Eat Your Math
The philosophies behind healthy eating and math instruction share interesting similarities that provide useful insight into the direction educational policymakers should take. Healthy eating means consuming the right amount from each of the food groups. It is systemically more beneficial when the food is as close to its natural state as possible, as opposed to having been heavily processed in a factory and removed from its original source. Eating unprocessed food gives us important dietary components, such as vitamins, minerals, fiber, and protein, that are essential for staying healthy.
While we know we need these dietary components to stay healthy, it isn't the same to take them separately as supplements. For example, you wouldn't have a lunch of vitamin A supplements, a snack of fiber, and a plate of zinc for dinner. Instead, we must strive for balance and eat a variety of foods that combine such dietary components to form healthy meals.
With healthy eating, it seems obvious which option provides the best result. For math educators, however, the choice is not so clear. Many classrooms take the path equivalent to eating meals of supplements. Robust math problems are broken down into individual standards so that the lessons no longer have context, and skills are swallowed, in isolation, like vitamins. On the one hand, this makes it easy to ensure that students have consumed all the required skills. On the other hand, these math problems no longer resemble their original form; instead, they become a collection of disconnected skills.
Some classrooms do teach math by keeping their complex contextual problems intact. These problems are not heavily processed in a textbook factory, and they require that students incorporate a variety of skills necessary to solve them. Lessons taught in this context are rarely recipients of the dreaded when-will-we-ever-use-this question. The truth is that preparing healthy meals takes time and energy, and we are surrounded by options that are easier, though not as healthy in the long run. Additionally, without a checklist of healthful components, it is possible to shortchange one's diet.
My belief is that the answer to this problem lies somewhere in the middle of both extremes. We don't want, or need, to consume every nutrient at every meal. Nor should we consistently focus on a single nutrient when we sit down to eat. The best option is to have a diet rich in variety to ensure the highest level of nutrition within a given period of time. I can see how achieving that balance is difficult. What if I don't like broccoli? Even though I eat a fairly balanced diet, I would still avoid broccoli. As a result, vitamin K would be missing from my diet. To compensate and attempt to still stay healthy, I could maintain my broccoli-less diet by supplementing it with vitamin K. This would be pretty convenient, and I might soon realize that I could avoid more foods that I don't like. This might lead me down a path where I continue replacing healthy foods with dietary supplements, and as a result, I would no longer be eating a healthy, balanced diet.
Similarly, if we teach using robust mathematical problems, we have to be careful to make sure that by the end of the school year, students have had adequate exposure to each of the standards within a larger framework. Otherwise, we may lose balance and end up with a long list of skills, taught in isolation, for which students have no context. This eventually brings us back to an extreme: taking lots of dietary supplements, instead of maintaining a healthy, varied diet.
Educational policy has been skewed toward teaching each standard in isolation. It is difficult to do it differently when textbooks, pacing guides, and standardized tests don't allow for incorporating the robust meals of multiple integrated standards. The Common Core State Standards have the potential to shift policy to a much more balanced approach, depending on how they are ultimately implemented and assessed.
My recommendation for healthy eating and math educational policy is the same: everything in moderation. In general, try to eat balanced meals and teach complex problems in context. Every once in a while, it is OK to rely on a dietary supplement or a lesson on a specific standard. The problems come when that is the only choice you are making.
Vol. 31, Issue 33, Page 29