# 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 jerepst@att.net—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.

Im also trying to get assessment like the FCI on pre-algebra subjects, like fraction and proportional reasoning. We’ve got a math expert looking into this right now, I’ll let you know if we find anything.

This is a great idea, but I’ve never heard of such a broad-scale inventory, especially for geometry, algebra, and precalculus. Partly this may be due to the reality that there has been no consistent national understanding for what these courses are or should cover despite efforts of NCTM’s Standards over the past two decades. The adoption of the Common Core State Standards in Mathematics by 45 states may help. Still, someone, somewhere must have some inventories, even if small and not thoroughly statistically vetted.

I’d love to be wrong about the existence of large-scale inventories for secondary mathematics.

Hi John,

I’ve wondered about this too. My first assignment for my math classes is usually a diagnostic that I’ve adapted from various sources, and it gives me some information about what they know. What ends up being much more informative is having the first unit as a large scale review of topics.

For example, my first Algebra 2 unit consists of solving 1 variable equations, number properties, absolute value equations, and evaluating algebraic expressions. All of these are more Algebra 1 topics that I know they have seen before, but it gives me a chance to really dig in and understand what misconceptions they have, what their good/bad math habits are, and where I may need to fill in later on. It also gives me some space to give them some open ended and challenge questions to see how they approach these types of activities.

The fact that they have seen the content before helps reduce some of the anxiety about starting up again after the summer, but this also lets me push them to see just how far their understanding of these essential topics goes. While this doesn’t really fit the bill for a pre/post analysis of their development, it goes pretty far as far as helping me predict what they will need as we move through the curriculum. It isn’t normed as the FCI is, but I can compare students to others I’ve had in my experience, and that tends to work well enough for planning purposes.

Evan,

This is interesting, and it’s a different take on review than I’ve thought of before. In about a week or so, I’d love to put together some sort of G+ chat on Algebra II to brainstorm various approaches to this subject. Would you be interested in joining?

Of course – in Cleveland at the moment with downtime for the next week or so – let me know when.

The ARTIST project attempts to do this for Statistics. I’ve not yet applied it to high school students, but I intend to do so this school year as both a pre- and post-test for AP Statistics.

http://app.gen.umn.edu/artist/

Probably not what you’re looking for but there are a billion “Algebra Readiness” tests out there. I think we use something from the Mathematics Diagnostic Project http://mdtp.ucsd.edu/ There appears to be more than just Algebra but I haven’t looked.

There’s the Quadratic and Linear Conceptual Evaluation at http://physics.dickinson.edu/~wp_web/wp_resources/wp_assessment.html