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AN EPIDEMIC OF INNUMERACY
Quantitative illiteracy contributed to the financial crisis.
In our country, mainstream elementary and secondary education in mathematics serves students poorly in two key ways. It leaves them without an appreciation for the power and beauty of math as a human endeavor and, more importantly, fails to help them connect mathematical concepts to goals and needs outside the math classroom.
While No Child Left Behind has been beneficial in making basic computational techniques of arithmetic more widely and thoroughly taught, the law’s focus on exam performance robs the resulting knowledge of its true utility. For example, students need not only be able to divide 1 3/4 by 1/2, but need also to recognize when such a computation is necessary. Think of an occasion when you might want to perform a computation like 1 3/4 divided by 1/2. When I asked that of students in my First-Year Seminar—some of America’s fine young minds, many of whom aspire to technical careers—only about half of them could offer a correct scenario.
Liping Ma, author of Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States, discovered that among the elementary school math teachers she studied, only a small minority of those in America were able to offer an example of an instance when this computation would be called for, whereas a majority of those in China could cite multiple examples of applications (often distinguishing between those that demonstrate the partitive—1 3/4 is 1/2 of what number?—and quotative—how many 1/2’s are there in 1 3/4?—interpretations of division).
That is, typical American teachers, when asked “Why do we need to know this?” in a class about dividing fractions, are likely to respond with some variant of “Because it will be on the exam.” In China (and, I expect, in the many other countries delivering better math education than the United States) the same query often is met with multiple examples that not only motivate the computation but elucidate the concept.
An epidemic of innumeracy
Failure to connect mathematical ideas and techniques to uses outside the math classroom is part and parcel of a mathematical education that is an exercise in deferring gratification. Students are perpetually told that they will discover later why they need to know the math they are being taught. So, arithmetic’s importance is postponed until algebra class and algebra’s until calculus. Naturally, for most students this is an extremely unsatisfying experience, and massive attrition occurs, because we learn things we believe are important. How can children learn or retain mathematical knowledge that isn’t motivated by utility? A minority of young Americans appreciates the inherent beauty of the subject from an early age, but most can’t value, and so don’t learn, math. They never succeed in making more than the most rudimentary connections between math and their lives.
The result is an epidemic of quantitative (or statistical or financial) illiteracy, or innumeracy. Large segments of the American public are unable to infer facts correctly from a pie chart, for example, or appreciate the impact of compounding interest on the value of an investment. This incapacity is the most serious consequence of ineffective math education. Indeed, I suspect innumeracy played a large part in the willingness of borrowers to agree to mortgages they could not reasonably expect to repay, a critical element in the current financial crisis. Quantitative illiteracy was a partner to greed and unscrupulousness in setting the stage for our current difficulties.
More fundamental math
The solution? Give mathematics a higher profile across the curriculum and offer teachers—and not just math teachers—more professional development on math and its utility. At present, much professional development effort is devoted to pedagogical methods, but not enough to math as a subject that students struggle to learn. That is, teachers don’t need to know lots of high-falutin’ abstract math; they need a profound understanding of fundamental math, the kind Chinese teachers demonstrated in the example given earlier.
Virtually all teachers, regardless of discipline, need a deeper understanding of fundamental math. This will enable students to see math applications integrated broadly into their curriculum. For example, in elementary school, precious time in math class is spent interpreting graphs and charts; why not have more of that occur in science and social studies classes, where the visuals offer students valuable information? In the upper grades, have students apply more math and statistics in a wider variety of subjects so they get more immediate evidence of the utility of their math lessons. There is no shortage of examples that can be drawn from contemporary life; we live in a world drenched in quantitative information that can benefit the observant and self-reliant. And by really integrating math into the curriculum, schools can provide time in math class to delve deeper into the foundational math that, as we have seen, is lacking.
A deeper understanding of math and its applications by teachers is the key to an improved K-12 education that enables students to appreciate math’s utility and beauty more profoundly and motivates them to engage more deeply with math. This will prepare the college-bound for their next step while providing all students with practical math skills necessary to function successfully in jobs, in the marketplace, and in our democracy.