Putting the cart before the horse

School Science and Mathematics, Jan 2000 by Lederman, Norman G, Niess, Margaret L

Have you ever noticed that precollege teachers are expected to know almost everything about teaching but nowhere nearly as much about subject matter) On the other hand, college teachers are expected to know almost everything about their subject matter but very little about teaching. You may also have noticed that as you move from 12th grade down to kindergarten there appears to be a corresponding trend in emphasis toward less subject matter knowledge relative to pedagogical knowledge.

These relationships may just be an interesting oddity, or they could represent some underlying policy or philosophy. You may have noticed these relationships on your own, but we must admit to never having really thought about them until they were pointed out to us by a geologist during the final oral exam for the MS degree. The question that must be considered is whether the relationships present a critical problem.

Perhaps the most highly cherished emphases of the reforms in mathematics and science education are higher level thinking skills, such as inquiry and problem solving. These elusive skills and knowledge are difficult to promote during instruction but represent the knowledge and skills most useful to our future citizenry-for these are the skills and knowledge that allow individuals freedom of choice and freedom from dependence on others for many of the important everyday decisions we make throughout our lives. All too often, instruction that supposedly is designed to promote such knowledge and skills in students does little more than train students to use an algorithm to produce an acceptable answer. Students may still have no idea what they are trying to do. In this all too typical approach, students are provided with questions, procedures for answering the questions, and a variety of hints as to the correct answers (if they have read the assignment the night before). At its worst, the teacher has already provided the students with a detailed explanation of the phenomenon or situation under investigation, and the real purpose of the activity is to verify what the teacher has already stated. These types of activities are endearingly called "cookbook" activities. We find this an odd name, because neither of us can successfully follow a recipe. There must be some difference between thinking and cooking that we have yet to figure out.

When teachers are really trying to provide students with authentic inquiry and problem solving activities, they quickly find that one of the most difficult things for students to do is to come up with their own problems or inquiries of interest. This has perplexed educators for years, because the development of a question or problem to investigate is the first step and, at least intuitively, seems the easiest step. However, when you think carefully about what is needed to pose good questions for investigations in mathematics or science, the importance of background knowledge looms quite large. Quite simply, it is very difficult to ask a good question about anything unless you have sufficient general background knowledge in subject matter and specific knowledge related to the situation or phenomenon from which your question will be derived. In an attempt to provide such knowledge, for example, a science teacher might take her students on a field trip to a stream, so the students can get some idea of the environment and the potential variables present. More often than not, students will still have difficulty posing questions that are acceptable to the teacher. It just seems as if more background knowledge is needed than can be provided by the pre-investigation field trip.

In mathematics, teachers focus on particular problem solving skills such as guess-and-check, working backwards, looking for patterns, etc. Activities are provided for the students, in which a particular strategy elicits a pathway to a solution of a problem posed by the teacher. In fact, students typically default to guess-and-check as the first strategy for solving problems presented to them. Teachers often suggest that students look for another strategy, thus, emphasizing that the importance is on learning the different strategies rather than on problem solving. Again, the background knowledge needed for the problems is almost always the mathematics students have been currently investigating. This is NOT problem solving; this is investigating different problem solving strategies within the context of the mathematics currently being studied.

These field trip and problem solving scenarios have some implications for the geologist's observation. In the elementary grades, the general trend has been toward process and problem solving skills, as opposed to a set of core foundational concepts. We think most would agree with our general characterization. The root cause of this emphasis is not clear, but it is quite consistent with some other aspects of the elementary grade level experience. For developmental reasons, elementary students are believed to he less than ready for many of the abstract and complex foundational ideas in science and mathematics. Instead, the wisdom at large recommends that students should learn to appreciate mathematics and science in the early grades. They should be allowed to pursue their natural curiosity about the world, and above all, students should develop positive attitudes toward mathematics and science.