This article first appeared in the American Journal of Physics, Vol. 65, 45-54 (1997); ©1997, American Association of Physics Teachers.
The specific issues we investigate are the learning of the concepts of instantaneous velocity and Newton's third law. Facility with these concepts is essential to an understanding of mechanics and addresses general issues (such as the relation between a quantity and its rate of change and the nature of interactions) that play an important role throughout introductory physics. These concepts are known to be difficult for many students. We target each of these difficulties with one hour of active-engagement microcomputer-based laboratory (MBL) activities.
Of the previous work on this subject, the most relevant is the oft-cited paper of Thornton and Sokoloff. They report that introductory physics students' understanding of velocity graphs could be significantly improved using an MBL curriculum they developed. They evaluated the effect of their curriculum using a set of multiple-choice velocity questions (VQ) in which students were required to match a description of a motion to a velocity graph. They then demonstrated that students who were given four hours of group-learning guided-discovery active-engagement MBL proved significantly more successful in choosing the correct graphs than those who only received traditional instruction.
The results are dramatic, with a large fraction of the students missing all but the simplest of the five velocity graph questions after traditional instruction. After the MBL activities, the error rate drops to below 10% on all the questions. This result is strikingly robust and has now been confirmed at dozens of universities and colleges. In addition to confirming the difficulty reported by other researchers, a difficulty that many instructors find surprising, they demonstrate the existence of a solution. This work is often cited as an indication that interactive-engagement MBL activities are highly effective. Several questions remain to be addressed, however.
This study explores the first two of these three questions and touches briefly on the third. We encourage others to address the third.
To allow students to have more interaction with faculty, lecture classes are formed of 50-150 students with each class taught by a single faculty member. Each lecture class is divided into sections of about 25 for recitations and laboratories. The textbook and the approximate outline of the course content are chosen by a course committee, but otherwise, each faculty member acts independently. There are no common exams and there is no laboratory component in the mechanics course. The lecture hours tend to be traditional with little student interaction. Occasionally, faculty distribute in-class worksheets or engage the class with questions and discussion, but this is rare. The recitation hour typically consists of a graduate student solving problems at the board. Often there is a brief quiz (usually one of the homework problems) and sometimes the choice of problem discussed is based on student questions or requests. Teaching assistants typically receive no special training for these sessions.
We suspected that our traditional lecture plus recitation environment suffered the oft-reported problems of teaching mechanics: students appear to master algorithmic problem solving techniques but fail to make significant improvement in their understanding of the fundamental concepts. To try to improve this situation, we introduced an experimental research-based instructional technique which we refer to as tutorials. This method was developed by Lillian McDermott and the Physics Education Group at the University of Washington to improve student understanding of fundamental physics concepts in a cost-effective manner within the traditional lecture structure.
These tutorials have the following components:
The first tutorial was based directly on the MBL activities developed by Thornton and Sokoloff labs in Tools for Scientific Thinking. We extracted from their velocity labs what we considered the essential elements, following the guidance in their paper (ref 3). In the tutorial, students walk in front of a sonic ranger which provides immediate feedback and reduces data-collection drudgery. In the tutorial, students use their own bodies to
The second tutorial is based on suggestions of Laws, Thornton and Sokoloff. Newton's third law is explored by having students connect the force probes to two low-friction carts and observe the result of their interaction. The apparatus is sketched in Fig. 1.
Fig. 1: The arrangement for the Newton 3 tutorial.
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 In this paper, we use the term MBL to refer not simply to the use of a microcomputer to collect and display data, but to laboratory activities using microcomputers in which there is an attempt to actively engage students intellectually and to help them construct an understanding of the relevant concepts.
 Thornton, R. K., and D. R. Sokoloff, "Learning motion concepts using real-time microcomputer-based laboratory tools", Am. J. Phys. 58 (1990) 858-867.
 The poor results achieved by students on the velocity graph questions, despite traditional instruction in the subject, might be interpreted as difficulties reading graphs and not as a confusion on concept. However, the fact that students succeed at a much higher rate on position graphs, plus the reports of interviews from many researchers indicate that this is a confusion of concept, not just of representation.
 Thornton, R. K., "Tools for Scientific Thinking: Learning Physical Concepts with Real-Time Laboratory Measurement Tools", in The Conference on Computers in Physics Instruction, Proceedings E. F. Redish and J. Risley, Eds. (Addison-Wesley, 1990) 177-188.
 The textbook for all semesters reported was Tipler, Paul A., Physics for Scientists and Engineers, 3rd Ed. (Worth Publishers, NY, 1991).
 This was confirmed by the results of the Hestenes test reported below and by interviews associated with another project.
 L. C. McDermott, P. S. Shaffer, and the Physics Education Group, Tutorials in Introductory Physics (University of Washington, Seattle, 1991-present). For a description of tutorials as used at the University of Washington and an experimental result using them, see McDermott, L. C., Peter S. Shaffer, and Mark D. Somers, "Research as a guide for teaching introductory mechanics: An illustration in the context of the Atwoods's machine", Am. J. Phys. 62 (1994) 46-55; Shaffer, P. S., and L. C. McDermott, "Research as a guide for curriculum development: An example from introductory electricity. Part II: Design of an instructional strategy", Am. J. Phys. 60 (1992) 1003-1013.
 Morse, Robert A., "The classic method of Mrs. Socrates", The Physics Teacher 32 (May, 1994) 276-277.
 McDermott, Lillian C., "Millikan Lecture 1990: What we teach and what is learned — Closing the gap", Am. J. Phys. 59 (1991) 301-315.
 We used Intel 386, 486, and Macintosh SE personal computers. The ULI, sonic ranger, and force probes are from Vernier software, Portland, OR. Only the Motion and Datalogger software that comes bundled with the ULI were needed. Two Pasco carts or their equivalent are also required for the Newton 3 tutorial. The current cost of the required equipment is about $2500 per station.
 Thornton, Ron and David Sokoloff, Tools for Scientific Thinking (Vernier Software, Portland OR, 1992 and 1993).
 Ref. 3, Fig. 2.
 Laws,Priscilla, Ron Thornton, and David Sokoloff, RealTime Physics (Vernier Software, Portland OR, 1995).
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