The Magic Marker
Colleges want to judge their applicants fairly without using test scores. But should they rely on a subject that not every student needs and fewer still actually learn?
As the global pandemic recedes (though it’s not, according to my doctor), schools are finding their way back to a normal that is not actually normal, but close enough to 2019 that they can perceive it as normal, from a distance. Will colleges continue to allow test-optional applications? And, if they do, what kinds of data do colleges rely on to inform their admissions decisions?
One data point: Calculus. Taking Calculus in high school, I’m told, is significant, even for non-science students. A student who passes Calculus in high school is more likely to handle university-level material.
I smile at that thought.
I do agree that taking Calculus in high school is significant, but that its significance is partly misplaced. In addition to signifying that the student who took it is excellent, its presence on the transcript signifies that the school that student attended is wealthy. I moved from a high school that offered it in well-off Fairfax County, Virginia to a just-above-average Chicago public high school that didn’t. I took College Algebra in my senior year of high school. I was an underachiever, so I probably wouldn’t have taken Calculus in my senior year anyway–but, I never had the option.
I’d also remind everyone that it’s not just taking Calculus that matters: it’s what you learn from it. I’ve had some experience tutoring first-year Calculus with students at a franchise tutoring outfit. I’d like to share some of that experience.
First, for the non-mathematically inclined, what is Calculus? According to Google, it’s the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. According to me, It’s the study of limits as described by mathematical functions and the applications of said limits. (I told you I was an underachiever.)
Neither definition gives the reader a sense of the challenge, so I shall try again. Do you remember how difficult it was to adjust to Algebra after mastering (or, especially, not mastering) arithmetic? In order to understand polynomial operations, it helped (a lot) to really understand the four basic operations, to know factors of two- or three-digit numbers on the spot, and to master exponents, among other things. You just took your mastery of arithmetic and applied it to a new situation. In a sense, Algebra was proof that you knew arithmetic well enough to apply it to a situation out of context. Calculus is to Algebra what Algebra is to arithmetic, and, since most high school graduates could not ace a 9th-grade Algebra exam taken at graduation, one could understand how excited colleges would be to consider the applications of students who have passed Calculus.
Even then, it’s not that simple. The word “Calculus” on a high school transcript doesn’t mean that the school system offered Calculus in the same way that the college does, or that the student mastered it, or that the student even understood it.
When I took Calculus at the University of Illinois at Urbana-Champaign, it was a “weed-out” class for Engineering students and those who had visions of transferring to the college of Engineering (I’m a proud and happy graduate of the U of I, but I made a colossal mistake choosing it–don’t be a Liberal Arts Math major at a great Engineering school). However, the instructors allowed for partial credit on exam grades. I got through with low passing grades by solving every problem as far as I could and then writing out where I thought the problem was going, but that I couldn’t solve the rest. If this sounds like an exercise in another sort of discipline, it was, so I switched to Rhetoric in my junior year and kept Math as a minor. After I was hired to teach GED Math at a community college, I re-took three semesters of Calculus and aced all—it wasn’t easy, but I knew what I didn’t master at the U of I, and I corrected course.
The students I worked with recently didn’t have the option of solving as much of the problem as they could. They had online tools that used multiple choice, or, worse still, treated every answer that was entered incorrectly, even if off by one negative sign, or one exponent, or one variable, as incorrect. You could literally understand ninety percent of the problem but get zero credit for the answer.
In this context, my students were less interested in the “why” and too interested in the “what” and the “how;” those are bad signs for any class. I helped one student iron out the kinks and get at least half her homework correct, until this became impossible—her class shifted to second-year topics and she needed more than I could give her. (I’ve forgotten a lot of Calculus myself, and there are times when the textbook doesn’t jog my memory.) Another student was taking a MOOC (massive open online course) to get ready for the stress of freshman Calculus at her as-yet-unchosen college. This was slightly better, because the class had notes that we could read together, but answers to exercises weren’t given in outline form, so I had to do the problem for her and give my notes on the problem in the margins. The first student learned a little, but she got the word “Calculus” on her high-school transcript. The second student learned a lot more, and kept decent notes, but didn’t. Neither student seemed terribly interested in STEM (Science, Technology, Engineering, and Math) programs–which left me wondering whether this wasn’t money wasted. They could have gotten the same intellectual bang by a study and discussion of Tolstoy. I’d have had us read Anna Karenina.
So, what are we left with? Words on transcripts. If I were in an elite college’s admissions department, I’d ask for essays designed to allow students to demonstrate what they’ve learned, and I’d administer those essays in a way that they can’t be faked. You could then, by looking at the difficulty of the essay topic chosen, the student’s ability to solve the problem, the way the essay is organized, and the length of time that student spent, have a much better view of that student’s ability to deal with college-level work.
But, hey. That takes time, effort, and money. If colleges don’t have any more of those three to spend, they’ll just look for words on transcripts instead. The system slouches on.