1Nathematics Education Research /ournal

1994, Vol. 6, No. 2, 131-143

What Makes a Person Mathsphobic? A Case StudyInvestigating Affective, Cognitive and SocialAspects of a Trainee Teacher's Mathematical

Understanding and Thinking

Jean CarrollRoyal Melbourne Institute of Technology

'The negative attitudes of some student teachers towards mathematics and theinadequacy of their mathematical backgrounds have been a concern of mathematicseducators for many years. In an attempt to understand the interaction of cognitiveand affective factors in mathematics learning, this paper presents a case study of onepreservice early childhood/primary teacher education student's experiences oflearning mathematics. The study identifies issues which are of concern both toteachers and to teacher educators.

IntroductionThis research has arisen in response to observations and empirical research

conducted during ten years of working with primary school teachers and studentteachers who are learning mathematics. A significant aspect of this work is dealingwith the negative aspects of affective factors, such as attitudes, appreciations,emotions, feelings, beliefs and values, on classroom participation and performancewhen learning mathematics. Many people seem to be constrained by negativeattitudes, beliefs and feelings about mathematics and mathematics learning. Anumber of teachers and student teachers exhibit and report a high level of anxietyin relation to their own mathematics learning. This is often associated with poorperformance on tests of mathematical competency relating to a number ofmathematical concepts. The author's experiences of and concerns about theinteraction of mathematics learning and affective factors have been corroboratedby researchers in Australia and internationally.

McLeod (1992), in a wide-ranging review of research into affective factors andmathematics learning, identified problems in defining the terms used in discussingaffective factors. He noted that a lack of consistency in the definitions used resultedin a range of meanings for affective factors which often overlap each other, and alsothat the same terminology can be used to describe phenomena which areessentially different. Further definition of affective terms can be found in Corsini(1984) and Hart (1989). This study will not attempt to define components of affect.The meaning of the terms, as they arise, can be constructed from the context.

Investigations of the interaction of affect and mathematics learning have beenconducted by many researchers (see, for example, Bar-Tal, 1978; Buxton, 1981;Fennema, 1989; Hembree, 1990; Mandler, 1989; and McLeod, 1992). Researchreported by Hart (1993) on this topic focused on teachers and student teachers. Theeffects of affective factors on mathematics learning are now clearly acknowledgedand there is a growing body of research on the topic (see for example, Leder, 1993).

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In Semester one, 1993 the author taught an undergraduate subject inmathematics education to first year students who were preparing to be earlychildhood and primary teachers. In addition to their curriculum studies, thestudents in this subject were required to sit a test of primary mathematics andachieve a score of at least 70%. This requirement is often a difficulty for manystudents, but for one particular mature age student (who will be called Chris) itappeared to be almost an impossibility. On her first attempt at the test, early in thesemester, her mark was 3%. A subsequent attempt (three months later), after asemester of lectures on aspects of teaching and leaming numeration andoperations in kindergarten and primary school, resulted in a mark of 8%. Duringthe semester the author had a number of conversations with the student about herwork. She seemed well aware of her problems in mathematics, extremely anxiousand embarrassed to think that her peers would discover her lack of knowledge, yetshe was found to be highly motivated to succeed. This student agreed tocollaborate with the author on this study during Semester two, 1993.

This research is a case study of one person's experiences, understandings andfeelings about learning mathematics. A similar study, on a much larger scale wasconducted by Buxton (1981). He worked for 72 hours over a year with seven adultsin an attempt to explore the negative feelings that people had about mathematicsand to investigate the causes of these feelings. He was also interested in seekingways to overcome their anxieties.

Method

The study was designed to investigate Chris's understanding of mathematics,the structure of that understanding, and associated affective factors. Because of thedifficulty in accessing thinking and feelings, a range of approaches has been usedto collect the data. A series of interviews, a questionnaire, a diary, a mathematicstest and a mathematics curriculum test were used.

