Abstract
This paper describes elementary students’ awareness and representation of the aggregate properties and variability of data sets when engaged in predictive reasoning. In a design study, 46 third-graders interpreted a table of historical temperature data to predict and represent future monthly maximum temperatures. The task enabled students to interpret numbers in context and apply their understanding of inherent natural variation to create a generalised data set. Student predictions, representations, and written and verbal descriptions were analysed using two frameworks—Awareness of Mathematical Pattern and Structure (AMPS), and Data Lenses. While 54% of students used the variability of the given data table to predict temperatures that were within the historical range for each month, only 20% described the table by focusing on aggregate properties. Student representations varied from highly structured line and bar graphs to idiosyncratic drawings on weather-related themes. In total, 83% of student representations were either idiosyncratic or direct copies of the data table. These findings suggest a progression in students’ predictive reasoning, with an awareness of range and seasonal patterns emerging before a multifaceted aggregate view.
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Notes
As part of the next cycle of the design study, the same students were given a similar task 12 months later. This “turning of the axes” was also observed in five students, although not the same individuals as in this study. In the third and final cycle when the students were about to start fifth grade, there were no examples of this type of representation.
Pseudonyms used for all students.
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The research was completed in a manner consistent with the principles of the research ethics of the American Psychological Association and approved through Macquarie University Ethics (approval number 5201600461).
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Oslington, G., Mulligan, J. & Van Bergen, P. Third-graders’ predictive reasoning strategies. Educ Stud Math 104, 5–24 (2020). https://doi.org/10.1007/s10649-020-09949-0
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DOI: https://doi.org/10.1007/s10649-020-09949-0