Soccer is the world's most popular sport. It is played on the beaches of Brazil, on the grassless surfaces of Argentina, Uruguay, Chile, Africa as well as on the nap-inviting fields of Europe and North America. Therefore, soccer balls are objects, i.e. geometrical objects that are popular among college students, and can be used to connect the discrete and continuum scales through the “Soccer Ball Model.(SBM)” When studying the physics of transport, it is necessary to develop conservation equations for variables such as total mass, energy, and momentum. In order to accomplish this, the concept of a continuum scale must be introduced. Since most students have only been introduced to the physical and chemical concepts related to total mass, energy, and momentum, from a discrete scale point of view, this concept can be very challenging for the student (learner). This means that the students already have knowledge related to calculating the total mass, velocity, and momentum of a single particle (discrete scale domain). In addition to having an introduction to several scientific concepts from the discrete point of view, students have an adequate background in many complementary subjects, including calculus, integral concepts, and algebra. It appears that the instructor should use this strong background to identify an approach that catalyzes the transformations. So, how does the instructor use the students' experience with the discrete scale domain and relate it to the continuum scale domain?

Most textbooks do not address this issue, assuming that the mathematical steps and concepts are familiar to the learner ¹ , when in fact, they are not. This can be frustrating to the student and does not enable them to fully understand or capture the importance of this important idea of a continuum scale. An alternative approach is to design a student-centered activity (Arce and Schreiber, 2004) to engage the student in every step from one scale to the other. Thus, we propose an approach that uses soccer balls, to help with this transformation process, in conjunction with geometrical domains, mathematical principles, and physical properties. In this contribution, the authors will discuss the soccer ball model from a student's point of view along with its advantages and compare it to more traditional, familiar methods for introducing the concept of a continuum scale. The important role of the SBM as a POK (Arce, 1994; 2000) will be highlighted.

References: Arce, P. and L. Schreiber, “High Performance Learning Environments, Hi-PeLE”, Chemical Engineering Education, 286-291, Fall 2004.; Arce, P. “The Colloquial Approach: An Active Learning Technique,” Journal of Science Education and Technology, 3 (3), 145, (1994); Arce, P.; Oyanader, M.; and Whitaker, S. “The Catalytic Pellet: A Rich Learning Environment for Up-Scaling,” Chemical Engineering Education, 41(3), 187-194 (2007); Arce, P., “Principal Objects of Knowledge (POK's) in Colloquial Approach Environments,” Annual Conference Proceedings, American Society for Engineering Education, ASEE (2000, CD-ROM).

1. In fact, textbooks suppressed the student opportunity to learn the concept by directly telling the answer. (See Arce et al, 2007).