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The Validity of Kolb LearningStyles and Neo-PiagetianDevelopmental Levels in CollegeBiologyAnton E. Lawson & Margaret JohnsonPublished online: 25 Aug 2010.

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Studies in Higher Education Volume 27, No. 1, 2002

The Validity of Kolb LearningStyles and Neo-PiagetianDevelopmental Levels in CollegeBiologyANTON E. LAWSONArizona State University, USA

MARGARET JOHNSONMesa Community College, Arizona, USA

ABSTRACT The Kolb learning styles and neo-Piagetian development levels of 366 students enrolledin a non-majors college biology course were assessed. Students then completed a one-semesterlecture/lab course within one of two instructional methods—inquiry or expository. The predictedinteraction between Kolb’s thinking/feeling learning dimension and instructional method was notfound. Instead, as predicted by neo-Piagetian developmental theory, the thinking/feeling dimensionand developmental level both correlated positively with course achievement under both instructionalmethods. Also as predicted by developmental theory, a signi� cant correlation between the Kolbthinking/feeling learning dimension and developmental level was found. Thus, the value of attempt-ing to match instructional method with Kolb’s thinking and feeling learning styles, which may in factre� ect differences in developmental level, is questioned. On the other hand, the � nding thatdevelopmental level did predict success within both instructional approaches supports neo-Piagetiantheory and implies that instruction should be designed to improve reasoning abilities.

Introduction

During the past several years, learning style—a student’s preferred way of acquiring and usinginformation—has been an active research area in adolescent and adult education. A generalintent of learning style research is to identify student learning styles and match them withinstructional methods to optimize learning (e.g. McCarthy, 1980; Berman, 1982; Kolb,1984; Merritt & Marshall, 1984; Posey, 1984; Boylan, 1986; Claxton & Murrell, 1987;Bonham, 1988; Green & Parker, 1989; Hudak & Anderson, 1990; Rhem, 1992; Harasym, etal. 1995; Kreber, 1998; Raschick et al., 1998; Drew, et al. 1999). A variety of instrumentssuch as the Can� eld Learning Inventory (Can� eld, 1980), the Kolb Learning Style Inventory(Kolb, 1985), and the Myers–Briggs Type Indicator (Myers, 1976) have been developed toassess learning styles. The Kolb inventory, which was developed primarily for use with adults,remains one of the most widely used (a recent electronic survey found 746 papers citingKolb’s work) in spite of serious questions about its validity (for a review and critique, seeReynolds, 1997).

ISSN 0307-5079 print; ISSN 1470-174X online/02/010079-12 Ó 2002 Society for Research into Higher EducationDOI: 10.1080/0307507012009938 6

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80 A. E. Lawson & M. Johnson

According to Kolb (1984), learning styles are expressions of human variability. Kolbclaims that just as natural selection has produced differences in skin and eye colour, it hasalso produced preferred ways of learning. In Kolb’s view, two dimensions underlie learningstyles. The � rst involves a preference for learning by thinking versus a preference for feeling.The second involves a preference for learning by doing versus a preference for observing.These two dimensions are assessed by a 12-item inventory in which each item asks learnersto rank four sentence endings. For example, one sentence begins: ‘I learn best when …’ andthe learner is asked to rank the following endings: I rely on my ideas; I rely on my feelings;I can try things out for myself; I rely on my observations. A summation of rankings thendetermines one’s overall preference or learning style.

Kolb (1984) and Karrer (1988) elaborate the four learning styles in the followingmanner. A high thinking score represents one who relies on logical thinking. Thinkers aremore oriented toward symbolism and less toward people. A high feeling score representsreceptive, experience-based learning that relies on feeling-based judgments. Feeling students� nd theoretical approaches unhelpful, but rather prefer to treat each situation as unique.They learn best from speci� c examples and peer discussion. A high doing score represents anactive orientation that relies on experimentation. ‘Doers’ presumably learn best with projects,homework, or in small group discussions. They dislike passive situations, such as lectures. Ahigh observing score indicates a tentative, impartial approach to learning. Lectures arepreferred.

