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Ponce and Montserrat Rebolledo. For further information regarding the present study, the first author may be contacted at: Junio 11, Revisado: Septiembre 9, Aceptado: The major purpose of the present study was to assess the effects of practice and reinforcement on letter string problem solving. College condicuonamiento were exposed to printed letter string problems. In the first experiment correct answers could be reinforced, punished, ignored, randomly reinforced or presented without a previous example.
Data showed punishment significantly decreased the number of correct answers produced by the subjects; additionally practice significantly increased the number of correct answers in one reinforced condition and lowered the number of correct answers in the punishment group. A second experiment assessed behavioral momentum theory in the solution of letter string problems.
Subjects were reinforced for producing a determined answer during 12 consecutive problems; subsequently the answer selected for reinforcement changed. Results showed the probability of producing a correct answer significantly decreased when reinforcement contingencies changed.
Coondicionamiento from both experiments suggest that approaching letter string problem solving from an operant, rather than cognitive perspective, could allow a better understanding and control of the phenomenon. Letter string problem solving, reinforcement, practice, behavioral momentumcollege students.
Estudiantes universitarios recibieron problemas impresos de secuencias de letras. When an individual uses a previously learned procedure to solve a problem in a context that differs from the original learning situation, cognitive scientists suggest that analogical transfer may have occurred. The negative findings produced so far have been relatively “shocking” to cognitive scientists because most of them have occurred in college students, and the experimental procedures have been relatively simple.
Thus the paradoxical nature of the phenomenon, it is assumed as general and fundamental for human adaptive behavior, yet it remains basically irreproducible under basic laboratory conditions. Previously, the experimental group had received a problem that required operabte application of the same procedure as the test problem but within a different context. The control group was required to solve a problem condivionamiento was unrelated to the test item.
In a final effort to produce evidence of analogical transfer, these scientists used a hierarchical taxonomy developed to classify algebra problems based on their difficulty. College students were exposed to the easiest problems of the aforementioned taxonomy but analogical transfer effects remained elusive.
These scientists used as test problem Duncker’s radiation problem see Duncker, The authors manipulated several aspects of the procedure, designed to favor analogical transfer, however analogical transfer effects could not be evidenced. In view of the continuous failure to produce analogical transfer, some scientists have suggested that the phenomenon should be explored using very simple problems.
For instance, Burnsstudied analogical transfer using letter string problems. In this type of problems, a particular sequence of letters is changed in a deliberate way for instance ABC is changed to ABD subsequently, the experimental subject is asked to change a new sequence using the previously presented model for instance: Using letter string problems, Burns found clear evidence of analogical transfer; given his success, other scientists have used this procedure to explore the phenomenon.
For example, Pulido attempted to replicate Burns’s findings in Mexican college students. In general Pulido’s findings agreed with those produced by Condicinamiento, however Pulido’s results also showed that slight procedural variations for instance changing the model casico sequence”vaporized” all evidence of analogical transfer. Other studies have assessed the effects of superficial similarities similarities between problems that are not essential for the solution of a problem on letter string problem solving by analogical transfer.
Results showed analogical transfer condiciknamiento considerably hindered in the group where the practice problem was superficially different from the test problem thus confirming the findings of fondicionamiento other scientists, see for example: In conclusion, contemporary research on analogical transfer suggests that the phenomenon is difficult to produce in the laboratory; additionally, results suggest that the independent variables the module it have not yet been accounted for; results also suggest that analogical transfer is rarely based on the structural characteristics of the problem, instead, it appears that superficial similarities play an important role for the establishment of analogies between problems.
Given the current status of the literature on the subject, one is prone to ask if there may not be something fundamentally wrong with the way analogical transfer has been conceptualized and studied.
One possibility would suggest that, at some point during the last thirty years, the scientists interested in this phenomenon have forgotten that the establishment of an analogy is basically a learning process.
As such the learning research produced during the last hundred years should not be put aside. As a matter of fact, a number of studies have assessed practice effects on analogical transfer by exposing subjects to more than one practice problem usually two or threebefore presenting them with the test problem. This finding alone, suggests practice could play an important part in solving letter string problems and possibly other problems tooand thus a parametric extension in the manipulation of this independent variable could be scientifically relevant.
Due to the fact that practice and reinforcement effects have not been systematically assessed in the study of analogical transfer, and considering that some studies have showed that practice may enhance analogical learning, the purpose of Experiment 1 was to evaluate the effects of these independent variables on clasick string problem solving.
It was hypothesized that both practice and reinforcement should considerably enhance letter string problem solving. A total of 79 undergraduate students from a university from Mexico City participated in the study; both male and female students were recruited.
Students from all schools and semesters were invited to participate. Additionally, these same studies have shown that presenting or not the complete alphabet to the students, previous to their solutions of letter string problems, has no statistical effects on their ability to solve vondicionamiento thus no attempt was made to measure alphabetical abilities in the students, previous to their participation in the experiment.
Subjects received the letter string problems in printed white booklets. Two different booklets were designed. The first booklet consisted of twelve different letter string problems. For further references in this text ABC: Only the first experimental group received the first booklet, all other experimental and control groups received a second booklet that contained 15 different problems of the following type ABC: The purpose of the problems contained in the first booklet was to assess the solution of an inverted letter string, in the solution test; different studies have suggested that when inverted letter strings are presented in the test phase “correct” responses rarely occur.
In the second booklet the model letter string was always presented in alphabetical order and test problems could be in either in alphabetical or inverse order for example ABC: The purpose of the development of the second booklet was to assess the effects of the independent variables on different types of problems, and thus assess their effects in a more general fashion.
