April 2002 Issue
Overcoming Or Preventing Math Anxiety
That Causes Learned Helplessness In Mathematics
By Gary K. Probst
Email:probstgk@pg.cc.md.us
There are many reasons given why students are not successful in learning math. One reason usually given is the students have a condition referred to as math anxiety. Math anxiety can be defined as a state of being uneasy, apprehensive, or worried about what will happen when taking a mathematics class. The effect of math anxiety is a feeling of being powerless and unable to cope with the threat of taking a mathematics class. What has happened is the student has become what is called learned helpless in mathematics. The student who is learned helpless in mathematics has learned that no matter how hard he or she studies, he or she will not be successful. If you are not familiar with learned helplessness, you should learn more about the cause and effect of this terrible condition on an individual. A discussion of learned helplessness is beyond the scope of this article.
There are many reasons given why students have not been successful in mathematics. However, one reason is the method used to teach mathematics this past decade. This method went by names such as new-new math, fuzzy math or rain forest math. Because of the failure of this approach, the term now used to describe this method is referred to as the constructivist approach. For a review of the difference between the constructivist approach and the traditional approach to mathematics, read the outline given at http://www.wgquirk.com/Massmath.htm. For a good overview of what went wrong this past decade in mathematic education, go to the following web site where there are many articles http://www.mathematicallycorrect.com. If you do a web search using the term “mathematically correct,” additional sources of information can be found.
When a student comes to college deficient in mathematics, it is not helpful to know why they are deficient. What must be done is to immediately place the student into a program of remediation so that the student quickly becomes successful in mathematics. The purpose of this article is to give suggestions regarding what must be done to give the deficient mathematics student the skills and confidence to develop the ability to become successful in a college level mathematics course.
By using the definition of math anxiety, an approach to begin remediation can be developed. What must be asked is why is the student (1) uneasy, (2) apprehensive, (3) worried, and (4) feeling powerless and unable to succeed in mathematics. What is required in a college remedial mathematics class is to remove and prevent the learned helpless condition in mathematics that has persisted for many years.
To overcome and prevent a learned helplessness condition
in mathematics, an approach to remediation should be developed that addresses
the following six areas:
 | Multiplication Tables |
| Prerequisite Skills |
| Vocabulary Skills |
| Accuracy |
| Practice Time |
| Study System |
*~*~*~*~*~*~*~*~*
Multiplication Tables
There was no emphasis or very little emphasis in public schools using the new-new math approach to learning the multiplication tables. In fact, teachers were told not to teach the multiplication tables through drill and practice. Teachers were told the students should learn the tables through “discovery.” Since the calculator was used in all mathematics classes, learning the multiplication tables was said to be a waste of time. The problem with students becoming calculator dependent is that calculators do not factor. A calculator does permit you find the LCD of 8, 14 and 21 in a mathematics course. In algebra it does not help you factor a trinomial. If the student does not know the multiplication tables and is not familiar with using them, he or she is helpless when trying to add and subtract fractions and solve a trinomial.
Suggestion:
Give a two part timed factoring test to students. Part One has numbers to
factor such as from 4 to 40. Part Two of the test has numbers above 50.
If the score on Part Two is lower than Part One and/or the student takes more
time on Part Two than on Part One, the student needs to review the
multiplication tables that need to be learned or relearned.
*~*~*~*~*~*~*~*~*
Prerequisite Skills
Usually students are placed into a mathematics class by having a certain score on a standardized mathematics test. What a standardized mathematics test does not reveal are the specific mathematics skills a student is lacking. The result is that some students score high enough on the standardized test to be placed into a higher level developmental mathematics class or are not required to take developmental mathematics. These students could have several specific weaknesses such as not knowing how to divide fractions. When a mathematics skill is introduced in class that requires knowing and applying a prerequisite mathematics skill that is not known, the student is helpless if he or she does not know the required prerequisite math skill.
Suggestion:
Develop a criterion-referenced test for placement into developmental algebra
that measures all of the mathematic skills covered in a basic mathematics
textbook. This test would be similar to the diagnostic test found in the
beginning of some algebra textbooks. If a student needs to learn only a
few basic mathematics skills, they can be taught through a individualized
computer-assisted instructional program. If a large number of mathematics
skills must be learned, the student should not be permitted to take algebra and
be required to take a mathematics class.
*~*~*~*~*~*~*~*~*
Vocabulary
There are three reasons why vocabulary skills are lacking in mathematics students. One, mathematics like any course has a specialized vocabulary that must be learned. In a basic mathematics textbook there are around 300 mathematics terms introduced. Instructors in most subject areas, especially mathematics, do not see themselves as vocabulary teachers. Therefore, new mathematics problems are usually introduced and worked without any development of the specialized vocabulary that is required to understand and apply the concept of how to solve a specific type of problem.
