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Reasoning Fallacies in Preservice Elementary SchoolTeachersJudith Bransky a , Rina Hadass a & Aviva Lubezky aa School of Education of the Kibbutz Movement, University of Haifa , IsraelPublished online: 07 Jul 2006.

To cite this article: Judith Bransky , Rina Hadass & Aviva Lubezky (1992) Reasoning Fallacies in Preservice Elementary SchoolTeachers, Research in Science & Technological Education, 10:1, 83-92, DOI: 10.1080/0263514920100107

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Research in Science & Technological Education, Vol. 10, No. 1, 1992 83

Reasoning Fallacies inPreservice Elementary SchoolTeachers

JUDITH BRANSKY, RINA HADASS & AVIVA LUBEZKY,School of Education of the Kibbutz Movement, University of Haifa, Israel

ABSTRACT One of the reasons given for failure in science studies has been a deficiency in students'reasoning capabilities. A remedial science program incorporating instruction in basic conceptualknowledge with reasoning strategies has been taught to large groups of preservice elementary schoolteachers in Israel for over 10 years. In the present study an attempt is made to compare thereasoning capabilities of preservice elementary school teachers before and after their involvement inthe above mentioned program. This report deals with two reasoning skills: (a) control of variablesand (b) drawing logical conclusions. The improvement in reasoning is evaluated by means of aquestionnaire administered to 221 students, all high school graduates, 97 of them having completedthe remedial course. The results point out some persistent logical fallacies. An average improvementof 18% in the control of variables skill and 10% in the drawing of logical conclusions skill isreported. It is suggested that teachers address these reasoning skills in any basic science course, be itin high school, in college or in teacher education.

Introduction

Efforts to enhance science studies in elementary schools and to start these studiesat an earlier age, necessitate the inclusion of a science course in the trainingprogram of preservice elementary school teachers (ESTs). These students usuallylack any scientific inclination. Most of them have a negative attitude towardsscience and some suffer from real anxieties, created by their previous failures.

Failure in science studies has been related to a deficiency in basic reasoningcapabilities (Arons, 1976, 1983; Karplus, 1977; Wollman, 1977; Lawson et al.,1978; Shadmi, 1981; Lawson, 1985; Linn et al., 1989). Other researchers (Gott,1984; Black, 1989; Perkins & Salomon, 1989) focus on the interaction ofreasoning capabilities and the mastery of concepts.

Besides being a tool for a better understanding of science, the development ofanalytical skills in prospective teachers seems to be a goal in itself. As observed byLawson & Snitgen (1982), preservice ESTs are, to a great extent, concreteoperational thinkers. According to these authors' findings, classroom instructionof specific formal reasoning skills is advisable.

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84 J. Bransky et al.

Linn & Thier (1975) and Jungwirth (1987) pointed out that the development ofreasoning capabilities is an outcome as well as a prerequisite to science studies.This situation is confirmed by our long teaching experience. In Israel preserviceESTs are little, if at all, exposed to science studies in their precollege education;hence, a deficiency in reasoning and process skills may be expected, and isactually found in our preservice ESTs. It is important for science instructors ofpreservice and in-service teachers to be aware of these deficiencies, as well as ofpossible cures.

The objectives of the study are:(1) to find out the extent to which preservice ESTs lack certain basic

reasoning skills;(2) to assess the effectiveness of an intervention program aimed to

develop these reasoning skills;(3) to suggest some implications arising out of the results for future

preservice and in-service courses.A remedial science program has been devised by Shadmi (1983). It is desig-

nated as "Basic Concepts in Science and How to Teach Them". The programincorporates science concepts and some basic reasoning skills. It is inquiry based,'hands-on' and follows an inductive approach. It builds on concrete, familiarexamples, usually through laboratory activities, then proceeds to formal generali-zations. The analysis of the experimental results is performed by directly employ-ing the relevant reasoning strategies. As these strategies are employed repeatedlyin the presentation of several new concepts, they gradually become part of thestudents' reasoning inventory and in turn facilitate future conceptual understand-ing.

