Concrete Operational Students (Third Grade - Fifth Grade)

Preoperational (Kindergarten - Second Grade) --->>> Concrete Operational (Third Grade - Fifth Grade) --->>> Formal Operational (Fifth grade - Adult)

Concrete Operational Students (Third Grade - Fifth Grade)

Develop conservation

Class inclusion Use of classification and generalization to solve problems (all dogs are animals, only some animals are dogs. A tree is not an animal, therefore it is not a dog. A collie is a dog, therefore it is an animal.)

Serial ordering Can arrange a set of objects or data from smallest to largest or by other criteria and create a one-to-one correspondence. Arrange people from smallest to largest and and relate to age.

Conservation is the ability to question perception and reason about reality. To use logic instead of perception to make determinations for what can appear obvious, but is not.

Conservation of number - five is five no matter if it is five elephants or five mice. No matter if the five horses are gathered by the fence at the barn or if they are spread out across the whole 10 acre field.

Conservation of length - Perception of two wires of equal length, a bent wire and a straight wire, suggests the straight wire is longer.

Conservation of liquid/volume - Perception of two drinking glasses, of equal volume, with one being tall and narrow and the second being short and stout, would visually suggests the taller has a greater volume. Abstract reasoning might cause us to represent the two by imagining the tall one shrinking in height as it increased in girth.

Conservation of solid/mass - a ball of clay will have the same amount of solid material or mass if it is rolled out as a snake, pounded as a pancake or rolled into a ball.

Conservation of area - My favorite one to act out. Mr. Smith and Mrs. Jones. Both have a farm yard with the same amount of grass. (Put down two identical pieces of green construction pieces.) Which farm yard has more grass? (neither they are the same.) Okay good. Now on with the story. Mrs. Jones decides one day that it is time for her farm to grow and builds a barn ( I place one Monopoly hotel on the green piece of construction paper). Mr. Smith, wanting to keep up with the Jones build a barn exactly the same size ( I place one Monopoly hotel on the other green piece of construction paper). The next year Mrs. Smith decides that things are even better and builds two more barns along side of the first barn ( I place two more Monopoly hotels on the green piece of construction paper right beside the first). Mr. Smith again wanting to keep up with the Jones and builds two more barns, but spreads them out across the barn yard ( I place two more Monopoly hotels on the green piece of construction paper so that all three are spread across the page). The following year Mrs. Jones has another good year and builds two more barns again side by side her original ( I place two more Monopoly hotel on the green piece of construction paper beside the other three). Again Mr. Smith keeping up with the Jones builds two more barns only he decides again to build his barns spread out across the farm yard ( I place two more Monopoly hotel on the green piece of construction paper spread apart from each other as much as possible). If there are more hotels, I continue until all of them are placed on the green construction paper. Then say Mrs. Jones goes out and buys a cow. Mr. Smith, wanting to keep up with the Jones, goes out and buys a cow. When both cows are let out into the farm yards, which cow is going to have more grass? Most people that have never heard of this before will have as their first hunch or answer the cow in Mrs. Jones. Just look at all that green. The image of the red (barns) hotels spread across the green page and image of the green page with barns huddled together in a corner can create a preoperational non conservation of area response or Mrs. Jones based on the visual evidence. However, if you are skeptical enough or whatever to ask yourself to just wait and think here. You might reason that the amount of green covered by the same number of barn/hotels is equal and each cow would have the same amount of grass. If you are still not sure, act it out. Or get two pieces of graph paper and pencil in two squares for each barn. On the one sheet color them all in a corner and on the other spread them out. Are they the same area? Is the amount of grass the same. Can you see that in order to conserve area a person needs to be able to stop their egocentric thinking (maybe someone else would think of this differently than just by looking at the grass for each), decenter (how else can I think about this problem rather than by looking at the amount of green and comparing), transformation (think what would happen if all the spread out barns/hotels started together and were moved/transformed to where they are now) or (what would happen if all the grouped together barns/hotels were moved/transformed to where they are now). It wouldn't matter where they were they are still sitting on the same about of grass. Reversibility - If I can move the barns to spread them out, then they can be returned to being together. Egocentric thinking is replaced by logical-mathematic reasoning.

Being able to use these operations enables people to make direct references to familiar objects and actions and explain them with asssociations. Example garduckals. Using associations allows them to create simple hypotheses, follow step by step directions or explanations, and understand others may have a different point of view or use a different reference point that they have or are using at the present.

Because concrete operational students begin with their concrete experiences and associations, rather than with a formal operation their abstractions are not as comprehensive and flexible with respects to generalizing to less or unfamiliar situations. Hence:
Concrete operational students can identify some variables that interact with an object or system, but do not use a systematic process to identify them, usually resulting with an insufficient list of variables, and do not consistently plan and hold variables constant that are not manipulated or responding variables.
Knows the difference of observation and inference and can make inferences from observations, but considers a limited amount of possible inferences for an observation.
May apply a related, but inaccurate procedure or algorithm as a solution to a problem.
Apply a process without applying his or her own validation of the application of the process against the data, conclusions, or whatever information the situation provides for checking and validating a particular method.

Formal Operational) Sixth Grade - Eighth Grade

The characteristics of formal operational thought is not abstract reasoning. It is formal operational thinking and the two are different. Remember abstract thought was a characteristic of the preoperational child. Abstraction is the ability to use symbols or other representations to think and reason. Formal operations requires abstract though, but it is more than just thinking with abstractions. It is being able to understand a mental operation or procedure that can be performed on information in an efficient systematical way. Operations and procedures that can be indicative of formal operational thought include isolation and controlling of variables, hypothesis, combinations, probability, correlation, proportion, and formal logical reasoning. ( formal operational information)