2. The Development of Reason
At this age, children’s reasoning evolves from a focus on the concrete world toward increasingly abstract problems. Children make progress by way of challenges that force them to think more abstractly.
Parents can help by supplementing their school learning with games, discussions, and problems that exercise their emerging abilities.
In terms of reasoning skills, children aged 10 to 12 undergo a stage between the “concrete operational stage” (where children reason only with immediately present objects) and the “formal operational stage” (where abstract reasoning detached from the sensory world becomes possible).
It is worth reiterating that from the age of nine or 10, children improve their ability to conceptualize and create lines of reasoning that still nonetheless require a direct relationship to concrete factors. A certain degree of abstraction also allows children to grapple with disciplines like mathematics beyond arithmetic. It becomes possible for them to resolve problems involving numbers and reasoning, but which still involve immediately present objects. The ability to systematically resolve abstract problems involving several variables is rare at this stage.
From the age of 11 to 12, children gradually develop what Piaget called “formal operations.” The new capacities that come with this stage, such as working logically with if-then statements and establishing abstract relationships, are generally mastered around the age of 15 or 16. At the end of this stage, teenagers can, like adults, use formal and abstract logic, but only if they have learned the language of logic (“if,” “then,” “therefore,” etc.) and have practiced using it. Teenagers also become capable of extrapolating and generalizing on the basis of concrete situations.
Therefore, between the ages of 10 and 12, children should be stimulated intellectually and pushed to reflect on and establish lines of reasoning. In this way parents can help them gradually move beyond the everyday logic based on action and observation onto logic based on rules of deduction that are independent of the situation at hand.
Our mind develops concepts by extracting shared features from a variety of different objects. For example, young children who hear the word “tree” spoken by others every time they encounter a dry plant 1 to 2 meters tall (dry climate trees like the Sahelian tree) will automatically extract shared features in order to produce a model of the concept of a tree.
But they have never had a formal definition of the word. If we take these children to a temperate climate for the first time, stand under a verdant 20-meter oak tree, and tell them it is a tree too, their previously established model will collapse. This immense object, very leafy and very green, with a central, vertical trunk, does not respond to their “visual concept” of a tree—based only on small, dry plants. This collapse forces the cognitive system to revise its concept of tree, defining it with more complex and increasingly abstract properties that are common to the large, green oak tree and the small, dry plant.
Case Study 1
We learn about our environment and our native language in this way, departing from concrete situations and creating an assembly of memorized links between words and sensory representations.
It would be convenient to have a formal, universal definition for a tree and to simply insert it into a child’s cognitive system. But this is impossible: on the one hand, because children have yet to master basic language and even less so logical language; and on the other, because children are not yet capable of learning by deduction.
But children can train themselves to identify and extract invariable properties of increasing complexity—creating a mental representation of the world by repeatedly calling into question and refining the concepts created by the cognitive system. Through this process and through the progressive accumulation of vocabulary, children become capable of extracting representations not only from sensory fact, but also from previously memorized representations.
One way to define thinking is the articulation of representations combined at will through language in one’s mind. When this combination of representations is structured by links of deduction (if-then statements), this thought becomes reasoning.
A field of immense possibilities opens up before teenagers, who become able to reason toward universal conclusions in unfamiliar contexts.
Near age 10, situations requiring logical deduction will be gradually encountered at school. Students will be forced to consider when and how to use basic operations to resolve concrete problems. These situations are also sometimes encountered in a family setting, if the child’s parents promote an environment favorable to reasoning and if they take the time to make sure it benefits their child.
Through encountering situations requiring deduction, in which we collect data, work through it rationally, and reach a conclusion, children will gradually manage to identify invariable properties in the data and to internalize the rules for deduction.
This begins developing slowly but surely around the age of 11 and stabilizes toward the ages of 14 to 15. This is how children reach the formal operational stage. Reasoning no longer requires imaginable, concrete situations. It no longer requires concrete elements, and it is even freed of the need to draw on memories of previously resolved problems. A field of immense possibilities opens up before teenagers, who become able to reason toward universal conclusions in unfamiliar contexts.
But this only happens if they are spurred on by having problems to resolve. Logical ability only improves with training. Adults must therefore encourage children to resolve problems. The struggle will create multiple new neural pathways and networks in the brain. These challenges are indispensable for the development of the brain and the capacity for reasoning.