Understanding and overcoming number difficulties

Across schools in the United Kingdom (UK), it is common for teachers to identify children as having significant difficulties with mathematics. The authors’ experiences in schools suggest that, despite interventions, these children continue to have significant mathematical difficulties. Currently there is little research and a lack of agreement across literature as to the aspects of mathematics that children find difficult and the characteristics of these children. In this paper, the authors provide a preliminary review of the literature in this field and propose a study in UK primary schools to address the gaps identified. The proposed study aims to investigate: (i) the characteristics of children who are identified as having significant mathematical difficulties; (ii) the mathematical profiles of these children; and (iii) different perspectives about the nature of a child’s number difficulties. With a clearer understanding of these children, we can suggest more appropriate ways to support their progress

Effect of Pictorial Depth Cues, Binocular Disparity Cues and Motion Parallax Depth Cues on Lightness Perception in Three-Dimensional Virtual Scenes

Surface lightness perception is affected by scene interpretation. There is some experimental evidence that perceived lightness under bi-ocular viewing conditions is different from perceived lightness in actual scenes but there are also reports that viewing conditions have little or no effect on perceived color. We investigated how mixes of depth cues affect perception of lightness in three-dimensional rendered scenes containing strong gradients of illumination in depth.Observers viewed a virtual room (4 m width x 5 m height x 17.5 m depth) with checkerboard walls and floor. In four conditions, the room was presented with or without binocular disparity (BD) depth cues and with or without motion parallax (MP) depth cues. In all conditions, observers were asked to adjust the luminance of a comparison surface to match the lightness of test surfaces placed at seven different depths (8.5-17.5 m) in the scene. We estimated lightness versus depth profiles in all four depth cue conditions. Even when observers had only pictorial depth cues (no MP, no BD), they partially but significantly discounted the illumination gradient in judging lightness. Adding either MP or BD led to significantly greater discounting and both cues together produced the greatest discounting. The effects of MP and BD were approximately additive. BD had greater influence at near distances than far.These results suggest the surface lightness perception is modulated by three-dimensional perception/interpretation using pictorial, binocular-disparity, and motion-parallax cues additively. We propose a two-stage (2D and 3D) processing model for lightness perception