Six one-hour interviews were conducted over a period of three months inwhich the subject was encouraged to recall incidents which involved or wererelated to learning and using mathematics, and to describe them in detail. She wasencouraged to think about her experiences in primary school, secondary school, indaily life and at university.

A method similar to the narrative inquiry approach used by Chapman (1993)has been used in this study. In her research Chapman had teachers write storiesabout their personal experience of teaching, including as many details as possible.She then reviewed them for themes or patterns underlying the behaviour.(Chapman also had the participants review their own narratives; this study doesnot include that aspect of the analysis).

The interview approach described by Hoyles (1982) was also employed. Hoylesset out to collect subjective descriptions and interpretations of learning situationsusing a loosely structured interview which allowed for probing and reiteration ofdetail. Aspects of interviews were revisited in subsequent interviews when it wasfeit that more detail was necessary. The interviews inciuded the presentation anddiscussion of mathematical tasks. This discussion related to the subject's reactionson first seeing the task, her memories of similar tasks in the past, along with the

What Makes a Person Mathsphobic? 133

feelings that these memories evoked, and how she would do the task.The questionnaire used in this study required Chris to recall past instances of

mathematics learning and to elaborate upon them. Some examples of the questions

are:

Try to remember a time when you were learning mathematics in secondary school.What was happening? How were you feeling then?Can you remember a time when you feit really good about learning mathematics?

What do you think about the way that you have been taught maths?Do you think that another way would have been more suitable?

It was feit that the use of a questionnaire would allow her time for deepreflection, rather than asking the same questions under the pressure of aninterview situation.

After each interview session the subject was asked to record her reflections onthe interview in a diary. She was also asked to write down any other thoughts andfeelings that arose between sessions in a diary. This provided a less structuredavenue of investigation as she was free to write about anything rather than feelconfined to address questions posed in the interviews and questionnaire.

Samples of Chris's work on mathematical tests were collected to provideinformation about her mathematical understanding. These consisted of her workon a test of primary mathematics which included questions like:

Write 0.53 as a common fraction.Name the unit which you could use to measure the area of a postcard.Jeff has been given 30 daffodil bulbs. If he put 2/3 out the front of his house and 1/3out the back, how many wilt go out the front?Write the name of this number in words: 10 455 002.

Draw a rectangular prism.

The tasks discussed in the six interviews were also of this type. In addition, herwork on a test of preschool and primary mathematics curriculum was examined.Questions were based on the content of the first semester mathematics educationsubject on numeration and operations in the primary school—the unit that Chrishad completed. The following are examples of the questions:

Describe the place value system.Describe the area concept of multiplication.Why is the ability to rename numbers an important skill?Preschool children participate in activities and games which have the potential todevelop many mathematical ideas. Discuss the strategies that you would use tomaximise the mathematical potential of the activities. Give examples.

Analysis of the Data

The six interviews were taped and transcribed. All of the data were analysedusing a technique derived from a phenomenographic approach described byMarton (1993). In this method, data collected from interviews with a number ofdifferent subjects were analysed by disregarding the barriers between the subjects,

13.E Carroll

treating all of the data as a whole and identifying patterns in the data which werecalled "categories of description." In the present study the data collected has beentreated as a whole, disregarding the barriers imposed by different types of data(interviews, questionnaire) and different episodes of the same approach (forexample, different interview sessions). The data have been analysed to identifypatterns or themes.

Results

The analysis of the data revealed three broad categories into which much of thedata could be classified. Cognitive and affective factors were anticipated but, aftersorting, a third broad category—social factors—which related to Chris'sinteractions with other peopie, also emerged. A fourth category, which wasclassified as "teachers' questions" related to the feelings aroused during questiontime in the classroom and seemed to be connected with both affective and socialfactors:

Affective Factors

A number of affective factors were identified in the study. Chris's reflectionsabout her experiences in learning mathematics were closely linked with strongfeelings like anger and frustration:

I tend to get really frustrated, angry and frustrated and get red in the face and justfeel like walking out but I never do ... It just got too hard and too complex. I wasgetting too frustrated. I don't think 1 was learning that much.

