Academic excerpt on Piaget’s concrete operational stage and uncertain inference

11.4 Piaget’s Stages in the Context of Uncertain Inference 197 Stage 2:Concrete Operational \ Inference Rules 1 ; Knowledge about World “ Inference Control Strategy | Knowledge about how to control inference New Knowledge Fig. 11.5: Uncertain Inference in the Concrete Operational Stage 1. Conservation tasks, such as conservation of number, 2. Decomposition of complex tasks into easier subtasks, allowing increasingly complex tasks to be approached by association with more easily understood (and previously experienced) smaller tasks, 3. Classification and Serialization tasks, in which the mind can cognitively distinguish various disambiguation criteria and group or order objects accordingly. In terms of inference control this is the stage in which actual knowledge about how to control inference itself is first explored. This means an emerging understanding of inference itself as a cognitive task and methods for learning, which will be further developed in the following stages. Also, in this stage a special cognitive task capability is gained: “Theory of Mind," which in cognitive science refers to the ability to understand the fact that not only oneself, but other sentient beings have memories, perceptions, and experiences. This is the ability to conceptually “put oneself in another’s shoes” (even if you happen to assume incorrectly about them by doing so). 11.4.2.1 Conservation of Number Conservation of number is an example of a learning problem classically categorized within Piaget’s concrete-operational phase, a “conservation laws” problem, discussed in [Shu03] in the context of software that solves the problem using (logic-based and neural net) narrow-AI techniques. Conservation laws are very important to cognitive development. Conservation is the idea that a quantity remains the same despite changes in appearance. If you show a child some objects and then spread them out, an infantile mind will focus on the spread, and believe that there are now more objects than before, whereas a concrete-operational mind will understand that the quantity of objects has not changed. Conservation of number seems very simple, but from a developmental perspective it is ac- tually rather difficult. “Solutions” like those given in [Shu03] that use neural networks or cus- HOUSE_OVERSIGHT_013113