US News – which, to be honest, I didn’t realize was still around – has an excellent article about the argument about whether to emphasize pure or applied mathematics when teaching it.
In the OECD study, researchers looked carefully at survey questions on how often students said they encountered pure math tasks at school, such as solving an equation like 2(x+3) = (x + 3)(x – 3). They were also asked how often they encountered applied mathematical tasks, such as calculating how many square meters of tiles you need to cover a floor, or how long it would take to get from one place to another using a train timetable.Disadvantaged students tended to report having more exposure to the applied tasks. Students from wealthier families tended to say they had more exposure to solving equations. OECD analysts explained that this exposure to equations indicated that the students had been taught pure math that emphasized conceptual understanding.
The surprising thing, though, is that students taking the pure math approach seemed to do better on tests, even those whose questions took an applied-math approach.
Consider how dividing fractions is taught. Instead of thinking through what it means to divide a fraction by a fraction, students, especially low-income students, are often immediately taught gimmicks, such as “Yours is not to reason why, just invert and multiply” or “Keep, change, and flip.” (Translation: keep the first fraction as it is, change the division sign to multiplication, and flip the numerator and denominator of the second fraction.)
Briars added that the new Common Core standards are aimed at boosting conceptual understanding, and that’s one reason teachers are asking students to draw all those crazy pictures that are lampooned in the media.
Read the whole piece here. It’s quite good.