Miriam E Hurley, Thomas M D Sheard, Ruth Norman, Hannah M Kirton, Shihab S Shah, Eleftheria Pervolaraki, Zhaokang Yang, Nikita Gamper, Ed White, Derek Steele, Izzy Jayasinghe
A correlative super-resolution protocol to visualise structural underpinnings of fast second-messenger signalling in primary cell types
Methods (San Diego, Calif.)
proportional reasoning important yet difficult many students often use additive strategies multiplicative strategies better suited research explore potential interactive touchscreen tablet application promote proportional reasoning creating conditions steer students toward multiplicative strategies design application mathematical imagery trainer inspired arguments embodiedcognition theory mathematical understanding grounded sensorimotor schemes study draws corpus previously treated data 911 yearold students participated individually semistructured clinical interviews solved manipulation task required moving two vertical bars constant ratio heights 12 qualitative analyses revealed frequent emergence visual attention screen location halfway along bar twice high short bar hypothesis arose students used socalled attentional anchors aaspsychological constructions new perceptual structures environment people invent spontaneously heuristic means guiding effective manual actions managing otherwise overwhelming task case keeping vertical bars proportion moving assumed students aas mathematically relevant points crucial progressing additive multiplicative strategies seek farther promote line research reanalyzing data 38 students aged 911 ask 1 quantitative evidence emergence aas 2 transition additive multiplicative reasoning take place solving embodied proportions tasks interaction touchscreen tablet app found aas appeared students b aatypes across students c aas mathematically relevant top bars halfway along tall bar interacting tablet crucial aas emergence e vast majority students progressed additive multiplicative strategies corroborated oral utterances conclude touchscreen applications potential create interaction conditions coordinating action perception mathematical cognition