Identification of student misconceptions in genetics problem solving via computer program

JOURNAL OF RESEARCH IN SCIENCE TEACHING VOL. 25, NO. 9, PP. 747-761 (1988)

IDENTIFICATION OF STUDENT MISCONCEPTIONS IN GENETICS PROBLEM SOLVING VIA COMPUTER PROGRAM

MARK E. BROWNING

Department of Biological Sciences, Purdue University, West Lafayette, Indiana 47907

JAMES D. LEHMAN

Department of Education, Purdue University, West Lafayette, Indiana 47907

Abstract

A genetics problem practice program and tutor on microcomputer was used by 135 undergraduate education majors enrolled in an introductory biology course at Purdue University. The program presented four genetics problems, two monohybrid and two dihybrid, and required the users to predict the number and type of each class of offspring. Student responses were recorded on diskette and analyzed for evidence of misconceptions and difficulties in the genetics problem-solving process. Three main areas of difficulty were identified: difficulties with computational skills, difficulties in the determination of gametes, and inappropriate application of previous learning to new problem situations.

Introduction

According to Trembath (1984), educators have been investigating student misconceptions for some 100 years. Piaget (1951) reported on significant work concerning the origins and nature of “child artificialism,” or what today would be called children’s misconceptions, as early as 1929. But it has only been in the last decade or so that educational research has seriously considered the issue of misconceptions (DiSessa, 1987; Mintzes & Amaudin, 1984).

Science educators now recognize that deeply engrained misconceptions often pose problems in physics, chemistry, and biology (e.g., Renner, Marek, Abraham, & Grzybowski, 1987). In physics, for example, the simplicity, familiarity, and congruence with common experience of many common misconceptions contributes to their persistence (Champagne, Klopfer, & Anderson, 1980; Champagne, Klopfer, & Gunstone, 1982). Often, student misconceptions resemble views once considered valid in the history of science such as the Aristotelian view of physics. Similarly, in chemistry, Ben-Zvi, Eylon, and Silberstein (1986) report that students’ perceptions of the chemical structure of matter are like those of the ancient Greeks. Others

0 1988 by the National Association for Research in Science Teaching Published by John Wiley & Sons, Inc. CCC 0022-4308/88/09747- 15$04.00

748 BROWNING AND LEHMAN

have noted similar premodern views in the biological sciences (Bishop & Anderson, 1986; Clough & Wood-Robinson, 1985b; Wandersee, 1985).

Yet not all problem areas that are labeled misconceptions in the literature fit the picture of persistent erroneous concepts arising from common experience or a primitive world view. Especially in the biological sciences, it is clear that formal instruction may promulgate or at least fail to rectify misconceptions (Barrass, 1984; Cho, Kahle, & Nordland, 1985; Griffiths & Grant, 1985). The fault may lie in instruction that is too simplistic, too cognitively advanced, inconsistent, or insufficiently oriented toward conceptual linkages and the proper sequencing of concepts. In biology, one area of particular concern that may involve conceptual difficulties arising from instructional practice is the study of genetics.

Research into student misconceptions and learning difficulties in the area of genetics is a relatively new endeavor (Hildebrand, 1985). The literature of this new field is generally centered around two themes: the identification of misconceptions and their elimination. Several techniques have been used to pinpoint areas of student difficulties. These include audiotaped structured interviews (Clough & Wood-Robinson, 1985a, 1985b; Deadman & Kelly, 1978; Hackling & Treagust, 1984; Longden 1982); videotaped problem solving (Smith & Good, 1984); essay questions (Brumby, 1982, 1984) and "think-aloud" techniques (Stewart, 1982, 1983; Tolman, 1982). While effective, these techniques often are difficult and time consuming in practice. A computer might provide a more efficient means of identifying and addressing student misconceptions. This article reports on the results of a study in which a microcomputer program was utilized to identify student misconceptions and problem- solving difficulties in genetics.

Background

Genetics is a central part of the secondary and collegiate biology curriculum. The understanding of genetics is important not only to the understanding of biology but to the impact of biology on society as well. Recently, several researchers have begun to examine student problem solving in genetics. This research has shed light on student misconceptions and problem-solving difficulties.

