- Education and Science
Problems Encountered with Mathematics
Finding Confidence and Help with Math
Problems Encountered with Study Skills in Mathematics
Mathematics is a source of problems for many people. This article is devoted to assisting students with their studies in mathematics regardless of the level. It is not written in equations, so please open it and read. You may find something of value.
Good Students Who Place Low in Mathematics when Entering College
Some years ago I was sitting in a mathematics faculty meeting at a university when the Assistant Dean of Science presented the mathematics faculty with a problem. Many students are taking advanced mathematic in high school in accelerated programs, but these same students often place in developmental mathematics. What is even worse is that many of them fail to pass the developmental course into which they place. The challenge was to figure out what might be the problem, and fix it.
This indeed seemed at first to be a contradiction. However, after some reflection it became evident that the most likely source of the problem could be the time lag between taking algebra and taking the placement test. The placement test for algebra was the first one given, and if a student passed it additional testing for trigonometry and calculus were in order. It appears that, while these students have many mathematical skills, they tend to become rusty in the skills they have learned several years prior to entering college. And, when a student is placed in the wrong class, as they assume they have been, they often have a tendency to assume there is no need to study. This can lead to the low grades that cause the gifted students to languish is developmental mathematics.
The remedy is quite simple. Review the basics before taking the placement test. Once a person learns mathematics it is often a simple matter to bring that understanding back. But how could this be accomplished? I recommend Algebra Review Before College. This is available on Amazon and as a Kindle book.
Preparation for the mathematics placement test at a college may save several courses, and prevent damage to self-esteem.
Books to Overcome Math Anxiety
I am the author of three of these.
Studying Math: Overcoming the Anxiety and Fear
Many students have an unusual fear of math. Frustration and lack of past successes often are the causes of math anxiety.
How can a student overcome math anxiety?
First, it is necessary to determine what study skills are necessary for success.
Second, it is necessary to believe success is possible. This means POSITIVE THINKING!
Third, it is necessary to stop worrying about the past.
The study skills for math require that one realize math is learned differently than most other subjects. Math cannot be learned by memorizing facts. Math involves developing a process of logical thought. The good news is that math can involve using skills already developed. The only way to get past math anxiety is to develop appropriate study skills.
1. Practice. While other subjects might require reading, math requires practice. But practice in a way that reinforces the skill. It is inappropriate to practice problems, if they are being done incorrectly. NEVER work a problem that you cannot check! Reinforcing the wrong technique increases frustration and wastes time. NEVER work a problem until you have checked the last one, or you may repeat the error. NEVER work past a problem with an error until you either get it correct, have looked at an example, or found other help and have corrected the problem.
2. GET HELP! Often there are several ways of working the same problem. Search until you have found a method you understand. Your resources include:
a. Notes from class,
b. Ask a friend,
c. Ask your instructor,
d. Go to tutoring,
e. Read examples in the text carefully, and
f. Get in a study group. Peer learning is effective.
It is sometimes best to go to different sources of information simply because you then have several options to choose from. But be careful not to blend different approaches and add to the confusion.
Believe in yourself! Get that POSITIVE ATTITUDE
Ask yourself, did I study? Did I work each type of problem until I could work it correctly? If you answer yes then why would you not duplicate your success on a test? So, if you have prepared properly, expect to succeed.
Ask yourself, am I not as smart as others in the class? Were there students no more intelligent than myself who have passed
this class in the past? Of course there were, so why shouldn't you?
Don't dwell on past failures. Do you own a calculator? Did you bother to learn how to use it? Delegate the arithmetic, and eliminate many careless errors. With the careless errors gone you should miss more problems and pass, with a good grade. So stop worrying and prepare to succeed.
Reduce the problem length by adding one or two ideas to what you already know. Looking at an example of solving a quadratic equation can be
intimidating. However, realizing that only one or two new steps gets you to solving linear equations makes the problem reasonable. Increase your problem range by building on what you know rather than starting from scratch. SIMPLIFY!
Work in as few steps as possible. Every step is a potential careless error. Fewer steps means higher grades! Higher grades eventually lead to POSITIVE THINKING!!!
Improve you test taking skill. Work the problems you know first. If there are enough of these that you are confident of passing, RELAX! This will increase your grade. If you can reduce the tension your grade should respond.
So, recapping the significant points:
Take tests in a way to help your grades.
Forget the past.
Build on old material rather than become overwhelmed with complex problems.
• BELIEVE in yourself.
Why Am I Not Able to Learn Mathematics?
This is a question many good students ask. It is not uncommon for a student to have excellent grades, yet find difficulty with mathematics. Why is this so?
The problem may not be in lack of intelligence, nor an inability to learn mathematics. The problem, most likely, is that the wrong study method is being used.
Mathematics cannot be read with great concentration and produce the same results as reading with understanding would in disciplines such as history or literature. Employing valid study skills that work fine in those disciplines will usually result in disaster. Mathematics is learned by exercising the mental task of solving problems. Reading mathematics is only valuable to understand the definitions and theories, the tools with which you can work. And rote learning, the technique that gets so many people by the lower grades, fails when the problems are all different. Unfortunately, rote learning, mimicking problems that are given as examples in the book, may just be enough to get by in a high school where thought is not fully being challenged. But, college mathematics requires taking the parts and coming to a logical conclusion called the solution, based on reasoning.
The best advice is to practice! Practice the problems for which answers are given, for it is counter-productive to work problems wrong and not know there is a problem. Working problems without checking them can, in fact, reinforce the wrong technique.
With the practice should come the enlightenment. With the enlightenment should come the end to the disillusionment.
The key is to believe in yourself, not the study method. Change the study method and become reassured in your ability.
There are two things that can help with the process. Take a philosophy class in logic. The skills will carry over to mathematics. For a technique that is more fun, play chess. Knowing the consequences of a move is a very similar skill to the results in applying a mathematical operation. Look what can happen if different pieces are moved, and develop the mental process needed for mathematics.
Math Study Guides
Math Study Guide
Support Material for College Textbooks
For some reason publishing companies do not advertise the support material for textbooks. But an abundance of support material is out there. Even if your textbook does not have support material, a similar book does.
Support material consists of videos, which are great for making up missed classes or for getting a second opinion, Study Guides that outline the important material for you so you need fewer notes and can listen more attentively in class, and Solution Manuals that give WORKED OUT solutions to many problems. If properly used, these can be invaluable. And most are inexpensive.
To find these go to the Amazon link that follows this article and click on any book shown. Then type the name of your textbook into the key word search. Do not use the author's name, since these items are often produced by other authors working on contract for the publishing house.
Do you have a greater insight into why mathematics is difficult?