What is the math equivalent to the FCI?
One of the great things about teaching physics is how well developed the Physics Education Community is. Hundreds of researchers have investigated nearly every question and developed assessments for nearly skill or concept one can imagine. One of the most important assessments is the Force Concept Inventory (FCI), a 29 question multiple choice test of basic mechanics concepts. This assessment has been given in thousands of classrooms and serves as the de-facto standard for measuring increases in student understanding in physics course. It’s not without its flaws, starting with the fact that it doesn’t assess anything other than understanding of Newtonian Dynamics, but its influence in physics teaching has been huge.
A second, much less well assessment is the Colorado Learning Attitudes about Science Survey, or CLASS. Rather than measure student understanding, the CLASS is designed to measure student believes about learning and science in general, and these results are then studied to look for correlation with student performance in the class.
There are dozens more assessments out there in physics education research for measuring understanding of different areas of content or attitudes, but these two form a pretty good basis for trying to measure the effects of a first year physics class.
Now that I’m teaching math, I’m wondering if anything like this exists in the math world. Are there conceptual inventories of mathematics, that rather than measuring a particular skill like graphing conic sections or binomial expansion measure some sort of more generic mathematical understanding (whatever that may be)? The nice thing about the FCI is that even students without any physics experience can read and understand the question enough to be able to offer an answer, which is then useful for pre/post testing.
Secondly, are there any assessments of mathematical attitudes out there? I’d love to give even a rough quantitative measure of a student’s preconceptions about the subject of math, their comfort with it, and their ideas about the best ways to learn math.
So if you know if these things, I’d love to hear about it in the comments.
Follow up: actually, a lithe bit of googling has already helped me find some possibly useful links:
- Mathematics Attitude Survey from Oregon State
- Math Skills Inventory
- The Calculus Concept Inventory
- The statistics concept inventory
- The Basic Skills Diagnostic Test: This looks closest to what I’m looking for. I’ve written the author, Jerry Epstein for a copy. He’s responded, and if you would like a copy, you can email him at firstname.lastname@example.org—you need to agree to a number of conditions about preserving the security of the exam for him to send it to you.
- Precalculus Assessment:This Precalculus Concept Assessment (PCA) instrument is a 25-item multiple-choice instrument that assesses a student’s understanding of the central ideas of precalculus mathematics.
So it looks like the BSDT, along with one of the attitudes studies will be just the tools I’m looking for. Thanks to everyone who sent in ideas.