Using think-aloud techniques, Stewart (1982) examined the knowledge and problem solving abilities of 14 ninth-grade biology students as they worked three types of simple genetics problems. The subjects attempted about 100 genetics problems with only about 10 failures. Stewart maintains that the high success rate was due to the fact that the problems were similar to those the subjects had seen in their genetics instruction. The main finding of this study was that meaningful problem solving in genetics is based in part on an understanding of the role of meiosis in genetic inheritance. In addition, Stewart, like Longden (1982), found that some subjects had difficulty stating the relationship between certain genetic terms such as gene and allele, allele and chromosome, etc.

Stewart (1983) reported another data-gathering study that utilized 27 high school biology students. This study focused on the procedural and conceptual knowledge evinced by the subjects as they each solved a monohybrid and a dihybrid problem. Stewart found that three of the subjects could not even begin the monohybrid problem because they could not construct a proper allelic key. These subjects had similar difficulties with the dihybrid problem. Another seven subjects successfully

IDENTIFICATION OF STUDENT MISCONCEPTIONS 149

completed the monohybrid problem, but had difficulty with the dihybrid task. Among other problems, these seven had difficulties constructing allelic keys and determining the genetic composition of the parental gametes. Although 17 subjects produced correct solutions to both problems, Stewart warned that most were not meaningfully solving the problems because they were unable to connect meiosis to the problem solutions.

Another study of secondary school students was reported by Tolman (1982). He studied the problem-solving performance of 30 high school students who had completed a sophomore-level biology course. The subjects were asked to solve a monohybrid problem, a codominance problem, and a sex-linked problem. Only 20% of the subjects solved the monohybrid problem, 40% the codominance problem, and 63% the sex-linked problem. A common error committed by the subjects in the monohybrid and codominance problems was that the gametes contained both genes from the pair in question. Interestingly, Tolman found that his subjects were less likely to make the same error in the sex-linked problem.

While Stewart (1982, 1983) and Tolman (1982) studied American students, Longden (1982) examined the problems faced by 10 well-motivated British high school students while learning genetics. He discovered that students had trouble with the relationships between genes and alleles, chromatids and chromosomes, and DNA synthesis and meiosis. Some students, like those in a study by Stewart (1983), found the proper assignment of symbols to alleles a difficult task. Finally, Longden writes, “the most frequent unsolicited explanation of difficulties in genetics was related to the mathematical elements of the topic” (1982, p. 137).

At the post-secondary level, Smith & Good (1984) analyzed the problem- solving behavior of I 1 undergraduates and nine graduate students and instructors who were asked to solve seven genetics problems. The investigators discovered 32 problem-solving behaviors in which novices differed from experts. Some behaviors were related to problem solving in general; for example, novices were more likely to view problem solving as a task requiring the use of memorized patterns of response. Experts, on the other hand, approached problems using task analysis and reason as tools. Other behaviors were more domain specific, such as the tendency of experts to make fewer errors concerning gene number than the novices. Also, experts had a better grasp of gametogenesis and fertilization, which are biological processes vital to genetic inheritance.

The studies cited above have shown that specific misconceptions and difficulties in the genetics problem solving process can be identified. The goal of the study reported herein was to examine the genetics problem solving of a large sample of undergraduate nonmajors using a new methodology, specifically, the use of a computer program.

Computers already have demonstrated value as tools for open-ended genetics exploration; a number of genetics simulations for education now are commercially available. A microcomputer program was chosen as the data-gathering tool in this study for several reasons. With a computer program, student responses can be recorded on floppy disk and easily retrieved for analysis. Since the data-gathering program can be reproduced exactly, a number of subjects can participate in the study simultaneously. Additionally, precise reproduction of the program insures consistency of response to students showing signs of the same misconceptions or difficulties. The time savings relative to methodologies such as individual interviews


are significant, so that a large sample can be examined. While computer-based data accumulation will not replace other methodologies, it represents a significant research tool that can complement or supplement the sorts of information gleaned from more in-depth techniques such as interviews. Finally, identification of misconceptions and errors in the genetics problem solving process via computer represents the first step toward the development of an “intelligent” genetics tutoring program. Such a program would identlfy student problem areas and then provide corrective instruction tailored to the specific, idiosyncratic errors of each individual student. Indeed, one research group now reports work on the development of an intelligent tutoring system for genetics (Streibel, Stewart, Koedinger, Collins, & Jungck, 1987).

