Final answer:
Christian's misunderstanding of conservation indicates that he's likely in the preoperational stage of Piaget's cognitive development theory, which is characterized by a lack of conservation understanding.
Step-by-step explanation:
The question presents a scenario where a child named Christian doesn't understand the concept of conservation, which is pertinent to Jean Piaget's stages of cognitive development. The specific stage in question where children lack conservation is the preoperational stage, ranging roughly from 2 to 7 years old. During this period, children are known to struggle with the idea that quantity does not change with the physical arrangement or appearance of objects. In the given situation, Christian believes he has more to eat only because the carrots were cut in half, showing that he has not developed an understanding of conservation. Therefore, the answer is (a) Preoperational / conservation.