Reformed text: UM uses a reformed calculus
text (Hughes-Hallett et al.), which emphasizes conceptual
understanding, the rule of four, etc., and de-emphasizes more
traditional skills in the course.
Reformed course: UM calculus I and II are
taught in sections of 30, with group homework assignments and
required graphing calculators.
Uniform exams
are highly conceptual, and allow use of graphing calculators.
(And so are written so that calculators can't give the answers.)
Highly uniform: about 40% of course grade
comes from classwork and team homework; about 60% from uniform
exams
Courses using gateway testing: are
precalculus, calculus I and calculus II, all of which use
reformed texts and/or methods.
Gateway Tests
Rationale: Gateway testing was introduced to
the introductory program to ensure the acquisition of algebraic
and computational skills in the reformed courses.
Results: Assessment of gateway testing at the
time of its implementation indicated that students learn and
retain the skills on the tests. [Megginson, A gateway testing
program at the University of Michigan, in Preparing for a New
Calculus, MAA Notes #36, A. Solow ed.]
In-Class Test: The gateway test is given and
graded once in class by the instructor.
Time Frame: Thereafter, students who did not
pass the test in-class have two to four weeks to pass the class
in the UM Math Lab.
Policies
Time Limit: tests are capped at 20 minutes, and
tests are time-stamped when they are handed out and
returned.
Cap on Repeats: students are allowed only one
attempt per day, to encourage studying between attempts.
Passing Grade: students must get 6/7 problems
correct to pass.
Proctors: student proctors check student IDs to
ensure that the student taking the test is who they say
they are.
Graders: student tutors in the Math Lab grade
the tests (after the student taking the test has left) and
return them to the instructor.
Incentive: Students who do not pass the
gateway test by the end of the testing period have their course
grade reduced by 1/3 of to a full grade point.
Gateways Given: Precalculus entry gateway,
Calculus I entry gateway (discontinued; to be reintroduced),
Calculus I differentiation gateway, Calculus II entry gateway,
Calculus II integration gateway.
Difficulties with Traditional Implementation
Grading Time: because of the volume of
students (about 2000 calculus I students in the fall), gateway
tests cannot be graded and returned fast enough.
Retaking: students sometimes retake the exam
before knowing their previous results.
Reviewing: students suffer from not knowing what
they did wrong when they did it.
Instructors' time: in peak times, instructors
may end up having to grade gateways for their students.
Accountability: even with student proctors and
oversight, 100% accountability is not attained with this system.
On-Line
In-Class Test: The gateway test is in most
cases given and graded once in class by the instructor.
Time Frame: Thereafter, students who did not
pass the test in class have two to four weeks to pass the class
in a computer testing center.
Policies:
Time Limit: because students are having to work
with the computer, the time limit is increased to 30
minutes. This limit is tracked by the computer.
Cap on Repeats: students are allowed more than
one attempt in a day, but only if they review their test
with a tutor between attempts.
Proctors: students from the Math Lab are used as
proctors for the on-line exam.
Grades: are stored and reported to the student
immediately once they have completed their test.
Practice Tests: students are able to practice
the gateway test from any computer with Web access.
Incentive: students still lose 1/3 to a full
grade point for failing to pass the gateway.
Technical Details
Software: In F00 UM Ann Arbor tested the use
of eGrade
(from John Wiley &
Sons) and WeBWorK
(from the University of
Rochester). eGrade was designed as a gateway testing
platform; WeBWorK had to be tricked to be effective in
that context. In W01 and hereafter eGrade is being used
for gateway testing.
Course Numbers: In F00 seven sections of
calculus I used the on-line system to take the derivative
gateway test; in S01, about 11 sections of calculus I took the
derivative gateway and about 11 of calculus II took the integral
gateway on-line. In F01 we hope to have all courses taking the
gateways on-line.
Lab Space: We expect to need about one
computer in the testing lab for every 20 or 30 students taking the
gateway test, or about 60 computers for full implementation. We
are in the process of adding a 30 computer lab for F01 and W02,
to use in conjunction with existing lab space. We will be
reassessing needs thereafter.
Additional Features: We have added a
tutorial
component to the practice derivative gateway, and are this
summer adding similar features to the other on-line gateway
tests.