I had, that student presenters might not be well prepared or able to hold the class's interest, hardly ever came to pass; my other major concern, that the class would either not ask any questions of a peer or, the opposite, that they might give the presenter a "hard time," were also unfounded. These were high-energy classes with lots of questions, comments, wide-ranging discussions, and humor. One highly idiosyncratic, brilliant student presented a very effective "class" to the accompaniment of rock music. The students learned a lot, had fun, and, most important to me, came to realize that learning comes from within.
I was also fortunate to have had the chance to teach an English class, an independent study course called "Books in Translation," focusing on modern fiction in translation. Several students joined me a few times each week to discuss some of my favorite books written by authors such as W. G. Sebald, Bruno Schulz, Fernando Pessoa, and others. My goal was not to "teach" these books, whatever that means, but to encourage students to react to what they were reading, say what they thought of each book and why, both in our classroom conversations and in short papers they wrote after we finished each book. The discussions we had were lively, interesting, and lots of fun. The classroom dynamic changes entirely when the teacher's goal is not to transfer her knowledge to the students, but to work collaboratively to learn together.
As education focuses less on the accumulation of factual information, more educators are recognizing that collaborative learning is an effective way for students to learn to problem solve, recognize patterns, develop successful research methods, communicate with peers, and improve writing skills. These are the skills and habits of mind that students will need most to live confident, productive, successful lives in the 21st century. Education should now be about students growing from the inside out, not the outside in, developing their unique sense of self, not simply fitting in. Collaborative learning, with its emphasis on students taking much more responsibility for their learning and the learning of their classmates, can help our students find the individuality that is so crucial to living fulfilling lives. Helping our students along that path should be the goal of modern education.