In theory, learning styles interact in important ways with learning environments, suchthat speci� c styles are favored within speci� c environments. For example, ‘feelers’ arepresumably favored when the learning environment includes personal feedback, sharedfeelings, application of skills, teacher as coach/helper, and the learning is self-directed andautonomous (e.g. Kolb, 1984). In the sciences, these are characteristics associated withinquiry instruction (Lawson et al., 1989; Lawson, 1995). In Kolb’s view, feelers are hinderedby learning environments that involve theoretical readings. On the other hand, ‘thinkers’ arepresumably helped by such environments and hindered by precisely those factors favored byfeelers. Hence, Kolb’s learning style theory leads to the prediction that feelers should performbetter than thinkers within an inquiry instructional setting. Conversely, the theory leads tothe prediction that thinkers should perform better than feelers within the more commonexpository (inform–verify–practice) setting because it (1) directly informs students of what isto be learned, and (2) introduces new terms via less personal and more theoretical lecturesand textbook readings.

Neo-Piagetian Developmental Theory and Reasoning Levels

Another active area of research aimed at adolescents and adults involves the development ofreasoning systems. Much of this research in the sciences was initially conducted within theframework of Piagetian developmental theory (e.g. Inhelder & Piaget, 1958; Renner, et al.,1976) and more recently within the context of what has been called (by some) neo-Piagetiandevelopmental theory (e.g. Case, 1984; Commons et al., 1984; Lawson, 1985, 1995; Kuhn,1989). In general, children are thought to � rst develop reasoning systems based on manipu-lations of classes, relations and quantities. These descriptive systems relate to observableobjects, but not to verbally stated causal hypotheses. At the more developmentally advancedlevel, at least some adolescents and adults acquire systems that allow reasoning about thehypothetical, the causal, and involve deduction of the logical consequences of the hypotheses.Thus, reasoning is hypothetico-deductive in form and can lead to the effective test ofalternative causal hypotheses.

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Validity of Kolb Learning Styles 81

FIG. 1. Predicted pattern of achievement by thinkers FIG. 2. Predicted pattern of achievement by thinkers(T) and by feelers (F) in learning cycle and expository (T) and by feelers (F) in learning cycle and expositoryinstructional methods based on developmental instructional methods based on learning style theory.

theory.

The general intent of such research has been to better understand the nature of advancedreasoning and to identify factors that contribute to its development, so that instruction canbe carried out to help students become more effective reasoners (cf. American Association forthe Advancement of Science, 1989; Lawson et al., 1989; Adey & Shayer, 1990; Shayer &Adey, 1992; Lawson, 1995; National Committee on Science Education Standards andAssessment, 1995). The educational implication of such research is that instruction shouldtake into account students’ initial reasoning patterns, much as learning style theorists arguethat instruction should take into account students’ learning styles. However, the developmen-tal intent is not to present instruction in a student’s preferred learning style, but to actuallyprovoke the development of improved reasoning abilities.

Kolb’s Thinking/Feeling Dimension and Developmental Levels as Alternatives

There is reason to believe that Kolb’s thinking/feeling dimension and developmental levelsmay be related, because many of the terms and descriptions used by Kolb and others tocharacterize the thinking/feeling dimension are also used by researchers to characterizedevelopmental levels. Indeed, we wish to advance the hypothesis that responses on Kolb’sthinking/feeling dimension actually re� ect learning preferences of students at differing devel-opmental levels. More speci� cally, it may be that students at the ‘descriptive level’ ofintellectual development believe they learn best in a feeling mode, while more advanced‘hypothetico-deductive’ students believe that they learn best in a thinking mode. Thus, whileKolb learning style theory predicts that feelers should learn more than thinkers within inquiryinstruction, and that thinkers should learn more than feelers within expository instruction,the current hypothesis leads to different predictions. More speci� cally, if Kolb’s thinking styleis in fact a developmental advance over his feeling style, then thinkers should learn more thanfeelers under both inquiry and expository instructional methods. These alternative predic-tions are shown graphically in Figs 1 and 2. Note that Fig. 1 also predicts that inquiryinstruction should be superior to expository instruction. This prediction is based on boththeory and evidence reviewed in Lawson et al. (1989).

To summarize, Kolb’s theory leads to the following predictions.

(1) Thinkers should learn better than feelers within expository instruction. Feelers shouldlearn better than thinkers within inquiry instruction.

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82 A. E. Lawson & M. Johnson

(2) There should be no correlation between scores on the thinking/feeling dimension andcourse achievement (i.e. the thinking/feeling dimension re� ects learning styles ratherthan learning abilities).

(3) No correlation should exist between scores on the thinking/feeling dimension anddevelopmental level.

However, neo-Piagetian theory views Kolb’s thinkers as developmentally advanced overfeelers. So neo-Piagetian theory leads to the following alternative predictions.