Methods and Materials

The subjects were 132 female and three male undergraduate students, all of whom were elementary education majors enrolled in the second semester of a two- semester course in introductory biology at Purdue University. Approximately 28% of the subjects were freshmen, 41% were sophomores, 22% were juniors, 7% were seniors, and 1% were unclassified.

A major focus of the course was an examination of genetics. Prior to engaging in this study, the students had completed a seven-week experiment using Drosophilu. The students had conducted a dihybrid cross experiment with flies carrying an autosomal and a sex-linked recessive trait. Offspring were examined and the results tallied by the class through the F2 generation. Each student was then to write a major paper in which he or she proposed a symbolic model that could explain the results of the experiment. The model was to be used to predict the expected numbers of offspring from the crosses, and these predictions were to be compared to the actual results for goodness of fit.

From a teaching standpoint, the emphasis of the Drosophila experiment was on discovery as opposed to expository learning. Students were expected to derive aspects of their symbolic model (two genes, gene dominance, etc.) from the ex- perimental evidence and, thereby, “discover” modern gene theory. As such, it is important to note that the subjects in this study differ from those in more typical biology courses in that they were not exposed to formal instruction in genetics problem solving. However, prior to taking part in this study, the subjects had been through a class exercise in the construction of a symbolic model, prediction of genotypes and phenotypes from crosses, and the prediction of number of offspring from crosses.

The microcomputer program used in the study was a pilot version of a genetics problem practice program and tutor designed by the investigators and written in Turbo Pascal (Borland International) for a 256K IBM-PC or compatible.* From a curricular standpoint, the object of the program was to review the components of the genetics model developed in class and to give the students practice in predicting the results of genetic crosses. Two traits, body size and color, of an undefined

* Interested readers may obtain a compiled copy of the current version of the program used in this study, suitable for MS-DOS or PC-DOS computers, by sending a blank, double-sided, 5W’, 360K diskette and a self-addressed, stamped mailer to the authors.

IDENTIFICATION OF STUDENT MISCONCEPTIONS 75 1

organism were considered in both monohybrid and dihybrid crosses. Reference to specific Drusophila characteristics was not made to avoid confusion with the students’ experiment. Consideration of sex linkage was omitted for simplicity.

The program presented four genetics problems: two of the monohybrid type and two of the dihybrid type (see Figure 1). Each problem began with a presentation of the genetic cross being made with parental genotypes and phenotypes given, and a total number of offspring set (a randomly selected multiple of 1600). Using the parental characteristics and the given number of offspring, each subject was asked to make a prediction concerning the physical characteristics and numbers of each type of offspring (i.e., the F1 generation).

The subject entered the prediction into the computer to be recorded and judged for correctness. If the prediction was correct, the subject received a congratulatory message from the program and then was allowed to try another genetics problem. On the other hand, subjects whose responses were judged to be incorrect were directed by the program through a step-by-step solution to the problem. The solution steps involved a determination of the following: the genetic composition of the parental gametes, the genotypes of the zygotes using a Punnett square, the phenotypes associated with selected zygotic genotypes, the ratio of those phenotypes, and, once

P r o b l e m 1 M o t h e r F a t&r

P h e n o t y p e Long Long

G e n o t y p e A a A a

P r o b l e m 2 M o t h e r F a t h e r

P h e n o t y p e G r e e n B1 u e

G e n o t y p e b b B b

P r o b l e m 3 M o t h e r F a t h e r

P h e n o t y p e L o n g , B l u e Long , B l u e

G e n o t y p e AaBb AaBb

P r o b l e m 4 M o t h e r F a t k c

P h e n o t y p e L o n g , B l u e S h o r t , B 1 u e

G e n o t y p e A a B b a a B b

Where: A = l o n g a l l e l e ( d o m i n a n t ) a = s h o r t a l l e l e B = b l u e a l l e l e ( d o m i n a n t ) b = g r e e n a l l e l e

Fig. 1. Genetic crosses presented by the program.


