Learning Integral calculus with NASA Classroom of the Future

By Gloria Faus, Jim Botti and James E. Coffield *

With the purpose of having students learn integral calculus, professor Ing. Ind. Gloria Faus of the High School, Guadalajara Campus made some changes in teaching methods to use Problem Based Learning (PBL). PBL centers on real-life problems that are present in a variety of out-of-school contexts. Problem-based learning (PBL) is a constructivist instructional strategy that simultaneously develops both problem-solving strategies and disciplinary knowledge bases and skills. Students become active problem solvers as they tackle an ill-structured problem that mirrors real-world problems (Finkle & Torp, 1995).

To succeed in their chosen careers, students need practice in solving ill-structured problems that reflect life beyond the classroom. They must develop the ability to confront ambiguous, ill-defined situations and make sense of them. They must recall concepts and techniques and apply them in this sense-making process. Further, they need to engage in and develop an effective inquiry process. By solving problems, students practice learning, address multiple contents, and overcome obstacles. Instead of memorizing facts that reflect a collection of random information, they use meaningful facts relevant to solving actual problems. (Botti & Astengo, 2004)

Professor Faus looked for the support for these changes from two experts in PBL education: Jim Botti, Ph.D. and James E. Coffield, Ph.D., both of the NASA classroom of the Future and the Center Educational Technologies at Wheeling Jesuit University in West Virginia . The NASA professors suggested an actual situation that they thought would be of interest to the students. The suggested problem involved an actual Comet, C/2002 T7 (LINEAR) passing through the solar system. Th is open ended problem was beyond the learners' immediate capabilities, requiring inquiry for appropriate methods and information not only of mathematics, but also of other disciplines of the High School like a multimedia for the presentation of results. Students addressed the problem and worked towards a solution involving history, ethics, geometry, algebra, differential calculus, integral calculus, physical, sciences of century XX and disciplines not known for them like astronomy that they had to investigate and to learn.

Not all the information was given, nor did the learners have enough prior knowledge to solve the problem. During the process, the students had communication via email with Dr. Jim Botti and Dr James Coffield, who guided them providing information on pages of Internet of NASA where the students could find the answers to their questions. This PBL approach caused the students to exceed all of our expectations. The students' high level of performance motivated Drs. Botti and Coffield to make the closing by video-conference. During the videoconference they asked the students directly about their problem solving processes, the physical and mathematical information that they involved in their work, and what they thought of this form of learning. The students enunciated very favorable commentaries as a result of their experience. The students said it was very rewarding that at the end of the PBL process, the NASA professors congratulated them not only for their efforts, but also for their knowledge in the matters of mathematics and physics, as well as the reasoning and programming they used to present their solutions.

The Comet scenario and PBL process contains seeds of interest and roles that provided the opportunity for learners to face the application of their values with an attitude of responsibility in the delivery of their work. The students demonstrated a deep respect in the communication with the NASA professors and showed a genuine preoccupation to take care of and to maintain the harmony, the responsibility to make sure that the information that they successfully obtain outside is the truth and is possible to use for to find a solution feasible, to take into account in the solution. Finally, in the solutions that the students presented were based not only on sciences but also on their own values.

Because life outside the classroom is filled with complex problems, it makes sense to mimic similar conditions in the classroom. Complex problems offer many advantages. First, complexity helps ensure that there is no one “right" answer. Having multiple correct answers that approach the problem from various perspectives and solutions can springboard to class discussions that stimulate student higher-level thinking. Also, complex problems often allow for the integration of interdisciplinary solutions, a common occurrence in solving real world problems (Albanese & Mitchell, 1993).

Rather than seeking right answers, PBL is more about seeking appropriate resolutions to questions, issues, and or situations. Typical problem solving taught in schools often tends to be situation specific: There are well-defined problem parameters that lead to predetermined outcomes with one correct answer. In these situations the procedures required to solve the problem are often the focus of instruction. Unfortunately, students skilled in this method generally are not adequately prepared when they encounter problems in which they need to transfer their learning to new domains, a skill required to function effectively in society.

Albanese, M., & Mitchell, S. (1993). Problem-based learning: A review of the literature, its outcomes, and implementation issues. Academic Medicine, 68 (1), 52-81.

Botti, J. A., and Astengo Noguez, Carlos (2004) PBL Scenario Essentials , Proceedings of the PBL International Conference, Cancun, Mexico, June (2004)

Finkle, S., & Torp, L. (1995). Introductory Documents. Aurora, IL: Center for Problem-Based Learning.

* Gloria Faus coordina el área de Cálculo Integral en la preparatoria del campus Guadalajara; Jim Botti y James E. Coffield trabajan en el Salón del Futuro de la NASA (Centro de Tecnologías Educativas, Universidad de Wheeling). El artículo se publicó en inglés a petición de los autores.

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