We have been using this program successfully in our teacher education collegefor over ten years. The success is 'measured' by the consistently large number ofstudents (about 50%), choosing optional science courses following the basic one.

For the present study, an effort has been made to construct an assessmentinstrument that is based on everyday, familiar topics; this is in order to focus onthe improvement in reasoning skills, without interference of subject matterknowledge.

This report deals with two of the several reasoning skills addressed in theprogram:

I. Control of variables.II. Drawing of logical conclusions.

The first skill has been extensively reviewed in the literature (Lawson et al.,1975; Lawson, 1980, 1985; Shadmi, 1981; Wollman & Chen, 1982; Linn andLevine, 1978). The second skill has not been reviewed to the same extent.Nevertheless, many examples, in which this reasoning skill occurs in scientificanalysis, can be given (Jungwirth, 1987).

The Study

The scope of the logical fallacies and the improvement in reasoning abilities,gained by the instruction of Shadmi's program, was evaluated by means of awritten questionnaire. The questions are mainly based on everyday experiences,with no direct reference to the scientific topics of the program

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Reasoning Fallacies 85

The questionnaire contains 12 multiple choice questions relevant to the tworeasoning skills. Some of the distractors are purposely designed to representcommon fallacies. The scores for all answers were analysed so as to detect popularmisconceptions.

The questionnaire was administered to 221 students, 97 of them after havingcompleted the course (within a year). It is worth mentioning that because ofcertain specific characteristics of our college, the average age of our students is25-7 years as compared to 22'4 reported for equivalent institutions in the US.

Part One: control of variables

The control of variables is a fundamental reasoning procedure for investigationsof any kind. It is important in all the sciences, as well as in social studies. For ascience curriculum, which is of a 'self-discovery' type, it is indispensable. Linn etal. (1989) recently reported on the benefits of the instruction of this reasoningstrategy to adolescents in which they employed a medical, biological subject.

The teaching method of the control of variables in Shadmi's program wasdescribed in detail elsewhere (Shadmi, 1981). It is based on a series of 'sink orfloat' experiments. The task is to find the variables which control the 'sink orfloat' phenomenon. Two sets of cylindrical, uniform bodies are provided; one setis comprised of equal mass bodies, the other of equal volume bodies. The ideasconcerning the control of variables are derived by means of guessing games,trials, conclusions and generalizations. At the end of the activities, the concept of'density' is derived by the students.

In the present study, the main features of this reasoning skill can be classifiedinto three processes, as follows:

11 The choice of an appropriate experiment to study a phenomenon,i.e. changing only one variable at a time.

12 The drawing of conclusions on tested variables only.13 The legitimacy of drawing a negative-limited conclusion on an un-

tested variable.

The word 'limited' emphasizes the fact that the conclusion includes the wordonly or alone.

The last process, 13, is relatively complex, so we present here a clarifyingexample: Let's assume that for a 'sink or float' investigation, all the experimentsare performed in water. In one case, bodies of equal volume and different massare thrown into the water. Some of the bodies sink while others float. Thefollowing conclusion: 'The sink or float phenomenon does not depend on the typeof liquid alone', would be a correct one. This conclusion implies that thephenomenon depends on other variables than the type of liquid, which is a factestablished by the experiment (in the present example the 'other' variable is themass). We shall denote this type of conclusion by ULN: 'Untested variable-Limited Negative conclusion'. When the word 'alone' is omitted, the aboveconclusion becomes unfounded and belongs to process 12: a negative conclusionon an untested variable (UN).

A 'Limited Positive' conclusion on an untested variable, which we denote byULP, makes no sense. In the above example this would be: 'The sink or floatphenomenon depends only on the volume'. It is not expected that adult students

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86 J. Bransky et al.

would consider this a logical option. The drawing of a limited conclusion, positiveor negative, on a tested variable is also unacceptable. In the present example, thatwould mean concluding: 'The sink or float phenomenon depends (or does notdepend) only on the mass of the bodies'. These conclusions will be denoted byTLP and TLN, respectively. Contrary to ULP, such fallacies might well occuramong our students.

