Introduction To Statics - Teacher's Guide

Helen L. Plants and Wallace S. Venable

West Publishing Company, St. Paul, 1975

Note: This is a supplement to the full-length programmed textbook Introduction To Statics



Part 1 -- Introduction to Programs

Part 2 -- Teaching with Programs

Appendix I -- Objectives for Introduction to Statics

Appendix II -- Example Post Tests

Appendix III -- Student Comments on the Programs


This is about a book that works.

How do we know that it works?

We know because it has been tested in repeated versions and iterations upon more than a thousand students in a half dozen schools over a period of six years. Students from the programmed format and students from traditional lecture sections have taken common final examinations graded on a common scale. In all but one reported instance the programmed students have earned a higher mean score than did the conventional students. In some instances the difference was significant. In some it was not.

Why does it work?

It works because it actively involves the student in the learning process. By continually demanding his response to the material and continually evoking and reinforcing his correct response, it involves him in a dialogue with the study material that holds his interest and enhances his self-confidence. (By carefully considering student achievement, it starts where the average student is, and guides him to a pre-determined level of proficiency.) By minimizing the number of times he is wrong it teaches him the habit of being right.

It works because it begins with what the student can do easily and leads him gradually to difficult and complex work. Beginning each new topic with simple common-sense responses to simple questions it progresses gradually to single concept problems and finally to complex terminal problems. It leads the student through many problems with a minimal effort by asking the student to take only the critical steps, leaving the workout to the program, but in the end it asks him to do involved problems by starting at the beginning and working through to the end.

Where does it work?

It works in Junior Colleges and in Universities. It works in community colleges and in Tech schools. It works in conventional classrooms with a teacher up front. It works in self-paced situations with the teacher guiding from the side. It can even work for some rare individuals who want to do it all alone with no teacher anywhere.

For whom does it work?

It works for all sorts and conditions of men -- and women, too. It has been greatly praised by very bright students and by far from bright students -and has been soundly damned by students from both groups. Its success seems to depend more upon the personality of the student than upon his scholastic ability. The students who enjoy it most are those who prefer steady daily study to the crash cram system and those who prefer relying on their own developing abilities to relying on the authority of the teacher. Even those students who dislike the book intensely, admit to learning from it and the exam scores bear this out.

It is a book that works and that is a proven fact.

Morgantown, West Virginia, March, 1975

Part 1 - Introduction to Programs

This Teacher's Guide is designed primarily to help the prospective user of the programs understand how they work and how he may best use them. This is not an answer book in the usual sense. Its purpose is to help the teacher anticipate certain questions and to help him find his own answers. It attempts to transmit to other teachers some of what we know about the book and what we have learned from our experiences in using it.

This guide is, quite frankly, a sales pitch for a style of teaching as well as a book. We have produced it because we feel that when a teacher who is sold on doing an enthusiastic job of working with his students goes into a classroom with good materials, good teaching is the usual result.

An Introduction to Statics is quite different from other books on statics. It differs from text books in style and organization more than it does in content. It differs from other workbook approaches in many detailed aspects. In this Teacher's Guide we will briefly explain some of the advantages in style we feel that this book has over others.

What is Programmed Instruction?

Programmed books share features which obviously set them off from conventional texts. First, they consist of a series of questions and blanks. This is a feature that they share with the workbooks which have been popular at the primary school level for at least a quarter of a century. This form is chosen because it is well known that people learn easily by doing things. In the words of the behavioral scientist, they learn through active responses. A programmed book requires an active response to each item to be learned.

In addition, programs have a feature which sets them apart from most workbooks at an obvious level. A program contains the answers to its questions in a readily accessible location. The student is able to find out whether he is correct or incorrect as soon as he answers a question. He gets immediate confirmation of his response and can use this feedback to correct his work and to guide him in formulating answers to following questions. Immediate confirmation has been found to facilitate learning.

Good programs also have features which are less easily observed. In an effective program, the student progresses through a series of steps of increasing difficulty. A program dealing with verbal material may begin by asking a student to complete sentences with a single word, and progress through questions to be answered with a phrase, a sentence, and finally a paragraph. In engineering, an effective program may begin with questions which require the student to interpret only one term in an expression or to evaluate a single piece of data. The sequence may then lead him through calculations involving multiple terms and solutions of ever more complicated equations until, at the end of the program, he is working complete problems from beginning to end. In short, good programs consist of a series of steps which are graduated in size so that the student progresses from the simple to the complex.

