G.V. Ramanathan asks, How much math do we really need? in the weekend Washington Post. Jeff Solochek, a reporter for the St. Petersburg Times who pointed out the Ramanathan op-ed locally, claims that he hasn't used calculus in his job on the education beat. This comes up every few years in an op-ed column, so this is a repeat lesson, except for some recent events in my family: a relative of mine had a mild systematic infection earlier this month, and the doctor prescribed antibiotics… but miscalculated the dosage for her weight. The result was a pretty nasty reaction. Dosage-weight relationships are almost but not quite linear, and while there are short-cuts to prescribe the correct dosage (in the form of charts), maybe if the doctor prescribing the antibiotic had a better handle on algebra (you know, the non-elementary course where you learn about ratio relationships), the prescription would have been identified immediately as incorrect.
So, yes, Professor Ramanathan, I think understanding proportions matters.
Or another example from another field: the number of pregnant women in the 1980s and 1990s who agreed to AFP prenatal testing presumably for the risk of spina bifida… but unless testing for a rare condition such as spina bifida is much more accurate than standard commercial tests were at that point, a positive test is far more likely to be a false positive than a true positive. (Yes, the medical literature acknowledges the risks of false positives, including the risk of conducting additional, costly, and unnecessary testing.)
So, yes, Professor Ramanathan, I think probability matters.
One more example: the economy's liquidity trap we're all now in. It is absolutely true that our collective misunderstanding of economics could be cured by understanding relatively simple explanations of why a country's economy is not the same thing as a household (and why government budgets are not the same thing as household budgets). Good economics writers do that all the time. But the general principle is figuring out where to apply a balancing equation. In an economy, someone's debt is always owed to someone else, and therein lies one way of slicing the liquidity-trap dilemma.
Yes, Professor Ramanathan, a deeper understanding of algebraic principles (and how to apply them) matters. And while a few smart folks may remember those principles for their entire life with a semester of algebra, most of us (including me) can benefit from repeated exposure and continued application of those principles. Where might you get them except in courses beyond algebra? Maybe we don't need the exact sequence that's common in schools today, but I don't buy the elitism where we only worry about advanced math courses for the few.