Chapter 3

Chapter III

Analysis of Student Writings

Difficulty with mathematics in general, or difficulty in learning algebra is not necessarily something to be proud of. Quite possibly it may even be quite traumatic, and the individual may unconsciously repress the entire experience. Lerner (1986) writes of the beginning medical practice of Sigmund Freud:

Freud began this private practice as an associate of another physician, Joseph Breuer. Breuer had been working to a great extent in the treatment of hysteria, a disease believed to afflict only women because it was held that the source of the disease was damage to the uterus. Breuer had successfully treated this disorder through the application of what he termed the "talking cure" (Boring 1950). Breuer hypnotized his patients and allowed them to talk about the emotional events associated with their difficulty. Thus, through use of the catharsis, or emotional release, Breuer was able to cure his hysterical patients. Freud readily adopted this method but soon modified its use. He found it equally, if not more, effective to allow his patients to talk completely freely about whatever was on their minds. Thus, by supporting such free association in his patients, Freud found that the same emotional releases could be produced without the use of hypnosis. Freud soon found that once such emotions were released, his patients would talk about things that they themselves thought they had forgotten.

With this use of the free association method, Freud was able to get his patients to reveal to him, and to themselves, what he termed repressed memories. These were memories of unpleasant feelings (affects, or emotions) or events that patients had experienced and because of their negative emotional valence, had actively kept out of their awareness. Because of the negative affective connotation of these experiences, they had repressed the memory of them; they had actively kept these unpleasant memories in an area of their mind, the unconscious, that contained only material normally not present in awareness.(p.108)

As a mathematics educator, the author was profoundly interested in why some students have disproportionate amounts of difficulty learning algebra compared to other mathematical topics. In an attempt to measure the effects of this "Algebra Anxiety", the author first tried to randomly interview people at a shopping mall. He found that many people did not want to be interviewed at all, and that many more refused after the topic of algebra was mentioned!

The author then constructed a survey based on the work done by Sheila Tobias in Overcoming Math Anxiety, revising several of the questions to specifically measure problems relating to difficulty in algebra, and more specifically the presence of letter variables. The surveys were then given to students beginning Math 080 classes at Minot State University. Math 080 is a remedial algebra class intended for students who did not take algebra in high school, or for some other reason have a lack of background in algebra skills. Instead of getting a response indicating frustration with algebra or variables, the responses indicated a positive identification with both topics! This the author believes to be a result of two factors. First, as the survey was given by the regular instructor on the first day of class, the students may have answered with the responses they believed their instructor wanted to receive. Second, it may well be an indication of what Freud called "repressed memories".

As an alternative plan, the author decided to parallel the work of Dr. Freud. As the author is not a clinical psychologist and cannot interview students individually using free association, he decided to set up conditions which should have essentially the same effect. Dr. Holmen, chairman of the Department of Mathematics and Computer Science at Minot State University, agreed to allow the author to teach the Math 080 course during the summer term. One class on campus in 1994, one class on campus and one at neighboring Minot Air Force Base in 1995, and again one class on campus and one on the base in 1996.

In each of the classes, the first class day was devoted to a discussion of attitudes towards mathematics, and the assignment at the conclusion of the class was for each student to write about their personal experience in mathematics. They were asked to write about either one of two topical ideas: 1. I hate math because. . ., or 2. I need to take this class because. . .

Because this is not an exercise in clinical psychology, the author felt it necessary to direct the comments in the area of mathematics, but as no specific requirement related to algebra, the responses should reflect free response within the area of mathematics. The students' responses are presented in full in Appendix 2. They have been edited only to take out references to individual names; grammatical errors made by the students remain intact.

A strategy had to be developed to classify responses. There was a total of 59 students in the five classes. In a general sense, 39 or 66% described a personal situation which would fall in the category of math anxiety. 20 or 34% simply said that they had a lack of background in mathematics

Figure 1. Total Math Anxiety

Of the 39 (66%) students who responded with math anxiety, 18 or 30% of the total responded in a way typical of general math anxiety. The other 21 students (36%), responded in a way that would indicate the math anxiety came from specific causes, namely, teacher actions in the classroom, and problems unique to studying algebra, or "Algebra Anxiety".