If a program is effective, the observer will generally find that most students answer most of the questions correctly. This is a part of the designer's plan since people tend to repeat behaviors they have already performed. If a man is encouraged to make a mistake once, it is quite likely that he will repeat his mistake when he is asked to perform under pressure. If, on the other hand, he has always done an operation correctly in the past, he will probably continue to do so in the future. Therefore, most programs have their questions organized and stated in such a manner that students will rarely make mistakes during study.

To insure these characteristics, programs are tested for effectiveness during development. While he is preparing a program, the programmer evaluates his materials through the use of quizzes and by examining the student's responses to individual questions. When students fail to perform correctly, the programmer considers himself at fault and accepts the responsibility for the student's error. He must correct his program to prevent recurrence of the error.

These characteristics are all reflections of the basic difference between text books and programmed instruction. In the development of a text, the author concentrates his attention on organizing the content of his subject matter. In writing programmed instruction, the author focuses on organizing the behavior of his students. Because of the unusual organization of the subject matter a program is not likely to be particularly remarkable as a reference work, however the focus on the development of behavior makes programs outstanding tools for instruction.

What Does This Package Teach?

This particular set of programs was developed to do some very specific things. It is intended to teach the student to use a limited number of procedures and a limited vocabulary in solving problems with a high degree of reliability.

As a potential user of this work, you have a right to know exactly what topics and ideas are included. These areas are delineated in two different ways in the back of this guide.

Appendix I contains a list of behavioral objectives. These objectives detail the skills which a successful student should be able to demonstrate when he 'has completed the course. They are listed for the course as a whole rather than on an assignment by assignment basis. We have found that several assignments are required to achieve the desired outcome on some of the more complex problem-solving objectives, while others require only a portion of a programmed unit.

Appendix II contains a set of sample quizzes, or post tests. These are included to provide explicit examples of the questions on which student performance has been evaluated. They give evidence of the overall level of achievement which can be expected at the end of a particular study unit. A study of the post tests will show that several topics have been split between units so that the student alternates between closely related topics but achieves an increased level of sophistication on each iteration.

The primary consideration in splitting and combining topics has been to assure that the student will have sufficient practice on each objective while studying assignments of reasonably uniform length.

This is the outcome of a focus on the needs of the learner rather than on the relationships between concepts.

No attempt has been made to give the student a comprehensive survey of all topics in statics. Instead, the focus has been on helping the student develop a thorough working knowledge of selected procedures and concepts which the authors feel comprise the basic skills needed for more advanced work in mechanics.

How Well Do These Programs Teach?

The performance of students using these programs has been the subject of several different evaluations over the period in which the experimental editions were in use. These evaluations were conducted in order to obtain information which we needed in order to improve our instructional materials and methods rather than as a public demonstration of the comparative effectiveness of the programs.

Our experience has been that the biggest improvements in class performance are an increase in the number of students earning the grade "B" and a reduction in the number of students who are unable to begin to attack problems in a systematic manner.

Post Test Data

The largest volume of data in our files consists of scores on tens of thousands of post tests, or daily quizzes. However it was not considered appropriate to attempt to subject "lecture" classes to the large number of testings that would have been needed to establish the norms required for evaluation of the relative effectiveness of the programs on the post tests. The data on our use of quizzes is, therefore, a measure of the absolute performance of the classes on the criteria reflected by the collection of post tests in Appendix II of this Guide.

A typical post test study analyzed the post test scores of a group of seventy-two students. These students took a total of 2084 tests and had an overall average of 86.9 out of a hundred. Of this collection of post test scores, 87 percent received grades of seventy or higher, 74 percent of the scores were over eighty, and 60 percent received grades over ninety.

To evaluate such data it is necessary to know a little about the meaning of our numerical grade. Like most organizations involved in the grading of subjective answers, we and our staff are a little more variable in our performance than we would like, however, we feel that a paper must be exactly correct to receive a "hundred." Ninety to ninety-nine indicates that the paper includes arithmetic or notational mistakes. Scores above seventy indicate that the student is able to set up a problem solution even if he is unable to reach the correct answers. Papers which display evidence that the student has memorized formulas but is unable to apply them are likely to receive grades in the fifties.

Common Examinations

A second source of performance data has come from common examinations taken by students in both "programmed" and "lecture" courses at West Virginia University. Subject to scheduling priorities, students and instructors are given the opportunity to take statics in a class using the method of their choice. On several occasions, a common final examination has been given to all sections of the course.

In our early trials instructors were only asked to report section averages on each problem, hence our records do not contain the data needed for detailed analysis. On the basis of the available information we do know that, in every case, the average score of the programmed sections was somewhat higher than was that of the lecture section, although the significance of these results cannot be established statistically.

