Visual-spatial processing in young children: Mathematical models, cognitive correlates, and cross-disciplinary implications

这项研究是应用数学研究如何用于告知与视觉空间处理相关的跨学科问题的一个例子。虽然对幼儿的计算能力和算术能力（特别是数数）发展的方式进行了大量研究，但对视觉空间处理（或几何推理）和相关数学模型进行的实验研究相对较少。然而，视觉空间推理已经与许多领域密切相关，如技术、医学（即细胞学、运动障碍、数字医疗干预）和城市规划，仅举几例。先前的研究表明，幼儿的视觉空间处理在工作记忆、阅读（如阅读障碍）、执行功能（如注意力）和学习（如视觉空间学习者的差异化教学、学习障碍）等领域都有影响，但不限于此。由于对视觉空间处理的理解和研究存在这种差距，本研究项目对12至60个月大的儿童视觉空间处理的发展进行了实验研究。指导本研究计划的广泛研究问题是：(1)给定一组视觉空间任务（或几何结构），12个月至72个月的幼儿视觉空间处理是如何发展的？(2) 12 ~ 60月龄儿童视觉空间加工的发展涉及哪些相关的认知过程？(3)哪些数学模型可以解释这一现象？(4)这些模型如何为与视觉空间感知相关的生物科学和计算机工程研究提供信息？这种应用数学研究基本上是跨学科的，涉及数学、认知科学、心理学、健康科学和教育。未来的研究方向包括与遗传学家和神经科学家的交叉合作。

This research is an example of how applied mathematics research can be used to inform cross-disciplinary issues related to visual-spatial processing. While much research has been conducted on the ways in which numeracy and arithmetic (particularly counting) develops in young children, comparatively less experimental research has been conducted on visual-spatial processing (or geometric reasoning) and the related mathematical models. Yet, visual-spatial reasoning has been linked to many areas of intense interest such as technology, medicine (i.e., cytology, movement disorders, digital medical interventions), and urban planning, to name a few. Previous research has shown that visual-spatial processing in young children has implications in the areas of, but not limited to, working memory , reading (e.g., dyslexia), executive function (e.g., attention), and learning (e.g., differentiating instruction for visual-spatial learners, learning disabilities). Motivated by this gap in understanding and research in visual-spatial processing, this program of research investigates experimentally the development of visual-spatial processing in children ages 12 to 60 months old. The broad research questions guiding this research program are: (1) Given a set of visual-spatial tasks (or geometric structures), how does visual-spatial processing develop in young children from 12 months to 72 months? (2) What associated cognitive processes are involved in the development of visual-spatial processing in children 12 months to 60 months of age? (3) What mathematical models explain this phenomenon, (4) How can these models inform research in the biological sciences and computer engineering related to visual-spatial perception? This applied mathematics research is fundamentally interdisciplinary drawing on mathematics, cognitive science, psychology, health sciences, and education. Future directions in this research program include plans for cross-collaborations with geneticist and neuroscientists.