 |
 |
 |
 |
 |
 |
 |
|
The Decision Sciences Journal of Innovative Education
Use of Brief Collaborative Quizzes on New Quantitative Lecture Material
Creighton University College of Business Administration
2500 California Plaza
Omaha, NE, 68178-0308
Department of Mathematics and Computer Science
Creighton University
2500 California Plaza
Omaha, NE, 68178-0308
Overview
College students continue to be challenged by quantitative models and applications that appear in most majors and many courses across the curriculum. Failure rates in quantitative courses are substantial in many schools. Even successful students often express dissatistfaction with this material. We use out brief collaborative quiz (BCQ) process to promote student learning and increase student satisfaction in the study of difficult quantitative topics. The BCQ process combines several aspects of teaching effectiveness: peer interaction, active learning, assessment, effective grading, instant feedback, time management, student responsibility, attendance, and motivation. We have used the quizzes for many years with much success in statistics classes and in mathematics classes such as calculus, trigonometry, algebra, and finite math, with class sizes ranging from 10 to 120 students. Other application areas would include economics, accounting, finance, operations management, and any course with quantitative components such as psychology and sociology.
Literature review
Recent emphasis on teaching has shown the benefits of collaborative learning (Thomchick, 1997; Slavin, 1990), assessment (Angelo and Cross, 1993), and effective grading techniques (Walvoord and Anderson, 1998). A number of variations on and alternatives to the classic lecture format have been found to enhance learning. A primary feature of these methods is to engage the student actively (Salemi, 2002; Silberman, 1996). While unannounced or pop quizzes have been used for many years to try to increase student preparation, they are not popular with students. Athough any specific piece of the BCQ may not be new, the innovation is the specific combination of the several parts to simultaneously address multiple learning goals both efficiently and effectively.
The BCQ Process
At the end of a standard lecture, students are given a quiz over the material just presented. They may use notes and texts, and are encouraged to confer with classmates in answering. Quizzes are usually worth five or ten points and cannot be made up. They take ten to twenty minutes at the end of class, and are given one to three times per week, beginning with the first or second day of class. Students know that a BCQ can be given at the end of any class section at the discression of the professor. Thus from a student point of view, the BCQ are random. They find out only when it actually occurs. BCQ questions may be prepared in advance, or prepared on the spot. They are very simple, direct, and just like class examples. They help students learn challenging new notation, terms, concepts, and methods. The professor answers queries only about previous class examples, class notes, or clarification about the problem. After a quiz paper is collected from each student, the answers are presented just before the end of the class. Graded quizzes are returned at the start of the next class, and solutions may be shown again as a review and to enable quick response to student queries.
The purpose of the quiz is threefold. Because the instructor may pause several times during the course of the lecture and ask whether the students understand the process well enough to replicate it on a BCQ or if they need more examples, student response is elicited immediately and attention level remains high. Finally, the experience of the professors allow them to pinpoint topics likely to cause ‘thinking snags’ which may trip up students on homework and tests if not caught quickly. [A very simple example is the tendency of students to reduce (2x+3y)/2x to (1+3y).] These snags seem to be ironed out much more readily with simple quizzes worth points than with repeated warnings in a lecture. Also, it is easier to form a correct firms impression in the student mind than to overcome a previously anchored incorrect view.
There are several collatoral benefits to the BCQ process. Typically, scoring BCQ quizzes occurs just after class and takes very little time. This gives the professor a quick assessment of the exact nature of any misunderstanding about the new material. We use this feedback to guide continuous improvement activities in the course. Because students confer with eachother, anxiety is reduced and a more relaxed and friendly classroom atmosphere is produced. The students appreciate the instant feedback and the chance to get on top of the day’s material right away, while help is available from classmates.
In other words, the BCQ provides a bridge to assigned homework problems, which are typically more complicated and demanding. BCQ points are seen as a reward for attendance and paying attention, and frequently students request a BCQ or additional questions. Over the past twelve years of use, student response to the BCQ (as recorded on anonymous end of semester classroom evaluation forms) has been universally positive.
Differences
Some important variations from methods previously reported in the literature should be noted. Formal student groups or teams are not formed for the BCQ in-class activity. We encourage students to discuss with eachother, they may either seek help or give help. We allow them to make their own contacts, they are not forced to do so. Contrary to classical assessment methods, our BCQ has points attatched. Points motivate attendance, active participation, and learning. Quizzes cannot be made up because the situation of fresh material and peer help cannot be replicated. Finally, a BCQ covers material freshly presented. They do not involve previous lectures or assigned homework problems. The idea is to engage the student immediately to improve learning and student satisfaction.
Of course, the use of the BCQ does not preclude the use of formal groups, standard assessment, or other learning enhancement techniques. We expect professors to match our success using the BCQ, and they may even create modified versions to fit their own situations.
Sample BCQ Questions with Response
BCQ questions are very simple and straightforward, to engage students thinking about the new material. BCQ is ‘bare bones’ whearas homework assignments rapidly progress in context and variety. Let us take for example a statistics class period introducing the Central limit Thereom (CLT). This is a ‘statistical law of nature’ for our world of variation. In the class notes the concept is defined and examples given. CLT gives the sampling distribution of a sample mean random variable. When sampling from a Normally distributed population, the sample mean also has a normal distribution. When sampling from a population of unknown distribution, the sample mean has an approximate Normal distribution if the sample size is large enough (twenty five is large enough for practical purposes). Sample queries with a correct response are given below. Students’ written response must show understanding of the modeling method or process to get credit. Making a diagram for a distribution is a must, showing values on the number axis and identifying probabilities as areas under the curve.
1a. CLT: Random sample of n=25 from X~(50,5), then Xbar~N(50,1), find P(Xbar<52)
Response: P(Xbar<52) = P(Z<(52-50)/2)~.9772. Diagram shows the area to the left of 2.
1b.CLT: As above with n=100, find P(Xbar<51.5).
Response: sigma/Sqrt(n) = 5/SQRT(100) = .5, Xbar=N(100,.5)
P(xbar<51.5)=P(Z<(51.5-50)/.5=3)=.99865. Diagram shows area to the left of 3
1c. CLT: As above with n=10, find P(Xbar<54)
Response: n too small, CLT does not apply!!!
References
Angelo, T.A.;Cross, K.P. Classroom Assesment Techniques 2nd, 1993, Jossey-Bass, San Francisco
Salemi,M.K. An illustrated case for active learning. Southern Economic Journal.
Jan 2002, 68:721-729
Silberman, M. Active Learning, 1996, Allyn & Bacon, Massachusetts.
Slavin, R.E. Cooperative Learning. 1990. Englewood Cliffs, NJ. Prentice-Hall
Thomchick, E. The use of collaborative learning in logistics classes. Journal of Business Logistics. 1997,18:191-205.
Walvoord, B.E., Anderson, V.J. Effective Grading, 1998, Jossey-Bass. San Francisco.