Individual problem scores were subjected to analysis in a recent departmental final examination. On each of the three problems on material covered in these programs the performance of the programmed sections was significantly better than that of the "non-programmed" sections (P < 0.05).

Each of the common examinations was comprised of problems representing a consensus of the entire staff's goals for the course. They were, in a sense, a set of minimum standards. It is our feeling that the performance of students using the programs might have been more dramatic if they had been given an examination especially selected to emphasize their strengths.

National Tests

In the spring of 1968 our exam questions were selected from the master list prepared by F. L. Singer for the "Evaluation Study of Mechanics." A comparison of the performance of the programmed class with the national performance included in Singer's "Interim Report" shows that our students appear to have been above the national average on eight of the nine items selected, and significantly above that average on two items. They fell below the national average on only one question and we have since made several drastic revisions of the related programmed units.

A Few Words About Format

The authors are overjoyed that the publisher has agreed to produce this book in the same format used in the experimental editions of the work. It is a format which places economy of student effort ahead of economy of production. In this connection your attention is directed to the paper on which the book is printed. It was selected to provide a satisfactory surface for writing either with pencil or pen, so that the student is encouraged to use the book properly by writing his responses.

Each page of the program contains a single "frame." That is, a page deals with a single idea or relation and has only closely related questions on it. The response to that frame is on the following page. This means that no mask is required to hide the answers from the student. There is no awkward shield to lose or slip out of place.

The use of one frame per page also means that there is space for students to do nearly all of their work in the book itself. The student needs only a pencil and a pocket slide rule or a calculator in order to complete his assignment. He can work with the book while sitting at a desk, lounging in an easy chair, or sprawling on the floor without losing the benefits to be gained from writing out complete solutions and answers.

The use of one frame per page also means that there is little need to spend time hunting through the book for answers, references, or the next question. We have attempted to make it easy for the student to give his answers by providing him with quick answer "check-a-box" questions wherever appropriate. Our purpose in designing the book for ease of use was to allow the student to spend most of his study time thinking about the material and working with problems rather than grinding through routine busy work. To this end we have often asked him to do only the crucial part of a problem rather than solving it completely.

Instructors who have looked the book over have sometimes suggested that we should provide the able student with an opportunity to take short cuts through the material which he already knows. This was tried in some of our earlier work. We found that the poor student needs all of the material and the good student reads all of the material just to assure himself that he isn't missing anything. Since the extra questions and directions necessary for a fast track required more work from both authors and students, that approach was abandoned in favor of the strictly linear format.

About the Notebook

The notebook has been designed to provide the student with concise recapitulation of the major points in the units at the same time that it provides an annotated index for ready reference and review.

It is an integral part of the programs so that the student is directed to work first in the programs, then to summarize his work in the notebook and to return to the programs for the next topic.

Every item called for in the notebook is referred to a frame in the program where the item is discussed. For example, a question followed by the notation (8-23) means that the answer will be found in Frame 8-23. This enables the student to check his reply and to build up a completely correct notebook for future reference, at the same time that it provides him immediate access to the programmed treatment of the topic should he wish more detail.

Since the entire notebook forms an annotated index to the material, it seems reasonable that the alphabetical index to topics should be included in the notebook. Thus, a student may look up a given topic in the alphabetical index. There, he will be referred to the appropriate page of the notebook for a concise treatment of the topic. Should that not be sufficient, the parenthetical numbers will direct him to the portion of the unit which gives a detailed treatment of the topic.

This is, admittedly, a very imperfect solution of the problem of providing the student with a book which is both a learning tool and a lifetime reference, but we feel it is a practical answer to the charge that programs are "worthless" as reference material and impossible to review.

Part 2 - Teaching with Programs

It is our belief that each teacher must find his own personal system for teaching with programs. We have arrived at ours and offer it to you as a point of departure.

Our system has grown up over a period of nine years in a sort of trial and error manner. We have tried many teaching systems and are convinced that the system we are currently using works best for our students and our materials. We call it Elastically Structured Teaching (EST) since it provides a great deal of elasticity for the individual within a rather rigidly structured course.

We attribute the success of the EST system to several causes. First, it provides for the student's need to interact with the teacher and provides the teacher with a chance to model proper problem-solving behavior. Second, it provides a strong feeling of structure to the class so that the student knows exactly what is expected of him and when he will be measured. Third, it provides almost continuous feedback so that a student can accurately assess his progress. Fourth, by providing considerable flexibility in the schedule it allows the student to make necessary deviations at the same time that it encourages him to get back to the class schedule as quickly as possible. (In a sense, he is thus encouraged to substitute self-discipline for teacher-imposed discipline.) Last, it reinforces persistence, self-reliance, and daily study.