On a number of occasions she refers to feelings of physical pain associated with thestress of doing mathematics. This is a description of how she feit when she wasasked to add two decimals:

... having to do this, I found it to be stressful because I guess I just don't know myown ability because these might be perfectly right but they are not right in my own,how I foresee it. I mean if I had to um and aah about something that is perfectly rightI'm just not sure of my own ability. It's like this real pain stricken thing.

Associated with these feelings is an attitude towards the mathematics which shedescribed:

I must have had such aversion to maths, such hate of maths ... I had some aversion toit that I just turned off. I still kept on doing it. Maybe at high school if they had got tothe root of the problem that might have helped me. I still think I developed at a veryyoung age that dislike of maths.

Two aspects of beliefs emerge from the data. The first is a belief about herself. Shesaid:

I always thought it was me, I have got problems but it wasn't necessarily me.

This theme of external attribution is followed up in the analysis of social factorslater in this paper. The second aspect, beliefs about mathematics, could easily

What Makes a Person Mathsphobic? 135

account for barriers to thinking about mathematics and also may relate tomotivation. When asked what mathematics meant to her she replied:

It is something that I have to do but then probably won't be useful for me later on ...it's not going to be useful.

Schoenfeld (1985) found that students' beliefs about mathematics determine howthey choose to approach a problem and may weaken their ability to solvenon-routine problems.

In all of her work on mathematical tasks Chris's lack of confidence wasapparent. Answers which seemed to be well considered were usually accompaniedby comments like:

Today I feit that I was struggling with the problems. When I saw the page my mindwent blank ... My mind always tells me my answer to any question presented to meis wrong ...

This might be really completely wrong but it is just my understanding ... 1thought I knew where it was but it's just a silly guess, no, I really don't know ... Icould_ but I don't think it would be right. This is just a real guess, this is such a wildguess anyway.

Her comments about affective factors revealed that Chris had strong negativefeelings about learning and doing mathematics particularly in relation to herprimary and secondary school experiences. A clear lack of confidence in her ownability to do mathematics combined with her belief that mathematics would not beof use to her, could have been a negative influence on her ability to learnmathematics. However, it is significant that she has now realised that the cause ofher problems in mathematics was not necessarily herself. Her lack of confidence inher ability to solve mathematical problems was evident in the interviews and onthe tests as shown by her reluctance to answer a question unless she was certainthat she was right.

The data reveal that Chris had experienced a positive change in the area ofaffect since commencing her university studies earlier in the year. In this excerptfrom an interview she spoke about enjoying learning mathematics now:

I must admit that for the first time in my life that I really enjoyed maths, having mytutor ... I enjoy going back to the basic maths that I remember as a child. I reallyenjoyed learning but then when it got really hard I stopped. I did enjoy the revisingand even though a lot of the stuff! knew 1 suppose I enjoy the one-to-one-ness with itand the fact that it's private.

She was also confident of her ability to succeed in passing the mathematics subjectsat university. This confidence was often linked with her appreciation of the supportgiven by teachers and her tutor who work with her in a one-to-one situation. Herincreasing confidence in her ability to succeed was evident in the followingcomments:

If you had asked me about maths last semester I would have said no way, 1 willnever pass, no way. I will never understand it but I feel that as time goes by; yes ...

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Well it might take me seven times to repeat maths to get there but it is confidence,support, like my tutor has really supported me and made me believe that I can do itwhich I found to be such a help. I just sort of feit by being at university, like thesupport of you Jean, like Maureen, having a really confident attitude about me doingmaths, and Cathy. It has just been such a help to me, just the support. It has reallybuilt my confidence. So that is really important to me, and it has taken a while.

