Students who “see the connections” are more likely to understand and remember what they learn. In the next several issues, David Perkins will explore ways to forge the link between thinking and learning as well as ways schools can use the various curriculum strands to teach thinking skills.
A while ago I found myself wondering: “When was the last time I solved a quadratic equation?” Not your everyday reminiscence, but a reasonable query for me. Mathematics figured prominently in my education; I have a technical doctoral degree; I pursue the technical profession of cognitive psychology and education; and occasionally I use technical mathematics, mostly statistics. However, it's been a number of years since I've solved a quadratic equation.
My math teacher in high school—a very good teacher—spent significant time on quadratic equations. Almost everyone I know today learned how to handle quadratic equations at some point. Yet most of these folks seem to have had little use for them.
All this relates to one of the more discomfiting findings from the research on how students use what they learn. Investigations show that most students just plain forget most of what they have been taught. They often do not understand well what they do retain. And what they retain and understand, they often do not use actively. Some psychologists speak of the problem of “inert knowledge”—knowledge that learners retrieve to answer the quiz question, but that does not contribute to their endeavors and insights in real, complex situations.
Why do these problems of forgotten, misunderstood, and inert knowledge occur on such a wide scale? While there are many reasons, here I want to single out the basic disconnectedness of much of what students learn in schools. A good deal of the typical curriculum does not connect—not to practical applications, nor to personal insights, nor to much of anything else. It's not the kind of knowledge that would connect. Or it's not taught in a way that would help learners to make connections. To symbolize the whole by a part, we suffer from a massive problem of “quadratic education.”
What's needed is a connected rather than a disconnected curriculum—one full of knowledge of the right kind, one taught in a way to connect richly to future insights and applications. John Dewey had something like this in mind when he wrote of “generative knowledge.” He wanted education to emphasize knowledge with rich ramifications in the lives of learners.
What is Generative Knowledge?
What does generative knowledge look like? Consider another cluster of mathematics concepts: probability and statistics. The conventional precollege curriculum pays little attention to these topics. Yet statistical information is commonplace in newspapers, magazines, and even newscasts. Probabilistic considerations figure in many common areas of life, for instance, making informed decisions about medical treatment. The National Council of Teachers of Mathematics urged more attention to probability and statistics in the standards established a few years ago. Faced with a forced choice, I would teach probability and statistics instead of quadratic equations. It's knowledge that connects!
Or for instance, a few months ago, The Boston Globe published a series on the “the roots of ethnic hatred,” the psychology and sociology of why ethnic groups from Northern Ireland to Bosnia to South Africa are so often and so persistently at one another's throats. It turns out that a good deal is known about the causes and dynamics of ethnic hatred. If I were teaching social studies, I might teach about the roots of ethnic hatred instead of the French Revolution. Or I might teach the French Revolution through the lens of the roots of ethnic hatred. It's knowledge that connects!
Tapping Teachers' Wisdom
Where are ideas for the knowledge in this “connected curriculum” to come from? For one rich source, teachers. In some recent workshops, my colleagues and I have been exploring with teachers some of their ideas about generative knowledge. We begin with these questions: What new topic could I teach, or what spin could I put on a topic I already teach, to make it genuinely generative? To offer something that connects richly to the subject matter, to youngsters' concerns, to recurring opportunities for insight or application?
- Justice in Literature. For example, To Kill a Mockingbird connects to adolescents' concerns with justice, to literature as social commentary, to current issues of justice such as the Rodney King case, and so on.
- What Is a Living Thing? Are viruses alive? What about computer viruses (some argue that they are)? What about crystals?
- The World of Ratio and Proportion. Research shows that many students have a poor grasp of this very central concept. Dull? Not necessarily. The teachers who suggested this pointed out many surprising situations where ratio and proportion enter—for musical notation, diet, and sports statistics.
- Whose History? This theme addresses point-blank how accounts of history get shaped by those who write it—the victors, the dissidents, and those with other special interests.
Powerful Conceptual Systems
It's important not to mix up generative knowledge with what's simply fun or doggedly practical. The most generative knowledge is a powerful conceptual system that yields insight and implications in many circumstances. Each of the topics listed earlier can be read as a particular piece of subject matter knowledge. But every one also is a powerful conceptual system. Probability and statistics offer a window on chance and trends in the world. The roots of ethnic hatred reveal the dynamics of rivalry and prejudice at any level from neighborhoods to nations. Patterns of justice figure over and over again in human affairs. The nature of life becomes a more and more central issue in this era of test-tube babies and recombinant DNA engineering. Ratio and proportion are fundamental modes of description. The “whose history?” question basically deals with the central human phenomenon of point of view.
If much of what we taught highlighted powerful conceptual systems, there is every reason to think that youngsters would retain more, understand more, and use more of what they learned. A maxim I have come to believe in can be put in a single phrase: Our most important choice is what we try to teach. To be sure, there are important choices of how to teach—instructional method, classroom layout, approach to assessment. Still, the fundamental fact remains that, no matter how we teach, many students will learn at least temporarily a fair amount of what we try to teach. If we teach within and across the subject matters in ways that highlight powerful conceptual systems, we will have a “connected curriculum”—one that equips and empowers learners for the complex and challenging future they face.
