This study investigated how children of different ages use counting to make numerical estimates. It was hypothesized that increased skill and strategy use in counting would be associated with greater accuracy in estimation. Children in kindergarten and Grades 1 and 3 played a game of "darts" on a microcomputer in which they had to estimate the ordinal position of a point along a vertical line segment on which only the endpoints were numerically labeled. Each subject was presented with 21 trials, representing all possible target positions along the line segment. Children were asked to report how they made their estimates and also were given an inventory of forward-and backward-counting skills. Results showed developmental differences in accuracy of estimation, fluency in counting, and sophistication of self-reported strategy use. Third graders were very accurate at estimating targets at both ends of the line segment and also relatively accurate at middle-range targets, whereas younger children were accurate only within the small range of target positions. It appears that the older children's flexibility to adjust the direction and starting point of their counting sequences provides them an advantage in estimating ordinal number. The results are discussed in terms of the relationship between children's counting skills and mathematical understanding.

Graphs are one of the primary means of exploration and communication in the practice of science, but students in science laboratories are customarily taught only the low‐level mechanics of constructing a single kind of graph when given a table of information. The use of a microcomputer can relieve the drudgery of plotting, allowing students to pursue higher‐level issues in the design and interpretation of graphs through repeated “thought experiments.” We introduced computer‐assisted graphical data analysis to inner‐city high school students with weak math and science backgrounds, emphasizing the dynamic manipulation of various kinds of graphs to answer specific questions. Drawing on extensive recordings and classroom observations, we describe examples of the performance of these students on open‐ended problem‐solving tasks in which graphs can be used to arrive at meaningful answers to applied data analysis problems.

Instrumentation, methodology, and analysis techniques were developed to measure changes in adolescent skills in the estimation of linear distance. Microcomputers were used to present and control the amount of information available to assist students in estimation. Three different levels of difficulty in estimating were developed and students estimated ten positions of a point on a vertical line within each level of difficulty. Strategies used by students to estimate were found, and a model was developed using regression analysis to allow for the separation of variance of trend and individual skill differences. This model was used to predict decreases in number of estimates and decreases in average time per estimate. The number of estimates per position decreased rapidly and a limit was soon achieved. Thus average time per estimate was used as a measure of skill. Students improved performance within the first two levels, but not within the most difficult level. Across levels, average performance improved in spite of increasing difficulty, and a transfer effect appeared to occur over time. It was concluded that microcomputers were a valuable instrument for gathering and recording data. The model using regression analysis was an effective tool to study estimation. Students used effective strategies and improved their estimation skill quickly. Learning did occur, but the level of difficulty of information or practice effect available while solving an estimation problem may limit the extent of improvement.0

Sixty-six seventh and eighth grade students were tested to find if group size was related to microcomputer problem-solving success and time to solution of problems. Individuals or groups of two, three or five students attempted to solve problems requiring the indirect linking of twenty clues. The microcomputer was used as a data presentation and recall device for students and a data gathering device for the researchers. The number of problems successfully solved significantly differed based on group size with students in groups scoring best. There were no differences in time to solve problems based on group size but practice significantly decreased problem-solving time for all.

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