| Fun with Probability!The Probable Pen in the Cereal BoxAbstract |
| Project Coordinator: | Michael Cornell |
| E-Mail Address: | mcornell@uiuc.edu |
| Permission to post on Satex Web Page: | Granted |
The Fun with Probability Project was a joint effort among interested schools worldwide to experimentally solve a simple probability problem. Simply stated, we calculated the number of boxes of cereal one needs to purchase to receive a complete set of six colored pens.
Each student rolled a six-sided die to simulate buying one box of cereal. Each face of the die corresponded to a colored pen. The students counted the number of rolls it took until each side (colored pen) had appeared at least once. The results were tabulated and submitted to the Fun with Probability! web site. The web site compiled averages to provide an experimental result. This was compared to the theoretical result which was calculated using statistical formulas.
The only required materials were a set of six-sided dice, one for each student in the classroom, and of course, access to the World Wide Web or E-Mail. In addition, the teachers might have used a large coffee can or cereal box and six colored pens or markers for the initial demonstration. Student, class tabulation and sample submission worksheets were provided in various formats to aid in presenting the lesson.
A complete curriculum guide was provided for the presentation of the lesson. The lesson was designed to appeal to a wide range of ages, from Kindergarten to 9th grade. The lesson stages were incremental and cumulative, allowing a teacher to stop the lesson at the point appropriate for the classroom. The subject was of course, probability, specifically averages, predicting results and expected values.
There are a tremendous number of Internet-based projects available, and due to the nature of the project, attracting the attention of a large teacher community would greatly increase the probability of success. In fact, the larger the participation, the better. The incremental lesson plan was developed in order to maximize the participation levels. The assumption was that by making the cost of entry low, but the potential value high, a large number of teachers would be enticed to participate.
However, a large participation group opened the possibility for superfluous hours of management time. Therefore a web-based form was developed which would spread the data entry responsibility out to the participants allowing the project coordinator the ability to focus on other aspects of the project.
The project went remarkably well, considering the magnitude of participation. Of the 100+ participants, only a handful had no web access at all, and of the remaining participants, problems were only experienced by approximately 10%. These problems ranged from Internet access issues, to lost results, to confusion about using web-based form submissions. All were resolved to everyone's satisfaction via E-Mail.
Actually, one concept which has been confirmed about Internet projects, at least at this stage of Internet development: The lowest common denominator continues to be electronic mail, if one is to reach the maximum audience. However, a new corollary has been identified: If 95% participation is sufficient, then web-based projects will be successful as well.
The project was well received by all participants, even those experiencing "problems." All participants seemed to recognize that this was a ground-breaking project, and were extra patient in their expectations. Many comments were received which indicated positive learning experiences. The project was enjoyed by students from five countries, and 19 of the United States. Class sizes ranged from 1 (a home school in Pennsylvania) to as many as six classrooms taught by one teacher.
Minor difficulties were encountered on the technological front, stemming primarily from unfamiliarity with the Macintosh serving environment and programming in AppleScript. All problems were resolved, though late in the project period. There should be no problems in executing a similar project on the LRS web server, based on the modifications performed at the end of the project. Overall, however, the concept of capturing data via a web form and pushing it into a spreadsheet for analysis and posting worked exceptionally well. Approximately 10 hours of data entry time were avoided because of this.