Student G was an elementary school student. He was in grade 6 when we started tutoring classes. He did not know multiplication table, and consequently, he could not learn how to divide numbers. He could not complete the academic requirements of grade 6 and the school decided to put him into the special education class with other weak students that require extra help.
The whole story:
I started to teach the multiplication table. I gave him all tips and tricks on memorizing multiplication facts. I explained how to use some facts that he remembers to calculate multiplication facts he doesn’t.
I can not agree more.
“In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures; so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended. John Fauvel and Jeremy Gray (eds.) A History of Mathematics: A Reader, Sheridan House, 1987.”
Have a nice summer!
Some middle school topics.
Recently, I was surfing the Internet and encountered an article written by professors of Mathematics that were sharing their experience with the middle school math curriculum. The article is called, “Why is it your job to teach your kid math?” The authors of the article were helping their children understand various alternative method offered by school teachers such as using grids, blocks, counters, or strips of paper to perform operations on fractions. The professors realized that children can not untangle themselves from the confusion created by these variety of methods without their parents and ended up organizing a Math club at home to help their neighbors’ and friends’ children to understand Math topics better. If you are interested in reading this article here is the link: “Why is it your job to teach your kid math?”
I understand that the developers of the school curriculum wanted to appeal to all psychological types of learners by creating all these alternative methods. But, I do not understand why children are tested on understanding and using these methods. For any math student it is important to be able to perform arithmetical operations quickly, correctly and with ease. Which method a student is using is supposed to be a matter of his or her choice, - whatever makes more sense for him or her. My tutoring experience proved that classical, “old fashioned” methods are more easily understood by children.
Student R. is a highly intelligent boy who is motivated to learn math. Moreover, he has an interest in and enjoys the challenge of the course. When a new topic is explained by the teacher in class he listens attentively and understands the algebra of the steps. But when it comes to apply the same steps to a different situation he gets stuck in the middle of the problem, which reveals that he does not have a deep understanding of the logic behind each step.
The problem with R. is that he does not know how to listen to the explanations of Math topics. He did not develop the “Math listening” skill which tells the mathematician to “think about the logical reasons of the steps not the algebraic simplifications”. Student R needs to understand the theoretical, abstract part of the concepts first. Then he has to solve a few more questions with different variations of the same concept applying his knowledge by himself.
How to think.
The difficulties of learning Mathematics are based, very often, on the inability to initiate, understand, trust and control mental processes by our consciousness. The brain is an instrument, but we have to learn how to use it. Our mind is capable of thinking and figuring out the solution to many Mathematical problems if we feed it with precise data, formulate the question clearly and listen to what the intuition is trying to tell us. Of course, we are assuming that a learner has strong foundations in previous knowledge and has acquired practical skills in applying it.
Two months of “Math torture” are over and some of you realized that marks are lower than you expected and aimed to get. You can improve your test performance by changing your studying routine. Here are some tips that, I am sure, will help you to do better.