Abstract
There has been considerable research into how children solve single-digit addition problems for more than a century now, which has brought about significant changes to the ways teachers’ support children to retrieve single-digit addition facts. In this project, we examine what makes an addition problem difficult to retrieve in light of contemporary teaching approaches, based on both student performance and teacher perceptions. Australian primary school students in Years 3 and 4 (n = 166) solved 36 single-digit addition problems under two different conditions during a structured interview. These data were then used to create the Difficulty Retrieving Addition Facts (DRAF) measure, which we propose as a contemporary measure of single-digit addition problem difficulty to supersede older measures developed in a different era of instruction. We then invited Australian primary school teachers (n = 49) to complete a questionnaire asking them to estimate the percentage of students who would be able to rapidly retrieve these same 36 single-digit addition problems to facilitate comparison between student performance and teacher perceptions. We found that although teachers were generally accurate in discerning which addition problems students would find relatively easy to retrieve and which they would find more difficult, they tended to overestimate student capacity to retrieve addition facts in general, particularly when the addition fact was comparatively difficult. We suggest that this overestimation resulted from teacher responses being shaped by curriculum expectations, which states that students should be able to recall single-digit addition facts by the end of Year 3.
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Notes
Note that the terms recall and retrieve are used interchangeably throughout this paper. When referring to the notion of “just knowing” the answer to a single-digit addition problem, whilst the Australian Curriculum uses the term “recall,” the research literature tends to use the term “retrieve” (e.g. Campbell & Oliphant, 1992).
This was achieved by subtracting the minimum score on the composite scale from each of the item scores on the composite scale.
The reason that the correlations between DRAF score and the various measures of problem size are lower than Wheeler’s (1939) study when doubles facts are included is because our study did not include “add zero,” “add one,” or “reciprocal” problems (e.g. we did not include both 2 + 9 and 9 + 2, only the former). The inclusion of these additional problems would have had the effect of strengthening these correlations.
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Russo, J., Hopkins, S. Not so Simple Addition: Comparing Student Performance and Teacher Perceptions of Retrieval. Int J of Sci and Math Educ 21, 2279–2301 (2023). https://doi.org/10.1007/s10763-022-10346-7
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DOI: https://doi.org/10.1007/s10763-022-10346-7