Figure 2. Math Anxiety Subdivided

Eight students (14%), cited specific incidents where the actions of a classroom teacher caused them to "hate" mathematics. Student C of the 1994 campus class writes, "I had no problem with basic math until 4th grade. My third grade teacher was 85 years old and not very instructive, so I must have fallen behind. In the 4th grade, I found I was behind in multiplication tables. Mrs. "Z" advised my parents when I earned my first poor grade of a "D", that I couldn't do math well. I must have believed that statement, as I found math a struggle from that point."

Student D (CC'94) said: "My math anxiety occurred when I was in the third grade. I was petrified of my teacher & I was called upon to stand and answer a problem which I was unable to complete. I started to cry & felt totally humiliated. Ever since that time I have had difficulty with numbers."

Student K (CC'94) said: "Third grade and Mrs. "X" was the beginning, I remember it vividly. I can still see her standing over me with her bird beak nose and that muscle that always twitched in her cheek."

The classroom activities chosen by the teacher can also be a problem. Student A from the Campus Class '95 writes: "I think it all started back in grade school. I liked math and found it even then a challenge and I love a challenge, until the teacher one day brought out "Flashcards" and made sort of a game out of it. When the first person in the far end of the room would stand beside the person behind him and see who could blurt out the answer first and whoever won would then go on, it wasn't that I didn't know the answers, I just never had the opportunity to win just once, and I think back then every kid wants to be able to win at least once. I believe that this is where my anxiety for math began and then continued on through high school where the dreaded "don't pick me", or the going up to the blackboard became the ultimate of all humiliation".

Student C from the campus class '95 mentions avoiding algebra, but not because of problems with the subject, because of problems with the teacher. "My worst teacher was Mr. H, who taught algebra during my 7th and 8th grades. (I don't remember ever thinking much about math one way or another up to that point.) Mr. H was the boys' basketball coach. (We didn't have girls' basketball back then.) It seems to me in retrospect, that Mr. H paid attention in class to the boys and the cheerleader-type girls. I, on the other hand, was skinny and shy, not a boy, and definitely not cute or popular. I somehow felt like I didn't fit into Mr. H's scheme of things; like I was "less than" the others there; attendance in his class became an increasingly difficult ordeal. Ever since then, I just haven't wanted much to do with algebra."

The classification of students coupled with poor teacher action, may cause the student to anticipate failure, and set low standards of achievement for himself. Student D (CC'95) writes: "In high school I had debated whether or not I should take Algebra or General Math. I attended a small school and had went to school with this same group of kids for years. Academically, I considered our group to be divided into four categories. First came the brains, which I was not a part of, second came the kids that obtained as good of grades as the brains, but had to work for it, I did not fit into this category either, third came the kids that worked but came up a little short (B's, C's and D's), this is the category I fell into. And finally, the fourth category was the kids that put no effort into school at all. I went into the algebra class knowing full well where I fit, but never the less I would give it a try. The fourth group I described above went to general math so now I was at the bottom of the class. I was still determined to learn this math. Within the first week of class I began to have trouble. I sought help from the teacher in the time provided before the end of the hour. This teacher was a single male, coach and as you described in class (I did not fit into his social class), he did not have the time for me nor did he want to take the time for me. He basically told me I would not understand the material and left it at that. Needless to say, I did not return to algebra class and finished my math credit with general math."

The primary significance of this type of math anxiety is that it is absolutely preventable. Teacher action can be changed, but only if the teacher is willing to change, and moreover, convinced that a change needs to be made.

Algebra anxiety, unique to the study of algebra, strikes the individual in a way that is unique to that individual, and quite commonly, the individual may not be aware that a unique problem exists. In some cases, it is obvious what the problem is. Student I (CC'94) writes: "I've always liked math (numbers). In high school I even got "A". Surprize! My freshman year I was introduced to algebra. I hated the class. I saw no reason to change all those interesting numbers to a + b =. I've survived for years without it. Now I face the challenge of it being a requirement to receive my degree. I've never been a quitter. I'll do this!"