The first reasoning process II is relatively easy for our students. The process12, though derived directly from the first, is often violated by students, mainlywhen they are misled to derive a negative conclusion on an untested variable. Thelast process 13 is not frequently used in scientific analysis and in everydaysituations; it is, therefore, less familiar and, perhaps, also less important. Never-theless, it is considered worth noting, since it does give another opportunity toenhance logical thinking.

Examples

We present a few examples from the assessment questionnaire, one for eachreasoning process. For the purpose of reporting, we will use the following legend:

T—Tested variable U—Untested variableP—the conclusion is a N—the conclusion is a

Positive statement Negative statement

L—Limited conclusion (phenomenon depends, or does not depend, on therelevant variable only)

Logically, the conclusions:

TP and TN are legitimate UP and UN are illegitimateTLP and TLN are illegitimate ULP is illegitimate

ULN is legitimate

11. Choice of Experiment: CE

Two different amounts of two materials were heated by the same heater. MaterialA reached 50°C sooner than material B.

It may be concluded:

(a) material A is inclined to warm up faster than B;(b) the specific heat of A is higher than the specific heat of B;(c) the amount of A is smaller than the amount of B;(d) none of the above conclusions can be drawn from the experiment.

12. Tested Variable-negative Conclusion

The breaking strength of some metal wires was tested in a laboratory. Wires ofthe same metal and of the same thickness, but of different length were checked.All the wires broke when a load of 50 Newtons was applied to them.

It may be concluded:

(a) the breaking strength does not depend on the thickness of the wire(UN);

(b) the diickness of the wire alone determines its strength (ULP);

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Reasoning Fallacies 87

(c) the breaking strength does not depend on the length of the wire (TN);(d) not the length alone determines the strength of the wire (TLN).

13. Untested Variable-limited Negative Conclusion

Two different amounts of the same liquid were heated by identical heaters for thesame period of time. A different temperature increase was measured in each ofthe vessels containing the liquid.

It may be concluded:

(a) the temperature increase depends on the heating time (UP);(b) the temperature increase depends on the type of liquid alone

(ULP);(c) the temperature increase does not depend on the type of liquid alone (ULN);(d) the temperature increase depends on the amount of liquid alone

(TLP).

Results and Discussion

For the sake of comparison and for a greater variety in assessment questions, weinclude in our summary the results of three questions from the Standard Pre-testand three equivalent questions from the Standard Post-test of the program. Theresults of these were collected over several years. The standard pre- and post-testswere administered to over 1000 students. We denote these questions by SI1, SI2and SI3 according to the relevant reasoning process. However, it should be keptin mind that the standard post-test was devised to assess the knowledge andunderstanding of scientific concepts as well as the reasoning skills, while thepresent study was aimed at assessing the reasoning skills only. The questions inthe pre- and post-tests, in most cases, were different ones. The questionnaire waspresented to the students before and immediately after studying the course. Inour study, the questionnaire, presented to different groups of students, was thesame; one group before learning, the other a year or so after the completion ofthe course.

The mean scores are presented in Table I.The main feature of the results, presented in Table I, is that the absolute

improvement is almost equal for all three reasoning processes. The spread in

TABLE I. Percentage of correct answers (iV=221 students)

Before learning After learning A R. improvementReasoning B A A - B (A-B)/(100-B)%

111213

SI2SI2SI3

(CE)*(TN)(ULN)*(CE)(TP)(ULN)

40-077-037-082-637-050-0

(s.8)

(s.9)

57-096-056-0

97-059-069-0

(s.12)

(s.7)

17-019-019-014-422-019-0

288330

833538

*Average of three questions,(s.) Spread.

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88 J. Bransky et al.

scores for several questions is small. This points to a consistency of the instrumentand gives some face validity to the results. The scores for 12 are derived from onequestion only; a second question, assessing the same process was discardedbecause of ambiguity. Thus, we regard the high scores of 12 with some reserva-tion and give more weight to the scores for this reasoning process in the pre- andpost-tests as shown in SI2. This is justified, as in this particular case, the post-testdid not include any specific subject matter discussed in class, but dealt with ballsrolling with different speeds after being hit by different forces. Thus, for all threereasoning processes (II, SI2, 13) the relative improvement is about a third of the100% final goal.