(1) Thinkers should perform better than feelers regardless of instructional method. This ispresumably because learning science concepts often requires the use of hypothetico-de-ductive reasoning patterns (e.g. Lawson, 1995).

(2) There should be a positive correlation between scores on the thinking/feeling dimensionand course achievement (i.e. the neo-Piagetian interpretation is that Kolb’s thinking/feel-ing dimension re� ects learning abilities rather than styles).

(3) A positive correlation should exist between scores on the thinking/feeling dimension anddevelopmental level.

Method

Participants

Participants were 366 students (242 women and 124 men; mean age 5 23.1 years, SD 5 6.05years) enrolled in 16 lab sections of a one-semester non-majors biology course at a largecommunity college in the south-western part of the USA.

Design

Measures of Kolb learning style and neo-Piagetian developmental level were administered inlab sections of approximately 24 students per section on the � rst day the sections met.Administration of the 12-item Kolb inventory took approximately 15 minutes. Administra-tion of the developmental level test took approximately 30 minutes. All students were thentaught the one-semester biology course, with eight lab sections taught with the expositorymethod (181 students) and eight with the inquiry method (185 students). The expositoryinstructors had extensively employed this method in the past and used it by choice in theirnormal teaching activities. The inquiry instructors received instruction in how to teach viainquiry, and had successfully employed the approach prior to the present study. Conse-quently, the inquiry approach is now their approach of choice and is used in their normalteaching activities. Weekly visits to each class checked compliance to the designated instruc-tional methods. Instructors in both instructional methods designed, administered and gradedtheir own quizzes and examinations during the semester. A common � nal examination, whichwas not previously seen by any of the instructors, was administered to all students on the lastday of the semester.

Kolb Learning Style

The 12-item Kolb Learning Style Inventory (Kolb, 1985) was used to assess learning style.A total score for each of the four learning styles (i.e. thinking, feeling, doing, observing) wasobtained for each student. Composite scores for the thinking/feeling dimension (i.e. thinkingscore minus feeling score) and the doing/observing dimension (i.e. doing score minus

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Validity of Kolb Learning Styles 83

observing score) were also obtained for each student. Split-half reliabilities (i.e. correlationbetween the sum of the student scores on the � rst half of the test with the sums an the secondhalf) of each learning style score were as follows: thinking 5 0.77, feeling 5 0.63, doing 5 0.82and observing 5 0.74. These coef� cients are similar to those reported by previous investiga-tors. Scores for each learning style were then used to derive two composite scores for eachstudent. The � rst composite score was derived by subtracting the feeling score from thethinking score, and the second by subtracting the observing score from the doing score.

Neo-Piagetian Developmental Level

Neo-Piagetian developmental level was assessed by use of a two-item pencil and paper test.The � rst item, shown in Appendix 1, required students to identify and control variables todetermine whether or not a dog’s age in� uenced the judge’s score in a dog show. The seconditem (after Karplus & Karplus, 1970) required use of proportional reasoning to estimate theheight of an imaginary � gure called Mr Tall, given information about the height of Mr Short.The item, which included a drawing of Mr Short, was worded as follows:

The � gure below is called Mr. Short. We used jumbo paper clips clipped end-to-endto measure Mr. Short’s height starting from the � oor between his feet and going tothe top of his head. His height was four jumbo paper clips. When we took a similar� gure called Mr. Tall and measured him in the same way, he turned out to be sixjumbo clips tall. Mr. Short measured with small paper clips turns out to be 6 smallpaper clips tall. What would the height of Mr. Tall be if measured with the samesmall paper clips? Please show (or explain) how you arrived at your answer.

Scoring. Items were judged correct (a score of one) if the correct answer and an adequateexplanation or set of calculations were present. Otherwise items were scored zero. Allresponses were scored anonymously by a single rater. Students who scored zero on bothitems were classi� ed as descriptive reasoners. Students who scored one of two were classi� edas transitional reasoners, while students who scored two of two were classi� ed as hypothetico-deductive reasoners. These labels correspond to what is believed to be the key feature thatseparates these two developmental levels—namely, the ability to initiate verbal argumentsabout causal situations and to reason in a hypothetico-deductive manner, rather than in thedevelopmentally earlier descriptive manner. Details of this theoretical position can be foundin Lawson (1995).

