A study of students' understanding of patterns and functions in grades 3-5
Looney, Susan Coppa
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The purpose of this study was to gain insight into students' understanding of the concept of function by assessing their abilities to continue a pattern, and to represent the functional relationship between an element in a pattern and its position in that pattern using words and symbols. The study also sought to identify differences in performance that could be attributed to grade level or the type of format, function or task. The population consisted of 228 subjects from Grades 3, 4, and 5, from three elementary schools in a suburban city in Massachusetts. To assess student's understanding of the concepts of patterns and functional relationships, the Generalizing Number Patterns (GNP) instrument was developed. The GNP consists of six problems. Two problems are presented in each of three formats: as tables of data, as pictures, and as arrays. Two different linear functions are presented within each format. Accompanying each of the six problems are three tasks: continue the pattern, describe the pattern in words, and generalize the relationship symbolically. Statistical analyses were performed to determine the effect of grade level, format, function type, and task type on performance on the GNP, and to determine the relationship between solution strategy and grade level, format, function type, and success in representing the functional relationship in words and with symbols. Analyses showed that grade level, format, and task type were significant factors for success. Subjects in Grade 5 performed significantly better than did those in Grade 4; followed by subjects in Grade 3. Scores were highest for the format of tables, followed by pictures, and then arrays. Subjects were significantly more successful solving continue type tasks followed by describe tasks and then symbolize tasks. The type of function was not a significant factor in overall success on the GNP. There was a significant relationship between solution strategy and grade level, format, and function type. Subjects who used the strategy of covariation were significantly more successful in generalizing relationships with both words and symbols.
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