The Effects of Selected Experiences on the Classification and Seriation Abilities of Young

MF-$0.65 HC-$3.29 Age Differences; classification; *Conservation (Concept); Educational Research; *Elementary school Students; Grade 1; Grade 2; Learning Processes; *Mathematical Concepts; Relationship; *serial Ordering; *Student Testing; Training The purposes of this study were to: (1) determine the influence of a series of experiences involving the equivalence relation "same length as" and the asymmetric transitive relations "longer than" and "shorter than" on the ability of first and second grade children to classify and seriate objects on the basis of length; (2) investigate the influence of such experiences on the child's ability to conserve and use the transitive properties of the length relations; (3) determine if the subject's ability to use the transitive property of the equivalence relation "same length as" was related to his ability to classify on the basis of the relations; (4) investigate the relationship between the child's ability to use the transitive property of the relations "longer than" and "shorter than" and his ability to seriate on the basis of these relations; and (5) determine if the ability to seriate linear objects is material specific or relation specific. The subjects were 39 first grade and 42 second grade children. Two instructional units were written and taught to acquaint the students with relations used in the study. Tests administered were: Criterion Test, Conservation of Length Relations Test, Transitivity of Length Relations Test, Seriation Test, and Classification Test. The results clearly confirm the hypothesis that seriation ability of "linear objects can be improved by training. (DB) SCOPE OF INTEREST NOTICE The ERIC Facility has assigned thn document for processing to: In our judgement, this document is also of interest to the clearing. houses noted to the right. Index. ing ShOuld reflect their special points of view. 4-1.S. DEPARTMENT OF REALM EDUCATION & WELFARE OFFICE OF EDUCAJION THIS DOCUMENT HAS BEEN REPRO. DUCE() EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGINATING IT POINTS CIF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRESENT OFFICIAL opricE OF EDUCATION POSITION OR POLICY The Effects of Selected Experiences On The Classi ication And Seriation Abilities Of Young Children Martin L. Johnson Rut e s The State University irtsent-day elementary school mathematics curricula include few activities in classification and seriation. Bruner (1963) believes such activities may be crucial to math matics learning. He has state( that "it might be interesting to devote the first two years of school to a series of exercises in manipulating, classifying, and ordering objects in ways that highlight basic operations of logical addi\tion, multiplication, inclusion, serial ordering and the like. For surely these logical operations are the basis of more specific operations and concepts of all mathematics @.4g The failure of current mathematics curricula to include activities such as proposed by Bruner may be due in part, to the almost non-existence of research showing how such activities are related or are prerequisite to the learning of specified arithmetic content. Guidelines are needed on which to b se curriculum innovations. Such guidelines can be given through r search that describes cognitive capabilities of elementary children, as is pointed out by Sigel and Hooper (1968). The acts of classifying and ordering objects may be analyzed both Cf) psychologically and mathematically. Piaget (1964) has attempted to rz.4 explain the e acts pt.le$. *1Ly by tion called "groupings". Eight major gteupin differences in the groupings residing in the various operati ns which are to be organized. Grouping I. addition of classes and grouping V, addition of asymmetrical retione provide models for the cognitive acts of combining individuals in classes and asseniblis the asymmetrical relations which express differences in individuals, respectively. More specifically, groupings I and V provide uodels for classifying and seriating. A Complete discussion of the groupie structures can be found in Flavell (1963) Mathematically, the act of Classifying a set of objects into disjoint subsets on the basis of some criteria involves the use of an equivalence relation. For in tance, givenastAof linear objects (e.g. sticks, string etc ) with the instructions "put all objects having the same length together, by using the relation same length as" (R) it can be found that for arbitrary elements a, b, and c contained in A (1) aRa (2) if aRb, then bRa and (3) if aRb and bRcf then aRc. "Same length as" satisfies the mathematical properties of reflexivity, symmetry, and transitivity and is by definition an equivalence relation; one of the many equivalence relations encountered by elementary sdhool children. On the other hand, linear order relations Stre involved in seri, ation. While these relations are transitive they do not possess tt mathematical properties of reflexivity and symmetry. "Longer than" and "shorter than" are both lin ar order relations and are commonly found in elementary mathematiTs. Inhelder and Piaget (1969) were among the first to systematically investigate classificatory behavior in young children. They report behavior related to classificatory acts ranging fr "graphic collecti ns" in which the child forms spatial wholes to true classification. True classification res lted when the child was able to coordinate both the intension and e tension of a class, which first appears somewhere a ound 8-9 years of age. Similar behavior was found in a series of studies by Lovell, Mitchell, and Everett (1962). In tl aforementioned studies children were asked to group objects on the basis of shaper size or color. The fact that verbal and pictorial stimuli can also out by Olver and also report that influence a child's strategy for gr uping was poinba Hornsby (1966). while this may be the case they young children base their group=ge on perceptible properties whereas older children use more functional based equivalence egardless of type of stimuli. Since every object is multidimensional, it seems logical that a child has a choice of criteria for classification. Maccoby and Modiano (1966) report that the criteria employed in f r ing classes are functions of cultural convention It has been shown that with