Selected List of Publication on Cooperative and Collaborative Learning Implemented in Calculus

A brief history of various Math Workshop Programs

Small-group Calculus workshops were first introduced by Treisman [1] in the 70’s at UC Berkeley. The program was originally called Professional Development Program Mathematics Workshop and was aimed at helping minority students to success in Calculus. Treisman then replicated the program at University of Texas Austin starting in 1988, which was then renamed Emerging Scholar Program (ESP). In both cases, results were extremely positive with measurable increase in student grades. [2]

In 1998 Duncan and Dick at Oregon State University [3] started a similar program, the Math Excel Workshop Program, and extended it to four different courses (college algebra, precalculus, differential calculus, integral calculus). Data analysis based on regression models over four different semesters and 19 workshop sections showed that the Math Excel sections received average grades that were .01 units higher on a 4-point grading scale than the average grades of other students.

Other workshop programs targeted at minority students were developed at California State University (Bonsangue, 1994, ref in [3]), and at University of Kentucky (Freeman, 1998, ref in [3]). In both cases, minority students enrolled in these programs not only received higher grades than other minority students not enrolled in the math workshops, but also a smaller fraction of these students had withdraw or changed to a non-math major within three years of entering the program compared to the non-workshop students.

Links to existing workshop programs:

Emerging Scholar Program, U. Texas Austin http://cns.utexas.edu/current_students/emerging_scholars_program/

Math Excel, U. Kentucky http://www.ms.uky.edu/~freeman/mathexcel.html

Merit Workshop, U. Illinois, Urbana-Champaign http://www.math.uiuc.edu/MeritWorkshop/workshop.html

Wisconsin Emerging Scholars, U. Wisconsin http://www.math.wisc.edu/~wes/

Typical Features of Workshop Programs

The overall goal of a mathematics workshop program is to increase student achievement by creating small communities of learners who work cooperatively on challenging mathematics [4]. A key aspect of most of these workshops programs is that it emphasizes honor-level mathematics, not remedial. Attempts to adapt the model to address underpreparation have met with varying degrees of success (at UC Santa Barbara workshops were extended to include participants with lower and lower levels of preparation and the effects were negative [4]). Most of these programs are directed to underrepresented students –women, students of colour, students with disabilities, students from rural background, however everyone is eligible to enrol in the program, but at the same time enrolment numbers are kept small.

A common feature of these programs is student voluntary self-selection. Before the beginning of the term or on the first day of class, students are invited to enrol in the workshop program. Because of the time commitment required by the program (see below), enrolment is mostly driven by student’s motivation to success.

Students in such programs attend regular lectures (and sometimes also regular weekly recitation sessions). In addition, they enrol in small size workshop sessions (no more than 24 students) that would meet 2 or 3 times a week for 1.5 or 2 hours per session (timing and scheduling vary across institutions).

The additional workshops usually carry one or two extra credits with Pass/No Pass grade awarded based on strict requirements of faithful attendance, punctuality, and participation by the students (typically attendance at less than 90% resulted in a No Pass grade).

Workshop sessions are not necessary linked to a particular lecture session. The level of integration of workshop material with lecture material is regulated by weekly meetings between the course instructor and the workshop leader.

For each workshop session, students work individually or cooperatively on carefully prepared worksheets, typically under the supervision of a graduate assistant who plays the role of facilitator. An extensive database of problems used at UT Austin and UK is available at http://betterfilecabinet.com

A study of some of the characteristics of a workshop worksheet is presented by Dick [5], who discusses the adaptation of the mathematical tasks framework proposed by the researchers involved in the QUASAR project (Quantitative Understanding: Amplifying student Achievement and Reasoning) to help create successful workshop problem sheets. In particular, he discusses the importance for good worksheets to maintain high cognitive demands, be relevant to class material, and offer a variety of tasks to keep students engaged.

None of these programs has ever been extended to an entire course section. Hake et al [6] experimented with the creation of a special section of College Algebra that required concurred enrolment in Math Excel in lieu of a recitation session and the replacement of TAs with course instructors at the workshop sessions. The analysis described in [6] is limited to the effect of enrolment in the workshops on student participation to subsequence math courses, effects on students grades are not analised. [1] Treisman, U., Studying Students Studying Calculus: A Look at the Lives of Minority Mathematics Students in College, The College Mathematics Journal, Vol. 23, No. 5 (Nov., 1992), pp. 362-372

[2] Moreno, s., Muller, C., Success and Diversity: The Transition through First-year Calculus in the University, American Journal of Education, Vol. 108, No. 1 (Nov 1999) pp 30-57

[3] Duncan, H., Dick, T., Collaborative Workshops and Student Achievement Performance in Introductory College Mathematics Courses: A Study of a Treisman Model Math Excel Program, School Science and Mathematics, Vol. 100, No.7 (2000), pp 365-73

[4] Hsu, E., Murphy, T.J., Treisman, U., Supporting High Achievement in Introductory Mathematics Courses: what we have learned from 30 years of the Emerging Scholars Program, M. Carlson & C. Rasmussen (Eds.), Making the Connection: Research and Practise in Undergraduate Mathematics Education. Mathematical Association of America [Good review of ESP workshops programs developed in the last 30 years, focus is on minorities. Programs is described in detail, lots of quotes from Asera (2001).]

[5] Dick, T., Lessons Learned in a Math Excel Workshop: The Importance of Maintaining High Cognitive Demands, The Journal of Mathematics and Science: Collaborative Explorations, Vol. 6 (2003), pp 65-74

[6] Hake, C.M., Crow, M.L. Dick, T., Persistence in Mathematics by Underrepresented Students: Experiences of a Math Excel Program, The Journal of Mathematics and Science: Collaborative Explorations, Vol. 6 (2003), pp 87 -101

Other references:

Asera, R. (2001) Calculus and community: A history of the Emerging Scholar Programs, New York: The College Board.

Herzig, A., Kung, D. T., Cooperative learning in calculus reform: What have we learned? In A. Selden, E. Dubinskly, G. Harel & F. Hitt (Eds.) Issues in mathematics education Vol 12: Research in collegiate mathematics education: Vol 5, pp 30-55

Emerson, J. d., Mosteller, F. Cooperative Leraning in Schools and Colleges I and II, Educational Media and Technology Yearbook, Vol. 29, pp 132-162 [Brief review of different programs in US universities (p 143)]

Springer L., Stanne M. E., Donovan, S. S. Effects of Small-Group Learning on Undergraduates in Science, Mathematics, Engineering, and Technology: A Meta-Analysis, Review of Educational Research, Spring 1999, Vol. 69, No. 1, pp 21-51. [Meta-analysis of small-group learning, effect sizes are compared, in all cases effects are positive and mostly significant.]