One might question whether something as complex as developmental level can bemeaningfully assessed with a relatively brief two-item test. Shayer & Adey (1981) concludedthat ‘Within certain limits set by the reliability of the tasks, it is possible from two or threesamples of a pupil’s performance to characterize his/her capacity in terms of the level at whichhe/she presently functions’ (p. 66). In fact, Lawson (1987a) found evidence that a single itemmay be suf� cient. High school students were � rst classi� ed into developmental level based onone proportional reasoning item. Following instruction in reasoning to a contradiction, 71%of the hypothetico-deductive reasoners, so identi� ed, but only 20% of the descriptivestudents, successfully applied the reasoning pattern to a new context. Con� dence in thevalidity of using only two items was further bolstered by the results of two pilot studiesconducted during two previous semesters. The studies utilized the 12-item Classroom Testof Scienti� c Reasoning (Lawson, 1978, 1987b) to assess developmental level. Percentages ofdescriptive, transitional and hypothetico-deductive students were similar in each of thosesemesters and in the semester in which the present study was conducted. The results of thepresent study also provide reason to believe that the two items constitute a valid measure of

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84 A. E. Lawson & M. Johnson

developmental level, because performance on the two items turned out to be a goodachievement predictor within both instructional settings. In other words, developmentaltheory led to the prediction that reasoning ability—if measured in a valid way—shouldsigni� cantly predict course achievement, and the results showed that reasoning ability, asmeasured, did signi� cantly predict achievement. Thus, the items have predictive validity—sometimes referred to as criterion-related validity (Anastasi, 1968).

Learning Cycle and Expository Instructional Treatments

Both inquiry and expository instructional treatments consisted of an entire one-semesternon-majors biology course. The course consisted of three 50-minute lectures and one 3-hourlab per week for 15 weeks. Two instructors (one male and one female) taught lectures andlabs using the inquiry method, and two instructors (one male and one female) taught usingthe expository method. Each instructor had approximately 48 students in each of two lecturesections and 24 students in each of four lab sections. Both treatments presented biologicalconcepts in the ‘micro to macro’ sequence (i.e. beginning with the atomic/molecular levels oforganization and ending with the ecosystem/biosphere levels). Both treatments used the textUnderstanding Biology by Raven & Johnson (1991).

Each instructor controlled his/her own class pace. One expository instructor assignedportions of 23 chapters, the other 17 chapters. One inquiry instructor assigned portions of 23chapters, the other 21 chapters. Thus, the number of chapters assigned in the two instruc-tional approaches was similar. All four instructors introduced the following topics: the cell,chemistry, organic molecules, bonds, genes, photosynthesis, cellular respiration, mitosis,meiosis, Mendelian genetics, natural selection and evolution.

Inquiry instruction employed an approach called the learning cycle—an approach � rstdeveloped by the Science Curriculum Improvement Study during the late 1960s and 1970s(see Lawson et al., 1989, for a brief history). Learning cycles consist of three phases calledexploration, term introduction and concept application. During exploration, students explorenew materials and phenomena that raise questions and encourage students to seek answers.Student exploration may involve the gathering of data that may reveal patterns or allow thetesting of hypotheses. This in turn leads to the term introduction phase, in which theinstructor introduces terms to label the identi� ed patterns or concepts. Lastly, during conceptapplication, new contexts are identi� ed in which the newly introduced terms can be appliedand consequently become better understood. For example, consider how the learning cyclewas used to introduce the concept of mitosis. During exploration, students attempted to � ndout how multicellular organisms grow by making microscopic examinations of preservedonion root tip cells in the lab. Those observations revealed what appeared to be either cells‘caught’ at different stages in division or different ‘types’ of cells. To test these alternativehypotheses, students � rst attempted to sequence the cell ‘types’ into possible stages ofdivision. They then observed a time lapse � lm of a single living root tip cell to discoverwhether or not it changed (i.e. if the cell ‘types’ represent a single cell type dividing, then the� lm should reveal changes similar to the proposed sequence; on the other hand, if the cell‘types’ are in fact different types of cells, then the � lm should reveal no changes inappearance). Once the � lm was viewed, students saw that the cell underwent changes similarto those in proposed sequence. Therefore, the cell division hypothesis was supported and thealternative hypothesis was not supported. The instructor now introduced the term mitosis torefer to the part of the division process in which chromosomes replicate and migrate to thenewly formed daughter cells. As part of the concept application phase of instruction, students

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Validity of Kolb Learning Styles 85

then observed other portions of both plants and animals to see if evidence of mitosis couldbe found there as well.