The system is based upon scheduled, required quizzes over each unit of programmed material. Classes are met on a regular schedule. The teacher begins class by distributing tests which cover the previous night's assignments. These tests are designed to be completed in about fifteen to twenty minutes. The instructor collects the tests and works them out for the class. He then discusses any questions which arise from the day's assignment, and may use any remaining time to show the class his personal tricks and applications for the concept.

Class days on which no tests are scheduled may be used for problem sessions, discussions, demonstrations or lectures.

If a student is dissatisfied with his performance on any of the daily quizzes, he may try again on an alternate version. All attempts are averaged to arrive at his score for the unit.

While classes and quizzes are held on a regularly scheduled basis, attendance is not required. Those students who fall behind may take a make-up quiz in a Self Study center. Students are expected to complete the material before the end of the course, and nearly all of them do. Those who need extra help are encouraged to visit the instructor in his office.

The instructors accept any excuse for a temporary delay in completing a study unit, but no one is excused from completing all work. The individual student seems to respond to this by setting up his own standard of permissible excuses for postponing an assignment.

Grades are based in large part on traditional style examinations, but the frequent graded quizzes and discussions keep each student informed of his mastery of each concept so that he may review knowledgeably for the more critical examinations.

Students have been reasonably happy with the system so that the programmed sections usually fill first at registration. A large proportion of those who have had one EST programmed mechanics course take a second one, and on questionnaires 59 to 90 percent indicate a willingness to take a second, were it available. There are, however, those who dislike the EST approach rather intensely. This seems to run at about 10 percent. About 25 percent are very vocal fans of the system. The remainder of the students are neutral in their feelings about the course.

Appendix III consists of student comments on the system garnered from evaluation forms for several semesters. The majority of the students made no comment at all but those who did provide a reasonable idea of the strengths and weaknesses of EST as seen by the students taught by it.

We would suggest that a reasonable approach to using An Introduction to Statics might be to teach it for one semester using EST. By the end of that time you should have formed your own ideas on how to do it better.

The following portions of this manual are aimed at helping you clarify your own ideas about the components of instruction with programs and the way that they fit together, as well as to provide help in trouble-shooting when it becomes necessary.

The Theory of Testing

From the beginning, programmed instruction has relied heavily upon behavioral psychology with its emphasis on reinforcement. Post tests provide the reinforcement for regular conscientious study of the units. The use of the programs requires a great deal of effort and self-discipline on the part of the student and he needs constant reassurance that this is paying off for him. His post test scores give him that reassurance. We find that it is a good idea to post an up-to-date tally sheet of post tests in the classroom or study area. For many students a string of good post tests seems very reinforcing-and scores are seldom really bad.

Each unit should be post tested. This seems to be absolutely necessary. The post tests should be graded and the grades should count toward the student's final mark. If you customarily consider assigned homework as part of the final grade, we would suggest you substitute the post test scores for the homework grade. It seems to us to be unfair to require homework in addition to the programs.

Post tests should be designed to allow the student to show, and be rewarded for, what he has learned. They should be straight-forward without being trivial. They should be closely tied to the material covered in the unit and geared so that the average student will feel somewhat challenged but will be able to meet the challenge successfully. Thus each post test will increase his confidence in himself and in the idea that his diligence in studying the units pays off. The entire post test system should be designed to encourage the student rather than embarrass him. (In this connection it is well to point out that material which appears only in frames with no response is not actually taught and its inclusion on post tests is considered a dirty trick by most students.)

Proper use of the post testing system allows the students to see their mistakes and correct them, as well as allowing you to direct your lectures or problem sessions at points that are being missed.

Hour tests and final exams are another matter. In this system, as in any other, they serve to find the differences between students and may be designed to test any ability the teacher wishes. In fact, you may find that using tests modeled rather closely after those you have used in the past will give you some information about the effectiveness of your new system of instruction.

If, however, you plan to use hour exams which are much harder than the post tests, common decency and sense of self-preservation both seem to indicate that the students should be warned that such is the intention.

Supporting and Supplementing the Programs

Perhaps at this point you are wondering what your role is in teaching a class with programmed instruction. The students learn the material on their own from the book and the quizzes can be distributed and graded by a teaching assistant. Is there still a need for a professor in such a system?

We feel that the professor has at least four major functions in such a system. Two of these functions are probably vital to the successful adoption of programmed instruction in an American college. Two, in our opinion, are what make the programs able to enhance the quality of the education provided to the student.

