Thai-Duong Tran, Huston-Tillotson University
Today computers and on-line resources can help us to collect a lot of information in a very short time. This was demonstrated in many presentations at the Faculty Resource Network's Symposium in San Francisco last November. We can use the Internet to find the meaning of a word, to translate a paragraph to or from another language, to find the definition of Lie algebra, or to find a proof of the Stone-Weierstrass theorem. Students can find many different proofs of that last theorem in a very short time, but the question is whether they understand them.
Our students are now making beautiful presentations by collecting information from the Internet even when they do not understand the information. They have little trouble finding the information but a lot more trouble making sense of what they find. An analogy is that the average person now eats some good food but mostly junk food; nutritionists say the general public is getting fatter because of mindless eating. Our students fail because of mindless reading; they do not think while they read, and we did not train them that way. I have seen students excel in my classes just because they can read the textbooks.
I gave my students a reading assignment; they complained that two weeks were not enough time to finish the reading. On a test later, however, they requested use of the reading material. I asked them "If two weeks is not enough, what can you do in an hour?" but allowed it anyway. Indeed, they read the assigned material very fast, turning the pages quickly, and in only a few minutes decided that the reading material had nothing that could be used to answer the questions in the test.
I know this kind of quick reading, or "scanning," because it is the first level of reading that we implemented in our computer programs with artificial intelligence to "understand" the input and to act upon it. They (computers and students) do not really read or understand anything, they just scan the input for some keywords, which can be done very quickly.
Our students have actually been trained as scanners. They have been given "fill-in the blank" questions where scanning is the best algorithm. When other types of questions are given for reading assignments, they are given side-by-side with the reading materials. Such questions have trained students to search for answers to specific questions instead of to read for understanding.
To illustrate the point, imagine the following reading assignment
…Socrates was a man
…a man must die
Question: Based on the text, must Socrates die?
Answer: This question is impossible! The only thing that the text says about Socrates is that he was a man. It does not say anything about if he ever dies.
Example: In basic geometry, the students are given the formulas to calculate the circumference (perimeter) and the inside area of a circle. As you know, C = 2pR and A = pR2 where R is the radius.
The following question is given:
Joe drives around a round lake and determines that the circumference is 10 miles. Find the radius of the lake.
Many students "scan" through the book and then decide that they cannot solve the problem because there are no radius formulas. Students who solve the problem figure out that the formula C = 2p R actually gives a two-way relationship between the radius and the circumference.
However, many students still give up on the following question:
Joe drives around a round lake and determines that the circumference is 10 miles. Find the area of the lake.
They cannot find a single formula or statement that gives a relationship between the circumference and the area because they need to work between both the circumference and area formulas. Scanning simply does not work in this case.
Another example: In college algebra, students are taught to solve the following problems in exponential population growth A = P ert;:
The initial population is 5000 and the population 30 years later is 11000. Find the rate of increasing.
Given the initial population and the rate of increasing, find the time that the population will be a certain number.
After solving these two problems many times they still find the following question is difficult:
Suppose the initial population is 5000 and the population 30 years later is 11000. Find the number of years for the population to grow from 6000 to 8000.
This is a combination of the two problems above; again, simple scanning will not provide the answer.
"Thinking" vs. "Feeling" Questions
Many times, students answer the feeling of a question, not by thinking carefully about its wording. For example:
y is 10 less than x" is translated to y = 10 - x, or
Would you mind if I use your restroom? Sure!
Focus! Focus! Focus!
To read efficiently, students need to concentrate on what they are reading. Multi-tasking can create problems with concentration. Some well-known examples of multi-tasking problems include using cell phones while driving, and having a conversation while counting items. Lack of concentration is often caused by environment and can lead to bad reading habits. This happens to students who study in a cafeteria, at a bus stop, while watching TV, text messaging and/or listening to an iPod.
Reading and Writing
Reading is essentially the work of the mind, not of the eyes or the mouth. It also requires organizing and re-organizing to remember the knowledge and to make it useful. Reading and writing have a very strong relationship. A student learns more and understands better when he or she tries to rewrite their notes and/or explains the material to someone else.
Every time I attend a presentation or read a term paper or research report, I check not only that it is understandable, but also if the student understands their topic and if they are using their own opinions. Many times students just repeat something they heard or read on the topic even when it differs from their own thoughts. They are not answering the question "what do you think?" but "what does the professor like to hear?" This is similar to a witness who says something just because he reads it in the newspaper.
Intuition of the Abstract
Students understand more as they read more and increase their understanding of fields with which they were initially unfamiliar. Gradually, they also have to get used to abstract concepts, to improve the "intuition of the abstract" spoken of by Jean Dieudonne.
Beginning students do not like abstract statements such as:
For any two real numbers a and b, their sum does not depend on the order; i.e a + b = b + a, or
Sooner or later, our students must learn that such an abstraction and general statement is unavoidable. Common daily speaking style alone is not enough to train them to grasp this concept.
When I was giving a talk on this subject in San Francisco's Chinatown, I thought of a famous line of my hero, Mr. Bruce Lee, who he taught his students "don't think, FEEL!" I imagine if he were still alive, he would tell us "don't just feel, THINK!"