The number of problems in the second booklet was increased from 12 to 15 to better assess practice effects. The experiment was conceived as a between groups design with 2 experimental groups and 4 control conditions.
In the experimental conditions subjects were presented by the experimenter with an example of how letter string problems are solved. The example problem was different from those presented in the booklet, and was only used to develop a general idea of the solution requirement. Once the example problem was presented, the subjects received the test problems, one classico a time.
The experimenter registered solution time, initiating timing when the problem was uncovered by a white card, and stopping the clock when the subject finished the last word of the answer.
If the subject gave the “correct” response to the problem, the experimenter said “very good, your strategy is correct;” if the answer was “incorrect,” the experimenter said “your answer is incorrect, please use a different strategy. In the first experimental group subjects received the first booklet; in the second experimental group and in all control conditions, subjects received the second booklet.
The first control condition was identical to the second experimental group, with the exception that subjects received random reinforcement. In operqnte to guarantee that condicionaniento subjects would receive random reinforcement, previous to the application of the booklet, a coin was tossed fifteen times.
The second control condition was identical to the second experimental condition with the exception that the subjects received inverse reinforcement. This means that “correct” answers were punished and “incorrect” answers were reinforced. The third control condition was identical to the second experimental condition with the exception that the subjects received no feedback for their responses.
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This means that independently of producing a “correct” or an “incorrect” answer the experimenter remained silent. Condicionamient last control condition was identical to the second experimental condition with the exception that the subjects did not receive the condicionaniento string problem example before answering the booklet. Table 1 synthesizes the experimental procedure. Subjects were recruited at the library, gardens and cafeteria of the university.
They were identified as students by means of their “student identity card.
The experiment will not take more than twenty minutes of your time and the results will be helpful for the development of theories regarding logical reasoning. Subjects that agreed to participate were randomly assigned to one of the groups and the application proceeded as was previously described.
Vondicionamiento also solved the problems in different order. Some subjects were randomly assigned to a condition where they initiated with problem 1 and ended with problem fifteen; other subjects received the problems in inverted order. Figure 1shows cumulative success as a function of solving consecutive problems.
The figure shows the experimental conditions on the left side, and the control conditions on the right. In order to facilitate the identification of the different experimental and control conditions, each graph is identified by the same number that was assigned to the condition in Table 1. Each graph shows in the “y” axis condicilnamiento number of correct answers; the “x” axis shows consecutive problems.
In general, experimental groups produced a condicionamientto homogenous performance than control conditions the exception was group five, the “no reinforcement” control condition that shows homogeneous performance by most subjects. With the exception of two subjects from the first group, all other participants in the experimental conditions increased the number of “correct” answers in a linear fashion, as exposure to the problems and reinforcement increased.
Control groups numbers 3, 4 and 5 random reinforcement, inverse reinforcement and no preliminary example show heterogeneous results, with some subjects increasing the number of “correct” answers in a linear fashion and others showing small or no increase. The number of “correct” responses is particularly low in the inverse reinforcement condition group 4. Figure 2 shows the average effects of practice, on both solution time condicionamietno “correct” answers.
The figure was designed by averaging the solution times and “correct” answers for all subjects in each condition during the first 5 problems; the second group of 5 problems and the third group of 5 problems in the first experimental group with only twelve problems, three groups of 4 problems each were formed.
The columns in the left side of the Figure show the average number of seconds for the solution of the problems; the columns in the right side of the Figure show the average number of “correct” answers. The Figure shows that response times decreased in both experimental and control conditions. In some groups times decreased in a steep way see for instance group 5 ; in other groups times decreased gradually see for instance group 6. In contrast with the consistently decreasing effects observed with solution times, the average number of “correct” responses varied across groups.
Correct responses increased consistently in both experimental groups more abruptly for the first experimental group than for the second ; “correct” answers decreased in the random and inverse reinforcement groups more abruptly for the inverse condixionamiento group than for the random reinforcement groupand have nil or small effects in the no reinforcement and no example control groups.
In order to further assess the effects of the reinforcement contingencies a one way Analysis of Variance was conducted to compare the means of the six groups. The average probability of emitting a correct response was used as dependent variable. The post hoc analyses showed that experimental groups, as well as the no reinforcement and no example groups differed from the inverse reinforcement condition condition that presented the lowest overall condicionamidnto.
The random reinforcement group did not differ from any experimental or control condition. In order to assess the effects of practice on the dependent variables, regression equations relating practice as independent variable and “correct” answers as dependent variable were calculated for each one of the six different groups.
Table 2 shows the groups in the first columns; the regression equation is shown on the third column and the statistical significance of the slope is shown on the fourth column.
Table 2 shows that two regression slopes attained statistical significance, those corresponding to experimental group 1 and control group 2 corresponding to the inverse reinforcement control group.
Condicionamiento Operante I: Elementos Básicos
These results suggest that practice significantly increases the number of “correct” answers in at least one experimental group the regression equation presents a positive slope ; the results also cladico that practice decreases the number of “correct” answers when those answers are labeled as “incorrect” by the experimenter the regression equation presents a negative slope.
Table 3 shows regression equations relating practice as independent variable and solution times as dependent variable calculated clsaico each one of the six different groups.
Table 3 shows the groups in the first columns; the regression equation is shown on the third column and the statistical significance of the slope is shown on the fourth column. Table 3 shows that four regression slopes attained statistical significance groups 1, 2, 3 and 4 ; groups 5 and 6 no reinforcement and no preliminary example control groups did not produce significant regression slopes. All regression equations in Table 3 show negative slopes.