First, someone must assume administrative responsibility for the operation of the system. Schedules, rules, and rolls must be made out, quizzes and exams must be written and graded, and, in most cases, grades must be assigned. Assistants can appreciably lighten this load, but there should be a professional in charge of the operation.

Second, even if the programs were perfect, students would not be. At some time or another during the course many of your students will want encouragement, consolation, advice, or help in completing your requirements. These jobs are also ones which are best performed by a professional instructor.

The professor's role can extend beyond the realms of record keeping and first aid more easily when teaching with programs than with lectures. This is possible because less class time is needed for elaboration and repetition of basic principles. The teacher becomes more free to show his class how the concepts can be used.

For instance, the teacher can model his own problem solving approach for his students. He can show them his favorite methods or ask for their help on a more difficult problem with a fairly accurate expectation that they will understand his reasoning and be prepared to contribute to class discussions.

Last, but not least, when students study "the basics" from the programs outside the classroom and still come to class, you, the professor, will have more time to talk about the things you always wanted them to know but were too busy to mention. You will have time to tell them how you drew a free body diagram as part of a stability analysis on your last consulting project, or how you used the equilibrium equations in a biomechanics problem.

In short, the programs deal with facts and procedures. The teacher's role remains as counselor, administrator, and inspiration to his students.

Helping The Students

Programmed instruction is often a new experience for the student and you will probably find that more students than before appear in your office. You may find that you can be of more help to them if you are aware of the difficulties they commonly encounter.

At the beginning students may be wary of this new attack. However, success on a few post tests usually convinces them that it is a valid approach to learning.

A more serious difficulty arises when a student attempts to read the programs like a text without making an active response. He will usually find that he retains very little by this method. It is important that the students actually work through each unit, rather than merely reading it. The regular post tests are primarily to insure this behavior, since the students who have done the units usually have no difficulty with the post tests. It may help if you point this out to your students.

Encourage your students to write their responses. The book was designed to be written in, since we feel certain that writing responses is a necessary part of learning from programs.

A related problem arises when a student skims the early "easy" parts of the unit and only begins work when it looks hard. Unfortunately the early material is usually vital and he finds he can't do the problems. The gradual build-up of difficulty is important in programs and diligent work on the early frames is as important to the student as a careful warm-up is to an athlete.

Be aware of the students' time problems and try to adjust to them when you can. Since a unit requires considerable time and provides practice on problems in the units, no additional homework should be assigned when units are given.

A few students tend to develop an over-dependence on the teacher. By all means, help the student who needs it, but first be sure he has really done all he can on his own. The programs have been carefully validated and most students can get through them with an absolute minimum of help. However it is admittedly easier to get an explanation from the teacher than to think through a difficult passage. You can help your students to built both confidence and competence if you are judicious in providing help.

We find that we can help individual students most efficiently when we act as trouble shooters. We make it our policy to help students only when they

present us with specific questions on the materials and with their own written responses to earlier frames. We generally will not answer a request to "explain this topic" but will readily deal with questions such as "how do you get this?" Sometimes it has proven useful to ask the student to show us his attempt at a solution before volunteering any information.

Most of the students' problems stem from one of the causes we have discussed. However there is another problem which will probably arise. You will find that the students' attitude toward you changes. They will tend to consider you an ally against the programs, and as a friend and adviser. The distance between you will probably decrease. We find this delightful but time-consuming, and at times we have wondered who is in charge here. Consequently, we would advise you to enjoy your new role but be prepared to draw whatever lines you must.

All in all, we and our students have found programmed instruction stimulating, challenging, frustrating, surprising, and fun. We hope you will, too.

Some Do's and Don’ts

If use for vital in so vital trouble arises as you proceed through the course you may find some the following lists. They cover points that we have found to be the successful implementation of our system. They may not be quite to your system but they probably merit your consideration.

DO encourage the student to write their responses.

DO encourage students to make an active response to each frame in the units - even the easy ones.

DO post test every unit.

DO let students know what you expect them to learn.

DO "play fair" with students. They must trust you.

DO encourage students to complete the notebook.

DO grade post tests promptly. post the post test grades.

DO make class attendance worthwhile.

DO design the post tests so that the average student will succeed.

DON'T make the post tests too hard.

DON'T make the post tests trivial.

DON'T post test over material which is not in the unit.

DON'T post test over material which appears only in "no response" frames (introductions, transitions, etc.)

DON'T post test over notebook material which does not also appear in the active response frames.

DON'T let your students walk all over you.