March / April 2007
Most MIT faculty have never received formal training in teaching, and the demands on our time make it difficult for us to go to the research to look for best practices. The purpose of this article, however, is to draw attention to one area in which there are some easily learned principles and techniques that anyone might try. My target is the dominant educational model in the Schools of Science and Engineering: the lecture, recitation, and weekly problem set model.
The typical distribution of time is three hours of lecture and one hour of recitation. This model dominates the culture. The pressure of weekly problem sets almost always wins out over the chance for students to think hard, to reflect, on what they are learning. The amount of enduring knowledge (a term used by education scholars Grant Wiggins and Jay McTighe in their book, Understanding by Design) that our students take away is disappointingly small. This article both spells out goals for lectures and gives specific examples and techniques to be used to improve recitations.
For most of my 32 years on the faculty, I have subscribed to the accepted lecture-recitation model, and I have enjoyed that feeling of giving a good lecture. But I have experimented in my own classrooms in the last few years and have come to believe that more real learning would result if we did less lecturing and spent more time in appropriately crafted recitations. I believe that well-run recitations are where the real learning happens. In order to create more time for recitations, we have to cut back on lectures and rethink the purpose of the lecture. A growing body of research indicates that lectures are best used to accomplish the following:
As faculty at an elite, expensive university, what is our justification for a residentially-based learning experience unless our students truly are gaining from their hours in the classroom? When our students do poorly, the explanation that “They did not work hard enough” has a hollow ring.
Might we do better to focus lectures on the goals listed above, and challenge our students to practice the skill of learning some material on their own? Such assignments can be explicit, augmented by well-timed, carefully selected problem sets, and supported by well-run recitations.
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I believe one of the most important purposes of the recitation is to get students to reveal what they don’t understand, so we can help them. Dr. Breslow puts it this way, “A good recitation allows the student to practice skills he/she will need to become the expert, under the guidance of an expert.”
This is not what happens in the typical recitation today. The normal course of events is to do a couple of example problems and then ask: “Any questions?” to an all too often apparently dumbstruck audience, or to an audience that is too afraid to admit they have any questions.
So how can we create recitations that are opportunities for novices to engage the material and learn valuable skills under the tutelage of an expert coach?
First, the lecturer and the recitation instructors need to be on the same page, so that the recitation instructors know what to emphasize. Ideally, the lecturer will have introduced the big ideas and told students what they need to learn on their own. The assigned problems should relate to the application of the big ideas, covered in lecture, as well as the concepts that the students need to learn from independent study. The well-prepared recitation instructor knows where most of the common traps and misconceptions are likely to arise. He or she comes prepared with techniques for getting students to ask questions and reveal what they don’t understand (an important skill for teachers to possess), to explain and illustrate those misconceptions, and to engage the students in deeper thinking about the concepts of the week.
Although the instructor who is getting students to reveal their questions has already gone a long way toward improving the recitation experience, research has shown that learning is strengthened when students are actively involved.
To give students the opportunity to engage directly with important skills and concepts, recitation instructors can ask students to work together in small groups in which they could:
A number of MIT faculty have already devised innovative pedagogy to strengthen recitations. Below are two examples: the first is based on my own experience, and the second from a number of experiments in Course 2 on small-group teaching.
In teaching recitations in various engineering dynamics subjects over the last five years (2.003, 2.06, and 2.060J/1.581J), I have had students present the assigned homework for the week. Typically, five students would each present one problem. With 20 students in the class, each student would have the opportunity to make a technical presentation to peers about three times in the term. The best technology I have found for doing these presentations is a Wolf Systems document camera (available from AV), under which the student places the solution written on plain paper. The image is projected on the screen through a standard computer projection system.
There are several keys to making this work:
Do not critique the student in front of the classDon’t reveal if the solution is correct or not (this is important to success)
Have the student sit down, leaving the solution on the screen
Ask the others to describe different answers or results
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Under the leadership of Professor Warren Seering, experiments in small-group teaching were conducted from 2004-2006 in six (2.001-2.006) of the 12 subjects that compose the Mechanical Engineering core. The experiments were assessed extensively by the staff of the Teaching and Learning Lab, and the data suggest four factors lead to effective, active learning experiences: the instructors create safe environments in which the students are not afraid to appear confused; the instructors ask conceptual questions rather than only questions that can be answered mathematically; they provide timely feedback; and there is a close alignment of lecture with recitation problems.
One of the most successful implementations was Professor Ely Sachs’s “Discovery Learning Model” in 2.001, which was studied during the spring semester 2005. Often recitations began with students relating lecture concepts to demonstrations or mini-lab experiences. After reviewing these concepts, students would get together in small groups and work through problems or discuss answers to conceptual questions Professor Sachs had posed. Professor Sachs would rotate among the groups asking and answering questions. During the last segment of the recitation, he would guide the class collectively though the solutions to the problems. Throughout the recitations, he stressed conceptual understanding, the role of visualization in learning, and the importance of hands-on experience to develop an intuitive feel for concepts.
Although data was gathered through surveys to understand which parts of the small-group experience contributed to the students’ learning, perhaps the following quotes from student interviews are more telling:
“The small group recitation helps me reach a deeper understanding. We start from scratch. We are actually doing the problems, not copying the solution. The TA points out equations/features not covered in lecture that helps us understand the concepts.”
“I am more engaged in small groups. We are accountable. You can't hide, fall asleep, or escape! You are always doing something.”
These responses echo ones that were made by students who participated in an experiment, developed by Professors Hal Abelson and Gerry Sussman in spring semesters 2002 and 2003, to bring case-based tutorials led by MIT alumni to 6.002. As one student said:
“The tutorials force you to take responsibility for figuring out the end point and the steps to take to get there. … They break things into pieces . . . If you don’t understand, you need to ask, and you have lots of opportunities to do so. It prepares you to ask the right questions beyond the material. That’s empowering!”
These techniques and others allow us to grapple with the students on the hard problems we ask them to master. In coaching them this way, they are bound to sense our commitment to their learning. And it has been my experience that once MIT students know you care about their learning, they will respond.
More information on using the recitation techniques described here can be found on the TLL Website at web.mit.edu/tll/teaching-materials/recitations/index.html
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