To Play Or Not To Play? A Writing Project That Enhances Students’ Learning Of The Basic Concepts Of Counting
ABSTRACT: As part of a general
introductory mathematics course targeted for non-mathematics majors, students
use the basic principles of counting in a variety of applications including
voting theory, graph theory and probability. To prepare the students for these
applications, the course begins with a unit in which the basic concepts of
counting, permutations and combinations are taught. To assure that the students
have mastered these concepts, they are required to write a letter to a friend
advising them whether or not to play their state’s lottery. In the letter,
students must describe the lottery game they have chosen, the rules for playing
the games, and the chance of winning. This talk will present the challenges
this written assignment posed to the instructor and students as well as the
results observed in student learning.
At Saint Joseph’s University, we offer a course called “Topics
in Contemporary Mathematics” to liberal arts students as part of the general
education requirement. The course is based on the text by Robert Tannenbaum and
Robert Arnold Excursions in Modern
Mathematics (Prentice Hall). Many of the topics covered in the course such
as voting theory, graph theory and probability involve the use of basic
combinatorial concepts. A brief description of the concepts needed is provided
within the context of each application.
In my course, I incorporated a unit on basic counting principles
at the beginning of the course. The unit covers the fundamental principle of
multiplication, permutations and combinations. To assure that the students have
mastered these concepts, a writing project is assigned at the end of the unit. In
this project, students are required to select a state that has lottery games.
(A list of states with their corresponding urls is provided.) They must select
one game, learn its rules and determine the chances of winning. Then each
student must write a 1-2 page letter to a friend advising them whether or not
to play this game in their state’s lottery. In the letter, students must
explain the lottery game they have chosen, the rules for playing the games and
the chance of winning. They are also asked to advise their friend as to whether
or not they should play.
Since these students are not accustomed to writing in
mathematics classes, they are challenged by this assignment. It is imperative that
the instructor provide detailed guidelines on what is expected, grading
procedures and feedback. Students must be made aware of the importance of
writing style, grammar and organization of the letter as well as the importance
of the mathematical “answer” and its interpretation. Allowing students to submit a draft for review is advisable.
The project has been well received by students and has improved
their performance in the applications taught later in the course. The extra work incurred by the instructor is
grading the reports is well worth it.