Yes Meiosis Tutor ia l

1 I

again, a prediction of expected numbers of offspring. At each step of the problem solution the subjects’ responses were recorded; these responses are the sources of the data presented in this article. (A simplified flow chart of the program is presented in Figure 2.)

The program was incorporated into the students’ normal laboratory work about midway through the 1986 spring semester. The study followed completion of the Drosophilu experiment and class genetics model-building exercise but preceded the writing of the genetics paper. The subjects’ participation in the study was mandatory and considered part of their laboratory work. Groups of six to eight students were

Yes Meiosis Tutor ia l

1 I

I

J, Yes

S e l e c t and d i s p l a y problem

nput gamete

I

Yes Display c o r r e c t p r e d i c t i o n

No 6-

I Display c o r r e c t r a t i o

No T

Input pheno tvpe r a t i o

1 phenotypes

Dominance Tutoria l

Phenotype

[ I d r i l l Phenotype i d e n t i f i c a t i o n T N o c l d r i l l OK?

Fig. 2. Simplified program flowchart.


TABLE I Number and Percent of Subjects with Incorrect Problem

Predictions on the First Attempts (n = 135)

P r o b l e m N o . S u b l e c t s P e r c e n t

8 4

3 4

8 8

6 2

6 2 %

2 5 %

6 5 %

4 6 %

rotated through a laboratory of eight Zenith 150 microcomputers (BM-PC compatibles) over a period of about two weeks. Each subject interacted with the program individually and was allotted two hours to complete it. The average completion time was about 50 minutes. One or the other of the investigators was present at all times during the study to handle hardware and software problems; however, the investigators did not assist with genetics problem solving.

Once all of the subjects had completed the program, the recorded data were printed out and then analyzed by the investigators who noted the types and frequencies of errors. The data were tabulated manually because program inadequacies led to procedural errors and format errors (i.e., unexpected yet correct inputs) that were judged as incorrect solutions by the program but that a human judge would ignore as trivial. To circumvent the format error problem, all student responses subject to such errors were checked by the investigators. The analysis showed that initially about 10% of the subjects committed format errors, but the percentage fell as they gained experience. A more recent version of the program has been designed to prevent these format errors.

Results and Discussion

Table 1 shows the number and percent of the 135 subjects who, for each problem, failed to correctly predict the physical characteristics and numbers of each type of offspring. Overall, the subjects’ performance on the first monohybrid cross and the first dihybrid cross, i.e., problems 1 and 3, was poor, as over 60% of the subjects failed to make accurate predictions. At least in part, the poor performance was probably due to the fact that the subjects’ coursework did not emphasize traditional genetics problem solving.

In spite of their poor start, the subjects showed improvement on the second cross of each type, i.e., problems 2 and 4. The improvement in performance on the second problems can probably be attributed to the assistance provided by the program when mistakes were encountered on the first problem. Since dihybrid crosses are generally more difficult than monohybrid crosses, it is not surprising that the subjects’ improvement in dihybrid problem performance was not as great as that in the monohybrid case.


An analysis of the specific errors for the first prediction may be found in Table 11. One error was found consistently across all first predictions, while others were more problem specific. The error noted across problems involved correct phenotypes but incorrect numerical predictions. Such a mistake accounted for 6%, 12%, 17%, and 15% of the prediction errors on the first, second, third, and fourth problems, respectively. This error, and a similar one to be examined concerning the second prediction attempts, indicate the likelihood that subjects committing such mistakes had some weakness in computation skills.

