From the Origin: Newsletter Opinion Section

Retaining Freshman Interest in Mathematics and Computer
Science Using Collaborative and Experiential Learning

Joanne Caniglia, Krish Narayanan,
Elene Tetras Contis, Kathleen Stacey

Eastern Michigan University

I. Introduction and Background

A three-year study to determine why undergraduate science, technology, engineering, and mathematics (STEM) majors switch to non-STEM majors was conducted by Seymour and Hewitt [1]. They found that the major reasons students give for switching majors were lack or loss of interest in science, belief that non-STEM majors hold more interest, poor teaching by STEM faculty, and feeling overwhelmed by the pace and load of the curricular demands. The authors recommend that STEM programs examine their curriculum, structure, and delivery if they want to increase student retention. Studies offer compelling evidence that effective teaching in science and mathematics education enables students to: construct their own understanding of concepts; internalize relationships between concepts and processes ([2],[3]); develop critical thinking skills; integrate learned concepts with everyday experiences ([4], [5]); and appreciate the study of science and mathematics as a valuable endeavor. Programs that attract and sustain student interest feature learning that is experiential, investigative, hands-on, personally significant to both students and faculty, connected to other inquiries, and suggestive of practical application to students’ lives. Such learning flourishes in a community in which faculty are committed equally to teaching, to maintaining their own intellectual vitality, and to partnering with students in learning, and in which institutional support for such a community exists [6].

Sheila Tobias and others ([7], [8], [9]) report that to retain students in engineering programs the focus should be on the first two years, offer cross-college course integration, provide service-learning opportunities and establish a records-tracking system to identify causes of retention problems. The Eastern Michigan University Creative Scientific Inquiry Experiences (CSIE) program integrates and innovatively adapts features of these successful programs to the teaching and learning of mathematics and science in general education and has the potential to become a model for producing more STEM graduates at such institutions.

Based on these explanations, data, recommendations, and Eastern Michigan University (EMU) demographics, an interdisciplinary project team developed a model to recruit and retain students in STEM majors. Figure 1 illustrates the CSIE model, which requires a university-wide support system: interdisciplinary course development, supplemental academic enrichment for students, and intense and sustainable faculty professional development.

Figure 1

Figure 1. The CSIE model.

The CSIE Faculty Fellows will

  • Earn released reassignment time to develop the theme-based integrated courses;
  • Train in Academic Service-Learning pedagogy, one that focuses on academic research in the community;
  • Participate in the Spring/Summer Institute for generating creative linkages with fellow faculty to explore interdisciplinary science connections and research opportunities;
  • Develop a team approach to research-oriented community-based research.

The CSIE Student-Scholars will:

  • Learn to partner with others on community-based research projects;
  • Experience career exploration with local practitioners in their fields;
  • Experience smaller class size and book/supplies subsidies;
  • Have access to an intense network of academic support services through the CSIE Program Office.

II. College Algebra-Computer Science CSIE

“Tell me, and I will forget. Show me, and I may remember. Involve me, and I will understand.” – Confucius, 450 B.C.

Our approach builds on the fact that a significant number of freshmen do not appreciate a particular field of study because of the lack of immediate application of learning concepts ([10], [11]). Such application is essential for their critical thinking and assessment of results to make appropriate connections between fundamental and applied concepts. The Computer Science department in particular faces this challenge with students who are pursuing a constantly changing field ([12],[ 13]). Even though EMU’s Computer Science and Mathematics curriculum recommends a senior, capstone project, it is too late for students, in their duration of study, to realize the practical applications of what they have learned. We believe that students need to be shown the significance of what they are learning from the beginning of their coursework, in order to sustain their interest in the field. Such students demonstrate a lack of understanding or misunderstanding of fundamental mathematical concepts and thereby lose interest.

To address the Mathematics-Computer Science issue, we have identified a freshman course in Mathematics (MATH 105-College Algebra) and linked it with JAVA Programming (COSC 111). Students in these linked courses will be able to comprehend the math concepts they learn in class by applying them immediately in labs and projects in COSC 111. Because of the reinforced mathematical foundation, it is hoped that students will be well-prepared to learn computer science fundamentals. In addition, students will apply their computer science and mathematical knowledge in serving the needs of community organizations in a one-credit course (CSIE 177-Creative Scientific Inquiry Experience theme-linked course; www.emich.edu/csie) that emphasizes service-learning and team work. Students attend the three courses in the same semester to benefit from the collaboration. Figure 2 shows an illustration of how these courses work in a cycle to reinforce students’ learning of fundamental concepts and application.

Figure 2

Figure 2. Cycle of reinforced learning.