Cognitive FactorsAlthough it was anticipated that it would be possible to chart the extent of

Chris's mathematical knowledge and understanding, the nature of herunderstanding was found to be a more significant discovery. Analysis of the dataregarding Chris's thinking and mathematics learning revealed that hermathematical understanding could best be described as instrumental (Skemp,1979). Instrumental understanding, in a mathematical situation consists of beingable to recognise a task as one of a particular class, for which one already knows arule. Skemp also detailed relational understanding, a more usable form ofunderstanding, in which mathematical problems are solved by relating elementswithin and outside the problem to appropriate schema. In any learning task, themost obvious immediate goal of the learner, according to Skemp, is to give theright answer. In relational learning, the right answer is an indication that thelearner recognises appropriate relationships between concepts, skills and theproblem situation. In instrumental learning it is the other way around=the rightanswer is the goal, and the rule is the means of getting it.

The *instrumental nature of the subject's understanding was repeatedlydemonstrated when working on mathematical tasks. For example she was asked towrite 0.72 as a common fraction and did this correctly. When asked to discuss howshe knew this she said:

There is two numbers on the top followed by three numbers on the bottom.

She seemed to be aware of the instrumental nature of this response as she thensaid, "I don't think this is a mathematical answer." This notion was followed up inher diary when she said:

... but I understand that I needed to know the process of how it works not just get theanswer.

An entry from her diary reflecting upon this episode and my subsequent attemptsto relate the question to decimal place value ideas, shows that she had someresistance to taking up a relational approach when an instrumental one would do,and also shows the extent of emotional involvement in the situation.

I feit frustrated and emotionally hurt that I was not able to understand or tackle theproblems. I walked away from the session wanting to cry. Questions that came tomind was why was Jean explaining something in such a long and difficult way,when all we were doing was common fractions and I knew how to get the answeranyway.

This excerpt demonstrates her desire to have a quick and easy way to get theanswer and her resistance towards connecting the underlying ideas together.

What Makes a Person Mathsphobic? 137

A further example of the absence of evidence of relational understanding wasdemonstrated when Chris was asked to place the decimals 0.801, 0.819 and 0.81 inorder from the smallest to the largest. Her explanation for ordering them 0.81,0.801, 0.819 was that the smallest number is 0.81 since 81 is closest to 0, then 0.801because 801 is smaller than 819. It would appear that Chris was restricted tomanipulating symbols because of a lack of underlying models or representations.

It is possible to use the data to determine the extent of mathematicalknowledge and understanding demonstrated. Examination revealed that Chrishad some understanding of whole numbers and the concepts of the fouroperations. Some detailed calculations performed while she was explaining herfortnightly budget revealed that she could add and subtract sums of money,although some facts, like subtraction of zero proved a problem. Mathematical taskscompleted in the interviews showed that, although she knew an algorithm formultiplication, having to derive the basic facts of multiplication made theoperation tedious. Her knowledge of measurement and her ability to apply metricunits appeared limited.

Chris's result on the test of preschool and primary mathematics curriculumwas 8%. The response to the question "describe the place value system" was "don'tknow concept" and was typical of many of her responses on this test. As the testmark suggests, Chris demonstrated very little understanding in this area. The dataprovides a number of factors which could account for this. The feelings describedin the questionnaire about being in this class do not seem to be conducive toeffective learning:

This was very difficult for me as I had not been doing maths for ten years. I feitashamed, small and intimidated by the classroom structure to mathematics.

Her work on tasks in the interview situation repeatedly revealed a great reluctanceto answer questions unless she was sure that the answer was correct. Thestatement, "I like to be one hundred percent sure when I do something," wastypical in her work on mathematical tasks. A distinct lack of confidence in her ownability has been discussed previously in the section on affective factors. It is evidentthat her lack of previous mathematical knowledge is only one way of accountingfor her performance on this test.