TABLE 11 Common Specific Errors on the First Prediction Attempt

Problem 1 (n=96) Prediction contained genotypes instead of

requested phenotypes ......................... 37% All offspring had "long" phenotype . . . . . . . . . . . . . . . . 27% Re s pond e d w i t h " 1 on g " phenotype mu I t 1 1' 1 e

times ......................................... 1 2 % Entered correct phenotype, but prediction of

number of offspring was wrong . . . . . . . . . . . . . . . . . 6 % Other (miscellaneous/no answer) .................... 17%

Problem 2 (n=37) Phenotype was correct, but ratio of offspring

Phenotype was correct, but number of offsprlng

Phenotype was wrong, i.e. "long" . . . . . . . . . . . . . . . . . . . 9% Other (miscellaneous/no answer) .................... 27%

was in a 3:l ratio.. .......................... 47%

was wrong and not in 3:l ratio . . . . . . . . . . . . . . . . 12% Only "blue" phenotype reported ..................... 6%

Problem 3 (n=90) Only offspring with "long, blue" phenotypes

Entered correct phenotypes, but prediction of

Phenotypes were monohybrid-like .................... 14%

"Long,blue" phenotype reported twice . . . . . . . . . . . . . . . 7% Only "lon9,blue" and "short,green" phenotypes

reported ...................................... 6% Reported dihybrid-like and monohybrid-like

phenotypes .................................... 5 % Other (miscellaneous/no answer) .................... 2 5 %

reported ...................................... 18%

number of offspring was wrong . . . . . . . . . . . . . . . . . 17% Certain phenotypes omitted ......................... 9%

Problem 4 (N=64) Entered correct phenotypes, but prediction of

Reported only "short,blue" and "long,blue" phenotypes .................................... 13%

Reported phenotypes in 9:3:3:1 ratio . . . . . . . . . . . . . . . 13%

Phenotypes were incorrect, but predicted

number of offspring was wrong . . . . . . . . . . . . . . . . . 15%

Certain phenotypes omitted ......................... 11%

offspring numbers were correct . . . . . . . . . . . . . . . . 88 Other (miscellaneous/no answer) .................... 41%


In three of the four problems, a noteworthy number of subjects incorrectly predicted that all offspring would show the dominant phenotype(s). For example, 27% of the subjects making errors on the first prediction of problem 1 thought all offspring would have the “long” phenotype. Similar errors were made by 6% of the subjects on problem 2 and by 18% on problem 3. This might be indicative of a fundamental lack of understanding of dominance and recessiveness. But, more likely, subjects making this error were probably incorrectly attempting to generalize the results of their genetics experiment. In their laboratory experiment, the subjects had first crossed fruit flies that were homozygous dominant for a particular gene pair with flies that were homozygous recessive. Although the resulting offspring carried both the dominant and recessive alleles, only the trait variation controlled by the dominant allele was evident. Apparently, some subjects were trying to apply these familiar results to new genetics problems, with little success.

Another example of improper generalization appeared in the first prediction of the second problem. It should be noted that the correct phenotypic ratio for the first problem was 3: 1, but for the second problem it was 1 : 1. Interestingly, 47% of those making errors on the first prediction of the second problem predicted the offspring types would be present in a 3:l ratio, in spite of the fact that the two problems were very different.

The first prediction of the first problem produced a somewhat puzzling error: 37% of the subjects apparently confused the terms genotype and phenotype. The error occurred despite the fact that the subjects saw examples of genotypes and phenotypes when the parental information was displayed at the beginning of the problem. This error probably resulted from the course’s “discovery” learning approach, which delayed introduction of common terms such as genotype and phenotype until relatively late in the term. This problem was quickly overcome, however, because the error was not repeated in subsequent problems.

A subject’s success on the first prediction, as judged by the program, determined what would happen next. If the program detected no errors in a subject’s prediction, the subject was then given the next problem to solve. However, if the program detected error(s) in a subject’s prediction, it assumed the subject could not solve the problem and proceeded to lead the subject, step, by step, to the solution. The first step toward the solution was a determination of the genetic composition of the parental gametes. After the subjects completed their work with the gametes, they were asked to use an on-screen Punnett square to determine the genotypes of a portion of the possible zygotes. Once the zygotic genotypes were established, the subjects were required to translate each unique genotype into a phenotype. The subjects next had to determine the ratio of those phenotypes. After determining the phenotypic ratio, the subjects then used the ratio information to produce a numerical prediction outlining the expected number of each type of offspring. The second prediction attempt was the final subtask in the solution chain.

