Piaget's theory of cognitive development proposes that children's intellect cognitive ability progresses through four stages in which individuals?

Not sure what you mean by "which individuals"? A child's intellect develops in these 4 stages:

˜ Sensorimotor Stage: (Infancy) This stage consists of 6 sub-stages. During this time, children display intelligence through motor activities and experience the world through their senses. Children acquire memory/object permanence at about 7 months, some language or symbolic development is acquired at the end of this stage.

˜ Pre-operational Stage:(Toddler) This period has two sub-stages. Intelligence is demonstrated as language skills mature and memory and imagination are developed. Thinking is however non-logical and Egocentric. Children learn to represent objects by drawings, images and Words.

˜ Concrete Operational Stage:(Prepubescent and early adolescence) Egocentric thinking diminishes and logical thinking is developed relating to concrete elements. Operational thinking develops. Important Processes during this stage are:

¯ }Seriation-the ability to sort objects in an order according to size, shape, or any other characteristic. For example, if given different-shaded objects they may make a color gradient.

¯ Transitivity- The ability to recognize logical relationships among elements in a serial order (for example, If A is taller than B, and B is taller than C, then A must be taller than C).

¯ Classification-the ability to name and identify sets of objects according to appearance, size or other characteristic, including the idea that one set of objects can include another.

¯ Decentering-where the child takes into account multiple aspects of a problem to solve it. For example, the child will no longer perceive an exceptionally wide but short cup to contain less than a normally-wide, taller cup.

¯ Reversibility-the child understands that numbers or objects can be changed, then returned to their original state. For this reason, a child will be able to rapidly determine that if 4+4 equals t, t−4 will equal 4, the original quantity.

¯ Conservation-understanding that quantity, length or number of items is unrelated to the arrangement or appearance of the object or items.

¯ Elimination of Egocentrism-the ability to view things from another's perspective (even if they think incorrectly). For instance, show a child a comic in which Jane puts a doll under a box, leaves the room, and then Melissa moves the doll to a drawer, and Jane comes back. A child in the concrete operations stage will say that Jane will still think it's under the box even though the child knows it is in the drawer.

Children in this stage can, however, only solve problems that apply to actual (concrete) objects or events, and not abstract concepts or hypothetical tasks.~ (Wikipedia.org, 2009)

˜ Formal Operational Stage:(Adolescence and Adulthood)This stage involves the development of abstract reasoning. It commences after puberty has started, around ages 11-15. Intelligence is demonstrated by the logical use of symbols related to an abstract concept, devising plans to solve problems and systematically testing solutions. During this stage adolescents start to think about the future and what they can achieve, they begin to understand concepts such as love, proof and values and shades of grey…

This is applicable to all children, although thay may not develop at the same rate, the stages remain in the same order.

There are also activities you can do with your children to encourage the development of these stages. such as running, drawing, painting, learning to play piano...