Our objective is that by the end of our presentation you will be able to describe and their relation to learning. You will be able to articulate the issues and applications of behavioral learning theory in the mathematics classroom.
What can you teach a dog, a cat, and rat? Mostafa Ewees
Watson changed the focus of psychology from introspection, to environmentalism.
The principles of learning would account for the largest share of behavioral development and are exercised almost exclusively through environmental learning opportunities provided for children. (reflected in cultural diversity & learning studies)
He believed that environmental shaping of behavior began prenatally, and focused his studies on infants and children.
He demonstrated the conditioned response in the case of “Little Albert”(Watson, 1925), who was exposed to an alarming noise and a rat at the same time, and developed not only a fear of rats, but transferred the fear to all furry objects.
Credited with “Definitional standards for stimuli and response and criteria for making objective and reliable observations can be traced back to Watson and continue to characterize acceptable investigatory practices today.”(Horowitz, 1992)
“ When a modifiable connection between an situation and a response is made and is accompanied or followed by a satisfying state of affairs, that connection’s strength is increased: When made or accompanied or followed by an annoying state of affairs, the strength is decreased.” (Thorndike, 1913b)
Note: Thorndike(1932) later modified the Law of Effect when research showed that while positive consequences strengthened connections, negative consequences did not necessarily weaken them.
“ Spare the reward, spoil the child” by E.L. Thorndike
As an organism is operating in its environment, it happens upon a reinforcing stimulus, or reinforcer. This reinforcer then causes the organism to continue the operant, or event that occurred right before the stimulus. If an operant is no longer followed by a reinforcer, extinction of the operant behavior will occur.
Continuous Reinforcement – every time the rat does the correct behavior, it is reinforced with food. Fixed Ratio Schedule – there is a fixed ratio between correct behaviors and reinforcement, i.e., 5 pedal pushes to one food pellet. Fixed Interval Schedule – rat can push the pedal at least once or possibly many more of times per every 30 seconds, but will get only one food pellet. Variable Schedules – variable ratio means you change the amount of pedal pushes needed to receive the food pellet, and variable interval means you change the time period.
Shaping can be used to help an animal to behave in a manner that it would never do in its ordinary daily patterns.
Shaping occurs when a reward is given if the animal does a behavior that is even slightly close to the desired behavior. Then, as the animal continues to exhibit the behavior that closer and closer resembles the desired action, rewards are given. Eventually, the desired behavior will exist. (ie. Pigeons that bowl or play ping pong.)
Learning is a process; you must know and understand lower level skills before advancing to higher level skills. Therefore to teach a skill a teacher must first identify its prerequisite skills and make sure that the students posses them.
It may be that some theoretical basis will one day be proposed to replace the “common- sense logic” which now underlies the designing of sequences of topics for courses. The idea of the “spiral curriculum” (Bruner, 1960, p. 52), for example, proposes that content topics be systematically reintroduced at periodic intervals. Two purposes areas served by such a scheme: First, the previously learned knowledge of the topic is given a review, which tends to improve retention. A second the topic may be progressively elaborated when it is reintroduced leading to broadened understanding and be explicated in detail, but it appears to hold much promise for future curriculum design efforts. (Gagne, 1974)
Pro- It is easily implemented. Such things as positive verbal reinforcement, or that look of “I’m tired of your nonsense” take little time or effort and usually bring about the desired behavior quickly.
Con- It has its limits. Michael Shayer and Philip Adey made the observation: “In two studies it was found that no evidence of formal thinking capacity could be found in children under the age of 10, no matter how clever they were.”(Shayer & Adey ,1981) – By clever they mean measured IQ scores in the 160 range.
Corporal punishment is more prevalent in rural areas. “Corporal punishment in public schools is indeed legal in Alabama, Arizona, Arkansas, Colorado, Delaware, Florida, Georgia, Idaho, Indiana, Kansas, Kentucky, Louisiana, Mississippi, Missouri, New Mexico, North Carolina, Ohio, Oklahoma, Pennsylvania, South Carolina, Tennessee, Texas, and Wyoming (Starr, 2002)