Piaget’s theory extends beyond intellectual development to include moral reasoning, which evolves as children move through the cognitive stages. In the Preoperational Stage, children's morality is characterized by a unilateral respect for rules and authority; they view rules as unchangeable and believe that breaking them invariably leads to punishment. This stage is often referred to as the "moral realism" phase, where children believe in immanent justice, thinking that any misfortune is a result of wrongdoing. As children enter the Concrete Operational Stage, they start understanding rules as social agreements that can be negotiated and changed. This shift reflects a more cooperative approach to morality, moving away from the rigid obedience to rules seen in earlier stages. Finally, in the Formal Operational Stage, adolescents develop abstract thinking, which allows for the consideration of universal moral principles, such as justice and equality. This stage is marked by autonomous morality, where moral decisions are based on personal principles and an understanding of the greater good, rather than just adhering to established rules.

Piaget's theory posits that language development is closely linked to cognitive development, particularly in the Preoperational Stage. He believed that thought precedes language, meaning that cognitive development drives language development, not the other way around. In his view, language is a reflection of a child’s underlying cognitive abilities and is used to express thoughts and concepts they have already developed. During the Preoperational Stage, children begin to use words and symbols to represent objects, but their language is influenced by egocentrism, resulting in communication that is more about expressing personal experiences than understanding others. As children progress to the Concrete Operational Stage, their language becomes more logical and less self-centered, reflecting their growing cognitive abilities to understand others' perspectives and complex concepts. However, Piaget’s view contrasts with other theorists, like Vygotsky, who argue that language plays a fundamental role in shaping thought, demonstrating the interactive nature of language and cognition.

Piaget's stages of cognitive development have significantly influenced educational practices by emphasizing developmentally appropriate learning. Educators, informed by Piaget’s theory, focus on creating learning experiences that align with the cognitive abilities of students at each developmental stage. During the Preoperational Stage, for example, teaching is centered on concrete, hands-on activities and symbolic play, accommodating children’s limited ability to handle abstract concepts. As children enter the Concrete Operational Stage, teaching strategies shift to include more structured, logical tasks that involve problem-solving and understanding conservation and categorization. Moreover, Piaget’s emphasis on the active role of learners has encouraged educational environments that promote exploration, discovery, and hands-on learning experiences. His theory underscores the importance of adapting teaching methods to the child's cognitive stage, rather than expecting children to adapt to conventional teaching methods, fostering more effective and engaging learning environments.

While Piaget's stages of cognitive development primarily focus on childhood and adolescence, ending with the Formal Operational Stage typically reached by early adolescence, some aspects of his theory can be extrapolated to understand adult cognition. Adults, presumed to be in the Formal Operational Stage, are capable of abstract thinking, hypothetical reasoning, and can understand and formulate complex theories. However, Piaget did not extensively explore cognitive development beyond adolescence. In adulthood, cognitive development may be more about the application and refinement of these abilities rather than the emergence of new stages. Cognitive growth in adults could involve the deepening of logical reasoning, problem-solving skills, and the ability to understand and process complex, abstract concepts. Nevertheless, some contemporary psychologists argue that there could be stages beyond Piaget's Formal Operational Stage in adults, marked by more advanced forms of reasoning and problem-solving, though these ideas extend beyond Piaget’s original framework.

Contemporary research has both challenged and supported aspects of Piaget's stages of cognitive development. One major challenge is the notion of fixed stages; many modern psychologists argue that cognitive development is more fluid and continuous than Piaget’s distinct stages suggest. Furthermore, research has shown that children may achieve cognitive milestones earlier than Piaget proposed, particularly in environments that provide appropriate support and stimuli. Piaget's underestimation of young children's abilities, especially in understanding symbolic representation and conservation, has been a significant point of critique. On the other hand, Piaget's emphasis on the active role of the learner and the importance of hands-on, exploratory learning experiences has been widely embraced and continues to influence educational practices. His fundamental concept that children think differently than adults remains an accepted and foundational idea in developmental psychology. Despite criticisms, Piaget’s theory continues to be a key reference point in understanding cognitive development.