## by Maria K. Robinson, Seattle University |

Traditionally, mathematics courses are not heralded as participation courses. Many students come to their math classes expecting simply to listen or at most take notes rather than to actively participate. Typically, they are rarely called upon to answer questions that have been asked by the professor. As the effects of Reform Calculus are hitting the country many professors are now expecting more interaction with their students. But how can this participation be assessed? This note describes a quantitative way of assessing class participation that reaches students with different learning styles and promotes interaction between the students and the instructor.

I believe that students learn better when they are actively engaged in the lecture. In order to promote this, I ask my students questions that I expect them to answer. I try to avoid ?yes/no? questions; the questions I ask are generally open-ended. I may ask a question to introduce the topic, or for an idea on how to approach a problem. In many classes the participation grade may be assessed at the end of the course when the instructor is trying to decide if students with a border-line grade should receive the higher grade or not. This system relies on the instructor?s memory of the entire semester. Others assess participation by recording the student?s name as soon as they participate. However this method interrupts the flow of the lecture and gives the appearance of grading students. I have devised a way of assessing the participation grade that does not rely on my memory and minimizes the interruption to the lecture. When a student answers a question, either correctly or incorrectly, I toss him a Koosh Ball. Also, when students ask their own questions or answer each other?s questions, I toss them a Koosh. I typically only let a student earn one Koosh per class meeting. An exception can be made if a student provides a really insightful response or asks a really insightful question. At the end of class the students who have received a Koosh come to the front of the classroom. While there they write the number of Kooshes they received during that lecture on a spreadsheet with their name and the date of the class. They also use this opportunity to return the Koosh to me. The spreadsheet facilitates tabulating each student?s participation grade. Since the participation grade is only 5% of a student?s total grade there is not much incentive to cheat.

I try to create an environment where every student is encouraged to participate in class. However, not all students are comfortable speaking in front of their peers. In order that these shy students not be penalized, I have devised other ways of awarding Koosh points. A shy student who has many questions can earn a Koosh point by attending office hours and asking questions about the material. If my office hours are inconvenient a student can also earn a Koosh point by emailing me questions. However, not all shy students will attend office hours or email me. They can also earn Koosh points by completing a variety of small written assignments. In a proof class, for example, these assignments might ask the student to prove a statement that is beyond the scope of the standard exercises. By this I mean that either the proof technique required has not been taught in class or the concepts in the statement have not been covered in class. In other classes I may ask the students to write a paper on a topic that was covered briefly during a lecture. For example, in a Calculus II class I ask the students to research Gabriel?s Horn. I may ask students in an Introduction to Linear Algebra class to write a summary of an article from either a journal or the Internet where concepts from linear algebra are used. They may choose any article they desire. I only ask that when they submit their written report that they also submit a copy of the article. Because these writing assignments are often more intense than answering a question in class or attending office hours, I will award up to five points per assignment.

I have used this system, with slight modification, for six semesters. This past year, I collected feedback from my students. The following questions had an answer that was significantly (a=0.05) above neutral. Students in my Introduction to Statistics course at the sophomore level agreed with the statement ?Participation of other students helps me learn the material.? Students in Calculus II also agreed with that statement. Students in Linear Algebra agreed with the following statements: ?I like the ?Koosh? method of assessing class participation? and ?I feel the ?Koosh? system is fair to all students.? Finally, students in Engineering Math, a junior level course, not only agreed to all the statements already mentioned, but they also agreed to the following: ?Participating in class helps my performance (grade),? ?The participation grade has encouraged me to pay more attention in class,? and ?I learn more by participating in class.?

I am quite excited by the results of the survey, especially for Engineering Math. I was apprehensive about incorporating the participation grade in this particular class because the stereotypical engineering student does not participate in class. Therefore they would thrive in environments where they only take notes. This particular class was comprised of hard-working individuals who really enjoyed the stimulating interaction of the class. I think that the participation grade actually made the course easier for some students because in order to participate in class they needed to stay current with the material that was being presented.

The survey to which the students responded also allowed them to make
additional comments or suggestions. Here are a few of these comments:

?In general, I like it. The class atmosphere tends to be
more enjoyable.?

?I know that there are some kids who are shy and don?t like to
speak up in class, and I think this encourages them.?

?People told me that it was a difficult class, but it has been
made so easy.?

?I like to participate when I want to, not have to for a grade.?
{I see this as a negative comment ? but it?s fine that not everyone is
happy with the system, particularly if the class learns more.}

?While the system did not completely motivate me to overcome
my reluctance to speak in class, it did help considerably.?

Overall, I believe that the Koosh system is a successful way to encourage
students to participate in a mathematics class and to assist students to
be successful in the class because they are motivated to stay current with
the material. It promotes an active-learning environment, most students
believe that they benefit, and it does not disrupt the flow of the lecture.

Maria Robinson (robinsonm@seattleu.edu) is an Assistant Professor at Seattle University. After graduating from Emory University with her PhD in 2000, she spent three years as a teaching postdoctoral fellow at the University of Arizona. Her interests include studying low-dimensional topology, research with undergraduates in the area of Knot theory, and working towards improving the teaching of undergraduate mathematics.

The Innovative Teaching Exchange is edited by Bonnie Gold.