From the Origin provides a forum for lively discussion of issues of importance to the mathematical community. The Michigan Section-MAA Newsletter solicits opinion pieces for publication in this column from anyone in the Michigan mathematical community. In addition, comments on pieces published in earlier issues are welcomed.
Items for From the Origin should be submitted to the editor by the beginning of October to be considered for inclusion in the December issue and by the beginning of February for the April issue. Main opinion pieces should be at most 1800 words long, and responses at most 400. The editors reserve the right to shorten responses, if necessary, in order to fit as many as possible within the available space.
The term “quantitative literacy” has different meanings even among, perhaps especially among, mathematical professionals. Is quantitative literacy the same as “mathematical literacy?” What is the relationship to “numeracy?” How different is it from “critical thinking”?
The term “mathematical literacy” is not used frequently, perhaps for several reasons. Some people may avoid it because it sounds more foreboding than quantitative literacy (QL). Also, some may use QL to broaden the ownership and spread the responsibility for it. I think of numeracy as a subset of QL which is involved with questions such as “Is this a reasonable answer?” or “What is a rough estimate?” As mathematicians, we like to think of many of our thought processes as “critical thinking”. Critical thinking specialists usually have something much more general in mind. Some would not even want to include our ways of thinking under the critical thinking umbrella. Perhaps this is because they have a narrow view of what mathematics really is.
For a number of years now, government leaders and others have voiced concern that our educational institutions are not doing a good job in teaching mathematics. National tests reveal weaknesses in mathematical preparation. In addition, international tests show that the United States lags behind many other countries in mathematical achievement. When these concerns arise, technological developments with both real and potential impact on what might be considered quantitative literacy (QL) often have moved to the center of the discussion. To some, these developments are viewed as wonderful tools, while others view the extensive use of technology as a siren song calling us to our destruction. Still others contend that technology has even obviated the study of mathematics. Although technology certainly has an impact on how we may accomplish whatever goals we set for QL, the goals themselves are not altered.
In an academic institution, who has primary responsibility for QL? Many institutions already have courses covering some aspects of QL scattered throughout the curriculum. Accomplishing goals of QL can best be done if it has the kind of emphasis that “writing across the curriculum” received over the past twenty years. However, even if such a commitment were made, we should not think that we no longer have primary responsibility. In fact, our job might grow due to needed coordination and consultation with other areas.
In this article, in order to take a fresh look at QL, I have tried to put aside what I have previously read or heard about QL. Frequently, at the first mention of QL, the initial reaction is a comment about the skills students do not possess. With this negative approach, the discussion then focuses on how we can improve the teaching of basic skills and how we can test for QL. At this point, if we are not careful, we narrowly define QL as successful performance on a test of a relatively few applications and thus delude ourselves with a kind of “pseudo-QL”. No one should interpret the above to imply that we do not have some serious problems with low skill levels. We do indeed have much work to do to foster better skills development. To not do this can severely limit the progress and prosperity of our nation. However, perhaps we need a different strategy and a different approach.
QL has many aspects; I will mention only a few here. Certainly skills are included, but much more. In addition, QL encompasses a way of thinking, an exploration and appreciation of big ideas, data analysis, and patterns. Let’s explore some of these in more detail.
First, we will focus on skills. To be sure, a certain level of skills must be acquired in order to accomplish much in the other areas of QL. In some sense, skills, like a language, are used to express the elements of the more important aspects of QL. Unfortunately, skill levels quickly drop without use. An interesting question is this: “When skill levels do drop, does that mean all the other goals of QL are in jeopardy?” I am not so sure that this is the case, especially if the skills have been taught not as an end in themselves.
QL is much more than symbol manipulation, although some such skills are needed. An excessive focus in this area often brings up the inevitable question, “When will I ever use this?” This, in turn, makes attitude change, another goal of QL, more difficult to achieve.
A change in attitude brought about by an expanded understanding of the role that mathematics or mathematically related concepts play in the world is itself an important goal of quantitative literacy. This is much in the classic tradition of a liberal education and is not that different from literacy in other areas. When a student studies about poetry, we do not necessarily expect her to become a poet. When a student learns about music, we do not necessarily expect him to become a performer. Many of us had courses in appreciation of art, but few of us can successfully put oil to canvas or form to clay. Although this comment may seem misplaced in an article about QL, it is the perception of mathematics as a hard taskmaster rather than as a guide to a greater understanding of the world that severely limits what we are able to accomplish.
QL should be at least as much about big ideas as it is about the acquisition of skills. We would not all agree on what these big ideas are. Many of us would choose the concept of rates of change or changes in rates of change, while others might choose to study what patterns and symmetries tell us about the order in our world. Still others might choose to study data analysis and its pitfalls. Many others might study codes which control our world or unlock its secrets. The impact of abstraction as a way of thinking should not be overlooked. How can we fail to marvel at the infinitudes about us? A conceptual approach to transformations and continuous processes might be another area of exploration.
As one who constantly struggles with students lacking proper skills, I am not overlooking the necessity of building skills. However, a major emphasis on skills without showing some of the beauty along the way is a strategy doomed to failure. When students say that they will never use what they are being required to learn, sadly this may be the case. Their method of learning (or perhaps our method of teaching) has not informed their way of thinking. I venture to say that probably all of us have been introduced to a new acquaintance who, upon recognition of us as mathematicians, quickly “brags” about not being good at mathematics. How much better it would be to hear them say that “although I was not very good at math [whatever that might mean], we talked about some of the most interesting concepts in my math classes.”
So then, what is quantitative literacy and why is it important? For most people, QL can be thought of, whimsically and a little irreverently, as the residue remaining with them when they have forgotten almost everything they were taught. If that residue includes the ability to recover skills as needed along with an appreciation of a truly exciting world with mathematics all around us, we really might not have done all that badly.
Back to the Fall
Newsletter
This page is maintained by Earl D. Fife