A significant aspect of Chris's use of mathematics was demonstrated when shewas asked, in an interview, about the mathematics she used in her daily life. Chrisexplained in detail how she calculated her fortnightly budget. Her approach to thistask was quite different to the "test-type" tasks that she had been working on andseemed very "business-like." The lack of confidence which usually accompaniedher work was absent. The task was completed in a detailed way and eachcalculation was double checked using a different method. Sometimes the checkwould be mental while at other times she would use a subtraction to check anaddition. Her feelings about this activity are described in a diary entry which canbe contrasted with the feelings associated with the decimal example:

I enjoyed showing Jean how I worked out my finances. This type of mathematics isrelevant to my life.

It is evident that Chris has two approaches to mathematics: the functional

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Carroll '

approach which can be applied with confidence in daily life, and the dysfunctionalapproach which is used in classes and tests, and is typified by a lack of confidence,hesitance and a reluctance to put forward an answer.

Social FactorsThis study began as an investigation of affective and cognitive aspects of the

subject's understanding and thinking. However, social factors emerged as animportant theme from the data as Chris described her experiences in learningmathematics. The social influences came from three main sources: the family,teachers and peer group. The influence of her family and of her teachers isdiscussed below; the role of peers emerges in the section on teachers' questions.

Chris referred to her family on a number of occasions in the study. Her parents'expectations for her in learning mathematics were always very high. They couldnot understand why Chris had problems learning mathematics when her brotherand sister did not. She recalled being teased and called a dummy as a child by herbrother and sister. In the first interview she spoke about her mother's experienceswhen learning mathematics. Her mother had been so terrified by mathematics atschool that sometimes she would not go to school. Chris said:

... I think 1 might have picked up her genes because she had quite a lot of problemswith maths.

Teachers played an important role in Chris's memories of mathematics learning inprimary and secondary school, as can be seen in the following comments whichhave been taken from the interviews:

I can remember one of my teachers saying: "Chris, if you don't master it now younever will," and that is all 1 remember ... It seems to be around the grade five, gradesix mark that things seem to become more evident that 1 was having a lot ofproblems with maths ... I realised in probably grade five that I was having problemsand it just seemed to get worse and worse and no-one seemed to help. 1 mean myparents knew but then again they thought well maybe when she gets to high schoolshe will improve that kind of thing but nothing did.

failed maths in form one [the first year of secondary school]. The teacher knew1 had a problem and through that whole year but they never did anything about it,but I still went up, 1 never repeated. They used to say to my mother: "Chris is havingproblems in maths." Well they didn't take me out and put me in the remedial mathsclass which was something 1 thought that they should have. I went to form six. Afterform three 1 then changed schools where 1 had an option to do or not do maths and Idid do maths but I did at a lower level....

1 just think it's terrible, appalling. l mean if I'd had a different approach to mathsaltogether 1 would probably be fine today but 1 think I had really terrible teacherswho didn't do anything with the problems that 1 had. Maybe the school situationallowed them to, maybe that was it but 1 mean 1 remember my parents came tostudent meetings and nothing much was said about my maths. It was said she washaving problems with science and she is having a bit of a problem with everythingthey never really pin-pointed on maths....

What Makes a Person Mathsphobic? 139

The teachers told me I wasn't particularly good at things so I lost a lot ofconfidence and I was only fifteen years old so they called my parents up to theschool, especially my mum, and said to her that your daughter cannot survive in thisenvironment you will have to send her to another school because she is not passingand she is obviously having quite a lot of problems in all of the areas and then I justchanged schools which was for the better because if I had have stayed I would havehad to repeat form three. I should have been doing form four but I was probablydoing grade six work. But I stil!, I mean from then onwards I was just seemed to be atthe same level of maths all the time....

I tried to engage with the material. I always tried to do it but by that stage I justtended to give up easily. I did try but the teachers knew I was having a lot of trouble,they did assist me but that attitude had already been built up—not being good atmaths. ... It just seems so strange that I got up to year nine and failed maths all theway through but nothing was done.

These recollections reveal Chris's feelings of powerlessness to do anything aboutthe situation. She describes years of studying mathematics in classes whereteachers have acknowledged that she was having problems but the recurringtheme is that nothing was done about it. Inherent in her description is theinevitability that, having built up a belief that she was not good at mathematics,that there was nothing that she could do about it even though she persisted.

