Instructional Flowcharting: A Tool for Teaching Science and Mathematics

Michael Szabo, Ph. D.

Have you ever felt that you were repeating the same verbal directions for laboratory or problem-solving sessions (especially after five straight classes of chemistry or algebra)?

Do you wonder whether the quality or clarity of what you say varies from presentation to presentation?

Have you ever become aware that you have omitted or overlooked some major point and that backtracking to cover it seemed to reduce the impact?

If you have experienced any of these quandaries, perhaps instructional flow-charting is for you.

Have you ever wished for a technique which would serve to handle classroom management functions-and even basic, knowledge-level learning functions-with a minimum of effort? Something that would give you time to work with individual students?

Do you wish for something which would encourage the self-initiative of your students and discourage their extensive dependence upon you, their teacher?

If so, perhaps instructional flow-charting can help.

FLOWCHARTING, the art of developing flowcharts, is a method of representing an algorithm for doing something. It has a beginning, some well-defined path or alternative paths, and an identifiable end point, or series of end points. Teachers with experience in computer programming quickly recognize the symbols and logic of flowcharting. Those without such experience have little or no difficulty in assimilating the operational skills of flowcharting.

A computer flowchart deals with the logic of programming computers. An instructional flowchart (IF) involves the logic of providing instruction for human learners. (The inference that human learners can be treated like computers is not intended by this analogy!)

Flowcharts have been used outside the field of computer science in popular texts, in systems analysis, in research models, and in instructional development. They can and do provide a fascinating instructional tool.

Instructional Flowchart Symbols

IFs use the five basic symbols shown in Figure 1. These and other symbols are available in plastic flowcharting templates, or stencils can be made easily.

The figure also gives the symbol name and the type of instructional act called for by the symbol.

Terminal. The oval terminal symbol represents either ENTRY into or EXIT from the algorithm. The ENTRY specifies the prerequisites (cognitive, physical, or affective) needed by the learner to engage successfully in the instruction. Prerequisites may be laboratory apparatus (Figure 2), courses (Figure 3), unknown samples (Figure 4), or completion of a unit of instruction (Figure 5). The EXIT symbol informs the student that he has completed the task.

Process. The rectangle, or process symbol, represents a direction requiring a response. Examples are:

Decision. A diamond, or decision symbol, represents a question which requires a yes or no answer (binary decision). For example, in a laboratory exercise, the following decision may be important. Complex decision sequences can be flowcharted by means of a series of interconnected diamonds. (See Figure 5.)

Connector. The connector provides an imaginary line to any specified point in the flowchart; it is often used to avoid messy diagrams when the chart becomes complex or "flows" onto multiple sheets of paper.

Arrow. The flow of action is indicated by connecting the symbols by arrows in a meaningful fashion. Consider the short segment on the right, which depicts a binary decision and different subsequent activities.

Arrows specify "flow." The basic rules applying to arrows are that one and only one arrow must emanate from a process, terminal, or connector symbol, while two and only two arrows emanate from the decision symbol.

A Sample IF

Suppose you wish to provide written directions to chemistry students on safely inserting glass tubing in a rubber stopper and use a bit of humor to focus upon safety. The flowchart in Figure 2 is such a device. The main flow is contained in the six steps at the left and is enclosed in dashed lines. Note that there are three decision points in the main flow. A negative answer to any of these directs the flow into one of three loops or paths which eventually lead back to the main flow. These loops can be used to direct the learner's attention to important points or concepts. The number and nature of loops are up to the discretion of the teacher. For example, some would include a decision symbol which asks if the tubing broke and was somebody cut. A "yes" answer to this would presumably branch the student to a first aid or "call for the teacher" loop. This loop and others were excluded in Figure 2 for the sake of simplicity.

When used in conjunction with a series of photographs or drawings illustrating correct and incorrect procedures and posted in an accessible place in the laboratory, this flowchart can provide a powerful safety impetus.

Using IFs

The IF is an extremely versatile instrument in that it can be used for many purposes. The purposes illustrated here include classroom management, laboratory classification, and decision making relative to environmental problems.

Classroom Management (CM). CM refers to tasks which the teacher must complete but which do not directly interact with the learning process. It includes such things as laboratory techniques (Figure 2), keeping the supply room stocked, checking out equipment, and meeting schedules.

Figure 3 is an example of a CM chart from the science methods course for secondary school teachers at The Pennsylvania State University. Since this methods course is taught on an independent study basis, students must have a hard-copy description of the way the course operates. In addition, the flowchart provides a model for the flowchart the students will construct during the course.