Lawson et al. (1989) identify three types of learning cycles that differ primarily in theextent to which students only describe and name what they � nd or explicitly generate and testalternative hypotheses to explain their observations. A key element of the learning cyclemethod is that lab activities precede lectures that deal with the same concepts.

As mentioned, lectures come � rst in the expository method. Thus, a concept, or groupof related concepts, is verbally introduced and explicated in lecture and then the lab activitiesfollow. Labs are used to establish the validity of and reinforce the previously introducedconcepts. Thus, to introduce the mitosis concept using the expository approach, the instruc-tors, during a lecture, told students that the process of mitosis was going to be discussed.They then described the stages in mitosis and only then allowed students to go to the lab tomake microscopic observations of dividing cells. In essence, within the expository approach,labs do not effectively initiate scienti� c inquiry because students have already been told whatconcepts will be exempli� ed in the lab.

Course Achievement

To evaluate course achievement, instructors developed and administered a series of labquizzes and three lecture examinations. These measures were not the same across instructors.However, all students took the same � nal examination, which consisted of 50 multiple-choiceitems from the 80 that appear in Version B of the 1987 National Association of BiologyTeachers/National Science Teachers Association High School Biology Examination. Theitems were selected by an independent evaluator and reviewed by a second evaluator toestablish suitability for use in the present study. Instructors did not see the items prior toadministration.

Results and Discussion

Descriptive Results

Based on responses on the test of development level, 131 students (36%) were classi� ed asdescriptive thinkers, 144 (39%) were classi� ed as transitional, and 91 (25%) were classi� edas hypothetico-deductive thinkers. Scores on the doing/observing learning style dimensionranged from 2 29 to 1 30. These scores were found not to be related to developmental levelor to course achievement and will not be discussed further. Scores on the thinking/feelingdimension also ranged from 2 29 to 1 30.

The Thinking/Feeling Dimension, Developmental Level, and Achievement within Each InstructionalMethod

Fig. 3 shows the relationship between the thinking/feeling scores and instructor-generatedachievement (lab quizzes and lecture examination scores) in both the inquiry and expositorysections. Only the achievement scores for students in the extreme thinking and extremefeeling categories are shown. Achievement scores for students in the intermediate learningstyle categories were between those shown. As can be seen, the results reveal the patternpredicted by neo-Piagetian developmental theory (Fig. 1) but not the pattern predicted byKolb learning style theory (Fig. 2). Neither of the main effects due to learning style orinstructional method reached statistical signi� cance (F4,322 5 0.96, p 5 0.43 and F1,322 5 2.74,

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86 A. E. Lawson & M. Johnson

FIG. 3. Pattern of course achievement (per cent) by thinkers (T) and by feelers (F) in learning cycle and expositoryinstructional methods.

p 5 0.09 respectively); and no signi� cant interaction effect was found (F4,322 5 0.12,p 5 0.98).

Relationships of the Thinking/Feeling Dimension and Developmental Level with Common FinalExamination Performance

Table I shows mean scores in each of the � ve thinking/feeling learning style categories andcommon � nal examination scores for students in both the inquiry and expository sections.Analysis of variance found a signi� cant effect for the thinking/feeling learning style(F4,322 5 3.04; p , 0.01), and for instructional method (F1,322 5 24.12; p , 0.0001), but notfor the interaction between learning style and instructional method (F4,322 5 0.15; p . 0.96).These results are essentially those predicted by neo-Piagetian theory and not those predictedby Kolb’s learning style theory. As mentioned, Kolb’s theory claims that the thinking/feelingdimension re� ects differences in preferred ways of learning, but not in learning abilities.Thus, no overall relationship should have been found between the thinking/feeling dimensionof � nal examination performance. On the other hand, the results in Table I supportneo-Piagetian theory as the thinkers, particularly those in the top category, achieved morethan the feelers under both instructional methods. Also as expected based on neo-Piagetiantheory, developmental level correlated positively with achievement. Hypothetico-deductivestudents averaged 65.78%; transitional students averaged 60.04%; and descriptive studentsaveraged 53.08% on the common � nal examination (F2,306 5 20.32, p , 0.001).

