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The ability to understand sequences of items may be an important cognitive ability. To test this proposition, 8 first-grade children from each of 36 classes were randomly assigned to four conditions. Some were taught sequences that represented increasing or decreasing values, or were symmetrical, or were rotations of an object through 6 or 8 positions. Control children received equal numbers of sessions on mathematics, reading, or social studies. Instruction was conducted three times weekly in 15-min sessions for seven months. In May, the children taught sequences applied their understanding to novel sequences, and scored as well or better on three standardized reading tests as the control children. They outscored all children on tests of mathematics concepts, and scored better than control children on some mathematics scales. These findings indicate that developing an understanding of sequences is a form of abstraction, probably involving fluid reasoning, that provides a foundation for academic achievement in early education.

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In the United States children receive instruction on recognizing patterns beginning most often in kindergarten and continuing on through early elementary school years. Although widely accepted and included in curricula, patterning instruction has not been based on empirical research. The current study is the first attempt to determine how the dimension, e.g. color or shape, in which a pattern is displayed impacts children's ability to understand the pattern. This study is also an initial exploration of whether the overall "rule" of the pattern impacted a child's ability to recognize a pattern. Five types of patterns displayed in five different dimensions were presented to 204 first grade children in a completely counterbanced order. Results indicated that the dimension in which a pattern was displayed made no difference to the children. Patterns with alternating elements were significantly easier than any others, and those with increasing numbers of elements were significantly more difficult. Implications for instruction in patterning were discussed.

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Current curricula in most school districts in the United States include some instruction on the recognition of patterns in kindergarten and continuing into the early elementary school years. Despite the fact that patterning is so common in school cirricua, very few reports of what types of patterns are easy or difficult for children to learn have been published. In an effort to address this issue, 121 first grade children from an urban school district were tested with 48 patterns that varied in dimension, orientation, position of missing items, and magnitude of the gap between items. An ANOVA for completely correlated factors was conducted. Results indicated that only the magnitude of gaps (i.e., "skips") made a significant difference. There were indications of an interaction between that factor (skips) and the position of a missing item. Implications were discussed.

A malamute-husky mixed-breed dog was trained to distinguish one object that differed from three others that were identical to each other. The dog progressed rapidly after an effective shaping procedure, requiring 37 training sessions to master 20 such problems to a criterion of 90 %. The dog subsequently scored 80 % correct on the first trials with new problems that required a reversal of previously correct choices. The dog then scored 70 % correct on his first trials with 20 new problems composed of entirely new objects. Both performances are far above chance. Consequently, we conclude that choosing the odd or least numerous object in a group is within the capacity of the domestic dog.