Math And Human Learning

sAINT LOUIS UNIVERSITY |
Human Learning |
Rate of Memorization Model |
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Luis Conca, Fabiola Mazón, Alvaro Comino |
2/6/2012 |

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Project: Human Learning
Abstract
The main purpose of this project was to obtain a mathematical model that allowed us to predict the memorization capacity of an individual after a certain amount of time. For such aim, several trials were done,involving memorizing complete lists of numbers in a certain time and comparing the results between them, so as to finally find a model that could include them all.
Introduction
In the ability of learning there are many factors that affect either for good or for bad.
Freshness is without doubt a very important factor, although not essential. In our graphs, freshness is important. Thus, it’s notsurprising the fact that at the beginning of each graph, the slope is really high, whereas while the time passes, the slope decreases more and more, taking into account the fact that the mind of the student will get tired because of the effort it’s doing. However, not only tiredness is a determinant factor in the change of the slope of the graph, but also, the type of information studied. For instance,it’s much easier to memorize a list of words with a determined order and meaning than an incoherent lit of random letters, or in this case, numbers. The association of ideas that the mind does when learning involves not only the quantity of the matter studied, but also its content. This is because the human mind uses the association of ideas as a method to retain information.
In our experiment,the student was forced to memorize 3 large lists of numbers, of 20 numbers each, being each number a 3-digit one. Undoubtedly, this is completely a challenge for anyone. The purpose was no other than to test the ability of human memorization with no other help than pure photographic memory. Due to the lack of time, no extraordinarily helpful patterns could the student find in the list of numbers,and thus, the amount of numbers he learned depended only on his ability to retain information.
In our experiments, as well, a very important factor was taken into account. Not everyone has the same memorization ability, and thus, several students were used to memorize the lists of numbers. Finally, three graphs were obtained. In each of the graphs, a model of how the learning progressed alongtime can be observed. As well, the rate of change at every moment is showed. From both graphs, the fact that the learning process has a maximum peak is deduced. Certainly, at the moment of starting, the freshness allows a quick absorption of the data, but still, that very freshness causes a little distraction. The student is not as concentrated as he is able to be just at the moment of sitting downand learning, and some time must pass until that maximum is reached. Of course, after that maximum is reached, the first signs of tiredness appear. They appear as a slow but inexorable decrease of the slope, after a small period of remaining constant. After the trials of memorization, it was observed that the best way of obtaining a “perfect” graph of learning was after a small rest in the middleof several trials of memorization.
Each trial took a time of 10 minutes of memorization, divided into 10 1 minute periods. After each 1 minute period, the student was given time to write down the numbers he remembered, and then, another 1 minute period started. A total of 3 trials were used in the final calculation and modeling, which sum a total of 30 minutes of memorization. Of course, each ofthe trials was done taking into account several factors, such as freshness, pressure, and stress. Thus, the data gathered would serve as initial condition for a future mathematical model.
Experimental
The experiment was divided into two main parts: information gathering and mathematical modeling.
During the first part, the student was sat in front of several lists of numbers, and in 1...