Rate of Memorization Model Human learning is, to say the least, an extremely complicate...

Rate of Memorization Model

Human learning is, to say the least, an extremely complicated process. The biology and chemistry of learning is far from understood. While simple models of learning cannot hope to encompass this complexity, they can illuminate limited aspects of the learning process. In this lab we study a simple model of the process of memorization of lists (lists of nonsense syllables or entries from tables of integrals).

The model is based on the assumption that the rate of learning is proportional to the amount left to be learned. We let L(t) be the fraction of the list already committed to memory at time t. So L = 0 corresponds to knowing none of the list, and L = 1 corresponds to knowing the entire list. The differential equation is

Your report: In your report, you should give your data in Parts 1 and 3 neatly and clearly. Your answer to the questions in Parts 2 and 3 should be in the form of short essays. You should include hand- or computer-drawn graphs of your data and solutions of the model as appropriate. (Remember that one carefully chosen picture can be worth a thousand words, but a thousand pictures aren’t worth anything.)

Four lists of three-digit numbers are given in Table 1.9, and additional lists can be generated by a random number generator on a computer. Collect the data necessary to determine your personal k value as follows:

(a) Spend one minute studying one of the lists of numbers in table Table 1.9. (Measure the time carefully. A friend can help.)

(b) Quiz yourself on how many of the numbers you have memorized by writing down as many of the numbers as you remember in their correct order. (You may skip over numbers you don’t remember and obtain “credit” for numbers you remember later in the list.) Put your quiz aside to be graded later.

(c) Spend another minute studying the same list.

(d) Quiz yourself again.

Repeat the process ten times (or until you have learned the entire list). Grade your quizzes (a correct answer is having a correct number in its correct position in the list). Compile your data in a graph with t , the amount of time spent studying, on the horizontal axis, and L, the fraction of the list learned, on the vertical axis.