Table I11 summarizes the percents of incorrect solutions to each of the problem subtasks for each of the four problems. [Note: The discrepancy between the numbers of subjects who made incorrect problem predictions on the first attempt as reported in Table I and the higher numbers who attempted the problem subtasks as reported in Table I11 is due to a program flaw. Several students, a total of 12 (96-84) on problem 1 for example, produced valid predictions but made some sort of format error when they entered their predictions. Review of the data recorded on diskette


TABLE III Percents of Incorrect Solutions to Problem Subtasks*

P r o b l e m S u b - T a s k

P r o b l e m Number 1 ( n = 9 6 ) 2 ( n = 3 7 ) 3 ( n = 9 0 ) 4 ( n = 6 4 )

D e t e r m i n a t i o n of gametes 489, 5 9 % 9 3 % 7 3 %

D e t e r m i n a t i o n of z y g o t e s 2 % 3 % 79, 1 4 %

- ~ _ _ _ _ -

D e t e r m i n a t i o n of z y g o t i c p h e n o t y p e s 109, 11% 5 % 3 %

__-___

D e t e r m i n a t i o n of p h e n o t y p i c r a t i o 299, 7 1 % 1 4 % 2 7 %

P r e d i c t i o n of cross o n 2 n d a t t e m p t 2 3 % 359, 3 6 % 5 3 %

*Note: Only those subjects whose first prediction attempts were judged to be incorrect were required to complete the problem subtasks.

by the researchers identified these errors. The format errors caused the program to judge the predictions as incorrect. As a result, these students were forced through the problem subtasks although they had actually predicted correctly. The inclusion of these students may have biased the subtask data to some extent.]

Table I11 indicates that the subjects who attempted the problem subtasks had difficulty with many of them. Only in the case of the determination of zygotes and the determination of zygotic phenotypes were the percents of incorrect solutions relatively low. The subjects’ success with these subtasks is understandable. The zygote-determination task made use of the ability to understand and use the Punnett- square heuristic. The ability to properly assign phenotypes to genotypes requires only a reasonable understanding of the concept of dominance.

In contrast to the zygote and phenotype tasks, the subjects had great difficulty with the gamete-determination subtask. In the best case, problem 1 , 48% of the subjects made errors in determining the parental gametes, while in the worst case, problem 3, 93% of the subjects made errors. Table IV shows the specific errors made in the gamete task.

In the first problem, 72% of the subjects completing the gamete-determination subtask put two genes in each gamete. The same error was committed by 32% of the subjects in problem two. Such two-gene gametes have also been reported by Tolman (1982). Something analogous occurred in the dihybrid problems; some subjects placed four genes in each gamete. Such errors indicate that the subjects were unaware of allelic segregation and/or the importance of the reduction of chromosome and hence gene number during gametogenesis. The errors in gene


number are consistent with the problem-solving patterns of novices identified by Smith and Good (1984).

Two other serious gamete errors arose in the dihybrid problems. In problem three, 20% of the subjects completing the task generated gametes that contained two genes from the sume pair. In problem four, more than half of the subjects performing the gamete task made the same mistake. These subjects did not recognize that each gamete should contain one gene from each pair. A second error was committed by 46% of the subjects involved in the gamete task of problem 3 and 17% of those in the problem-4 task. These subjects thought each gamete should contain only one gene, like the gametes of the monohybrid crosses. This appears to be another case in which some subjects were trying to inappropriately apply old information to a new situation.

The results given in Table 111 indicate that the subjects also had some difficulty with the determination of the phenotypic ratio. However, except in the case of problem 2, where the number of subjects was comparatively low, the percent of errors was not nearly as great as with the gamete-determination subtask. This is probably just a function of the relative ease of this task.

