Mathematics and attitude to it; all children can do well
You often hear people saying mathematics is difficult, or beyond them. Amazingly that so many people do not consider that they can improve their performance by working at it. Round about ninth grade I learned to work, and put myself into it. There is no magic to it at all. It simply means that I would write down my homework and then in the evening I would try to do as much of it that I could possibly do: mostly I did all of the homework, including any assigned reading.
Yet in order to pass above ground level I decided to do more than what I was given to do, so I would practice more mathematics than I was given. It did not take long to realize that I would have to do my reading beyond what the teacher had given me. My brother saw me studying and suggested that in order to keep interest level optimal, I spend an hour per subject, instead of spending a long time on one, then move on to another subject. At that point I wrote the simplest of schedules for the week. I would do each evening perhaps three or four subjects spending more time on the more difficult ones. By this time I had come across a book on studying and that helped me to improve my technique even more. It taught me things like making notes since, it said, making notes allowed you to sink the point into the mind by both reading and writing it. Working like this I would complete all homework and then engage in additional work. In mathematics that means that I would do more practice than my teacher had given me. It was the same with literature.
Blaming the teacher seems a popular sport today but one has to wonder if it does our students any good. The suggestion that we evaluate our teachers according to how their students perform in tests seems like a morally questionable idea since one corollary of that idea is that the student has little responsibility for his academic performance in school. I have met a number of students, and among those many black ones, who show great ability in mathematics, yet who seem to assume that raw ability is enough to do well at mathematics; they, or most of them, simply do not commit to the subject enough to do well. As a consequence these students do not achieve their full potential, not by a long shot. With the kind of ability many students have they could really do well but they seem satisfied with getting along on very little, crumbs. I see potential engineers, scientists, computer scientists, survey technicians, nuclear scientists, but they don’t seem to realize what they could do with a little commitment to hard work. It cannot be forced on them. A number of reports state that students finish high school and then do poorly in university and eventually they drop out.  The attitude of perseverance which comes from studying is an important part of success in university.
Indeed I feel that this one of the reasons why American students perform the way they do on Pisa tests, they have not been stretched.
There are three levels of math practice that I have encountered. At the end of a section in the book or end of a chapter the first problems are usually such that the student can get through. This is important for you do not wish the student to get discouraged. These problems serve for the student to grasp the main ideas of the topic, reinforce what was learned, and for him or her to acquire facility with the basic moves. Then comes the next level which consists of more challenging problems demanding more thinking on the part of the student.
The difficult problem constitutes the third level; these are the problems which will stand toe to toe with the student exchanging blow for blow with you and will not give you their secret without serious and strenuous input of time and concentration. They demand that you read the problem a number of times to ensure that you understand the problem and exactly what it is asking. They force you to look up definitions and theory thereby ensuring that you understand the topic better, and insist that you consult worked examples for guidance; and they will resist you. They take up your time and when you meet them you know you are in a battle. Often times when working on them the concentration demanded is such that you are oblivious to your surroundings and need all your attention to be focused on the problem at hand; deeply pleasurable. Sometimes the answer comes when you wake up the following morning. They vary in how much they demand from a student but they ask much more of the student than the first two sets of problems. These problems are absolutely important for the development of the student. When one encounters a difficult problem he knows because the answer is not forthcoming. Without doing the difficult problems the student cannot claim some mastery of mathematics.
Study is the word used in acquiring this kind of attitude and it indicates, for me, that the young person is beginning to take care of his or her learning. He or she has work to do and once home in the evening will dedicate the necessary amount of time to getting the work done on time; and then do the work for excelling. He has now acquired a work ethic which will be with him for life in all his pursuits.
For many people the skill gained is the product of effort and they recognize that achievement takes an input from them. There are books which will help the student acquire the necessary skill in studying and streamlining his efforts in learning. So when I speak of education and learning I include the effort made by the student in his acquisition of knowledge and thinking skills. The attitudes and skills go far beyond the knowledge itself and include perseverance when the problems are difficult, keeping deadlines, and using one’s time wisely.
Once parent and student understand that this is necessary for mathematical skill and for educational growth in general then there is every chance that the student will do well in school. There are people of course who are just gifted and no amount of studying will make us surpass them. But our objective in studying is to be the best we can and not to run races with those types. Many then, of our students, can vastly improve their mathematical achievement by simply studying and practicing more at mathematics. This is a foolproof plan and never fails.
Let me quote from ‘Gifted Hands’ by Carson. “I’ve decided you boys are watching too much television,” she said one evening, snapping off the set in the middle of a program. Mother had already decided how we would spend our free time when we weren’t watching television. “You boys are going to go to the library and check out books. You’re going to read at least two books every week. At the end of each week you’ll give me a report on what you’ve read.” So then the mother made a decision, something which parents have to do at some point in their children lives. At first Ben obeyed, but without joy, however he noticed that he was improving in school and states: ‘As I continued to read, my spelling, vocabulary, and comprehension improved, and my classes became much more interesting. I improved so much that by the time I entered seventh grade at Wilson Junior High, I was at the top of the class.’ This is an incredible transformation, but it is my deepest conviction that it is something which can happen to any number of students who decide to work at their school work; that included mathematics. Good schools and teachers can so a lot but in the end the student has to do it.
This development is important for higher education since the organization and study skills gained in upper high school will carry over into higher education and indeed into life itself. One of the important things in university is the use of time. Since in university there is ‘free time’ and there is no one to push the student then only if the student has developed time management habits will he know how to use time. He should already have learned that such time is to be spent in the library of if at home he or she should be doing his work. If not his work piles up and he fails eventually.
 Weissman, Jordan (2014): America’s Awful College Dropout Rates, in Four Charts. Available online at http://www.slate.com/blogs/moneybox/2014/11/19/u_s_college_dropouts_rates_explained_in_4_charts.html
 Gifted Hands, Ben Carson, p 35, 36.