Addressing preservice student teachers’ negative
beliefs and anxieties about mathematics.

Ms. Sirkka-Liisa [Lisa] Marjatta Uusimaki
B.A., Bed (Secondary)

Centre for Mathematics, Science and Technology
Queensland University of Technology

April 2004

A 72 credit point thesis presented in fulfilment of the requirements of
the Master of Education (Research) ED12


DECLARATION
I, Sirkka-Liisa (Lisa) Marjatta Uusimaki, hereby declare that, to the best of my
knowledge and belief, the work in this dissertation contain no material previously
published or written by another person nor material which, to substantial extent, has
been accepted for the award of any other degree or diploma at any institute of higher
education, except where due reference is made.

Signature……………………………….

Date…………………………………….

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ACKNOWLEDGMENTS
I wish to express my sincere gratitude to my principal supervisor Dr Rod Nason,

Senior Lecturer in Mathematics Education, Queensland University of Technology for
his brilliant ideas, excellent support and guidance throughout this study. His
assistance in the structuring and editing of this thesis has been greatly appreciated.
I would like to also thank my associate supervisor Dr Gillian Kidman, Lecturer in
Science Education, Queensland University of Technology for her outstanding
contribution to this study that included advice and support in the analysis of the
quantitative and the qualitative data, and in the formatting of the thesis to meet
American Psychological Association (APA) guidelines. I am truly grateful to Gillian
for her encouragement and time she so freely gave.
I would like to also thank and acknowledge Mr Andy Yeh for his assistance in the
programming of the Online Anxiety Survey.
Special thanks also to Mr Paul Shield who helped with the quantitative analysis of the
Online Anxiety Survey data.
Sincere thanks to the Director of the Centre of Mathematics, Science and Technology
Education, Professor Campbell McRobbie for his kindness and support that he so
generously offered throughout this study.
Finally, this thesis is dedicated to my son Marcus Uusimaki whose unconditional love
and support inspired me to research issues of quality in education and to give my all
in this study.

ii


ABSTRACT
More than half of Australian primary teachers have negative feelings about
mathematics (Carroll, 1998). This research study investigates whether it is possible to
change negative beliefs and anxieties about mathematics in preservice student
teachers so that they can perceive mathematics as a subject that is creative and where
discourse is possible (Ernest, 1991). In this study, sixteen maths-anxious preservice
primary education student teachers were engaged in computer-mediated collaborative

open-ended mathematical activities and discourse. Prior to, and after their
mathematical activity, the students participated in a short thirty-second Online
Anxiety Survey based on ideas by Ainley and Hidi (2002) and Boekaerts (2002), to
ascertain changes to their beliefs about the various mathematical activities. The
analysis of this data facilitated the identification of key episodes that led to the
changes in beliefs. The findings from this study provide teacher educators with a
better understanding of what changes need to occur in pre-service mathematics
education programs, so as to improve perceptions about mathematics in mathsanxious pre-service education students and subsequently primary mathematics
teachers.

iii


TABLE OF CONTENTS
DECLARATION ………………………………………………………………..
ACKNOWLEDGMENT ………………………………………………………
ABSTRACT ……………………………………………………………………..

Chapter 1
1.1 Introduction ………………………………………………………………
1.2 Background of study ……………………………………………………..
1.3 Overview of literature ……………………………………………………
1.3.1 Maths-anxiety ……………………………………………………
1.3.2 Teacher beliefs …………………………………………………...
1.3.3 Overcoming maths-anxiety ………………………………………
1.3.4 Assessment of maths-anxiety …………………….........................
1.3.5 Pre-service mathematics education courses ………………………
1.4 Significance of the study …………………………………………………
1.5 Chapter overview ………………………………………………………...
1.6 Summary …………………………………………………………………

Chapter 2
2.1 Introduction ………………………………………………………………
2.2 Maths-anxiety …………………………………………………………….
2.3 Consequences of maths-anxiety ………………………………………….
2.4 Teacher beliefs about mathematics ………………………………………
2.5 Prior school experiences and the origins and the development of negative
maths-beliefs ……………………………………………………………..
2.6

