Question

Research the keywords “shaping by successive approximation” on the Internet. Shaping is a method used in behavioral psychology to train pets and shape the behavior of people. How does this method relate to the way we use successive approximation in algebra?

Answer 1

The definition of "shaping" is: "a behavioral term that refers to gradually molding or training an organism to perform a specific response by reinforcing any responses that come close to the desired response.  

Lets take an example of a rat. Here, a researcher can use shaping technique to train a rat to press a lever during an experiment.

To start, the researcher may reward the rat when it makes any movement at all in the direction of the lever. Then the rat has to actually take a step towards the lever to get rewarded. Similarly again the rat gets a reward when it goes over to the lever and so on, until only pressing the lever will produce reward. Here, the rat's behavior was 'shaped' to get it to press the lever. So as per the example, each time the rat is rewarded, it is being rewarded for a "successive approximation" or for acting in a way that gets closer and closer to the desired behavior/result.

Similarly algebraic equations are also steps of succession and step by step advancement helps solve the problem.