III. Academic Service Learning in College Algebra and Computer Science

With this model in mind, the College Algebra and Computer Science courses teamed with the Meals on Wheels Organization. After meetings with the director of the Ypsilanti Meals on Wheels (MOW), not only would we serve the organization with data displays and trend analysis, but also the combined classes would develop an efficient routing system for a volatile client list. As an abstraction of the routing system, we used the “Traveling Salesman Problem”, which can be formalized as: Given n locations, find a tour of minimum total length. (A tour is a path that visits all the required locations and then returns to its origin.) The TSP is a famous problem because it is simple to understand but hard to solve, at least for instances of realistic size. For a survey of solution techniques, see Lawler et al. [14].

The Ypsilanti Meals on Wheels program delivers prepared lunches to persons who are unable to shop or cook for themselves. As it is for many nonprofit organizations, the funding for MOW is unstable, chronically insufficient and occasionally desperate [15]. The routing system is relatively accurate and inexpensive; consequently it has more implementations throughout the world than any other commercial routing system [16]. Materials are basic and consist of a map, a table of θ values, and two card files. The map is an official map of Ypsilanti and surrounding townships. It is mounted under a plastic grid so that one can read the (x,y) coordinates for any location. Thus adding new or subtracting clients is not difficult. A JAVA program produced a table of values of θ.

The Sierpinski space-filling curve is the limit of the series of recursively-constructed figures shown below. Each is built upon the preceding figure by dividing the square into quadrants and filling each quadrant with a shrunken copy of the preceding figure. The limiting figure is a one-dimensional curve that is continuous and visits every point in the two-dimensional square [17].

Figure 3

Figure 3. Sierpinski space-filling curve.

IV. Conclusion

Although Ypsilanti Meals on Wheels creates formal routing sheets based on mapping systems, volunteer drivers deliver meals using informal visualization methods based on their knowledge of Ypsilanti. As students ride along with volunteer drivers, they discover the complex nature of mathematical modeling. Students realize that human factors play key roles. They discover the difference between “real-world” applications and theoretical results.

We have found that the goals of promoting inquiry, encouraging reasoning, and making connections can be achieved in the seminar. Many students comment that the seminar is an important aspect of the course and helps students to see the connection between the mathematics and computer science programming.

Why should anyone take this type of experience (given it is not required)? We find that these types of courses are good both for the students and for us. We learn from each other and from the students. This mode of teaching is rejuvenating and if organized properly, is possible to be institutionalized.

REFERENCES

  1. Seymour, E. & Hewitt, N.M. (1997). Talking about leaving: Why undergraduates leave the sciences. Boulder, Co: Westview Press.
  2. Cobb, P. (1994). Theories of mathematical learning and constructivism. Paper presented at Symposium on Trends and Perspectives in Mathematics Education. Institute for Mathematics, University of Lagenfurt.
  3. Resnick, L. B. (1987). Learning in school and out. Educational Researcher, 16(9), 13–19.
  4. Thorton, R.K. (1985). Tools for scientific thinking: microcomputer-based laboratories for the naïve science learner. (ERIC Document ED 264 130).
  5. Laws, P.W. (1989). Workshop Physics. FIPSE final report. (ERIC Document ED 352 252).
  6. What works: Building natural science communities. Vol. 1, Project Kaleidoscope, 1991.
  7. Tobias, S. (1992). Revitalizing undergraduate science: Why some things work and most don’t. Tuscon, AZ: Research Corporation.
  8. Workforce 2000: Work and workers for the twenty-first century. William B. Johnston and Arnold E. Packers. Indianapolis, INP: Hudson Institute, 1986.
  9. Davis, James R. (1995). Interdisciplinary courses and team teaching: New arrangements for learning. Phoenix AZ: Oryx Press.
  10. Carter, L. Why students with an apparent aptitude for computer science don’t choose to major in computer science. In Proceedings of the Thirty-Seventh SIGCSE Technical Symposium on Computer Science Education. Houston, Texas, USA. March 2006.
  11. Frailey, D. What math is relevant for a CS or SE Student? – An employer’s perspective. ACM SIGSOFT Software Engineering Notes, 31, 3. May 2006.
  12. Shackelford, R. Why can’t smart people figure out what to do about Computing Education? CS and IT Symposium, St. Louis, Missouri, U.S.A. February 2005.
  13. Tester, J. et al. Developing Recruitment and Retention Strategies through “Design4Practice” Curriculum Enhancements. In Proceedings of the 34th ASEE/IEEE Frontiers in Education Conference. Savannah, Georgia, USA. October 2004.
  14. Hadlock, C. Mathematics in Service to the Community: Concepts and Models for Service-Learning in the Mathematical Sciences. The Mathematical Association of America. 2005.
  15. Ypsilanti Meals on Wheels – Annual Report, 2006.
  16. Platzman, L.K. and Bartholdi, J. J III. Spacefilling Curves and the Planar Traveling Salesman Problem. Journal of the Association for Computing Machinery, 36, 4. 1989.
  17. Bartholdi J. J. III Routing System Based on Spacefilling Curves. Atlanta. Georgia Institute of Technology. http://www2.isye.gatech.edu/~jjb/mow/mow.pdf, 2003.

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