What Can We Expect from Research?
Hiebert, James, Teaching Children Mathematics
As reform recommendations collide with traditional practices, the questions on the minds of many interested teachers and parents are these: Should we really adopt this new textbook series? Should we change the way we teach? What mathematics should students really be learning? It would be nice if research could give clear and simple answers to these kinds of "should" questions, but it does not and it cannot.
Research can be a powerful tool for making informed decisions in mathematics education, but it can never answer questions that have more to do with values and priorities than with the likelihood of effects. Failure to recognize the appropriate role of research leads to false optimism or disillusionment. To harness the real power of research and use it wisely, it is essential to understand both its limitations and its promise.
Many questions that are raising the temperature of current debates, questions similar to those mentioned here, are about goals and values. At the heart of many local disputes about curricula and teaching methods are unsettled issues about the kind of mathematics that the school district wants its students to learn. Questions about learning goals must be answered by public debate and consensus. Research can inform the debaters, but the final decisions must be made based on what society values most.
For example, many mathematics teachers and educators say that students should have opportunities to invent their own methods for solving mathematical problems. Research augments this discussion by identifying the kinds of problems for which many students can invent solution methods, describing instructional practices that support students' efforts, revealing the kinds of methods likely to be invented, and even showing that students learn something different by inventing than by watching a demonstration. But research does not say whether students should invent their own methods. The answers to "should" questions depend, ultimately, on what kind of mathematics is most valued.
Once the learning goals for students are set, a meaningful debate can begin about the most effective ways to reach these goals. Now research can play a more significant role in deciding which curricula and teaching methods support students' efforts to meet these goals. It would be misleading, however, to say that research can provide simple, straightforward answers. Classrooms are very complicated places, so complicated that the best ways to reach the goals will not be determined quickly or easily. This situation is not surprising, nor should it be discouraging.
The same dilemma is true in other fields; we live with these kinds of uncertainties every day. Health professionals have promoted the goal of a healthful life for years and have conducted a great deal of research but are still unable to specify the best way of meeting that goal. Exactly how much exercise do we need? Are seven servings of fruits and vegetables each day required, or would five be enough? What is your optimal weight? Our bodies are too complicated to specify the best path to a healthful life. The same is true in mathematics education. Teachers cannot expect to get clear and specific answers from research for exactly which textbooks or activities to use.
Does this uncertainty mean that research is useless? Not at all. Research can provide some very useful general guidelines for staying healthy and for designing classrooms, and as more research is conducted, more details are filled in. Many important decisions on the part of health professionals and of educators can be made using these guidelines. Although research can rarely prove that a particular course of action is the best one for all people and for all time, it can help boost the level of confidence with which decisions are made.
Here is a guideline for designing mathematics classrooms about which we can be quite confident: Students learn best what they have an opportunity to learn. …