Piaget

    The following article "Applying Piaget's Theory of Cognitive Development to Mathematics Instruction" by Bobby Ojose, discusses concrete stages of cognitive development in children.  Jean Piaget is a primary focus in children's psychology and has contributed a great deal of information in that field.
    All together, there are four primary stages of development.  They are sensorimotor, preoperational, concrete operational, and formal operational.  Some of this information is a summary to me because I have taken two psychology courses here at Dutchess Community College.  Each course discussed Piaget and the stages that were mentioned above. 
    The sensorimotor stage is “characterized by the progressive acquisition of object permanence in which the child becomes able to find objects after they have been displaced, even if the objects have been taken out of his field of vision”.  This stage is also important for a child to link numbers to objects. It’s interesting to know children at such a young age are able to have this concept of numbers and counting.  Mathematics starts early and it is just the beginning.
    The next stage is the preoperational stage.  Now, children engage in problem-solving tasks. Children can use materials such as blocks for building and sand and water for measuring. 
    The third stage is the concrete operations stage.  Cognitive growth in this stage is remarkable.  Hands-on activities are great because they have mathematical ideas and concepts which is useful for problem-solving.  Manipulative materials include: pattern blocks, Cuisenaire rods, algebra tiles, algebra cubes, geoboards, tangrams, counters, dice, and spinners.  These are all great items to contribute to growth in mathematics. 
    The last stage is the formal operations stage.  Children develop abstract thought patterns where reasoning comes into play.  Such reasoning skills include clarification, inference, evaluation, and application. 
    With these stages, teachers have the opportunity to develop lesson plans based on where a child stands.  Teachers are able to know what children know math wise and can provide proper materials that children will know how to use.  At certain stages, I would only focus on what type of growth is occurring.  For example, in the sensorimotor stage, one can read books to the children that show objects linked to numbers.  There could be a picture of three dogs with the number three right next to them.  Children could easily begin this concept and make the necessary connections. 
    I always wonder where things would stand if people like Jean Piaget never discovered stages of development in humans.  Piaget made it possible for teacher's to teach math at a proper level to children. This was an interesting article and it really refreshed my memory.