Development of model-based learning in first year mechanics

Development of model-based learning in first year mechanics David Sands, Department of Physical Sciences, University of Hull

Anyone who has ever built a computer model to investigate a difficult concept will appreciate the power of computers in fostering understanding. As described so eloquently by Chabay and Sherwood1; „Perhaps the most significant advantage of writing programs from scratch is that there are no “black boxes”: students write all of the computational statements to model the physical system and visualize the abstract quantities. In doing so students must bring together various components of their physics knowledge; for example, identify all interactions, describe them mathematically, and correctly write and apply fundamental principles such as the momentum principle. All the physics is nakedly exposed in the program.‟ In short, if it can be modelled it must be understood. The key word here is “understanding”, which is not the same as knowing. Students might know Newton‟s laws of motion in the sense that they can state them when asked, but they do not always understand them in as much as they cannot apply them to mechanics problems. David Hestenes2 was the first to identify the tension between naive beliefs about the world and understanding Newtonian concepts and developed the Force Concept Inventory (FCI) to measure students‟ understanding of the latter. Hestenes has shown that functional understanding of mechanics correlates with scores on the FCI and that his instructional methodology, which he calls the “modelling theory of instruction”, produces better results than conventional instruction by lectures3. Having students construct their own models produces better understanding than having students listen to lecture. The purpose of this development project was to establish resources that would serve as both demonstrations of concepts and as the basis of students‟ models for a course in mechanics that replaces a conventional 20-lecture course delivered in the second semester of the first year. The change was brought about by retirement of the existing member of staff rather than a revision of teaching methods, so the course had to satisfy a number of constraints, including course content and syllabus, which remained unchanged. It was decided therefore to implement a blended system of instruction which utilised elements of both Chabay and Sherwood‟s and Hestenes‟ approaches combined with demonstrations of mechanics principles through computer models. The medium for construction of the models was VPython, the 3-D visual extension to the Python programming language used by Chabay and Sherwood. VPython is ideally suited to modelling mechanics and includes a class of variables called vectors which have all the properties of vectors in mathematics. The models the students were to construct were based on the approach described by Hestenes and included uniform motion, uniform acceleration, variable acceleration, such as motion of charged particles under Coulomb‟s law, collisions and simple harmonic motion. SHM served as vehicle for the introduction of uniform circular motion. The FCI, taken three times during the course, was used as a means of evaluating learning. The first FCI established the baseline, the second was taken after the first assessment exercise, and the third at the end of the course. The purpose of the second test was to determine whether changes in the FCI occurred after completing the first modelling exercise designed around specific principles. In total two modelling exercises were set; one involving kinetic principles and the other involving Coulombic

interactions and Newton‟s third law. The class was split into two randomly assigned halves with each half being asked to do one exercise before swapping over. After the first exercise the class re-did the FCI. By many measures the course was success. On a personal note, I found this to be an enjoyable way to teach mechanics, as it is possible to demonstrate quite complex ideas through simple programmes. Moreover, the majority of the students enjoyed using VPython, though some struggled initially to get the hang of it. Some of the work produced for the assignments was very good and the majority of students passed the exam. Poor performances in this component of the module correlated with poor performances elsewhere. This indicates a substantial spread in both prior knowledge and abilities within the class rather than any especial difficulty with this type of instruction. This spread of abilities complicated the evaluation of the course. A breakdown of the proportion of correct responses on each question in both the pre- and post-instruction FCI scores showed very similar looking profiles. There was a general improvement in the post-instruction scores, but the FCI alone does not tell the whole story. The FCI does not test knowledge of either vectors or SHM, which together comprise a large element of the course. Therefore the FCI does not reflect all the learning that has occurred. Moreover, with some students already appearing to have a good working knowledge of mechanics, the capacity for improved FCI scores across the whole class is also limited. These factors indicate some modifications for the coming year. The FCI will be augmented by elements of the Vector Evaluation Test4, but there will also be greater emphasis on self-paced learning to allow for the individual differences. Although the construction of computer programmes will remain a central feature of the course, there will be a shift in emphasis to allow students develop modelling skills in general. Chabay and Sherwood have been teaching computational physics for over ten years and report; “After a decade of work on developing computational activities for the introductory course, we cannot claim that our instructional sequence realizes the full educational potential of computation that we have outlined in previous sections. Much research and development still remains to be done in this area.” Research and development, or rather development and research is the key idea. There is no complete and general theory of modelling in the educational literature but there is a lot of work on different elements of modelling in science education. This development project has laid the foundations for an interesting research project to integrate these different elements of modelling theory in an attempt to maximise the educational benefits of computational modelling using 3-D visual programming.

References [1] Chabay, R. and Sherwood, B. (2008); Computational physics in the introductory calculusbased course, Am. J. Phys. 76 (4&5) 307 [2] Hestenes, D., Wells, M., & Swackhamer, G. (1992); Force Concept Inventory, Phys. Teach. 30, 141-158 [3] Hestenes, D., Notes for a modelling theory of science, cognition and instruction, Proceedings of the GIREP conference 2006, Modelling in Physics and Physics Education, August 20-25, Amsterdam 2006, pp34-65 [4]

Redish, Edward F., Teaching Physics with the physics suite, John Wiley & Sons, 2003