The belief that she was not good at mathematics and her tendency to give upeasily suggest that there was an expectation of similar results in the future. Chris'smemories of teachers during her schooling tended to be negative, but more recentexperiences with teachers have been much more positive. The attribution of failureat school to the teaching, an external cause which is not stable (Bar-Tal, 1978), couldaccount for the change in her expectations. in mathematics in the university context.

The university context is providing an environment conducive to attitudechanges. Chris has teachers whom she views as supportive and has sought out theone-to-one teaching situation which the data suggest she prefers. This descriptionof her work with her tutor provides an example of this:

My tutor has really supported me and made me believe that I can do it which I foundto be such a help. "Of course Chris you have really improved s 9 The otherthing about my tutor, something I wrote here yesterday in the questionnaire is thatshe never made me feel like I had a problem with maths, you know, she never sort ofsaid look: "Chris you have got this problem and this problem." She just said: "Okaylets do it!" And we have done it which I have just felt - so good about.

She never sort of laughed at me and said: "you have all these problems." I justfeit that she had a really good attitude and I adopted that. I never feit like, oh, I don'tknow how to do this or don't know how to do that. To begin with I was reallyself-conscious and told her to never tell anybody about our meetings.

A significant issue raised here is that her tutor did not classify Chris's mathematicslearning as "a problem" to be overcome. This made Chris feel good and thebusiness of learning some mathematics has been addressed without dwelling onthe negative aspects.

140 Carroll

Teachers' Questions

A technique which is often used in lectures to try to keep tertiary students ontrack is to ask specific students to answer questions. The idea that this techniquecaused so much anguish was a surprise to the author. Chris describes her reactionsto the author's questions in lectures:

There was no way I was ever going to miss a maths class unless I was sick. I wasn't,and 1 always came to classes, but I dreaded you asking me questions. ... Wheneveryou would ask someone to answer a .question, I would write down the response andthen 1 would retain in my head the answer to the question that you are going to askme and then if you didn't I would think "phew" she didn't ask me. Then when youdid ask me out of the blue, I would answer anyway, I seemed to come up with theanswer.

You would only ask a certain amount of questions. I mean, this is a real strategy,Jean. It must seem really silly but I would always have nearly the answer to any ofthe questions or roughly an answer close to it, even half right, like just a few pointsjotted down or just a few noten. To begin with 1 used to write out these lengthyanswers and think: "Jean didn't ask me that question." So I'd start on the next oneand if you didn't ask me that question I would start on the next one. I mean I was justsilly. I was so embarrassed that people would piek up on my ability in maths. Therewere stages when I was in that classroom I feit so frustrated that I just wanted to cry 'and walk out and go to the toilet....

I would always make sure they were right because the fear of getting it wrong. Idon't think the students in the class would have laughed but there would have justbeen eyes on me getting it wrong. You know that feeling which relates back tosecondary and primary school.

Words like "dreaded," "embarrassed," "frustrated," and "fear" provide an insightinto the agony that this situation created for Chris. These feeling were rememberedvividly months after these experiences occurred.

The reference to being laughed at connects with another incident which sherecalled from secondary school:

It came to me that I was in year seven. There was a classroom full of students and theteacher asked me a question and I couldn't answer her. I can't remember what thequestion was at all but I remember the classroom and the maths book we were usingand I just remembered all of the other students laughing, you know, "she is a dumboshe doesn't know her maths," kind of thing. In those days everybody laughed outloud if you got anything wrong and they laughed and 1 just feit really embarrassed.