Table V summarizes the errors made by the subjects who completed the phenotypic ratio task. Ignoring what were essentially errors of interpretation of the program, such as reporting numbers rather than a ratio, it is interesting to note that a common error was reporting an incorrect phenotypic ratio such as 3:l for problems 2 and 3 or 9:3:3:1 for problems 1 and 4. This suggests a certain fixedness in the subjects’ attempts to apply these familiar ratios to new and different problems.

TABLE IV Specific Errors in the Determination of Gametes

P r o b l e m 1 ( N = 4 6 ) Two g e n e s p e r g a m e t e .............................. 7 2 % Responded w i t h p h e n o t y p e s ......................... 1 3 % O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) ................... 1 5 %

P r o b l e m 2 (N=22) Two g e n e s p e r g a m e t e .............................. 3 2 % R e p o r t e d same g a m e t e s f o r b o t h p a r e n t s ............ 2 3 % Responded w i t h p h e n o t y p e s ......................... 1 4 % O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) ................... 3 2 %

_____ Prob lem 3 ( N = 8 4 )

On ly o n e g e n e p e r g a m e t e ........................... 4 6 % R a , B b o r s i m i l a r g a m e t e s ........................... 2 0 % F o u r g e n e s p e r g a m e t e .............................. 11% Responded w i t h p h e n o t y p e s .......................... 5% O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) .................... 1 8 %

P r o b l e m 4 ( N = 4 7 ) Aa,Bb o r s i m i l a r g a m e t e s ........................... 5 1 % Only o n e g e n e p e r g a m e t e ........................... 1 7 % F o u r g e n e s p e r gamete .............................. 6 % O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) .................... 25%


TABLE V Specific Errors in the Determination of Phenotypic Ratios

Problem 1 ( N = 2 8 ) E n t e r e d number of o f f s p r i n g , i n s t e a d of r a t i o ...... 43% Responded w i t h “ 1 ong “ phenotype mu 1 ti p 1 e

t imes ......................................... 3 2 % Responded w i t h g e n o t y p e s i n s t e a d of phenotypes . . . . . 7 % Responded w i t h 9 :3 :3 :1 ............................. 4 % O t h e r ( r n i s c e l l a n e o u s / n o a n s w e r ) .................... 1 4 %

Problem 2 (N=30) Repor ted 3:l r a t i o ................................. 57% Kepor ted number of o f f s p r i n g ....................... 23% R e p o r t e d 2 : 2 r a t i o ................................. 7 % O t h e r ( r n i s c e l l a n e o u s / n o a n s w e r ) .................... 1 3 %

Problem 3 (N=13) Repor ted 3 : l r a t i o ................................. 1 5 % Repor ted number of o f f s p r i n g i n s t e a d of r a t i o . . . . . . 1 5 % C e r t a i n phenotypes o m i t t e d ......................... 1 5 % Phenotypes were c o r r e c t , b u t r a t i o numbers were

n o t . . ......................................... 8 % O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) .................... 46%

Problem 4 (N=17) E n t e r e d c o r r e c t p h e n o t y p e s , b u t r a t i o was

i n c o r r e c t ..................................... 2 4 % C e r t a i n phenotypes o m i t t e d ......................... 18% R e p o r t e d a 9 :3 :3 :1 r a t i o ........................... 1 2 % Repor ted number of o f f s p r i n g ....................... 1 2 % O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) .................... 35%

From the Table I11 data, it is clear that many subjects had difficulty correctly making the cross predictions on the second attempt, despite having been “walked through” the steps to the solution. Table VI shows the specific errors committed in each problem. As with the first prediction, the most common mistake was an incorrect number of offspring, even though the predicted phenotypes were correct. While these errors could have roots in conceptual difficulties, the simplest explanation again would seem to be basic problems with mathematics. Indeed, the researchers observed a number of instances in which students could not successfully generate numeric predictions even when they clearly understood the proportions of various offspring types and knew the total number of expected offspring.

