A Spreadsheet Approach to Mathematical Modelling for Engineering Students

This project was concerned with developing and evaluating spreadsheet-based materials for teaching algebra. functions and graphs and mathematical modelling to engineering technicians. The project has confirmed our starting hypotheses.
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  1 A Spreadsheet Approach toMathematical Modelling for Engineering Students Final ReportRosamund SutherlandAlison WolfInstitute of Education, University of LondonApril 1995  2 A Spreadsheet Approach toMathematical Modelling for Engineering StudentsFinal Report April 1995 This project was concerned with developing and evaluating spreadsheet-basedmaterials for teaching algebra. functions and graphs and mathematical modelling toengineering technicians. The project has confirmed our starting hypotheses. Thesewere (1) that many 16-18 year old engineering students have serious weaknesses intheir mathematical skills; (2) that use of computers for mathematics teaching is particularly relevant for vocational students because of their widespread use inindustry and (3) that educational institutions involved in technician engineeringtraining have the facilities with which to implement computer and spreadsheet-basedmethods in a routine fashion.The project has resulted in a book for engineering technicians,  A Spreadsheet  Approach to Maths for GNVQ Engineering  which was delivered to the publisher Edward Arnold, a division of Hodder Headline, at the beginning of April. The book should be published in September 1995. We took the advice of Anthony Tomei andmade contact with potential publishers at an early stage in the project and our  publisher has been very supportive throughout the production of the book. A selectionof pages from the manuscript (as submitted to the publisher) appear in Appendix 1.At the beginning of the project we were undecided about whether to producematerials for teachers or for students. However as the project progressed we becameconvinced that FE students would be more likely to take responsibility for learningmathematics if an appropriate text book were written for them. The book has beendesigned so that students work on both computer and non-computer activities.Throughout the last phase of the project our main energy was directed towards the publishing of the book. However there are a number of other important aspects of the project which we shall briefly report here and which we will actively disseminate over the next 9 months. Two articles for submission to academic journals are in preparation. One discussed the formal, quantitative evaluation of the materials (seesection C below), and one focuses on particular issues related to algebra learning, asillustrated by individual answers and error analysis.  3 A. Process of Curriculum Development We have taken a particular approach to curriculum development which has involvedworking closely with 5 Further Education colleges. The colleges represented a spreadin terms of: previous experience with computers; commitment of lecturing staff; typeof engineering students; computer provision. The materials were first evaluated withtwo groups of students in one FE college (phase 1). These students were taught by thedevelopment team, with the cooperation of the college lecturer. Materials were thenrewritten into booklet form and were used in 4 FE colleges by 5 groups of students.The FE lecturers were the teachers and the research/development team made regular classroom observations of students working on the materials (phase 2). The totalnumber of students trying out the materials was approximately 150.The effectiveness of the materials was evaluated by a) observations by thedevelopment team b) analysis of students' written responses in the booklets c) analysisof pre and post tests. After phase 2 the materials were rewritten as a book. In thecompleted book approximately three quarters of the materials have been intensivelytrialled and the remaining materials were written to fit with the new GNVQspecifications for engineering mathematics.The project was assisted by a steering group which met three times. Regular attendersat these steering group meetings included Professor Alan Davies, University of Hertfordshire; Sue Burns, Nuffield A-level Project; Peter Winbourne; University of theSouth Bank; Nigel Carruthers, West Herts College; Chris Boys, NCVQ; RosemaryWaite, Engineering Council. This group provided us with invaluable feedback on thematerials which were being produced. B. Visits to Engineering and Engineering-based Industries The Engineering Employers‘ Federation was extr  emely helpful in contacting member companies and arranging visits. These were supplemented through individual contacts.The following companies were visited throughout the project: Rolls Royce; JohnBrown Engineering; British Airways Brose, Technik für Automobile; Dormer Tools;AE Pistons; Brown & Holmes Tamworth; JCB, Uttoxeter. These visits provided uswith a wider understanding of current engineering practice. They also established that there is a general desire in industry for engineering technicians‘ c ourses to incorporatecontinuing mathematics instruction to a level well beyond GCSE. The visits were alsoused more specifically to:  4 • establish the general mathematical skills required of young workers andapprentices (including requirements for progression) • determine what problems, if any, young entrants from National Diploma backgrounds have with mathematics • investigate how spreadsheets are currently used in the engineering sector  • develop ideas for authentic engineering modelling problemsThese visits have highlighted the need for more substantial collaboration with industrywhich is the focus of our current proposal to the Nuffield Foundation, GeometricalModelling and Industrial Statistics for Engineering Students. C. Evaluation of the Materials in Terms of Student Learning andImprovement As specified in the srcinal proposal, the success of the materials was evaluated usinga formal pre-test and post-test (reproduced in Appendix 2). This involved all four colleges participating in the trialling, plus one control group. The pre-test was given tosix groups from the four colleges, but in one college (which srcinally volunteered twogroups) the materials were eventually used only by one. The post-test was therefore given to five ‗experimental‘ and one ‗control‘ group. There was also considerable attrition in numbers between pre- and post-test. Some students had dropped out of thecourse; others were absent on the second occasion (which was close to the end of theacademic year). Full pre- and post- test data were obtained for 72 ‗experimental‘ students. The small numbers; the groups‘ different experiences with different teachers; the fact that the control group was small (N=22) and turned out not to be very highly ‗matched‘: —  all these factors mean that the results cannot be seen as a definitive examination of the ‗effectiveness‘ of the materials. We would, in fact, emphasise thatit is not in any case appropriate to talk of materials‘ effectiveness separate from the way in which they are used by teachers. In this case, we were engaged, with our collaborating teachers, in developing, evaluating and modifying materials as the year   progressed. Obviously, therefore, this was far from a classical ‗treatment versuscontrol‘ design.  Nonetheless the results are in a number of ways both highlyencouraging and suggestive. They have also been fed directly into the modification of the materials for publication.  5  Patterns of change and improvement in participating colleges In our initial analysis each question was assigned a facility rating by determining the percentage of students who correctly answered that question. An unweighted averageof these facility rates was obtained and is presented in Table 1. Table 1Average facility rates for the whole sample Pre PostAverage facility rate 51% 57% Overall, this suggested a slight improvement overall in students‘ performance, but not a very great one. However, more detailed analysis revealed underlying patterns whichsuggested that for lower-achieving students, the results were positive and significant.For analysis, the group was split according to the GCSE grades of the students, asshown below. • B or C at GCSE (43 students) • D or E at GCSE (17 students)(A very small number of students had grades A or F. These, along with those who didnot give GCSE grades, were excluded from this analysis.) Table 2Facility rates according to GCSE gradeGroup B/C Group D/E Pre Post Pre PostAverage facility rate 56% 59% 37% 52%As might be expected, the pre-test scores were much lower for the students whichgrades D/E than those with grades B/C. However   , the D/E group showed a muchlarger increase between the two tests . The average facility rate for this groupincreased by 15 percentage points, or almost half: from 37% to 52%.Further information on differential patterns of improvement emerged when we compared ‗easy‘ and ‗hard‘ questions. In general where an individual question had a facility rate of more than 70% there has either been very little increase or even a slight
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