Slate.com recently ran a series on “Favorite Classes.” I thought that it would be worth sharing, and briefly commenting on, their perspective on mathematics and statistics.
First, I love the title on their post about mathematics: You’re Not Actually Bad at Math. Here are some excellent quotes:
The idea that someone can be bad at math is wrong, and it hides several harmful assumptions. It’s an excuse to justify individual failure, rather than a real understanding of mental capabilities. Giving up on math means you don’t believe that careful study can change the way you think. No one is born knowing the axiom of completeness, and even the most accomplished mathematicians had to learn how to learn this stuff. Put another way: Writing is also not something that anyone is “good” at without a lot of practice, but it would be completely unacceptable to think that your composition skills could not improve.
I agree with the author that the phrase “I am not a math person” is used largely as an excuse to help the self esteem of a person who has had difficultly in mathematics. The reality of the situation is that difficulty and struggle are inherent in the process of doing mathematics well. The only reason a person would think that their initial failure to grasp a concept makes them ‘not a math person’ is that they have come to understand the practice of mathematics as solely about obtaining ‘correct’ answers. This leads to a second key quote:
It seems that the origin of math phobia is not the content of math itself; it cannot rest solely on someone’s inability to sit through logic puzzles, because people exercise careful abstract reasoning in every other field without the same sort of fear. Instead, I think the form is largely to blame. All of high school math is basically a one-way linear staircase that leads to calculus. If you fall off at any point, you’re doomed. Calculus prep has infiltrated the curriculum to such a degree that I think people conflate doing algebra with all of math. Students spend so much time memorizing computational tricks that they don’t get to see anything else—that those algorithms have a logical derivation, and that plenty of math isn’t even like that.
In short: the form of teaching matters, not just the content that is taught. I have discussed the form of teaching before. If math is taught purely as algorithmic thinking that leads to a single ‘correct’ solution then it should not be surprising to hear the people who don’t get the ‘correct’ answer to label themselves “not a math person.” As I have discussed before on the topic of the form of teaching, we as math educators need to be mindful of not just the content we teach but also how the manner in which we teach it is shaping student perspectives on mathematics. On this note I encourage you to search for articles on “Productive Struggle” in mathematics. Here is one such article from a colleague at Texas State University that was recently published in the Journal of Mathematics Teacher Education.
Finally, I believe this last quote speaks directly to the mindset we as math educators should be seeking to instill in our students:
Not every educated person needs to be a mathematician, but no educated person should be afraid of the steps it takes to get there.
The second article is titled: “What are the Odds? To learn to think critically, take a statistics class.”
If there’s one skill almost everyone agrees schools should be teaching, it’s critical thinking, although what, exactly, critical thinking consists of is conveniently left undefined. For the longest time, I preferred to believe that it meant learning to be skeptical about words, specifically the arguments, exhortations, and beguilements foisted upon the public by politicians, advertisers, corporations, and the dodgier elements of the press. As a former English major, I figured I had this one nailed; if there was anything I mastered in college, it’s the ability to find the hidden and sometimes manipulative meanings in language.
What I, in my complacency, chose to ignore is just how much of the persuasion now aimed at the average citizen comes in the form of numbers, specifically numbers that tell us about the future, about how likely something is to happen (or not happen) based on how much it happened (or didn’t) in the past. These numbers sing to us the siren song of cause and effect, humanity’s favorite tune. Why do we like it so much? Because knowing what causes events and conditions is the first step toward controlling them, and we human beings are all about controlling our environments. That’s how we ended up ruling this planet, and it’s how some of us hope to save it.
…Statistics and the science of probability represent the ultimate in critical thinking, because they teach us how to criticize the ways we habitually think
I have written before on the Myth of Critical Thinking in Mathematics. To “think critically” is by definition “to be critical of thoughts” or in other words “to critique ideas” as they arise rather than accepting or rejecting them blindly. Critical thinking means thinking rationally and reasoning through arguments with care and consideration of the options on the table. This, of course, sounds all well and good until we as educators stop and actually consider the reality of the situation in the math classroom.
A critique can only be meaningful if you already have a standard by which to judge something. I can’t critique an argument as “true” unless I know what it means for something to be “true.” I can’t critique a painting as “beautiful” unless I know hat it means to be “beautiful.” I can’t critique an act of charity as “good” unless I know what it means to be “good.”
There is an underlying standard of judgment that is being instilled in students (whether knowingly or unknowingly) and this is the root of what is occurring in mathematics classrooms. The way in which students implement their “critical thinking skills” upon the completion of their mathematics courses is simply a symptom of a deeper reality that is being formed within them. That reality can be formed from a Christian perspective where it is God who sets the absolute standards for Truth, Beauty and Goodness, or it can be formed by very humanistic standards of relative truth, subjective beauty, and goodness defined by utility.
The humanistic standards that are pervasive in our educaitonal system is what I believe leads to the last part of the quote above: “We human beings are all about controlling our environments. That’s how we ended up ruling this planet, and it’s how some of us hope to save it.” A Christian perspective realizes that we as human beings are indeed all about controlling our environments, but that is as a result of sin and brokenness and not a trait to be admired. We wound up ruling this planet not by innate ability but by God’s granting to us the stewardship of His creation. And we can never save this planet – we can only rest in the promised hope of future redemption in Christ.
I strongly support the claims made by this article on the need for an understanding of statistics, especially in this age of digital media. However I believe we also must always be mindful of the worldview that we bring to the table in understanding statistics.