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Differential performance of third-grade and sixth-grade children in solving open mathematical sentences
The study had three purposes: (1) to investigate the difference in performance between third- and sixth-grade children on a sixteen-item test of verbal problems with certain open-sentence patterns; (2) to investigate the differences in performance of 64 children on the four open-sentence types according to grade level; and (3) to investigate the differences in performance of children from a low-economic public school and from a middle-class private school. The 64 children were randomly selected: 16 third-grade and 16 sixth-grade children from the private school and 16 third-grade and 16 sixth-grade children from the public school. Each problem situation involved an open sentence of the following types: (1) □ + b = c, (2) a+ □ = c, (3) a-□ = c, and (4) □-b = c, where □ was a placeholder and a and b were constants. The 16 problem situations were crossed with respect to the factors of number domain and context. The verbal problems were presented in the same order to all children on an individual basis. The data were recorded and later used in providing information for the statistical analysis. The t-test was used for comparing the means between the performances of the 64 children. The t-test rejected the null hypothesis for all three stated purposes.