Creating a mental image of our spatial environment is a key process for further abstract geometric thinking. Building a mental representation can be understood as a part of the process of visualisation. From the wide concept of visualisation, in this article, we will focus on the part where the mental representation of spatial relations, mental objects and mental constructions are created, and their manifestations as a 3D physical object and its plane representations arise. Our main goal is to follow the transition between 2D and 3D representations of physical objects and also to observe how and when such a transition happens in students’ thinking. For that purpose, we also use Tangram, because manipulation with the Tangram pieces in space and filling out planar figures by them indicates the transition between 3D and 2D. Our research, using an action research methodology, was conducted on the students of three 5th grade primary school classes as a part of a larger long-term project. We pointed out a relationship between spatial abilities and the perception of 2D–3D relationships in students’ mind.

In this paper, a neural network-based optimal control synthesis is presented for distributed optimal control problems. We deal with solutions of systems controlled by parabolic differential equations with control and state constraints and discrete time delays. The given optimal control problem is transformed into a discrete nonlinear problem and then implemented into a feed-forward adaptive critic neural network. We propose a new algorithm to reach optimal control and an optimal trajectory using a feed-forward neural network. We present a concrete application of this simulation method on the SEIR (Susceptible—Exposed—Infectious—Recovered) optimal control problem of a distributed system for disease control. The results show that the adaptive-critic-based neural network approach is suitable for the solution of optimal distributed control problems with delay in state and control variables subject to control-state constraints and simulates the spread of disease in the SEIR system.

Information about the paper titled "CREATIVITY AND SPATIAL SKILLS IN SOLID GEOMETRY AND PLANE GEOMETRY IN PRIMARY SCHOOLS" at IATED Digital Library