Calculus Readiness Assessment and Remediation

Maplesoft’s online assessment system, Maple T.A.,facilitates a win-win situation for students and faculty at EasternConnecticutStateUniversity

Calculus Readiness Assessment and Remediation project results in increased student accountability and better course curriculum

Introduction

The problem that EasternConnecticutStateUniversity’s (ECSU)Mathematics Faculty faced in its three-course calculus sequence is mirrored across the country. As students move through the sequence, they forget skills and concepts learned in earlier courses and often have an unrealistic expectation that their present instructor should review all previously learned material relevant to the course. Thus, they try to hide their lack of knowledge, which can lead to disaster at the end of the semester. Frustrated by this situation, the Mathematics Faculty at ECSU decided to take action in the form of instituting calculus readiness exams and remediation at the start of each course in the calculus sequence.

The faculty’s objective wasto ensure that studentstake responsibility forreviewing materialfrom previous courses before starting new ones. This would save a lot of time and effort on the faculty’s part and make new courses more efficient by bringing students up-to-date before the start of the course.

When they chose Maple T.A. -a Web-based system for creating tests, assignments,and exercises that automatically assess student responses and performance - little did the faculty realize that the successful outcome would go far beyond the anticipated increase in student responsibility.

Commenting on their selection of the software, Dr. Salvatrice F. Keating and Dr. Marsha Davis, the two faculty members that led the project at ECSU, said, “A salient feature of this assessment software is that Maple T.A. can identify and correctly grade equivalent forms of student answers. In addition, Maple T.A.’s randomly-selected-constants design feature is useful in creating different questions with the same mathematical structure. Given that the Mathematical Association of America (MAA) and Maplesoft are presently collaborating on online assessment/placement exams is further endorsement that we made a wise choice in selecting Maple T.A.”

The Maple T.A.Success

The MathematicsFaculty offered their collective resources to aid Dr. Keating and Dr. Davis’ preparation of entry exams and tutorials for students. Everyone gave inputs on their core topics, thus taking complete ownership.For the calculus courses, the Maple T.A. Question Bank Editor was used to create question banks for each exam and tutorial. More often than not, the algorithmically-generated Maple-Graded questionswereused. Assignments (in a variety of formats – exams, mastery sessions, study sessions, etc.) were created by selecting questions from a question bank. Once the questions were selected,assignmentpolicies were set.Such policies can include restricting the number of attempts a student is allowed to complete the assignment, setting the beginning and ending dates, and specifying whether students can view hints during the assignment or solutions at the end of the assignment.

The Maple T.A. Gradebook records student statistics consisting of student names, identification numbers, dates when the assignmentswere accessed, the time it took to complete the assignment or mastery session, grade earned, and so forth. The instructor can access assignment statistics such as the mean and standard deviations of the scores, as well as the lower quartile, median, and upper quartile of the scores. At the question level, instructors can view the success rate, the p-value and the d-value, and they can view individual student assignments.

Entry exams for Calculus I,Calculus II, and Calculus III are now administeredto incoming studentsat the beginning of the semester. For students who do not earn a passing grade of 75 percent, mandatory tutorials are provided. Revised assessment exams and tutorials are administered at the beginning of every semester. To date, more than 350 calculus students have been assessed by the Maple T.A.-based Calculus Assessment System. The success of the exams has led the faculty to make them mandatory for the start of certain courses.

“We see significant changes in student response because of the Maple T.A. readiness exams. Students now realize the immense benefits they get from taking the tests and assuming accountability for their readiness for the next course. Their complaints about ‘instructors going too fast’ have now changed to ‘I am not well-prepared for the new course’,” said Keating and Davis. “The courses themselves are getting better and much more efficient. We are able to identify deficiencies much earlier and addressthem productively.”

Going beyond

The positiveresults from using Maple T.A. readiness exams did not stop there. Another big win for ECSU was the way in whichthis exercise acted as a catalyst to enhance the unified efforts of the entire Mathematics Department. The faculty discussed student weaknesses together and arrived at ways to best address them through changes in the curriculum, as well as in teaching methods. They moved from asking “why don’t they know it?” to “where do they see it?” and planning the curriculum accordingly.

Maple T.A.alsoprovides an abundance of statistical information at both the course level and individual student level. For example, on the entry exams, in addition to a list of students’ final scores, faculty can access the dates on which students took the exam and the amount of time they spent on it. The percentage of students who answered each question correctly as well as an individual student’s answers can be determined. This type of information is extremely useful in identifying weaknesses in the calculus sequence, as well as weaknesses for individual students.Access to such data brought a great deal of ownership to the instructors who started taking responsibility for ensuring courses better address student needs.

Dr. Keating and Dr. Davis have presented their strategy and demonstrated their Calculus Assessment System at a number of conferences and at several universities. Their novel approach in the use of technology to assess student retention of prerequisite course material and their provision for remediation will be featured by author Peggy Maki in her revised textbook on assessment. Dr. Keating and Dr. Davisplan to continue their jointwork in assessment. In particular, Dr. Keating has been awarded a spring 2008 sabbatical to continue her research in assessment and its application to the use of online technology.

ECSU’s success with the Maple T.A.assessment system is now encouraging the Connecticut State University System to move to the same model. ConnecticutStateUniversity has already purchased Maple and Maple T.A. for use at each of its four campus locations.One goal is to ultimately create an assessment consortium consisting of the four CSU campuses. Dr. Keating and Dr. Davis advise them to start small and build from there, because the flexibility of Maple T.A. allows the system to grow at their pace.

“The use of technology has brought us amazing results,” said Dr. Keating and Dr. Davis. “We are getting so much more out ofour students. Once the results were visible, there was no turning back. We work together as a team to make the benefits available to both students and the faculty. In the end, it is a win-win game for all.”