Two, mathematics textbooks often give poor definitions of terms. It is a joke among the developmental mathematics faculty at my community college when a new program is demonstrated by a sales representative. I always ask the sales representative to give me the definition of numerator and denominator as used in the program. Most textbooks define these terms as the number above the line and the number below the line. This is not a definition of these terms. Sometimes the book will give examples of a numerator and denominator using pie charts. When this is done, a student has to develop a definition of a numerator in his or her mind. It is difficult to develop a definition from an example in mathematics. Examples used in place of definitions are found frequently in mathematics textbooks and expensive mathematics software programs.
Three, new concepts are developed in which the student does not have the prerequisite vocabulary. For example, a developmental course in beginning algebra starts out with the following rule:
Solve: a/4 = 3
Rule: Replace a/4 by 1/4a since division by 4 is the same as multiplication by ¼. Get a alone by multiplying both sides by 4, the reciprocal of the coefficient of a.
In order to understand this rule the student must know why division by 4 is the same as multiplication by ¼. Also, the definition of “reciprocal” and “coefficient” must be known in order to recognize an example of these terms. If an example of these two terms cannot be recognized, it is impossible to apply the rule.
If a student does not know the terms used in a mathematics class, he or she cannot understand any of the information and apply the rules. Thus, learning mathematics becomes impossible.
Solution:
Developmental mathematics instructors must introduce the new terms used in
mathematics. Practice should be given in recognizing examples of each
term. A list of terms that are introduced in each chapter in the mathematics
textbook should be given to each student if the textbook does not list these
terms.
When constructing a mathematics test, divide the test into two parts. Part One would be a test on the vocabulary terms introduced in the chapter. Part Two would be a test solving the problems introduced in the chapter. If the student knew he or she would have to know the vocabulary terms in order to pass the test, he or she would have an incentive to learn them. Also, if the students has not learned the definition of the terms used in the course, the student, not the instructor, is accountable for not being successful in the course. This is an excellent way to shift the accountability for success in mathematics to the student.
*~*~*~*~*~*~*~*~*
Accuracy
In some public school approaches to mathematics, credit is given for setting up a problem but not getting the correct answer. The student soon learns that accuracy is not necessary to pass in mathematics. However to solve 5 7/8 + 2 ¾ - 3 thirteen steps are required. If you miss one of these steps, this problem cannot be solved. Accuracy is very important and required in mathematics. Most mathematics problems’ solutions require many steps to be successfully completed. Each of these steps is a lower level mathematics problem. In mathematics the higher level skills always require several lower level skills be accurately performed in order to solve a problem.
Solution:
Require students to be accurate in mathematics in order to pass. Ask them
what accuracy rate they expect in their doctor, tax accountant, auto mechanic,
cook, etc.
*~*~*~*~*~*~*~*~*
Time – Practice
Mathematics, like the winning University of Maryland basketball team, requires much drill and practice. Can you imagine any coach telling the basketball team that drill and practice are not important. However, in new-new math it was called drill and kill. Practice was not emphasized. In order to become proficient in mathematics much drill and practice is required to maintain the skills learned. If any skill is not practice, it is soon forgotten. It is a waste of time to learn a skill then never practice it.
Solution:
Emphasize that retaining any skill learned requires practice in order to
maintain the skill. Inform the students that in order to learn mathematics
they will have to spend more time studying than is usually required in most
college courses. Also, the frequency of studying should be emphasized
because of the affect of the learning curve.
*~*~*~*~*~*~*~*~*
Study System
A student needs to learn how to learn the information in his or her mathematics textbooks. He or she needs to learn what to do before, during and after reading the information and doing the practice exercises in his or her mathematics textbook. . Developmental mathematics instructors in college must teach the study skills required to learn the information in their textbook. This has already been started in my community college.
Solution:
Along with the mathematics faculty the instructors of reading and study skills
should be used as consultants in developing the study skills required to be
successful in mathematics. However, the study skills should be taught by
the mathematics instructors. If the mathematics instructors introduce
study skills along with the mathematics skills, the students will see why they
are required.
*~*~*~*~*~*~*~*~*
With the current low percentage of students passing developmental mathematics classes and continuing on to credit mathematics courses, it is imperative that these six areas be addressed in any college developmental mathematics program. With the proper instructional design taking into consideration these six factors, students will have a chance of overcoming their math anxiety and becoming successful mathematics students. A program to reduce math anxiety without removing the causes of the math anxiety will only produce greater math anxiety.
To see how I address these six factors in my online developmental mathematics classes, click on http://academic.pg.cc.md.us/~gprobst/DVM%20005%20Prevent%20Failing.htm
*~*~*~*~*~*~*~*~*
Please send comments on this article to probstgk@pg.cc.md.us
http://academic.pg.cc.md.us/~gprobst/
*~*~*~*~*~*~*~*~*