Age 11 - adult, sixth grade and up developmental information (formal operational)
How does formal operational thinking fit with the way adults think?
Being formal operational for the adolescent means for the first time in his or her life he or she has the mental capacity to think as well as adults and the ability to solve all classes of problems.
While formal operational thinking requires time for the brain to develop; time alone is not sufficient to guarantee formal operational thinking will develop and one should not assume that all adolescents and adults fully develop formal operations. In fact a majority of adults never advance beyond concrete operational reasoning.
While formal operational thinking provides ways of thinking about problems and information comparable to any advanced adult's way of thinking about the same problem; it doesn't mean the number of experiences a person has engaged in during his or her life time doesn't make a significant difference in his or her ability and efficiency of solving problems with or without formal operational thinking.
Additionally one may have the ability to use formal operational thinking in one or more particular areas and still not be able to generalize or transfer their formal operational knowledge to other areas. Hence, they must rely on concrete operational thinking in those areas.
What does it mean to be formal operational?
Piaget claimed, when adolescents develop formal operations, further gains in their reasoning abilities is made only with the application of logical operation to specific events. Each application improves the efficacy of use of the operation (mental structure) or combination of operations.
In other words, there is no higher level of reasoning beyond formal operational thinking. Differences in reasoning among formal operational thinkers depends on the construction of accurate logical procedures, the ability to mentally manipulate information from one form to another with appropriate procedures, and the creativity or flexibility to solve problems and think critically. All achieved by experiences to recognize what procedure fits with a particular situation.
Formal thought and concrete thought are similar in that they both use logical operations. However, there is a clear difference in the greater range of reasoning with the type of logical operations used at a higher level of understanding, described as formal operational thinking.
A level of understanding, described as concrete thinking lacks systematic analysis, depth and range of comprehensive power, imagination, and flexibility of reasoning. In addition a formal operational thinker is aware logically derived conclusions have a validity different than conclusions directly derived from only facts and observations.
Formal operations include:
- Reasoning with complex verbal propositional reasoning that is not tied to a personal past or present experience.
- Reasoning about hypothetical problems not tied to a personal past or present experience and can project into the future without being tied to a personal past or present experience.
- Can use theories, models, and hypotheses to create solutions to problems. Hypothetical reasoning goes beyond the confines of everyday experience to things for which we have no experience. Reasoning beyond perception and memory about things which we have no direct knowledge. Young adolescents with formal operations can reason about hypothetical problems entirely symbolically in their minds and can deduce logical conclusions.
- Is able to think about his or her own thoughts and feelings (metacognition) as if they were objects.
- Reasoning can be independent of content. Can argue on the logic of an argument (solution or problem) independent of its content.
- Complex problems can be dealt with simultaneously and systematically by coordinating multiple thinking and reasoning strategies and or variables to derive solutions.
- Can use inductive reasoning by combining similar solutions to create generalizations, principles, models, and theories.
- Have a highly developed understanding of causation.
- Can use deductive reasoning. The use of a premise to create conclusions or the use of general ideas to create specific ideas. Inferences or conclusions created with deductive reasoning are true only if the premises used to create them are true. However, reasoning can use false premises and create logical conclusions.
- Can use hypothetical deductive reasoning or reasoning with the use of a hypothetical premises (rather than facts) to create conclusions.
- Combinatorial reasoning is thinking that systematically considers all possible relations of experimental or theoretical conditions, even though some may not be realistic.
- Identify and control all variables when attempting to validate a relationship or inference. Designs a test that controls all variables, but the one being investigated.
- Proportional reasoning
- Probabilistic reasoning
- Can use correlational reasoning to recognize a comparison between the number of confirming and disconfirming cases of a hypothesized relationship to the total number of cases.
These understandings combine to enable an individual to accept an hypothesized statement or assumption as a starting point for reasoning about a situation. He or she is able to reason hypothetic-deductively. OR... Able to imagine all possible relationships between the variables, deduce the consequences of those relationships, then empirically verify which of those consequences, in fact occurs. Daniella in the transportation puzzle demonstrates this.
Sample problems
What kind of reasoning is needed to solve each problem?
- A<B; B<C what is A compared to C?
- Chris is left of Sam and Sam is left of Ben, Where is Chris in relationship to Ben?
Formal operational can solve this kind of problem in these forms. Concrete operational can not. Unless, the relationship is transfered to a concrete representation: physically arrange three persons, draw a picture, label a picture, create a mental picture, ...
Young adolescents with formal operations can reason about hypothetical problems that are believed to be false and still come to logical conclusions that can be inferred from the hypotheses.
Hypothetical: Suppose snow is black.
Formal operational can reason logically or analyze the structure of an argument, independent of the truth or falseness of its content.
Understand correlation.
Example:
- A random sample of 100 people is selected.
- The number of people with blonde hair and blue eyes and the number with brunette hair and brown eyes are counted and added together.
- The number of people with brown eyes and blond hair and the number with blue eyes and brown hair are subtracted and then compared to the total number in the sample.
- If the comparison is by division, then the result will be from 0 to 1 for a positive correlation and from -1 to 0 for a negative correlation.
- A correlation of a +1 means a sample with all blonde/blue or brown/brown matches. Or the entire sample correlates with the hypothesis.
- A correlation of a -1 means a sample with all blonde/brown or brown/blue matches. Or the entire sample doesn't correlate with the hypothesis.
- Or a 50 50 result means a correlation of zero or no correlation with the hypothesis.
Understand relationships between multiple variables simultaneously.
Given an equal arm balance, constructed so that the weights can be hung at equal increments from the center. If three weights of the same mass are placed six units from the center how many weights of equal mass have to be placed three units on the opposite side to balance?
Control multiple variables.
Students are given the following equipment and asked to investigate and find what effect the kind of material, the thickness of the material, and the length of the material have on the flexibility of the material. Equipment: thick rods of aluminum and wood, medium rods of aluminum, steel, and wood, thin rods of wood and steel. All rods are the same length about 25 cm.