Once again the vividness and clarity of the memory of the feelings is a feature ofthis episode. She went on to describe the approach that she developed in secondaryschool to avoid these situations in the future:

I always went to maths classes. I used to hide at the back of the classroom. I didn'tlike teachers sort of asking me questions so I would always hide right up the backwith a coat on. Because I was too scared in case she asked me and I didn't know theanswer and I looked so obvious with this coat and I think a lot of the time theyobviously realised that I was hiding ... 1 remember doing it in French classes which isreally strange because I really loved French. I remember just hiding up the back andjust like if she ever asked me the question I couldn't answer it. I think I developed amentality, I just looked at the teachers and 1 couldn't even say anything in the end.

What Makes a Person Mathsphobic? 141

Buxton (1981, p. 101) also found that questioning could lead to tension andembarrassment. One of his subjects echoes Chris's feelings:

I always sat at the back of the class and prayed that I wouldn't be asked a question.There's a dim recollection of some pain associated with being asked a question, butit's too deep to come to mind.

As Buxton says, the role of questioning needs to be examined. It is a standard andlargely unchallenged practice in classrooms. Both of these students have attemptedto distance themselves from the teacher in order to avoid the negative effects ofbeing asked to answer a question. This relates to behaviours described by Mandler(1989), who found that people prefer to generate positive emotional states andavoid negative ones and hence they will seek out situations or conditions whichgive rise to positive states. This, he said, accounts for why students avoidmathematics as a result of early unhappy experiences or, as in this situation, try tohide at the back of the classroom.

Conclusions

The study was designed to investigate Chris's understanding of mathematics,the structure of that understanding and associated affective factors. It was foundthat her understanding of mathematics was mainly instrumental and limited toconcepts which are usually taught in lower primary classes. A range of affectivefactors such as lack of confidence, feelings of frustration, anger and embarrassmentas well as her beliefs about herself not being good at mathematics and mathematicsnot being useful to her, influenced her ability to learn mathematics and herperformance on tests.

Social factors involving her interaction with other people were identified as asignificant aspect in the study. Chris came to attribute the causes of her failure inmathematics to the teachers she had had at school, who identified that she hadproblems in mathematics but did nothing to help her overcome them.Improvement in her confidence, in her ability to succeed in mathematics in theuniversity context, seem to be linked to her perception that the teachers .there arewilling to work with her, particularly on an individual basis.

Chris views both the teacher and the teaching as the causes of her failure. Interms of attribution theory (Bar-Tal, 1978), her locus of control for success andfailure is external to the learner and unstable. Chris's external attribution of successin the university context, has contributed to her tendency to rely strongly uponlecturers and her tutor, rather than to develop her own internal resources. This mayprovide her with hope for the future, but if the teachers change or if one-to-onehelp is not available, this expectation may change. There is a need to encourage her'to attribute her successes to internal factors, over which she has control. Buerk(1985), when working with women who avoided mathematics, found that thedevelopment of a student's internal sense of power contributed to feelings ofconfidence, and of control over the material. Chris needs to experience this internalsense of power if her mathematics learning is to be enhanced.

The reactions of her peers in classroom situations was identified as animportant social factor at all levels of her schooling. Chris was determined not to

142 Carroll

make classmates aware of her lack of knowledge about mathematics, andmemories of them laughing at her when she could not answer a question in yearseven, were still vivid many years later.

Chris referred to the high expectations for her mathematics learning held byher parents and remembered the teasing she received from her siblings when shewas growing up. In a similar study of anxiety and performance in mathematics attertiary level, Evans (1987) found that relationships with parents and siblingscontributed to the development of mathematics anxiety.

Although this paper has presented a case study of one person's experiences inlearning mathematics, the results of this study highlight the importance of therelationships between students and teachers, the role of peers in the learningprocess, the effect of questioning techniques and the debilitating effect of negativeaffective factors on some students.

The research process, with the necessity for reflection upon less than pleasantmemories, has been demanding on Chris, but not without its rewards. The potionthat the process itself might be beneficial is supported by Buerk (1985). One of thestrategies Buerk used successfully with women, in working with them to overcomenegative feelings about learning mathematics, was to offer the studentsopportunities to reflect, on paper, about their ideas and. feelings aboutmathematics. She found that acknowledging negative feelings and reactions oftenallowed students to move on, as if relieved of a burden. In her final interview Chrissays:

Yes. It is really helping me. It is just like if I am to realise how totally stressed I was,what a nightmare, I'd feel terrible but now I just kind of feel a lot more calmer aboutit and I feel the reflection is the key.

