Problem-Solving and Science Teaching

Problem-Solving and Science Teaching

Hans 0. AndersenScience Education Center, Indiana University, Bloomin^toUf Indiana

Teaching science as a process of inquiry depends upon the teacher’sability to develop problem-solving skills. Teachers, like students, willneed training in the use of problem-solving skills before they can useany method involving the use of problem-solving skills effectively.

Science educators have been concerned by the slow development ofproblem-solving as a teaching method. Some have suggested that thismay be due to a lack of experience with this method in the teacherstraining. As such, it seems important to develop effective methods ofteaching teachers and providing them the know-how and experiencenecessary for this new role.

In this article, the author attempts to outline (a) the factors whichtend to influence the problem-solving process, (b) the problem-solv-ing process, and (c) some methods which have been used to improveproblem-solving skills.

FACTORS WHICH TEND TO INFLUENCE PROBLEM-SOLVINGThe multidimensional nature of the problem-solving process can be

segmented in various manners. Bruner, for example, prefers to studyproblem-solving through broad concepts which include hypotheticalmode, cumulative constructionalism, and intrinsic motivation [8].Discovery, according to Bruner, can be facilitated by the method ofteaching. If decisions concerning the mode, pace, and style are madeentirely by the teacher, the student becomes the passive listener [6].The teacher is the possessor of the ands, the ifs, and the alternatives.If a hypothetical mode of teaching is utilized, the student is forced toactively manipulate the content, search for alternatives, and makethe decisions. The latter method shifts the emphasis from extrinsic tointrinsic rewards. Emphasizing discovery in learning forces the studentto organize the content encountered in a manner which leads him to adiscovery of regularity and relatedness while avoiding the kind of in-formation drift which fails to account for the contexts in which theinformation may be applied. In this process of becoming a construc-tionist, the student encounters a variety of problem-solving proce-dures, practices transforming information for better use, and becomesfamiliar with the very task of learning [6].

Skinner views thinking and consequently problem-solving from adifferent vantage point. He feels that problem-solving is a highlyabstract process which must be reduced to its specific componentbehaviors before we can teach it. While Bruner is most concerned

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244 School Science and Mathematics

with the ^why^ of learning, Skinner is concerned with how we learnand the practical conditions which promote learning [8].Bloom and Broder in a study of problem-solving processes of col-

lege students examined the major sources of difficulty apparent inpersons with less problem-solving ability [3]. The five factors theycited as most important are as follows:

1. Lack of direction. The student proceeds directly toward trying to solvethe problem without either thoroughly reading directions or denning theproblem.

2. Lack of objectivity. The student allows dislike for the subject, feeling ofinadequacy, fear of complex problems, personal values, and lack of successin previous problem-solving efforts to interfere with any new attempts tosolve problems.

3. Lack of ability to think logically and systematically. The student’s problem-solving attempts are dominated by hunches, feelings, and guesses.

4. Lack of ability to follow a chain of reasoning. The student is capable ofinitial reasoning but cannot go beyond the first few steps in a logical se-quence.

5. Lack of knowledge. The student does not possess the knowledge necessaryto solve the problem.

Prior experience plays an important role in problem-solving.Saugstad and Raaheim indicate a subject will solve a problem if hehas the necessary functions [27]. Function is defined as somethingthat may be thought of in terms of a specific context or a much largercomplex consisting of a variety of contexts.Lapp pointed out that practice in solving physics problems in-

creased achievement in physics as measured by the ability to solvemore physics problems [17]. In a similar vein, other investigatorshave discovered that solving problems of a certain set tends to im-prove a students skill with problems which fit the set [12, 15]. Thebest approach to developing a students skill in solving a particulartype of problem seems to be by providing the student with practicein the particular type of problem. Jack Adams discovered that agroup trained on repeated presentations of the same problem wasmore proficient in solving a new problem of the same set than agroup trained on a number of different problems [1].