Discussion and Conclusions

In summary, the computer program proved to be an effective tool in identifying student problem-solving difficulties in genetics. Although there were some minor problems with the operation of the program, these now have been corrected, and the foundation is laid for the development of a computer program that can effectively address genetics problem solving with large numbers of students.

Three significant problem areas in the genetics problem solving of this undergraduate sample were detected. The first, evidenced by errors in the numeric predictions


of numbers of offspring of genetic crosses on both the first and second attempts, appears to be related to the subjects’ basic computational skills. This is consistent with the mathematical problems noted by Longden (1982). A small but significant number of students could not generate an accurate numeric prediction even after “walking through” a step-by-step solution to the problem. This argues for a core of subjects with profound difficulties in the problem-solving process. Fortunately, with a computer program such as this, such students can be identified and directed to the course instructors for assistance.

A second significant problem area related to the determination of the genetic composition of the parental gametes. Across all four problems, fewer subjects successfully completed the gamete task than any other. The observation that a number of subjects had trouble with the gamete task is consistent with the findings of Stewart (1983) and Tolman (1982). It suggests that an understanding of meiosis and its role in genetics is central to successful genetics problem solving.

Finally, there was ample evidence that many subjects attempted to apply previously learned information to new situations in rote or algorithmic and ultimately incorrect ways. The detrimental effect on problem solving of a reliance on memorization has

TABLE VI Specific Errors on the Second Prediction Attempt

- _ _ _ _ _ ~ P r o b l e m 1 (N=22)

E n t e r e d correct p h e n o t y p e , b u t p r e d i c t i o n o f number o f o f f s p r i n g was wrong . . ............... 6 4 %

Responded w i t h g e n o t y p e s i n s t e a d of p h e n o t y p e s . . . . . 1 4 % Responded w i t h 9 : 3 : 3 : 1 ............................. 5 % O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) .................... 1 8 %

P r o b l e m 2 (N=13) E n t e r e d correct p h e n o t y p e , b u t p r e d i c t i o n o f

number o f o f f s p r i n g was wrong ................. 3 2 % R e p o r t e d “ b l u e “ p h e n o t y p e o n l y ..................... 8 % P h e n o t y p e was correct , b u t r a t i o o f o f f s p r i n g

was 3 : l . . ..................................... 8 % O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) .................... 38%

P r o b l e m 3 ( N = 3 2 ) E n t e r e d correct p h e n o t y p e s , b u t p r e d i c t i o n o f

number of o f f s p r i n g was wrong. ................ 3 4 % R e p o r t e d “ l o n g , b l u e “ p h e n o t y p e o n l y ................ 9 % P h e n o t y p e s wrong , i e “ l o n g ” o n l y ................... 6 % C e r t a i n p h e n o t y p e s o m i t t e d ......................... 6 % O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) .................... 4 4 %

-__________ P r o b l e m 4 ( N = 3 0 )

E n t e r e d correct p h e n o t y p e s , b u t p r e d i c t i o n of

C e r t a i n p h e n o t y p e s o m i t t e d ......................... 11% P h e n o t y p e s were cor rec t , b u t r a t i o o f o f f s p r i n g

w a s 9 :3 :3 :1 ................................... 1 0 % O t h e r ( m i s c e l l a n e o u s / n o a n s w e r ) .................... 2 6 %

number of o f f s p r i n g w a s wrong ................. 4 7 %


also been noted by Smith and Good (1984). It is unlikely that the subjects who misapplied information understood the underlying principles that may be used to solve genetics problems.

The results of this and other studies of misconceptions in the genetics problem- solving process should provide biology educators with new means of approaching the subject. The apparent computational difficulties experienced by this college sample make it clear that basic mathematical skills cannot be assumed. A reasonable, general facility with mathematics and problem solving is important. Conceptual interrelationships, especially related to meiosis and genetics, need to be stressed. This may require curricular revision and/or modified teaching approaches. Also, educators need to take full advantage of the instructional power of computers and other promising technologies. The development of an “intelligent” genetics problem- solving tutor should be a step in that direction.

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Manuscript accepted February 24, 1988

Identification of student misconceptions in genetics problem solving via computer program

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