2.7
2.8

2.9
2.10
2.11

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1
1
2
3
3
4
4
5
5
6

6

8
8
12
13

15
Overcoming maths-anxiety in pre-service teachers
16
2.6.1 Beliefs ……………………………………………………………. 17
2.6.2 Conceptual understanding of mathematics ………………………. 18
2.6.3 Subject matter knowledge and pedagogical knowledge ………… 19
Assessment of maths-anxiety …………………………………………… 21
Pre-service mathematics education courses ……………………………..
23
2.8.1 Constructivist and social constructivist theories …………………
24
2.8.2 Collaboration …………………………………………………….. 25
Communities of learning and computer supported collaborative learning
27
Summary ………………………………………………............................. 29
Theoretical framework for the study ……………………………………... 30

iv


Chapter 3
3.1 Introduction ………………………………………………………………
3.2 Research methodology …………………………………………………...

3.3 Participants ……………………………………………………………….
3.4 Collection of data ………………………………………………………...
3.4.1 Semi-structured pre-enactment and post-enactment interviews ….
3.4.2 Online Anxiety Survey ……………………………………………
3.4.3 Knowledge Forum notes ……………..............................................
3.4.4 Written reflections …………………………………………………
3.5 Procedure ………………………………………………………………….
3.5.1 Phase 1: Identification of origins of maths-anxiety ……………….
3.5.2 Phase 2: Enactment of intervention program ……………………..
3.5.3 Phase 3: Summative evaluation …………………………………..
3.6 Data analysis ……………………………………………………………..
3.6.1 Analysis of qualitative data ……………………………………….
3.6.2 Analysis of Online Anxiety Survey quantitative data ……………..
3.7 Summary …………………………………………………………………

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43
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43
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Chapter 4
4.1 Introduction ………………………………………………………………
4.2 Results from interview data ……………………………………………...
4.2.1 Pre-interview results ……………………………………………...
4.2.2 Comparison of pre- and post-interview results …………………...
4.3 Results from reflection documents ………………………………………
4.4 Online Anxiety Survey results ……………………………………………
4.4.1 Introduction ……………………………………………………….
4.4.2 Overall analysis of the Online Anxiety Survey results ………….
4.4.3 Session 1: Number sense activity ………………………………….
4.4.4 Session 2: Space and measurement activity ……………………….
4.4.5 Session 3: Number and shape activity …………………………….
4.4.6 Session 4: Division operation activity …………………………….
4.5 Computer-mediated support tools ………………………………………...
4.6 Summary ………………………………………………………………….

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68
70
73
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Chapter 5
5.1 Introduction ……………………………………………………………….
5.2 Overview of study ………………………………………………………...
5.3 Overview of results ……………………………………………………….
5.4 Limitations ………………………………………………………………..

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83
87

v


5.5 Implications ………………………………………………………………. 88
5.6 Summary and recommendations …………………………………………. 89

References ………………………………………………………………………
Appendix 1: Phone interview questions …………………………………………
Appendix 2: Pre-enactment Interview …………………………………………..
Appendix 3:Post-enactment interview ……..…………………………………..
Appendix 4: Online Anxiety Survey …………………………………………….

91
103
104
105

106

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LIST OF TABLES
Chapter 3
Table 3.1

The four mathematical activities …………………………………. 37

Chapter 4
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table 4.5
Table 4.6
Table 4.7
Table 4.8
Table 4.9
Table 4.10
Table 4.11
Table 4.12
Table 4.13
Table 4.14
Table 4.15
Table 4.16
Table 4.17
Table 4.18

Table 4.19

The nature of mathematics ……………………………………….
Reasons for teaching mathematics ………………………………..
Teacher knowledge and qualities ………………………………....
Maths-confidence ………………………………………………....
The origins of maths-anxiety ……………………………………..
Situations causing maths-anxiety ………………………………...
Types of mathematics causing maths-anxiety …………………....
Perceptions of how to overcome maths-anxiety ………………….
Perceptions on how to reduce maths-anxiety in future students ….
The nature of mathematics ………………………………………..
The relevance of mathematics …………………………………....
Teacher knowledge …………………………………………….....
Maths-confidence …………………………………………………
Pairwise comparison: Overall results ……………………………..
Pairwise comparison: Session one results ………………………...
Pairwise comparison: Session two results ………………………..
Pairwise comparison: Session three results ………………………
Pairwise comparison: Session four results ………………………..
Perceptions of computer-mediated software ……………………...