Weir, using a game type activity, indicated that younger subjectsdeveloped problem-solving skills at a more rapid rate [29]. The in-vestigator claimed that all subjects of the study were motivated;however, only the young were rewarded extrinsically.

Problem-solving abilities of creative and noncreative college stu-dents were compared in a study by Eisenstadt who discovered thatthe creative student was much more efficient [11]. Students wereseparated on the basis of their scores on the Guilford Consequence andAnagram Test into creative and noncreative categories. The creativestudents did not prove qualitatively superior in spite of their abilityto solve the problems faster.

Problem-Solving and Science Teaching 245

Several investigators have noted the influence of stress on problem-solving. One investigator suggests that the influence of stress is re-lated to the subjects personality [18]. Another investigator indicatedthat stress increased motivation and increased performance slightlyon single-decision space problems, but interfered with the more com-plex and poorly learned cognitive strategies [26]. In examining prob-lem-solving behaviors of students, Cowen noted that his stress groupexhibited highly rigid problem-solving behaviors while his praisegroup exhibited significantly less rigid behaviors [7]. Reducing stressor avoiding placement of stress in a situation which potentially in-volves complex problem-solving behavior appears to be conducive toproblem-solving proficiency.

It has been demonstrated repeatedly that inflexibility of set,mind set, or the Einstellung effect, interferes with problem-solving[22]. The influence of set, as related to practice, was discussed earlier.It was indicated that practice in solving problems of a specific set,develops proficiency in solving similar problems of the set. Thegreater the similarity between the practice problem set and test prob-lem set, the easier it is to solve.Mind set or the Einstellung effect is a deterrent to successful prob-

lem-solving. Once established, set seems very difficult to surmount.Luchins and Luchins, for example, had very little success in prevent-ing or weakening the Einstellung tendency once it was establishedin students [19]. In analyzing set, Luchins points out several factorswhich tend to maximize set [20]. These are as follows

1. Increasing the number of set-inducing problems.2. Stress.3. Using set methods and procedures to solve problems.4. Presenting problems as isolated drill.

According to Luchins, set can be reduced if the following steps aretaken.

1. Increase the number of problems that demand direct solution as opposed toproblems for which a solution method is available.

2. Mix problems solvable by a method with some solvable only by directattack.

3. Add more complex detail to the problem.4. Discuss the nature of set and its possible deleterious effect on a student’s

problem-solving capacity with students,

Much of the evidence suggests that attempts should be made toavoid the establishment of set if improvement of general problem-solving skill is the objective.

THE PROBLEM-SOLVING PROCESS

When developing a method for improving problem-solving skill,the factors which govern the process become the paramount con-


cern. The process of problem-solving defies complete description forit is almost impossible to remember all the steps in the thought pro-cess and report them in the sequence in which they occurred. Thestudent describing thinking involved in solving a problem tends toedit the report and set forth the process as a logically proceedingseries of events. In editing, errors and ^dead ends77 are frequentlyomitted. Rarely does a student describe the process as it really oc-curred [3].Duncan defines problem-solving as the integration and organiza-

tion of past experience which leads to discovery of a correct response.He implies that almost any other definition leads into problem-solv-ing behavior or into theory [10].Dewey describes problem-solving as the five phase process outlined

below [9].1. The student is involved in a situation which is interesting to him.2. A genuine problem develops within the situation which challenges the

student.3. The student constructs hypotheses and collects data.4. The student arrives at several solutions.5. The student has the opportunity to test his solution.

Gross and McDonald point out that Dewey’s five phases involvethree essential functions [13]. These include:

1. An orientating function during which the student recognizes and accepts theproblem.

2. An elaborative and analytic function in which the student explores thedimensions of the problem and collects data.

3. A critical function in which the student tests his selections and evaluates hisresults.

Another scheme, similar in many respects to Dewey’s has beenadvanced by^Merrifield, Guilford, Christensen, and Frick to explainthe problem-solving process [24].

1. Preparation Phase. In this phase the problem arises, and is recognized as aproblem by the student who is then motivated to seek a solution.