The discrepancies between the scores of II and SI1 can be related, in part, tothe differences in the aims and technique of the assessment used for both cases,as explained above; but we tend to believe that the main reason for thediscrepancy is the context of the questions. SI1 happens to be a very familiarintuitive case, in which different amounts of water measured by 'cups' are heatedin an electric kettle, while example II uses scientific terms like 'amounts ofmaterial'. Saunders & Jesunathadas (1988) have already pointed out that thecontext and structure of questions have a major influence on the performance ofstudents. This is an inherent limitation of any written instrument of assessment.

Additional insight can be gained from the analysis of the scores of the wronganswers. The scores of the most popular ones show that the largest improvement(about 20% decrease in absolute score) is achieved in reasoning process 12; i.e. indiscarding answers of the type UP and UN. This corresponds to the averageimprovement (12 and SI2) shown in the correct answers. It may be inferred thatalmost the entire shift towards choosing the right option stems from a correctionof one common misconception.

The answers which deal with drawing conclusions from a wrong experiment(II) (uncontrolled variables), show an initially low score and a further decreasethrough the intervention.

About 17% decrease is detected in the scores for answers of the type TLPrelated to 13. Reasoning process ULP shows a decrease in score of about 10%.This means that at least 10% of the students did get, through the instruction, thegeneral idea that a positive limited conclusion (only variable X is . . . ) on a testedand untested variable is unacceptable. On the other hand, scores on conclusionsof the type TLN (only X is no t . . . , where X is a tested variable) show even a slightincrease after instruction. This might indicate that the teaching of the reasoningprocess ULN confused some of the students. The legitimacy of deriving anegative limited conclusion on an untested variable caused them to believe it isright to draw such a conclusion on a tested one. The shift of 19% of the studentsto the correct answer ULN, in this case, probably stems from discarding theanswers in which a positive limited conclusion has been derived.

Part Two: logical conclusions

The second issue addressed in this study is the drawing of logical conclusionsfrom information presented. Two basic cases exist:

III The information presented is sufficient to give a single, certainanswer to a problem.

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Reasoning Fallacies 89

For instance: if A is too short to reach X and B is shorter than A,then B is certainly too short to reach X.

Or: if A is long enough to reach X and B is longer thanA, then B is certainly long enough to reach X.

112 The presented information allows more than one possibility.For instance: if A is too short to reach X and B is longer than A, it

is possible that B is too short to reach X; it is alsopossible that B is long enough to reach X.

Though this logic might seem self-evident, our experience and the presentstudy show that this is not the case.

In Shadmi's program (1983) this topic is also tackled by a 'sink or float' quiz.The students are told that a certain body sinks (or floats) in water. Then they areasked to guess what will happen to an equal mass body which is larger (andsmaller). After recording their guesses, the students are urged to verify them bytrial. A set of four equal mass bodies is supplied. The bodies are made of fourdifferent materials, so that two of them float and two sink. The students have todecide how to fit their experiments to the required problem; i.e. they have tochoose the right body as their reference. If they choose as their reference thelarger of the two sinking bodies, they tend to conclude that a smaller body willcertainly sink (correct) while a larger body will certainly float (incorrect). Thestudents are then urged to choose the smallest body as the reference. In this casethey perceive that their last conclusion was wrong; more than one possibilityexists: one larger body floats, and another larger body sinks. The same verifica-tion procedure is repeated for a floating reference body. A similar quiz isrepeated for equal volume bodies, where the words 'larger' and 'smaller' aresubstituted by the words 'heavier' and 'lighter'.

The students are also asked to specify which of the trials gave an absoluteverification of their guess and which of them supplied just an example of theassumed rule. It is known that the absolute verification by experiment is possibleonly for the uncertain cases: when two possibilities exist, both can readily bedemonstrated; when only one definite answer exists, it cannot be verified by oneor even by many successful experiments. This last point is an important scientificissue. It emphasizes the fact that basic scientific rules cannot be verified byexperiment. They are accepted as rules, because they are never contradicted byexperiment.

The following are a few examples of questions on this issue included in thequestionnaire.

