A child in the concrete operational stage will have the most trouble understanding

Classification

Beyond conservation, Piaget also believed that children in middle childhood master hierarchical classification; the ability to simultaneously sort things into general and more specific groups, using different types of comparisons. Most children develop hierarchical classification ability between the ages of 7 and 10. For example, kids who collect superhero trading cards might be able to sort their cards by good-guy/bad-guy status, gender, and particular category of superhero powers. The ability to perform hierarchical classification is very useful to children in school, as they begin to understand and appreciate science and social studies concepts which involve making just such comparisons, for instance, sorting living creatures into different groups based on whether they are animals or plants, etc.

Seriation

Seriation involves the ability to put things in order based on quantity or magnitude. When we count numbers in order, we are demonstrating our ability to seriate, because numbers represent in abstract or generic form, specific quantities of things. When we count numbers in order, we are counting numbers in such a way as to arrange them so that the number we name immediately after another number will always represent a larger quantity of things than the previous number did. In the laboratory, Piaget tested children's seriation by showing that they could arrange sticks of different lengths into order from the smallest to the largest. However, children might also demonstrate their mastery of seriation by spontaneously arranging their stuffed animals or army toys from smallest to biggest on their bedroom shelf.

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In daily life, children often use their seriation skills in school contexts. Seriation is a fundamental ability, without which children cannot progress in math and science. You cannot appreciate what it means to measure the length or mass of something, for example (measurement being fundamental to all scientific endeavors) if you are incapable of reliably arranging things in order of their magnitude.

Spatial Reasoning

Finally, Piaget also suggested that kids develop spatial reasoning during middle childhood. Spatial reasoning is the ability to understand and to reason (to draw conclusions) using cues in the environment that convey information about distance or direction. During middle childhood, children become able to discriminate objects that are nearby and far away based on their apparent size. They learn that objects that are further away will appear smaller than objects that are closer. Younger children who have not mastered spatial reasoning do not appreciate this seemingly obvious perceptual rule. Younger children will instead typically assume that far-away objects really are tiny. They appreciate that closer and farther away objects do differ in size, but do not understand that the size difference is only apparent, a perceptual illusion caused by distance and the nature of vision.

For the first time in their lives, middle-childhood-aged children become able to give directions using another person's vantage point rather than their own. For instance, a boy who wants to indicate to a woman seeking directions that she should turn to his left would know to tell the direction seeker (who is standing facing him) to turn to her right. Younger children cannot do this sort of thing, instead being limited to providing directions from their own perspective only.

Children's development of spatial reasoning skills, including their ability to represent places from multiple perspectives helps them to form more accurate cognitive maps (mental pictures of their environment) than they could previously. This refined knowledge enables them to produce realistically accurate maps of their neighborhood that other people can understand, complete with appropriate landmarks and relative distances between locations. Younger children's maps are less sophisticated and less accurate.

Even though middle childhood aged children who have achieved concrete operations stage have made many gains in their thinking abilities, they have not yet reached the level of adult thinking. Adults can reason not only about things that are concretely in front of them, but also about more abstract concepts. By comparison, middle childhood aged children are not skillful at thinking abstractly. They cannot easily (or at all) consider complicated hypothetical situations, generalize a wide range of outcomes to vague situations, or make sense of intangible ideas like "liberty".

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