Student B (CC'95) said: "One of the main reasons I am afraid of "Algebra" is because I've never had it before. It's unexplored for me, so I feel a little insecure about it. I don't hate other math, but when I look at all the formulas with letters instead of numbers, as in algebra, I become nervous and feel I don't understand, so I've avoided it all these years because when I was in High school it was not a requirement to graduate, so I never bothered with it, not knowing that one day I would regret it."

The anxiety may even caused by circumstances beyond the control of the student. Student E (CC'95) sites an interesting case of mistaken identity: "It all started when I transferred from (a North Dakota) High School to a high school in Dallas, Texas.

When I transferred from ND to Dallas, I was taking "Introduction to Agriculture". When I arrived in Dallas, they misread my records and put me into algebra in the middle of the year. They thought that "Intro. to Ag." meant "Intro to Algebra". I was lost big-time. After a month or so I was placed back into a general math class and was doing just fine.

Two years later I transferred to (another North Dakota) High School. I started taking algebra as a junior in high school. I was always pretty good at math but found algebra to be hard. It wasn't long before I started to copy other people's assignments. The more I copied the further I fell behind. It wasn't long before I didn't have a clue to what I was doing."

It is not uncommon for students to fail to recognize the source of the problem, which is commonly the presence of letters among the numbers. Student C (BC'95) starts off by discussing her history with math classes, and acknowledges she tends to repress the memories, by starting off with: "Now that you've rattled my brain cells, I do have bad memories of math teachers in my younger years." She then goes into a rather lengthy discourse about her experience with math teachers, including problems at the College level. She concludes her statement with a post script: "P.S. Letters don't belong with numbers in math."

Occasionally, students will describe the fear of algebra in quite graphic terms. Student I (BC'95) writes: "Well, now that I'm older, I like to think of myself as a renaissance woman, but without mastering this fear of algebra I can never really adopt that moniker. I remember reading some place that E. Gordon Liddy was one of the great confronters of fear. He feared rats, so he ate one to overcome his fear. I have to give algebra another shot, so here I am. This has to be easier than eating a rat. Maybe?"

The extreme case may be in the student who hated algebra to such an extent, he felt justified in quitting school. Student H (CC'96) writes: "I've had no problem in any kind of math until 10th grade. In fact math was my favorite subject until 10th grade, that is until I met 10th grade algebra. 10th grade algebra ruined my chances of graduating from high school. I hated it so much, I decided to change my classes and I got so mixed up in my studies, I just quit."

A method of classifying the student responses was developed by the author. Although the responses were diverse, certain consistencies became observable.

They were divided into four major classifications:

1. General math anxiety

2. Math anxiety induced by teacher action

3. Algebra anxiety

4. Lack of mathematics background

The general classification of student responses is as follows: Note, student responses have been coded for identification and statistical purposes. For example CC94A, would represent a student in the on "Campus Class", in the summer of 1994, student A from the list of students in that class. BC95C would represent a student in the class at Minot Air Force Base, or the "Base Class", in the summer of 1995, with student C from the class list.

Figure 3. Sources of Math Anxiety

Table 1

Raw Data, catagorized individual responses

Figure 4. Anxiety by Class

Table 2

Response by class

Figure 5. Composite Results

Algebra anxiety appears to exist in 22% of the overall sample, and ranges from a high value of 33% to an apparent low of 11%. It is also interesting to note that lack of background accounts for 34% of the total sample, and there is no way of accounting for the reason for a lack of algebra background. Why would students not take a background in algebra? It would seem that a perception of algebra being a more difficult course than other options presumably kept students away. This could be due to a general math anxiety, algebra anxiety that is not recognized by the student, or simple lack of motivation. In either case, it would appear that algebra anxiety does indeed exist, and may be a factor in course choices as well.

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