Starting in the upper left corner of Figure 3, the student enters with the University prerequisites and attends the first six class meetings. The first diamond asks if the student has mapped out his own personal goals for teaching. A "no" response sends him into a loop which requests him to make such a list.

A "yes" response leads to two loops. In essence they ask the student to check his personal goals against the requirements of the course and to develop alternative requirements in the event that any of his goals are not compatible with the course requirements.

On the right side of Figure 3, the student is requested to submit the first requirement and check to see whether it meets the criteria. This decision loop is all-important in the mastery learning model since there are definite alternatives to an unsatisfactory grade should the requirement not meet the performance criteria. Note that this feedback loop appears twice.

This flowchart carries the main burden of describing how the course operates. Numerous questions can be answered by referring students to certain parts of the flowchart.

Laboratory classification. Methods students develop at least one IF as a requirement for the science methods course. Figure 4 shows a flowchart developed by a methods student and subsequently used during his student teaching. It describes identification of 10 specified minerals for classification

purposes.

The logic of this IF will be left for the reader to pursue. It should be pointed out that this flowchart is a deliberate attempt to combine previously learned skills and facts into a simple classification scheme. Having this classification scheme available in IF form (rather than stored in the mind of the teacher) provides impetus for the student to assume responsibility for his own learning.

Decision Making. Flowcharts need not be restricted to memory activities or routine tasks. They can be used to lead students into fairly sophisticated learning behaviors. One key to the complexity of IFs (in terms of the cognitive functioning elicited) is the level and nature of questions in the diamonds. Questions may require observation (Is the sugar dissolved?) or analysis (Is this conclusion based on empirical evidence?) In addition, questions may be convergent (Is the tube lubricated'?) or divergent and open-ended (Have all factors been considered?)

An IF designed to develop decision-making skills in students should emphasize thinking questions that are divergent and higher (than memory) level. The IF in Figure 5 provides a model for decision making relative to environmental problems. It is from the minicourse The Environmental Impact of Electrical Generation: Nuclear and Conventional, Pennsylvania Department of Education, 1973.

Some would argue that complex mental acts (such as decision making) are not amenable to performance on the basis of a mechanical method like flowcharting. But there are good strategies or heuristics for arriving at such acts even when no sure-fire mechanical method exists. The instructional flowchart can be useful in depicting salient components of the strategy, particularly to science students at the secondary level.

There seem to be two general rules which enhance the effectiveness of IFs. First, use each one in conjunction with a behavioral statement of what is expected of the student. Second, provide copies of each IF and the associated objective to students. One purpose of the IF is to communicate what the teacher expects the student to do.

And, speaking of students, it has been found that providing students with opportunities to construct their own flowcharts to describe scientific processes seems to help them to: (1) adapt more readily to using teacher-generated flowcharts and (2) identify with the logic of man's interpretation of those scientific processes.

The criteria for "good" flowcharts lie in the extent to which they help students achieve those science objectives for which the charts were designed. In this sense, IFs must adapt to individual differences. For example, students who require a high degree of structure and highly directed learning activities might find the IF in Figure 4 quite useful; the IF in Figure 5 might lack the structure and result in less than optimal learning for these students. Instructional flowcharting should be used in those situations where it is most appropriate relative to student achievement and attitudes.

Advantages

The chief benefits of IFs, from the point of view of the teacher or student, seem to be that they:

1. Require careful analysis of the activity to be covered.

2. Force the teacher to increase emphasis on being thorough and detailed (helps systematize classroom instruction)

3. Provide replicable and permanent means of communication and instruction which can be updated.

4. Portray to students what is expected of them (thus providing one opportunity for fostering student independence).

5. Are flexible in that they can cover a wide range of intellectual and psychomotor skills.

6. Lead students to participate through considering questions posed in the diamonds.

7. Can be used as a pedagogical tool that emphasizes what the teacher wishes to emphasize.

8. Provide a basic and inexpensive tool which can bring out creativity in teachers.

9. Are fun for many teachers (and students) to construct.

If you are skeptical, pick up or construct a flowchart template, and create

a flowchart which directs someone to:

1. Get candy out of a candy machine.

2. Make change as a sales person during a purchase.

3. Complete a simple laboratory write-up.

But be careful, it's infectious!

Source:

Szabo, M. (1974, January). Instructional flowcharting: A tool for teaching science and mathematics. The Science Teacher. (You didn't think I was that old, did you?)