Two-stage Testing for Second-year Math Students

For this activity, students are given four 2-Stage Assessments (tests) over the course of a semester. These 2-Stage tests are structured the same way. In stage one, students write the test individually. For stage 2, students are randomly placed in groups of 3 or 4. The topics for stage 2 are the same as stage 1, but the test questions are different. In their groups students collaborate to rewrite the test and are required to come to a consensus with their answers.  Each group submits one test booklet.

In each case the two stage tests take place on the same day, but there is approximately a five-hour gap in between. During the gap, students are encouraged to discuss individual test questions with their peers before the 2nd stage test is administered. The 2nd stage questions are only made available at the time of the test.

The tests are evaluated as follows: If a student’s 2nd stage weighted test grade is lower than their individual test grade, their final grade will be their individual test grade. In other words, taking a test in stage two does not lower their test grade.

At the University of Manitoba, this two-stage assessment strategy was conducted with 81 students. Tests were conducted on Fridays; the individual first stage was during the class lecture from 10:30 to 11:20 (85% of a student’s test mark), and the second stage was held during lab time from 4:30 to 5:20 (15% of a student’s test mark). In addition, students were requested not to upload any test question to any online website and or forum at any point.

The main learning objectives are:

• Understand functions of multi-variables and how to represent them using traces and level curves.
• Perform vector operations and calculate dot product/cross product of vectors.
• Determine equations of lines and planes and calculate distances between a point and a line/plane using projection.
• Understand vector-valued functions and how to parametrize a given curve.