2. Analysis Phase. During this phase the student becomes acquainted with theproblem; denning its limits and the type of activity necessary for solving theproblem.

3. Production. The student acts to generate alternative solutions to the prob-lem and selects one for testing.

4. Verification. The student rejects tentative solutions.5. Reapplication. In this phase the student returns to previous stages and

selects other tentative solutions for subsequent evaluation.

This model is considered more realistic than earlier models de-

signed to describe the problem-solving process because it indicatesthe potentially flexible nature of the problem-solving process; prob-lem-solving rarely occurs in sequential linear order. This model al-lows for the frequently repetitious nature of the problem-solvingprocess in its structure.


Problem-solving often progresses intuitively. Bruner indicatesthat intuitive problem-solving apparently operates by an implicitperception of the total problem, and employs leaps, skipping steps,and short cuts rather than rigid formulas or patterns [5]. Thoughsolutions reached in an intuitive manner require later checking byanalytic means, the value of intuitive thinking is not unrecognized.Development of intuitive thinking has become an objective of manyof the most highly regarded teachers in science and mathematics [5].The problem-solving process defies complete description at present;

however, several investigators indicate that it may be defined interms of the factors in the structure of intellect [24]. Thorndike in-dicates that there is no simple pattern or formula of problem-solvingwhich can be isolated and taught in the schools as a simple unitaryskill [28]. The lack of agreement concerning the nature of the prob-lem-solving process thus indicates that persons interested in develop-ing problem-solving skills should develop methods which willstrengthen a maximum number of the functions known to influencethe total process.

SELECTED METHODS USED TO DEVELOP PROBLEM-SOLVING SKILL

The scientific method of problem-solving was for years the prin-cipal means of teaching problem-solving in the science class. Thismethod was typically represented as the five steps outlined below:

1. Defining the problem2. Constructing hypotheses3. Experimenting4. Compiling results5. Drawing conclusions

The idea that a scientific method of problem-solving truly existed wasso well entrenched that one important science education documentcontained an apology because it was not possible to introduce a com-plete cycle of the steps in the problem-solving process in each specificsituation [14]. Since the publication of this document, employing thescientific method as the way to attack problems has waned in popu-larity. Recent writers in the field of science education generally agreethat there is no one scientific method, and there may be as manymethods as there are problems and scientists to solve them [16].

Using the scientific method or any other method involving steps,such as Dewey’s five classical steps in the processes of analyticalthought contribute. little to the. development of problem-solvingskill. Brownell discusses.two criticisms of. teaching a general methodfor solving problems [4]. These are:


1. The step approach presents problem-solving as a logical pattern of thinkingwhich may or may not characterize adult thinking but which has definitelynot been proven to be characteristic of good thinking on the part of stu-dents.

2. The step method places too much faith on the technique alone and ignoresother factors which may influence problem-solving.

MacLatchy indicates that many of the difficulties students havewith problem-solving arise from the invariability of the methods ofsolving problems and the over emphasis on following a pattern [21].She demonstrated that having the student solve the problem in asmany ways as possible had a positive effect on developing problem-solving skill.Methods of teaching problem-solving which involve short cuts that

sometimes work and methods which rely upon training in a singlefunction more or less related to problem-solving, should be avoided.The first method lacks value as a teaching method because the solu-tions reached are not consistantly reliable. Improving reading, be-cause many problems are presented through reading and are solvedfrom data obtained in reading, is an example of improving a functionrelated to problem-solving. This method could be used to improve theproblem-solving skills of good problem-solvers who are poor readers,but lacks other applicability [4],

