Plane thinking: Mental representations in number line estimation as a function of orientation, scale, and counting proficiency

• We compared children’s number line estimation in the horizontal and vertical plane.
• Individual analysis revealed developmental lag in estimation on the vertical plane.
• Similar patterns of responses in both planes by 6–7 year-olds.
• Estimation assessed alongside number familiarity (i.e. reciting and counting).
• Experimental manipulation provides added insight into numerical representations.

Young children typically show strong biases when estimating the placement of numbers on or along a scale. Number line estimation changes in accuracy and linearity across development. However, existing research is almost entirely based on a horizontal number line, which presupposes that numbers are scaled on a horizontal plane only. We present data that broaden our understanding of number line estimation by also including vertically oriented scales. This study presented 4- to 7-year-olds with the number line estimation task presented in both horizontal and vertical orientations and on different scales. Our results suggest that children store numbers as accurately in the vertical plane as in the horizontal plane, although some developmental changes are observed. Our results highlight how even simple experimental manipulations can reveal the complexities of internal representations of number.