This was reinforced when she wrote in her diary:

I don't have the "I hate maths" attitude any more. Now I want to learn maths andunderstand it.

ReferencesBar-Tal, D. (1978). Attributional analysis of achievement-related behaviour. Review of

Educational Research, 48(2), 259-271.Buerk, D. (1985). The voices of women making meaning in mathematics. Journal of Education,

167(3), 59-70.Buxton, L. (1981). Do you panic about maths? Coping with maths anxiety. London: Heinemann

Educational Books.Chapman, 0. (1993). Facilitating in-service mathematics teachers self-development. In I.

Hirabayashi, N. Nohda, K. Shigematsu & F.-L. Lin (Eds.), Proceedings of the 17thInternational Conference of Psychology of Mathematics Education (Vol: I, pp. 228-235).Japan: International Group for the Psychology of Mathematics Education.

Corsini, R. (Ed.). (1984). Encyclopedia of psychology (Vol. 1). New York: Wiley.Evans, J. T. (1987). Anxiety and performance in practical maths at tertiary level: A report of

research in progress. In J. C. Bergeron, N. Herscovics & C. Kieran (Eds.), Proceedings ofthe Eleventh International Conference on the Psychology of Mathematics Education (Vol. I,pp. 92-98). Montreal: International Group for the Psychology of . MathematicsEducation.

What Makes a Person Mathsphobic? 143

Fennema, E. (1989). The study of affect and mathematics: A proposed generic model forresearch. In D. B. McLeod, & V. M. Adams (Eds.), Affect and mathematical problem solving(pp. 206-219). New York: Springer-Verlag.

Hart, K. (1993). Confidence in success. In 1. Hirabayashi, N. Nohda, K. Shigematsu & F.-L Lin(Eds.), Proceedings of the 17th International Conference of Psychology of MathematicsEducation (Vol. I, pp. 17-31). Japan: International Group for the Psychology ofMathematics Education.

Hart, L. E. (1989). Describing the affective domain: Saying what we mean. In McLeod, D. B.& Adams, V. M. (Eds.), Affect and mathematical problem solving (pp. 37-45). New York:Springer-Verlag.

Hembree, R. (1990). The nature, effects and relief of mathernafics anxiety journal for Researchin Mathematics Education, 21(1), 33-46

Hoyles, C.(1982) The pupils' view of mathematics learning. In Educational Studies inMathematics, 13(4), 349-369.

Leder, G. (1993). Reconciling affective and cognitive aspects of mathematics learning: Realityor a pious hope? In I. Hirabayashi, N. Nohda, K. Shigematsu & F.-L. Lin (Eds.),Proceedings of the 17th International Conference of Psychology of Mathematics Education(Vol. I, pp. 46-65). Japan: International Group for the Psychology of MathematicsEducation.

Mandler, G (1989). Affect and learning: Cause and consequences of emotional interactions.In McLeod, D. B. & Adams, V. M. (Eds.), Affect and mathematical problem solving (pp.3-19). New York: Springer-Verlag.

Marton, F. (1993, April). Phenomenography. (A paper prepared for publication in InternationalEncyclopedia of Education) Paper presented at a research seminar at Royal MelbourneInstitute of Education.

McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualisation. InD. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning(pp. 575-596). New York: Macmillan Publishing Company.

Schoenfeld, A. (1985). Mathematical problem solving. California: Academie Press.Skemp, R. (1979). Intelligence, learning and action. Chichester: Wiley and Sons.

Author

Jean Carroll, Faculty of Education, Royal Melbourne Institute of Technology, Alva Grove,Coburg, Victoria 3058, Australia.