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LIST OF FIGURES
Chapter 2
Figure 2.1
Figure 2.2.

The process of solving maths problems ………………................
The theoretical framework ……………………………………….

11
30

Chapter 3
Figure 3.1
Figure 3.2
Figure 3.3

Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7

Intervention Program ……………………………………………..
Online Anxiety Survey …………………………...........................
MipPad model and tabular representation ………………………..
MipPad model, language and symbol representation …………….
Shape and measurement activity ………………………………….
Number and shape activity ………………………………………..
Division operation activity ………………………………………..

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39
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41
42
43

Chapter 4
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8

Figure 4.9
Figure 4.10

Box plots overall positive feelings…………………………………
Box plots overall negative feelings…….…………………………..
Number sense activity (positive feelings responses)……………….
Number sense activity (negative feeling responses)………………..
Space and measurement activity (positive feeling responses)……...
Space and measurement activity (negative feeling responses)……..
Number and shape activity (positive feelings responses)…………..
Number and shape activity (negative feelings responses)………….
Division operation activity (positive feelings responses)…………..
Division operation activity (negative feelings responses)………….

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viii


CHAPTER 1
INTRODUCTION

1.1

Introduction
The purpose for this research study was to investigate whether supporting

sixteen self-identified maths-anxious preservice student teachers within a supportive
environment provided by a Computer-Supported Collaborative Learning (CSCL)
community would reduce their negative beliefs and high levels of anxiety about
mathematics.

1.2

Background of study
A considerable proportion of students entering primary teacher education

programs have been found to have negative feelings towards mathematics (Cohen &
Green, 2002; Levine, 1996). These negative feelings about mathematics often
manifest in a phenomenon known as maths-anxiety (Ingleton & O’Regan, 1998;
Martinez & Martinez, 1996; Tobias, 1993).
Maths-anxiety can be described as a learned emotional response to, for
example, participating in a mathematics class, listening to a lecture, working through
problems, and /or discussing mathematics (Le Moyne College, 1999). People who
experience maths-anxiety can suffer from, all or a combination of the following:
feelings of panic, tension, helplessness, fear, shame, nervousness and loss of ability to
concentrate (Trujillo, & Hadfield, 1999). Maths-anxiety surfaces most dramatically
when the subject either perceives him or herself to be under evaluation (Tooke &
Lindstrom, 1998; Wood, 1988).
A review of the literature clearly suggests that teachers’ beliefs have great
influence on their students’ attitudes and beliefs about mathematics. Hence, of
concern is the persistent argument found in the research literature for the transference

of maths-anxiety from teacher to students (Brett, Woodruff, & Nason 2002; Cornell,
1999; Ingleton & O’Regan, 1998; Martinez & Martinez, 1996; McCormick, 1993;
Norwood, 1994; Sovchik, 1996) and the difficulty in bringing to an end its continuity.
The need for preservice teacher education mathematics courses to address the
related issues of negative beliefs about mathematics and high levels of anxiety
1


towards mathematics has long been recognised in the research literature. Many
mathematics education courses have attempted to reduce maths-anxiety by focusing
on methodology and mathematical content as well as on learners’ conceptual
understanding of mathematics (Couch-Kuchey, 2003; Levine 1996; Tooke &
Lindstrom, 1998). Others have focused on having the preservice teacher education
students re-construct their mathematical knowledge within the context of
constructivist frameworks. However, most preservice teacher education mathematics
education courses have at best reported limited success only in ameliorating
preservice teachers’ negative beliefs and high levels of anxiety towards mathematics.
Therefore, in this study, a three-phase Intervention Model was developed and
implemented to assist preservice student teachers to overcome not only their negative
beliefs about mathematics but also their high level of anxieties about mathematics.
The first phase of this model, the identification phase, involved both the identification
of the maths-anxious preservice students and the semi-structured interviews. The
interviews questions focused on issues, such as, the origins and causes of negative
beliefs about mathematics, preservice student teachers’ perceptions about the nature
of mathematics, what they believe characterize effective mathematics teaching and
their ideas on how to overcome maths-anxiety. The second phase, the intervention
phase, involved the enactment of the intervention program. This included the
participants working in groups in non-intimidating workshop situations, learning
novel mathematical activities with the help of innovative computer-mediated software
and taking part in an Online Anxiety Survey. The third phase, the evaluation phase,

the collection and analysis of data from interviews, an Online Anxiety Survey, and
written reflections about the preservice student teachers’ experiences in the project
that in turn, when analysed were used to ascertain and explicate changes in students’
negative beliefs and anxieties.

