Many undergraduate students enrolled in institutions of higher learning wish to connect their learning to real life experiences. By linking reality to academics, students see first hand the practical value in their studies. The purpose of this study was to critically analyze the practice of application projects in undergraduate mathematics courses to determine if, and if so how, students benefit from optional real world application projects. The study was limited to specific courses within a non-math major's undergraduate mathematics program of study at one large research university.
Until the appearance of "The Mathematics Umbrella: Modeling and Education" (Grinshpan, 2005), no research was available dealing directly with mathematically focused application projects, so this study is purposeful. A review of related literature suggests that projects provide a desirable method of learning. This researcher adopted the educational philosophy of pragmatism established by James, Dewey, Chickering and Gamson, and others. Pragmatism---doing what works---is appropriate to undergraduate mathematics education.
Quantitative and qualitative phases were performed sequentially on two distinct, but related, populations of undergraduate non-mathematics major students taking calculus courses. The first phase assessed whether completion of optional real world application projects was related to mathematics students' test grades. The second qualitative phase used individual interviews to capture students' opinions as to the value and desirability of the project process.
The overall goal of the research was to gauge the beneficial aspects of application projects. One strong finding concerned the relationship that may exist between application projects and students' levels of time on task. Project students reported greater time on task than non-project students, and increasing time on task may enhance the quality of students' learning experiences.
The numbers of reported incidences of feelings of course satisfaction and of increased positive perception toward mathematics were largely consistent between groups, with somewhat greater numbers within the project group. Pedagogical implications from this study point to the value of both faculty and student effort devoted to application projects in increased student understanding of, and appreciation for, mathematics.
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