June 20, 2010
June 20, 2010
June 23, 2010
15.201.1 - 15.201.10
Assessing Engineering Students’ Ability to Use the Mathematics They Have Learned
A Mathematics Applications Inventory (MAI) is being developed by engineering and mathematics faculty at Cornell University to assess students’ ability to apply the mathematics they learn in freshman calculus to engineering-related problems. This paper reports on three aspects of this work: (1) Development of the first draft of the MAI, (2) Pilot testing the MAI, and (3) Preliminary analysis of the pilot test data.
To develop the MAI, faculty of second- and third-year engineering courses were surveyed about how key concepts and techniques from single variable differential and integral calculus are used in intermediate-level engineering courses. Based on their feedback, as well as feedback from advanced undergraduate engineering students, an initial set of test items was developed. The resulting MAI consists of five open-ended questions with eleven sub-questions. The test is designed to be administered during one hour in paper-and-pencil format.
The MAI was administered during the first week of the Fall 2009 semester as a pre-test to a sample of first-year engineering students (N=51). Based on a review of their performance, a subset of 14 participants was selected to participate in follow-up cognitive interviews to probe their thought processes relative to the MAI items.
The pilot test data are being analyzed to determine patterns in students’ abilities to apply the mathematics they have learned, to gain insight into common gaps in understanding related to the application of specific mathematical topic areas, and to understand patterns of responses and performance by other background and status variables such as gender, race, SAT scores, and level of mathematics preparation. These data are being used to refine the MAI items and to develop a multiple-choice version of the MAI. Ultimately, the MAI is intended to be used as a pretest/posttest instrument to determine whether curricular changes affect students’ ability to apply mathematics to problems set in engineering contexts.
Entering engineering students at Cornell University have median SAT Math scores of approximately 750 and Verbal scores of approximately 685. Credit for the equivalent of first semester calculus is expected at entrance (i.e., the equivalent of a 4 or 5 on the AB Advanced Placement examination). The first mathematics course for half of the entering class, Math 1910, is the equivalent of second semester calculus, for the other half it is multivariable/vector calculus, Math 1920, or higher (Linear Algebra for Engineers, or Differential Equations for Engineers). By all the usual measures we have a very able and motivated group of students. Yet engineering faculty at our institution have reported consistently that students in introductory engineering courses have difficulty using even elementary mathematics to represent quantities and relationships between them. This inability to use the mathematics that they have apparently
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