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Adding + It Up: Helping Children Learn Mathematics
Describing data involves reading displays of data (e.g., tables, lists, graphs); that is, finding information explicitly stated in the display, recognizing graphical conventions, and making direct connections between the original data and the display. The process is essentially what has been called reading the data,137 and researchers have found that the majority of students in the elementary and middle school grades can read data displays accurately.138 Although children in the primary grades often give idiosyncratic descriptions of data, explorations with categorical and numerical data in instruction that incorporates technology produce more focused and less idiosyncratic descriptions.139
The process of organizing, and reducing, data incorporates mental actions such as ordering, grouping, and summarizing.140 Data reduction also includes the use of representative measures of center (often termed measures of central tendency) such as mean, mode, or median, and measures of spread such as range or standard deviation. Research on organizing data at grades pre-K to 8 is quite limited.
Most of the available research on data reduction by elementary school students has focused on their understanding of measures of center, particularly the mean. The most familiar measure of center is the mean, which is computed by adding up all the data values and dividing by the number of values. The median is the middle value when the data are sorted (or the mean of the two middle values). The mode is the most common data value. All of these measures of center are called “averages” for some kinds of data. With housing prices and incomes, for example, the preferred average is the median because the mean is easily skewed by a few very high incomes, giving a false impression of income for an “average” or typical family. With clothing sizes, the preferred average is the mode because it gives the best impression of the typical buyer.
First and second graders have informal conceptions of mode and median as measures of center, and they also have some conception of spread.141 Most elementary school students understand that the mean is located between extreme values.142 Nearly all realize that the mean is influenced by values in the data set and that the mean does not necessarily equal one of the actual data values. In a study of fourth, sixth, and eighth graders’ concept of average, the younger students interpreted the average as the mode.143 Although