Since the imposition of Common Core and ubiquitous propaganda that Common Core math standards require different methods of instruction (despite claims on the CC website that the standards do not prescribe how teachers are to teach), there has emerged an expression that causes me great anguish whenever I hear it. The expression is “to problem solve”, in which “problem solve” has become a new verb form.
It has caught on like wildfire and replaced older forms such as “solving problems”. The phrase has taken on specific meanings; it is a “dog whistle” of reform math (a term Tom Loveless of Brookings coined). It means a departure from the standard word problems that have been held in disdain by reformers as tedious, repetitious, “plug ‘n chug’, not relevant to students’ interest and not reflective of how math is used in the real world.
Case in point would be the type of word problems (which used to be called ‘story problems’ in simpler times) that one finds in great supply in older algebra books and diminishing to none in newer ones, about trains catching up with each other, people mowing lawns together at different rates, and so on. There has been universal agreement amongst reformers that these problems did not do anyone any good except the brighter gifted students who, as reform legend has it, would have learned math anyway by virtue of having been born that way.
The term “to problem solve” now means giving students so-called “rich” problems that cause them to “dig deep” into concepts, learn what is needed to solve the problems on a just-in-time, as needed basis, and other wonderful-sounding things that in the end are more often than not ineffective. Such problems are often open-ended, with multiple right answers, and students solving them in multiple ways. A classic example offered in this genre is “A rectangle has an area of 28 square inches; what are the possible dimensions of the rectangle?” Others are laborious one-off type problem which require intepretations of graphs that are then used to plug in to various formulae in order to answer various questions that the educators responsible think represent how people go about solving problems (collaboratively, of course) in the real world. These type generally fall into the category of problem-based, or project-based learning. There are those who make a distinction between problem- and project-based approaches. I am not one of them.
This is not to say that all such problem constructions are bad. And I recognize that there are teachers who are able to effect a good balance of different problem types, and hook in to prior knowledge and skills. I offer, however, something that veteran middle school teacher Vern Williams has said:
I have always stated that if a reform minded teacher produces competent, intellectually passionate students, they will absolutely escape any criticism on my part. But the opposite seems never to occur. Regardless of stellar results, the traditional teacher will always be criticized for being a self centered sage on the stage, controlling student learning and running a draconian classroom. Their students may be the happiest most accomplished students of all time but the teacher will never be good and pure until they cross over to the reform side.
In that vein, what I often hear are arguments that these “rich” problems justify the rejection of traditional type problems used over the years to teach students fundamental problem-solving skills–skills that are generalizable and transferable to many types of problems.
I happen to use the old type of problems in teaching my students how to solve problems–not problem-solve. People at my school marvel at how my students are challenged, and who show improvement in solving problems. I am often asked what I do to get such positive results. An answer I haven’t yet uttered but am tempted to do so is: “You know all those types of problems that they tell teachers we shouldn’t give students to solve? Well, that’s what I do.”