Analytical thinking is an important aspect of the total problem-solving process and some methods of improving this function of thetotal process merit consideration. Bruner points out that problem-solutions reached by other methods should always be checked bymore analytic methods [5]. Relying on improving analytic thinkingskills as the method of improving problem-solving ability in totalfails to account for the importance of intuitive skills and problem-solving attitude. While improving analytic thinking ability often willimprove a student’s analytic problem-solving ability, it generallywill not improve his intuitive ability. Development of a positiveproblem-solving attitude would depend upon the number of problemsof a solvable analytic nature he encounters as opposed to problemswhich he would have to solve by direct or intuitive methods.Bloom and Broder investigated a method of improving problem-

solving skills which avoided the analytic step method f3]. They as-sumed that students who consistently scored high on the comprehen-sive examinations at the University of Chicago were good problem-solvers and that students who consistently did poorly on the compre-hensive examinations would profit from a study of the problem-solv-ing methods used by the high scoring students. Students fitting bothcategories were given problems and then asked to explain exactly howthey began their attack and proceeded toward a solution to the prob-


lem. Because many students had difficulty recalling all the steps theyfollowed, they were given training in thinking aloud. At later sessionsthe remedial student reviewed the method he had used to solve theproblem, and then the method employed by the successful problem-solver was read. The remedial student was then asked to list any dif-ferences between his method and the method used by the successfulproblem-solver. At first the remedial students had difficulty notingany difference between his and the model student’s method of attack.An interviewer would then try to point out the differences. After afew practice problems, the remedial problem-solvers became pro-ficient in noting differences between his method and those of success-ful problem-solvers.

After several months of training, changes were noted in the mannerused by the remedial problem-solver in attacking problems. The prin-cipal change was in the extent to which these students became moreactive and aggressive in their problem-solving attempts. It was alsonoted that they were more confident in their ability to solve problems,tended to break problems into more workable subproblems, and weremore careful and systematic in reading directions and followingthrough a logical system of thought [2].

Utilizing brainstorming instructions as a means of improving prob-lem-solving skills of trained and untrained subjects has also beeneffective [23, 25]. The experimentation involved brainstorming withstudents enrolled in a creative problem-solving course at a university.Students in the experimental study were given two problems. Oneproblem was given under brainstorming instructions; the other undernonbrainstorming instructions. The brainstorming instructions con-sisted of encouraging the students to list all the ideas that came totheir minds without judging them in any way. The nonbrainstorminginstructions consisted of directing the students to list all the goodideas which came to their minds. A significantly greater number ofgood quality ideas were produced under brainstorming instructionsthan under nonbrainstorming instructions. The investigators con-cluded that brainstorming instruction was an effective method forincreasing the production of good ideas in problem-solving situationsand that this method becomes even more effective if preceded by ex-tensive training in its use.

SUMMARYThe scientific method of problem-solving was for years expounded

upon by science teachers. It was considered the way to attack prob-lems and students were encouraged to memorize its five steps;problem, hypothesis, research, results, and conclusion. When at-tempts were made to develop problem-solving approaches to the


teaching of science, it was realized that scientific research rarely pro-ceeded along the five linear steps portrayed as the scientific method.Instead, it was discovered that there probably were as many methodsas there are scientists and problems to be solved, and that intuitiveproblem-solving methods often produced results when analytic meth-ods had failed.The recent emphasis on problem-solving approaches to the teach-

ing of science in the secondary school places new and greater demandson the science teacher. His past experience in science has given himlittle opportunity to explore the problem-solving process and hisexperience with actual science problems is often limited. Yet, this in-dividual is expected to teach science as a process of inquiry and ac-tively involve students in the type of problem-solving activitycharacteristic of scientists.

Developing skill in solving problems has been a goal of most scienceteachers; but being a goal is not enough. The teacher must activelypursue this goal by providing students with the types of experienceswhich tend to develop effective problem-solving skills. To do this, theteacher must possess a functional understanding of the problem-solving process which he can communicate to the student. A func-tional understanding of the problem-solving process and developmentof effective problem-solving skills arises from training, practice, andan appreciation of the value of being a proficient problem-solver. Assuch, future science teachers should receive considerable practice andtraining in problem-solving.

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[11] EISENSTADT, J. MARVIN, "Problem-Solving Ability of Creative and Non-creative College Students," Journal of Consulting Psychology, 30: 81-83,Feb., 1966.

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Problem-Solving and Science Teaching