Learning
Integral calculus with NASA Classroom of the Future
With the
purpose of having students learn integral calculus, professor Ing. Ind. Gloria Faus of the High School,
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. This 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
(http://www.usc.edu/hsc/dental/ccmb/usc-csp/quikfacts.htm).
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.