According to Jean Piaget's theory of cognitive development, in which stage children gain the ability to seriate objects in a specified order ?

Piaget's theory of cognitive development: Piaget’s theory proposes that Cognitive Development universally follows a pattern of four stages. As a person progresses to higher stages, her/his thinking becomes more refined and evolved.

The first three stages span from birth to about eleven years; that is mainly during early to late childhood.
The fourth stage is the highest stage of cognitive development and is primarily located during pre-adolescence age till adulthood.

Characteristics of concrete operational stage:

'Concrete Operational Stage' lasts around 7 to 11 years of age which refers to the later childhood stage of child development.

In this stage, children can classify objects into groups and subgroups and gain the ability to conserve numbers, area, and volume.
Children show attainment of the concept of reversibility, seriation, and transitivity as a cognitive capacity.
Reversibility is the understanding that a child develops to know that things that have been changed can be returned to their original state.
Children can conserve numbers (age 6), mass (age 7), and weight (age 9). Conservation is the understanding that something stays the same in quantity even when its appearance changes.

From the above points, we can conclude that the concrete operational stage involves seriation or the ability of the child to seriate objects develop in the concrete operational stage.

Sensorimotor Stage: The developments that take place in this stage include Co-ordinating reflexes, Greater control over body movements, and Co-ordinating simple motor actions. Another important development that takes place during this stage is object permanence.
Preoperational Stage: The capacity to mentally do and reverse action is known as operations or operational thinking. Since this second stage comes before the development of such thinking, it is known as preoperational. This is the stage that prepares for such operational thinking. The first step in this direction is a development of a language system
Concrete Operational Stage: This stage is considered a significant turning point in the cognitive development of children. Concrete operational reasoning is much more logical, flexible, and organized than sensorimotor or preoperational thought. They apply their reasoning to concrete and specific information which can be directly perceived.
Formal operational stage: It is important to note that mathematics and grammar are subjects that demand higher abstract thinking as the student has to work with symbols and with ideas that may not be visible in concrete reality. It is only in this stage that children’s capacity to think mathematically emerges. Such thinking demands the ability for hypothetical (assumptions based), and deductive reasoning.