Electrocardiogram data, an example of measured signals. (Image courtesy of kenfagerdotcom on flickr. License: CC BY-NC-SA.)
By Peter Chipman, Digital Publication Specialist and OCW Educator Assistant
The syllabus for a typical MIT course spells out a familiar grading scheme that assigns fixed percentage weights to the different elements of the course: so many points for attendance and participation, so many for the quizzes or written assignments, and so many for the final exam or final project. Such a system is straightforward to implement and easy for students to understand, but there are times when both students and instructors want a little more flexibility. After all, not all students are the same, and they don’t all have the same needs.
In Spring 2018, Professors George Verghese, Alan V. Oppenheim, and Peter Hagelstein co-taught 6.011 Signals, Systems and Inference, an undergraduate course that covers a broad range of topics pertaining to communication, control, and signal processing. The material is complex, and the instructors support student learning in unique ways. We approached Professor Verghese for his insights on the course’s unusual grading system, and also on how the teaching team uses tutorials and an informal collaborative learning space called the Common Room to help MIT students succeed.
OCW: You offer three grading schemes in the course: regular, lower-friction, and project. This is so interesting! Tell us about your decision to offer students this kind of choice.
George Verghese: Ideally we’d like all students to attend all lectures and recitations, and for most students this is essential to their learning the material well and succeeding in the class. However, student lives can be complicated, their backgrounds and motivations are varied, and they optimize their trajectories through MIT in different ways. I know there is always a handful of students who can master the material with much less interaction, and I am fine with allowing them to do that, without getting in their way—hence the “lower-friction option,” in which the only components of the grade are their scores on the homework, the two quizzes during the term, and on the final exam.
Students who opt for this have access to all the material in the class, but not to the tutorial sessions, as we don’t want them using the teaching assistants to help them make up for lecture and recitation material they may have missed. Unfortunately, there are always a couple of students who opt for the lower-friction version who really should not have, and their grade ends up suffering for it. But there are others—and these are the ones for whom this option is intended—who end up near, or even at, the top of the class. More power to them! My only regret is that we lose the benefit of whatever they may have contributed to class discussions if they had attended lectures and recitations.
Those students who do not elect the lower-friction option are, in effect, signing on to attending most lectures and recitations, and 15% of their course grade is allotted to attendance. I don’t actually take attendance directly, but every few lectures I will have them pair up in class to work out some problem related to the lecture material, then turn in their answer sheets at the end of lecture (with their neighbor’s name on their sheet, so they know I’m not looking to grade them on their answers!). Any student who misses a couple of these gets a note from me to urge better attendance. And recitation instructors have a good sense of who is attending and who isn’t, even if they don’t take attendance formally.
An example of binary hypothesis testing from Lecture 22 (PDF).
There are also a few students each semester who feel they’d do better if they had a project to anchor their learning, and also to spread the course grade over (10% of the course grade is assigned to the project for students who choose this option, and the contributions of quizzes and the final exam are correspondingly reduced). Since there are typically only a few such students, I work quite closely with them over the semester, meeting at least every couple of weeks, to ensure the projects are related to course material and are moving along well. Some of these projects turn out to be good demonstrations for lectures in succeeding terms.
OCW: Please describe the tutorials offered to students and tell us about their role in the course.
George Verghese: Our tutorials are run by the teaching assistants on an optional, sign-up basis, limited to 5 students per session. Some students—perhaps a third of the class—attend them very regularly each week, others occasionally or not at all. The idea here is to actively engage the students, have them go the board to work things out, rather than having the teaching assistant give a summary of lecture at the board and then work out problems for the students. The teaching assistants go prepared with a small set of basic problems, simpler than those on homework, and illustrating points that have come up in lecture.
However, the tutorials are also teaching assistant office hours, and students are encouraged to come with questions they may have. Any general guidance that the lecturer or the recitation instructors may have for the teaching assistants usually comes at our weekly staff meeting, held on Monday to set plans and directions for the week and beyond, but we typically leave the teaching assistants to come up with specific problems for their tutorials, perhaps in coordination with each other. The teaching assistants also take turns helping the lecturer generate the problem sets and solutions.
OCW: Please tell us about the role of the Common Room in the course. What was the impact of having a space where students could informally ask questions and work alongside each other on course assignments?
