Lasting Laboratory Lessons

As stated by Alexander Pope, “A little learning is a dangerous thing.” Scientists and engineers will readily attest, a superficial knowledge of the theory can make us think we have more expertise than we really do, and thus at best will make us to look foolish and at worse cause tragic consequences. This paper describes the experience of a student who is able to perform well in courses in the physical sciences and engineering as indicated by grades, but who completes this education with only a shallow understanding of the subject. For the student, there remain gaps between theory and practice, and numerous assumptions necessary for a deep understanding are missing. We offer a solution to this problem in the form of a new approach to lab courses that emphasizes relevancy to the student and student participation in devising the lab. We maintain that labs designed with these two elements in mind, along with a set of guiding principles we discuss, increase the likelihood of deep and lasting learning in the student. We close with a proposal to implement labs of this nature not only in engineering and physical science courses, but in certain mathematics courses as well, with the intention of deepening student learning and retention of mathematical concepts. The Problem: Shallow Learning “Education’s what’s left over after you’ve forgotten everything you’ve learned.” James Conant As an undergraduate physics major, the first author took several lab courses, followed the instructions and was assigned good grades. He spent little to no time reflecting on each lab afterwards, instead going on to focus on the next problem set, paper or upcoming exam. While the labs were often designed to demonstrate theory that was introduced in lecture, there were many situations in which important underlying assumptions were not mentioned. Now, as a mathematics professor teaching courses with applications, such as differential equations, discrete mathematics, and linear optimization, the author’s interest in applied topics has been rekindled. It is apparent that his learning in undergraduate lab courses and the supporting lecture courses was not sufficiently deep and did not include the totality of the necessary theory required to make a circuit work or even to explain its operation. In some ways, the author was the teacher’s worst nightmare: he and his professors may have thought the learning was going well as indicated by the grades. But in reality, he was merely successful in imitating procedures to obtain results without any deep grasp of what was actually occurring. The second author, observed a similar phenomenon, except in the area of implementing a prototype. The prototype would be designed and implemented using the requisite theory and accepted practices, but when “turned on”, it rarely worked. After some minor tweaking, it finally worked. At first glance, the prototype’s implementation was almost exactly the same before and after the adjustments, but again, minor changes were required to make it fully operational. The presuppositions that went into the design and implementation were insufficient to achieve functionality. There is some recognition of this problem in the literature on engineering laboratories. Feisel and Rosa [1] point out the lack of consensus on what constitutes proper laboratory instruction and the overall lack of consensus on what constitutes an appropriate laboratory experience. They decry the dearth of literature on learning objectives associated with instructional engineering laboratories. In any earlier paper, Ernst [2] proposed as objectives that students “should learn how to be an experimenter”, that the lab “be a place for the student to learn new and developing subject matter”, and that the lab course “help the student gain insight and understanding of the real world”. As indicated above, this was not our experience in general. Ernst was aware that labs were not achieving their goals, pointing to symptoms such as an “apathy” in many students towards labs and a lack of resemblance between the tasks carried out in the labs and the real world. Since linking the real world to theoretical knowledge gained in lecture is supposed to be a goal of laboratory courses [1,2], this symptom is particularly troubling. In the book Shop Class as Soulcraft [2], Matthew Crawford writes “...science adopted a paradoxically otherworldly ideal of how we come to know nature through mental constructions that are more intellectually tractable than material reality, hence amenable to mathematical representation.” The theory we learned in undergraduate courses could represent reality compactly and elegantly with mathematical notation (e.g., kinematics, electricity and magnetism). Yet often times, even in electrical systems where often accurate models can be developed (e.g. SPICE circuit), it seemed divorced from reality. We were taught that an object traveling with a constant velocity exerts no force. Although obvious, it still took us a while to reconcile how a crash could cause damage if the vehicle was travelling at a constant velocity. Partly this was a failing of not thinking through the hand-off between the model and reality. But this kind of question was simply outside the curriculum. We were never asked questions like this in class, on homework assignments, exams, etc. What we were asked was to solve certain kinds of problems using the theory. We found that most problems could be solved neatly by the theory. Neatly doesn’t mean quickly or without tedium or clever mathematical tricks. It simply means without ambiguity, and without having to introduce additional assumptions into the problem. As youngsters, we thought the way the universe worked was some complicated mystery, understood only by grown-ups, or the experts. In high school and college science classes, we learned many explanations for how things worked, but something was missing. The sense of explanation often felt like: “Well, you can’t really understand reality as reality.” Instead we talked about this abstracted version of reality in which these models work well. And somehow, in applying these models to reality, the bridge between the abstract and real situations is crossed. But exactly how this happened did not seem to be as important an educational outcome as facility with the abstract models. After finishing up the physics major, the first author also found his skills were lacking in the hands-on practical application of what was learned. For example, in attempting to build an electromagnetic telegraph device many years after college, he encountered issues in which the voltage of the battery voltage output was lower than expected. With help from the second author, he learned the problem was due to the relatively high internal resistance of the battery. This is a case where the model was insufficient to describe reality, presuming that a battery was an ideal voltage source. This was a concept hardly mentioned in the coursework. The author went back to the physics text book and did find a brief explanation that a battery does indeed have internal resistance. There were even a couple of exercises to reinforce the explanation. The theory and the exercises all assumed the battery’s internal resistance was known and then led the student to calculate the actual voltage drop over the circuit factoring in the battery’s internal resistance. But for a real circuit, the internal resistance is not readily known. There was no discussion in the text on how to find it either. While this problem was eventually solved and the telegraph became functional, there is a great deal of frustration that the author’s prior education did not include these types of underlying assumptions. In the mathematical world, the assumptions that go along with a theorem are clearly stated and must always be checked. For example, the First Fundamental Theorem of Calculus about integrating derivatives requires that the function in question be continuous. Since the experiences recounted above, we have taken steps to address these issues of disconnect between theory and practice and potential for lack of depth in this type of education through a new approach to labs. This is discussed in the next section. Towards a Solution: Relevant, Student-Devised Labs What makes a learning situation deep and memorable? The two guiding principles for the kind of lab we propose are relevancy and student involvement in devising the lab. There can be many other factors in designing labs, some of which we list in the next section, others of which can be found in the literature in works such as Feisel and Rosa [1] and Ernst [2]. But given our experiences, we see relevancy and student involvement in devising the lab as central. This type of proactive student engagement in their learning is supported in the works of Olin College [3], and Montoya et al. [4]. Relevancy. When a lesson connects to something in a student’s life (past or present) or their aspirations for the future, their intrinsic motivation will be activated. They participate in the lesson with greater interest than if only motivated by external factors such as grades. This increases the chances of something from the lesson being retained. A great opportunity exists to better integrate the various threads of the educational experience by creating labs that are relevant to students and that they have helped devise. The labs are constructed around practical considerations that arise in applications of interest to students. Consider “Experiment 1” on “Transients in RLC Circuits” in the first author’s undergraduate Physics 231 A Laboratory Course. In the accompanying lab manual, the “Experimental Procedure” section begins “The circuit you will use is shown in Fig. 1-3 with the square-wave output of a function generator to drive the circuit.” This set-up had no relevance to the author. What is this circuit? When had he seen one in real life? Is he likely to be