Large Number Placements on a Bounded Number Line: The Importance of Explanations

Understanding large number data is essential for making sense of real-world problems. For the research reported here, our intent was to find connections between quantitative cognitive science studies and our prior qualitative study about participants' understanding of the relative size of large numbers. While all 23 cognitive science research studies that we reviewed focused only on participants' placements of large numbers on number lines, our study focused on preservice teachers' (PSTs; n = 128) strategies -- placements "and explanations" for their placements -- of one billion on a number line bounded by zero and one trillion. Our intent was to answer the following question: What are the connections between three plausible placements substantiated by cognitive scientists -- linear; log-linear; and segmented linear -- of large numbers on number line tasks and the nine strategies identified in our qualitative study? We highlight exemplars from the nine PSTs' strategies to show connections between the three plausible placements. In doing so, we illustrate that asking participants to place large numbers on number lines only gives a partial picture of their understanding. Their explanations expand the placements by revealing inconsistencies among the placements and explanations. Implications for future research are also discussed.