At the community college, it has been an on-going discussion and dilemma to determine how to diagnose a student’s mathematical skills so that they might be placed into the proper course. Diagnosing student mathematical ability is not an easy thing to do!

At the heart of the issue, in my opinion, is this…do we want to assess student ability to reason, make sense, problem solve, etc. or do we want to know what skills and procedures that they can remember how to do?

It seems to me that diagnostic tests only serve to reveal how little students can remember! Why is this so? I contend that because students have not developed a well connected understanding of the kinds of skills and procedures that are on the diagnostic or placement tests, they cannot remember well and/or cannot re-construct or problem solve their way through the diagnostic situation.

My strategy has been to not worry about diagnosing students and rather to work to develop thinking and reasoning skills and to work on students’ beliefs concerning sense making in mathematics. Then, when algebraic issues arise, I try a “just in time” mini-lesson to address that issue.

For example, recently in my Calculus II course, students needed to evaluate sin(0). Several students had no idea and their only recourse was to push buttons on the calculator. I used this as a teachable moment to do a mini-lesson on the meaning of sin(A). Most students do not have a mental image of sine being the vertical position of the endpoint of the corresponding arc on the unit circle. If they did, sin(0) would not really have to be something to memorize. Rather, they could draw on their understanding of the meaning of sin(0) and figure it out!

This is an important topic (diagnostic testing) that is worthy of discussion and debate. I encourage everyone to share their experiences, strategies, and successes!

Scott

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