When the students were asked whether a/5 or a/8 was greater, only 53 percent answered correctly. The authors believe that many of the participants could’ve been just guessing, since 36 percent were unable to explain why one was bigger.
The researchers said that since much of math education is just following formulas, students are incapable of tracking problems only slightly different than ones that they have encountered.
A student was asked in the study whether it was possible to check if 462 + 253 = 715. The student correctly answered that you could subtract 253 from 715, but when he was asked whether one could also do 715 – 462, the student “did not think so.”
Another set of questions checked to determine whether students would take advantage of relationships between problems to find easy solutions. These students were asked to solve the following problems: 10 × 3 = ; 10 × 13 = ; 20 × 13 = ; 30 × 13 = ; 31 × 13 = ; 29 × 13 = ; and 22 × 13 = .
Once problem two is solved, the third becomes easier by simply multiplying the answer by two. However, 77 percent of the students never took advantage of those relationships, and simply did the multiplication for each problem.
The researchers found that 77 percent of the students believed that math was not something that could be figured out, or that made sense. Instead, the students believed math was a step of procedures and rules to be memorized.
The team believes the results suggest that U.S. students may be able to do a lot better in math if they can develop a basic conceptual understanding.
“This finding helps make sense of the community college students’ lack of conceptual understanding,” Nate Kornell wrote in “Everybody is Stupid Except You,” published in Psychology Today. “They have been taught in a way that deprives them of the chance to work through the concepts they are being taught. No wonder they see math as an exercise in memorization.”
“The concepts are learnable. On the other hand, teaching mathematical concept is deceptively difficult. Teachers need high quality training, and more research (and funding) is needed to make that happen,” Kornell concluded.