mother, son, daughter, uncle, aunt, nephew, niece, placed one at each corner. One vertical face of the cube can be thought of as being marked +sex (for male),.
Quarterly Journal of Experimental Psychology (1973) 25, 504-510
A PRELIMINARY STUDY OF DISTINCTIVE FEATURES I N PROBLEM SOLVING
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DAVID WOOD AND JOHN SHOTTER Department of Psychology, University of Nottingham, University Park, Nottingham The abstract logical structure of family relationship problems, such as, “What relationshipto a man is his mother’s father?” was described in terms of a “distinctive-feature-transitioncount (dft)”, where the answer to the problem was characterized in terms of the distinctive features of descendancy, co-linearity, and sex. On average, it proved possible to predict the difficulty of such problems from such a count; thus tending to support the idea of a relational rather than an associative memory structure.
Introduction The aim of the present study was to find a way of describing the abstract structure of kinship problems that would reflect the difficulty that people have in solving them. One way to represent such problems is illustrated by Brown (1965),where, in Ch. 7, there can be found a diagram of a cube with eight kinship terms: father, mother, son, daughter, uncle, aunt, nephew, niece, placed one at each corner. One vertical face of the cube can be thought of as being marked +sex (for male), and the face opposite to it as being marked -sex (for female); the other pair of vertical faces are marked fco-lineal and -co-lineal respectively, while the upper of the two horizontal surfaces can be marked +descendant and the lower -descendant. Every corner can now be uniquely defined in terms of a triple and - signs denoting respectively sex, co-lineality, and descendancy. of Thus father is (+,+,+), mother (-,+,+), son (+,+,-), uncle (+,-,+), etc. More extensive relationships involving grandfather, say, may be thought of in terms of further cubes attached at the corners of such family relationship cubes. Now consider the problem relationships described below: ( I ) her father’s sister (aunt, niece); (2) his son’s son (grandfather, grandson) ; (3) her sister’s son (aunt, nephew). I n ( I ) the transition either way from her to father involves two distinguishing features, namely “sex” and “descendancy”, and the next transition from father to sister involves either way a further two, this time “sex” and “lineality”, making a total dft count of four transitions in the distinguishing features. This measure is a useful one and we shall call it “the distinctive feature transition count” (dft). I n the next example (2) the dft count is two; his to son, and son to son are both distinguished only by “descendancy”. And in (3) the dft count is three.
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Although all three features are to be subsumed under a single measure of complexity certain differences worthy of note exist in the effects which these different dimensions have upon the structure of the problems. The sex feature never contributes to the number of discrete items or elements in the problem whilst both of the other features invariably do, as an examination of the two lists of problems shown below will illustrate. Adding to co-lineality or descendancy invariably increases the “remoteness” of the relationship between the two elements at the ends of the problem statement. And, as an examination of the ThorndikeLorge tables shows (1944), there is an almost perfect correlation between the proximity of a relationship and its frequency of occurrence in English text. Thus, “mother” and “father” are amongst the most frequently encountered kinship words; “aunt” and “uncle” occur less frequently, whilst “great-aunt” and “greatnephew” occur extremely infrequently. Thus, whereas the sex feature may influence the internal complexity of the problem statement, it does not have a direct effect upon the number of discrete items to be handled or upon the remoteness of the relationship. Many previous studies of problem solving, e.g. Hayes (1965), have shown that increasing the number of items or “steps” in a problem does increase its difficulty. Hence it was predicted that the time taken to solve the kinship problems would be a function of the number of transitions in distinctive features (i.e. the dft count). Since studies with series problems (e.g. DeSoto, London and Handel, 1965) have shown that the nature of the question influences problem difficulty, this factor was also examined. We expected, on the basis of earlier studies (Wood, 1969a, b), that questions which reflect back from the last item to the first (e.g. “What relation to him is his . . .?”)would be more difficult than those that go forward (e.g. “What relation is he to . . .?”).
Method Design and materials Two lists of 10problems were drawn up, one a “low dft” and the other a “high dft” list. These are shown below: Problem nos. I 2
3 4
5
6 7 8 9 10
Low dft list Count Her sister’s daughter 2 His father’s brother 2 Her mother’s mother 2 Her mother’s sister 2 His father’s father 2 His brother’s son 2 His father’s brother’s son 3 Her mother’s sister’s daughter 3 His father’s father’s brother 3 Her mother’s mother’s sister 3
High dft list His sister’s daughter Her father’s brother Her father’s mother His mother’s sister His mother’s father Her sister’s son His mother’s sister’s son Her father’s brother’s daughter His father’s mother’s brother His mother’s father’s sister
Count 3 3 4 3 4 3 5 5 5
6
The low list comprises 10 problems in which the sex feature is constant. The high list contains basically problems matched to those in the low list but in these the sex feature frequently changes in the statement of the problem-leading to a greater dft count. By
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examining solution times to both lists, we can determine the effects of increased dft occasioned by the sex feature. Items within the low list vary by “descendancy” and “colineality”. By making suitable paired comparisons within the low list, with sex constant, we can determine the effects of the other two features upon solution times. It is possible to derive two problems from each of the items in the lists above, by asking either: (a) “What relation to him is his . .?” or (b) “What relation is he to his . . ?” The subjects were accordingly divided into two major subgroups, condition (a) and condition (b), who were given the questions in the two forms respectively. These subgroups were then divided again into the four groups described below, thus making eight groups in all: ( I ) given “low dft” list followed by “high dft” list-read top to bottom; ( 2 ) given “low dft” list followed by “high dft” list-read bottom to top; (3) given “high dft” list followed by “low dft” list-read top to bottom; (4) given “high dft” list followed by “low dft” list-read bottom to top. This procedure was adopted to control for learning effects, since we were primarily interested in the relation of dft count to overall performance.
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Subjects The subjects were 48 undergraduate students of the University of Nottingham. four were assigned at random to condition (a) and 24 to condition (b).
Twenty-
Procedure The experimenter read the following instructions to each subject: “I am going to read you a series of questions involving family relationships. Each of them follows a similar pattern, of which an example might be ‘What relationship to her is her mother’s mother?’ [in condition (b) this was changed to “What relationship is she to her . . . ?”I. The experimenters paused until the subject gave an answer. He then continued: “All the questions are like this one in that they ask for the relationship to him or her of his . . . or her so and so” [again this was changed for condition (b)]. “There are 20 questions in all.” When it was clear that the subject understood the task, he was presented with the problems, which were read at the rate of approximately one term per 0.5 s. After each problem the subject was asked if he was ready to proceed, and the next problem was given immediately he said “Yes”. The whole process was recorded on a tape-recorder, and after a session the experimenter played back the recording and timed, for each problem, the interval between his statement of the last term of the problem and the start of the subject’s reply. This procedure was repeated five times, and the mean of the five readings was taken as the solution time.
Results
The effects of dft count An overall picture of the effects of increased dft upon solution times is given by Figure I. It is evident that there is an overall increase in mean solution times with dft, and the differences between adjacent classes are significant in all but one instance. Using each subject’s mean time for each of the classes, the Kolmogorov-Smirnov test (Siegel, 1956), shows that the distributions underlying the 2 and 3 dft classes are significantly different ( N = 48,P < 0.025);and so are the differences between
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the four and five dft distributions ( P
