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Adding + It Up: Helping Children Learn Mathematics
the researchers claimed that these students did not see the data set as an entity that can be represented by a single value, an alternative interpretation is that the students used the mode because it is so easily identified in a graph.144 Some students consider the average to be a data point roughly centered within the data, that is, they conceptualize average as median.145 Students in the primary grades seem not to have the idea of center as a mathematical point of balance, a vital characteristic of the mean. They cannot use an algorithmic procedure to find the mean, let alone create a data set given the mean.146 Different measures of center appear to be important for different students; all need eventually to understand the different measures and their purposes.
Representing data in visual displays requires the generation of different organizations of data according to certain conventions. Many elementary students have difficulty creating visual displays of data.147 First and second graders’ knowledge of how to represent data appears to be constrained by difficulties in sorting and organizing data, and technology has been found to be helpful in overcoming those difficulties.148
Studies of middle school students have revealed substantial gaps in their abilities to construct graphs from given data.149 Processes like organizing data and conventions like labeling and scaling are crucial to data representation and are strongly connected to the concepts and processes of measurement. Given the difficulties students experience, instruction might need to differentiate these processes and conventions more sharply and utilize the potential of technology to make them more accessible to students.
The process of analyzing, and interpreting, data incorporates recognizing patterns and trends in data and making inferences and predictions from the data. It includes what has been referred to as reading between the data and reading beyond the data.150 Reading between the data requires students to compare quantities and use mathematical operations to combine and integrate data and to identify mathematical relationships expressed in the data or in visual representations of the data. Reading beyond the data requires students to make predictions or inferences from the data that are neither explicitly nor implicitly stated in the visual representation.