As a country, we make a lot of blunders, both publicly and privately. It’s no surprise, of course, because our population is 311,000,000 strong. Even if each person only made one-half of a mistake every other day, that would still be, like, so many mistakes being made. I might have a more exact number, but I’ve never been that good at math, and I am far from being alone in this country. As it happens, the teaching methods one learns by may play a large role in this.
A study published in the journal Educational Psychologist, itself taken from two previous studies, sheds some solar-powered calculator light on the steep downward spiral that this country’s mathematics education has taken. The subjects were community college students who placed into a remedial math class, so these aren’t just your everyday village idiots. But these tests weren’t the standardized standards either, and traded learned knowledge for applied knowledge. Traditional math problems can be solved purely by memorizing formulas and procedures, but when these formulas and procedures are themselves the subject of questioning, the understanding falls apart.
Here are some heart-stompingly depressing examples. Only 21% of students could correctly place the numbers -0.7 and 13/8 on a number line ranging from -2 to 2. Forty-seven percent could not answer whether a/5 is greater than a/8. Over 3/4 of those tested, when given a series of related multiplication problems, did not recognize the numerical relationships that would have made solving the problems easier.
The most glaringly disappointing example given was a student’s incomplete ability to figure out a simple addition concept. When asked to verify that 462+253=715, the student was indeed able to subtract 253 from the sum and got 462 as an answer, but denied the opposite — subtracting 462 from 715 — was possible, stating he’d been taught to only subtract the second number, not the first, from the bigger number. It’s like going through life eating under-seasoned food just because the recipe didn’t call for salting to taste. I’m not even sure who to judge more harshly in this situation.
A separate part of the study was focused on an improvement in mathematical learning, and included the TIMSS classroom video study of 8th grade math and science students. Seventy-seven percent of the students reported beliefs that math was not a sensible subject of logic, and that memorization was the only way to learn it. One was quoted as saying, “In math, sometimes you have to just accept that that’s the way it is and there’s no reason behind it.” This is a bigger problem, to me, than not knowing how to add fractions, because it is the complete antithesis of what mathematics is: i.e. the most logic-based thing to ever exist.
The video studies offered some insight into why students think this way, finding that lecture-based teaching and abstract examples probably don’t work as well as group activities and real-world examples. Studied deeper, it was found that higher-performing countries used no more conceptual problem-solving than procedural, but they discovered U.S. teachers were more prone to convert concepts to procedures, killing off the relatable aspect in a complicated math problem. Instead of informing students about the fascinating inter-connections found in all areas of math, the teachers are presenting bare-bones figures as the end all of educating.
Considering the problems given to these students were taught to me in a small-town Louisiana elementary school, I find it completely disheartening that schools in areas of higher educational funding and quality aren’t raising these averages anymore.
Wait, what’s an average?