As usual my thoughts tonight are focused on our latest class discussion on critical literacy. There's so much I could ramble on about dealing with this subject. But I've decided to approach it as it relates specifically to math. This is a topic I've dealt with in other classes in my major and the things I've learned and thought about have surprised me. Among other question I've considered things like, Isn't math just cold hard facts? Numbers can't lie right? and How on Earth could someone possibly know that? Unfortunately it's taken me until my college years to have these questions come to mind. I truly wish I would have been taught critical math growing up or better yet, critical thinking in a mathematical way.

I think the distinction between what I'll call critical math and critically thinking in a mathematical way is an important one. While both require interpretation and careful examination of the motives and context of a mathematical work, one is computationally driven and another is logically driven. I feel many teachers are scared away from critical literacy in mathematics because they interpret it only as teaching critical math. Critical math in my mind is mathematics that can be applied to mathematical claims to validate or disprove them. This falls into the realm of analysis which can get very complicated very quickly. Of this type of math I myself feel I've barely scratched the surface even after 4 years of college. In a sense I would call critical math the proofs behind mathematical claims. However, this is not the type of critical literacy I advocate for in a secondary education math class because quite frankly much of it goes well beyond high school math levels.

I advocate for my second category, critically thinking in a mathematical way. To me this is basically asking some very simple questions of any mathematical claim. These questions include things like, Does it make sense and why or why not? What would I need to know to determine if it is true or not? and What could contribute to bias in this claim? Questions like this don't require a student to know advanced math, only to be able to put the mathematical information into context. I think that it's ok for teachers not to always have the "right" answer and therefore we don't have to prove everything. Inspiring our students to question what appear to be cold hard facts is critical literacy at its finest and that is what we need to nurture in our students.

This practice lends itself particularly well to statistics. Student's don't need to know how to calculate the the joint frequency distribution for two exponentially distributed random variables in order to judge the validity of most statistical claims. While certainly we want them to apply what they have learned, basic principles are often the best grounds to stand on. I've heard statistics referred to as the study of mathematical lying and I can definitely see why that's true. There are so many ways to skew data sets that who knows what the truth really is. I certainly don't and nor do I always expect my students to. I only hope that they will be able to recognize the limitations of the claims and value them accordingly. That is critical literacy to me and that is achievable with any age group.