National standards and school science and mathematics

School Science and Mathematics, Oct 1997 by Bybee, Rodger W, Ferrini-Mundy, Joan, Loucks-Horsley, Susan

The Challenge of Understanding Inquiry and Problem Solving

When asked to describe what the NRC Standards mean by "science as inquiry," many educators respond with statements, such as "the process of science," "doing hands-on," "using kits," or "involving students in activities." All of these responses represent a conception of inquiry that centers on instructional strategies and omits the development of students ' abilities and understandings.

Careful review of the "science as inquiry" standard reveals the differences between the traditional "processes of science" and the contemporary perspective on inquiry. Although students use processes such as observing, inferring, and hypothesizing, the essential outcomes include cognitive abilities of using logic and evidence in formulating and revising scientific explanations, recognizing and analyzing alternative models, and communicating and defending a scientific argument. The NRC Standards present abilities that are aligned with the educational aim of critical thinking; in fact, they provide a substantial foundation for that aim.

A standard on science as inquiry might include what students should understand about inquiry. Here we confront another educational misconception. In many cases, individuals assume that if students experience "hands-on" activities, even good inquiry-oriented activities, then they will understand scientific inquiry and the nature of science. This is not necessarily the case. Although teachers do not have to plan entire lessons on understandings about scientific inquiry, they do have to introduce ideas; for example, "conceptual principles and knowledge guide scientific investigation," or "scientists rely on technology to enhance the gathering and manipulation of data," or "mathematics is essential in scientific inquiry."

There is a parallel set of issues regarding problem solving in mathematics. For many years, the interpretation of "problem solving" within the mathematics education community focused primarily on problemsolving strategies and heuristics for use in the completion of problems. In curriculum materials and in classrooms, problem solving was often relegated to a special section of the text or to Friday afternoon motivational activities. "Problems of the week" are still commonly used in mathematics classrooms, sometimes in contrast to what students and teachers consider the "real" mathematics of mastery of algorithms and procedures and learning of concepts.

Yet as early as 1989, the NCTM Standards contended in the introduction that "instruction should be developed from problem situations" (p. 11). The document emphasized a two-fold view of problem solving within the problem-solving standard at each of the three grade bands. The expected reference to formulating problems and developing and applying strategies is included. In addition, though, the standards emphasize the notion of problems as sites for learning mathematics: "In grades K-4 (5-8, 9-12), the study of mathematics should emphasize problem solving so that students can use problem-solving approaches to investigate and understand mathematical content" (NCTM, 1989).