We will again use abbreviations to denote the reasoning processes; the certainones (III), and the uncertain ones (112):

111 EM—even more so; and CN—certainly not.112 PY— possibly; and IP— impossible to know.

Examples

Ex. 1. Even more so (EM). Two motorcyclists went straight and without stopping,from Haifa to Tel Aviv (about a 100 km.). The first one drove faster than thesecond. The travel time of the first motorcyclist was a little over 2 hours. Howlong did the second motorcyclist take?

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90 J. Bransky et al.

(a) Less than two hours (CN).(b) More than two hours (EM).(c) Depending on the exact speed of the first motorcyclist (PY).(d) It is impossible to know (IP).

Ex. 2. Impossible to know (IP). You have two cylindrical containers equal in height.Assume you pour a certain amount of water into the first container and it is notfilled. Now you take the same amount of water and pour it into the secondcontainer. The second container will be completely filled:

(a) if the cross-section of the second container is larger than the cross-section of the first one (CN);

(b) if the cross-section of the second container is smaller than the cross-section of the first one (PY);

(c) if the volume of the second container is smaller than the volume ofthe first one (PY);

(d) it is impossible to know (IP).

Results and Discussion

The results of the questionnaire averaged for two questions dealing with thereasoning process EM, were 50% before and 64% after learning. The results forthe reasoning process IP (one item) were 6-5% before and 11% after learning.This means that reasoning process III, which deals with certainty, is clear to 50%of the students. The teaching improves the situation slightly. On the other hand,for reasoning process 112, where uncertainties occur, most of the students failedto choose the right answer. The intervention resulted in some improvement, butthe logical fallacy is still very persistent.

It is once more worthwhile examining the popular wrong answers. As can beseen from the second example, answers 112, b & c, present exactly the samelogical idea; in one case with the unfamiliar concept 'cross-section' and in thesecond case with the relatively familiar concept 'volume'. The scores for these twowrong answers were, before the intervention, 30 and 62%, respectively, and 28and 54% afterwards. The actual prevalence of this reasoning fallacy constitutesthe sum of these two scores, i.e. 92% before learning and 82% afterwards.Although these findings are based on a very limited number of questions, thecorrect scores are so low that the results must have some significance. This logicalfallacy (IP) seems to be widespread and it would be worthwhile to investigate it ingreater detail. It is interesting to note the 2:1 ratio in the number of students whopreferred the answer II2c (volume), to those who chose II2b (cross-section). Thispoints again to the inherent problem of the influence of the context on dieperformance of the students.

Implications for Teaching

The results of part one of this study show the resistance to change of some basicincorrect reasoning processes among adults. However, it should be kept in mindthat the modest gains of die intervention program include the transfer factor,from scientific to everyday contexts. The transferability of reasoning processes

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Reasoning Fallacies 91

from one area to another has always been a drawback of education (Lawson,1982, 1985; Lombard, 1982).

The authors share the view of most researchers in this area, that it is necessaryto explicitly address control of variables with all its different reasoning processes.In Shadmi's program, control of variables strategy is reused when discovering thefactors determining the temperature increase of heated bodies, in constructingthe equation of state for ideal gases and in deriving Ohm's law experimentally.Our teaching experience shows that the repetitive use of the control of variablesstrategy is very important in implanting the correct reasoning processes. Thestrategy applied to a variety of scientific topics also facilitates to a great extent theacquisition of new concepts.

The results presented in the second part of this report show that most of thestudents have difficulties in perceiving the possibility of an uncertain or ambi-guous answer; they do not see that there is not enough information to enablethem to draw a decisive conclusion. Conventional science education gives littleopportunity to such ambiguous cases. The small improvement achieved by theintervention, points to a strong resistance to change of this deficiency in logic.Unfortunately, this difficulty is often overlooked by teachers, although it seems tobe an important reasoning skill in any scientific analysis. Obviously, a lot more hasto be done in order to stimulate progress in this area.

Correspondence: Dr Judith Bransky, School of Education of the Kibbutz Movement,University of Haifa, Oranim, Tivon 36910, Israel.

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