George Verghese: I think the evening Common Room is one of the best elements of the class, for those students—around a third to half of the class—who take advantage of it. I got the idea for it many years ago when visiting another university campus center after dinner, and found clusters of students sitting at desks and working collaboratively on homework and projects, though with no instructors in sight. For 6.011 Signals, Systems and Inference, we reserve a classroom for the three or four evenings that precede the day homework is due, and guarantee that at least one of the staff will be present there for 1.5-2 hours; usually we have the lecturer or a recitation instructor, as well as a teaching assistant.
“Our staff invariably finds the Common Room to be the most rewarding of the various settings in which they interact with students.”—GEORGE VERGHESE
We find students working individually as well as collaboratively, and periodically interacting with the staff, either at the board or at their desk—very immersed and engaged in the homework problems, and in sorting out ideas and misconceptions related to these. The staff will typically respond to student questions with other (well chosen!) questions or hints that guide them along, rather than with answers—and that makes for a very fruitful dynamic.
We have never found the Common Room misused as a place to come and get fellow students to feed one solutions to the homework. I would absolutely recommend this to other faculty, if they have the staff resources and time. Our staff invariably finds the Common Room to be the most rewarding of the various settings in which they interact with students, and it is where they get to know their students best.
***
You can read more of Professor Verghese’s thoughts about teaching 6.011 on the Instructor Insights page of this course.
Keep learning! The following courses and Instructor Insights may be of interest to you:
More OCW Courses Offered by Professors Verghese and Oppenheim
Introduction to EECS II: Digital Communication Systems
An introduction to several fundamental ideas in electrical engineering and computer science, using digital communication systems as the vehicle. The three parts of the course—bits, signals, and packets—cover three corresponding layers of abstraction that form the basis of communication systems like the Internet.
The course teaches ideas that are useful in other parts of EECS: abstraction, probabilistic analysis, superposition, time and frequency-domain representations, system design principles and trade-offs, and centralized and distributed algorithms. The course emphasizes connections between theoretical concepts and practice using programming tasks and some experiments with real-world communication channels.
Discrete-Time Signal Processing
This class addresses the representation, analysis, and design of discrete time signals and systems. The major concepts covered include: Discrete-time processing of continuous-time signals; decimation, interpolation, and sampling rate conversion; flowgraph structures for DT systems; time-and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters; linear prediction; discrete Fourier transform, FFT algorithm; short-time Fourier analysis and filter banks; multirate techniques; Hilbert transforms; Cepstral analysis and various applications.
More about Communication, Control, and Signal Processing
This course, a prerequisite for course 6.011, covers the fundamentals of signal and system analysis, focusing on representations of discrete-time and continuous-time signals (singularity functions, complex exponentials and geometrics, Fourier representations, Laplace and Z transforms, sampling) and representations of linear, time-invariant systems (difference and differential equations, block diagrams, system functions, poles and zeros, convolution, impulse and step responses, frequency responses). Applications are drawn broadly from engineering and physics, including feedback and control, communications, and signal processing.
Analysis and Design of Feedback Control Systems
This course develops the fundamentals of feedback control using linear transfer function system models. Topics covered include analysis in time and frequency domains; design in the s-plane (root locus) and in the frequency domain (loop shaping); describing functions for stability of certain non-linear systems; extension to state variable systems and multivariable control with observers; discrete and digital hybrid systems and use of z-plane design. Students will complete an extended design case study.
Signal Processing: Continuous and Discrete
This course provides a solid theoretical foundation for the analysis and processing of experimental data, and real-time experimental control methods. Topics covered include spectral analysis, filter design, system identification, and simulation in continuous and discrete-time domains. The emphasis is on practical problems with laboratory exercises.
More on Assessment and Grading
Introduction to Electrical Engineering and Computer Science I
Professor Dennis Freeman reflects on the advantages and limitations of using oral exams to assess student learning, and considers how online exams might help instructors offer scalable assessments that are personalized and productive.
Teaching assistants Jessica Noss and Dylan Holmes describe the unusual grading system for this course, in which the final exam is optional, with each of its sections serving as a make-up exam for one of the course’s regular quizzes.
Project Laboratory in Mathematics
Project Laboratory in Mathematics is designed to give students a sense of what it’s like to do mathematical research. In the Grading section of this course, Professor Haynes Miller and Susan Ruff describe their approach to grading and their experiences in developing (and revising!) grading rubrics.
Find insights like these on many other teaching approaches at our Educator Portal.