Relationship between the Thinking/Feeling Dimension and Developmental Level

Table II shows the relationship between the thinking/feeling learning style dimension anddevelopmental level. Some students of each developmental level are found in each of the � vethinking/feeling learning style groups, ranging from extreme feelers in the top row to theextreme thinkers in the bottom row. Although there are some hypothetico-deductive studentswith a feeling learning style (i.e. 7 of the 43 in the top row 5 16%) and there are somedescriptive students with a thinking learning style (i.e. 2 of the 29 in the bottom row 5 7%),

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Validity of Kolb Learning Styles 87

TABLE I. Final examination scores (per cent) for students in each of the � vethinking/feeling learning style groups for each instructional method

Instructional method

Thinking/feeling Learning stylescore* Inquiry Expository group mean

2 30 to 2 10 60.88 55.50 58.362 9 to 2 1 61.74 53.80 58.180 to 10 62.16 54.42 58.4211 to 20 63.46 54.16 58.4021 to 30 71.12 65.86 67.92

* Low scores re� ect the feeling learning style. High scores re� ect thethinking learning style.

the table reveals a signi� cant relationship between the thinking/feeling dimension anddevelopmental level (c2 5 37.9, df 5 8, p , 0.001).

As a further analysis of the relationship between the thinking/feeling dimension anddevelopmental level, the mean score of the descriptive students on the thinking/feelingdimension was found to be 1.09, compared to 4.95 for the transitional students and 6.21 forthe hypothetical-deductive students (F2,363 5 7.36, p , 0.001). In other words, as expected,based on neo-Piagetian theory, the thinking/feeling dimension and developmental level donot appear to be independent variables.

Conclusions and Implications

Because the results are essentially those predicted by neo-Piagetian developmental theory,and not those predicted by Kolb learning style theory, they represent evidence for the validityof the former and not the latter. Contrary to Kolb learning style theory, thinkers were betterlearners than feelers under both instructional methods. Kolb’s theory argues that thinkers andfeelers do not have different learning abilities, just different learning styles. The � nding thatstudents with these styles did not do better when the instructional method presumablymatched their preferred learning style is evidence that Kolb’s learning styles, if they evenexist, do not interact with instructional methods in the expected way. In other words, Kolb’slearning style inventory appears to lack predictive validity (cf. Reynolds, 1997). Harasym, et

TABLE II. The relationship between Kolb’s thinking/feeling learning style dimensionand developmental level

Thinking/feeling Developmental level

Learning style score* Descriptive Transitional Hypothetical

2 30 to 2 10 19 17 72 9 to 2 1 39 25 10 to 10 46 58 3411 to 20 25 29 1921 to 30 2 15 12

c2 5 37.9, d.f 5 8, p , 0.001.* Low scores re� ect the feeling learning style while high scores re� ect the thinkinglearning style.

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88 A. E. Lawson & M. Johnson

al. (1995) found similar results in the context of a college-level anatomy and physiologycourse. The implication for college-level biology instruction, and perhaps for other levels andkinds of instruction as well, is that it may not be productive to try to match instructionalmethod with Kolb’s learning styles. On the other hand, the � nding that developmental leveldid predict success within both instructional approaches supports neo-Piagetian theory andimplies that instruction should be designed to improve reasoning abilities. As mentioned,several studies reviewed by Lawson et al. (1989) detail how this can be done within thesciences. Kral (1997) describes results of his use of the same pedagogical principles in atwelfth grade English course, which led to signi� cantly greater gains than control classes onboth the English and science sections of a widely used college entrance examination (theAmerican College Test). These results suggest that the inquiry (learning cycle) approach hasthe potential for successful application in wide variety of disciplines.

Acknowledgement

This material is based upon research partially supported by the National Science Foundationunder grant No. DUE 9453610. Any opinions, � ndings, and conclusions or recommenda-tions expressed in this publication are those of the authors and do not necessarily re� ect theviews of the National Science Foundation.

Correspondence: Anton E. Lawson, Department of Biology, Arizona State University, Tempe,Arizona 85287–1501, USA.

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90 A. E. Lawson & M. Johnson

Appendix 1.

1. Five different dogs were entered in a dog show. Each dog’s breed, age, weight, color and � nal judge’s scoresare shown in the table. Which two dogs would you select to make a fair comparison to � nd out if age makesa difference in the judge’s scores?

Dog Breed Age Weight Color Judge’s(years) (pounds) score

1 Collie 3 40 Tan 852 Bulldog 4 38 Brown 753 Collie 4 40 Tan 954 Bulldog 3 42 Brown 605 Collie 4 38 Yellow 75

I would choose dogs .Please explain your choice.

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