Dr. Stat

Dr. Stat is a Statistics Professor. This blog is his opportunity to share ideas and opinions about education (especially math education), politics, and whatever else comes up.

Monday, May 30, 2005

An Example of Economic Analysis

Jenny says in her comment below,
What do teachers do [to] produce in students acquired knowledge and skills? Are [t]here rules, protocols, studies? Do all teachers follow them, as do accountants and doctors? No, there is little if any uniformity of practice. So how can I design an economic model if I can't measure or quantify the inputs or the functions that produce the product? And if we can't measure them, then how can we generalize about them at all?

Teachers provide the management that enables students to produce knowledge and skills. Just as in any industry, there can be a great deal of variation in the management practices that are applied. Some may be more successful than others, and most are probably situation-dependent. What is successful with one group of workers in one environment may not be successful with another group in another environment.

In order to carry out a quality analysis of an educational process, we will have to focus on an example involving a specific product, that is, one lesson. Let us choose, for today's lesson, the introduction of the multiplication tables (facts). The students will have already done multiplication in the sense of counting up groups or rows and columns of objects. Now it is time for them to learn that we do not have to count everything all the time, because we can memorize some information that will always be true and useful to have at our "mental fingertips."

Managers make choices (decisions). Some theorists go so far as to say that is their primary function. So now the teacher, as manager, must begin to make these choices. First she must clearly define the product. What is it that the students will "know" or "do" after this lesson that they did not "know" or "do" before? How many facts should be introduced in the first lesson? What level of mastery should be expected? What will be expected of students who are "ahead" or "behind?" (The fact that the textbook authors have already determined some of these things will be ignored in this discussion. The teacher may not make all of these decisions on a daily basis, but still has the responsibility to determine what is appropriate, that is, whether the textbook should be followed or alternative lessons used.) Obviously we are talking about goals and behavioral objectives in educational terminology, and product specifications in industrial terminology.

Second, the teacher must design a production process, or in educational terms, a lesson plan. Should worksheets be used? flashcards? a computer program? Should the students work in groups and quiz each other? Should there be a contest, or should it be a non-competitive activity? Note that the teacher is planning how the students will WORK! (Remember the question, "Who are the workers?") Also, note that I have given a list of possible "rules or protocols" that are well established in the industry. Indeed, it is likely that there are numerous studies of the effectiveness of these techniques available in the education literature, as well as in the multitude of unpublished master's and doctoral theses in math education. To suggest that there are not well-established procedures or techniques available in education is absurd, and we are churning out research on the available alternatives at a rate unprecedented in educational history. Having alternative production procedures available should not be considered a bad thing. Uniformity in industrial practice might suggest, in some cases, that the best possible practice has been found, but it might also suggest a lack of incentive to improve. Indeed, improvement is impossible if uniformity is enforced. Furthermore, lack of uniformity in practice may be a reflection of varying conditions under which production occurs. That is to say, students are different, schools are different, and teachers are different. It makes sense that the process would vary as well.

Third, the process must be implemented. The workers must be informed of their functions, given motivation or incentives to accomplish the task, and the tools, materials, and environment to carry out the work. Again, these are management functions.

Fourth, Quality Control (or Improvement) must be carried out. In education, we call this assessment. Assessment occurs on two levels, and they have clear analogies in industry. One level is the assessment of individual students, or grading. This corresponds to product inspection. Management decisions must be made on how to handle defects. In other words, what should be done with students who did not meet the objectives? The other level is institutional assessment, which is really the goal of quality improvement. We want to evaluate the process, perhaps generating descriptive statistics of the performance of the group and compare them with statistics from other groups who used a different process. If we don't have numbers, we rely on the teacher's judgment of the results. Is she satisfied, or will she try something different next time? Unquestionably, this is the point where we want to apply statistical analysis and yet, will find we have great difficulty in the educational setting. In industry, the comparisons are done on data acquired from randomized experiments, so that hypothesis tests are a reasonable basis for a decision. Using data from non-randomized trials is extremely problematic, due to confounding variables and the inability to determine cause-and-effect relationships.

As for the question about "if I can't measure or quantify the inputs or the functions that produce the product," I would have to say that difficult does not equal impossible. Indeed, we can measure inputs and other aspects of the process. There has been a great deal of progress in the field of cognitive psychology recently, where carefully designed experiments are conducted, and the theory that develops can be applied to processes carried out in the classroom. Unfortunately, education theorists do not always take notice of the results from this field.