1.3

Overview of the literature
The conceptual framework to inform this study was derived from an analysis

and synthesis of the research literature from the following fields:

2


1. Maths-anxiety.
2. Teacher beliefs about mathematics.
3. Overcoming maths-anxiety in preservice teachers.
4. Assessment of maths-anxiety.
5. Preservice mathematics education courses.
To provide an advance organiser for the detailed review of the research literature that
follows in Chapter 2, a brief overview of each of these areas is now presented.
1.3.1

Maths-anxiety
In order to understand maths-anxiety and the development of maths-anxiety,

Martinez and Martinez (1996) emphasised the importance of understanding the
interactions between the cognitive and the affective processes of solving mathematical
problems. The development of confidence in contrast to maths-anxiety is dependent

on positive factors from the affective domain such as supportive environments,
empathy and patience. Positive factors from the cognitive domains of the problemsolving process involve the development of conceptual understanding of mathematics,
and mathematics relevance to real life. According to Martinez and Martinez (1996, p.
6), when negative factors dominate the mathematics problem-solving process, “the
by-product will be anxiety”.
1.3.2

Teacher beliefs
The research literature shows that teachers’ beliefs about mathematics have a

powerful impact on their practice of teaching. Schoenfeld (1985) suggests that how
one approaches mathematics and mathematical tasks greatly depends upon one’s
beliefs about how one approaches a problem, which techniques will be used or
avoided, how long and how hard one will work on it.
It is suggested that teachers with negative beliefs about mathematics influence
a learned-helplessness response from students, whereas the students of teachers with
positive beliefs about mathematics enjoy successful mathematical experiences that
results in their seeing mathematics as a discourse worthwhile of study (Karp, 1991).
Thus, what goes on in the mathematics classroom is directly related to the beliefs
teachers hold about mathematics. Hence, teacher beliefs play a major role in their
students’ achievement and in their formation of beliefs and attitudes towards
mathematics (Cooney, 1994; Emenaker, 1996; Kloosterman, Raymond, & Emenaker,
1993; Roulet, 2000; Schofield, 1981).
3


1.3.3

Overcoming maths-anxiety
An awareness of the learned negative belief[s] and affect[s] and then the


ability to monitor these emotions are necessary components to overcome and control
maths-anxiety (Martinez & Martinez, 1996; Pintrich, 2000). To overcome mathsanxiety, Martinez and Martinez (1996) state that “as with any negative behaviour,
effecting change must begin with admitting that there is in fact a problem” (p. 12).
Hence, the realization and the acceptance of negative feelings are essential in the
quest to overcome maths-anxiety. Thus, becoming maths-confident in contrast to
maths-anxious requires direct conscious action (Martinez & Martinez, 1996). To
reflect and to think about one’s thinking is referred to as meta-cognition. Martinez and
Martinez (1996) argue, the meta-cognitive approach challenges anxieties through: (a)
the analysis of thought processes about mathematics, (b) the translation of anxieties
about mathematics into thoughts; and then (c) the analysis of these thoughts over an
extended period of time.
To overcome maths-anxiety, it is also necessary to recognize particular
anxiety causing mathematics (Martinez & Martinez, 1996). For example, a person
who says that he or she ‘hates’ mathematics may find on further reflection, that he or
she ‘hates’ specific types of mathematics. For many prospective teachers learning
mathematics has meant only learning its procedures and may have, in fact, been
rewarded with high grades in mathematics for their fluency in using procedures
(Tucker, Fay, Schifter &. Sowder, 2001).
Also, for learning to be most effective it is crucial that the learning
environment is safe, supportive, enjoyable, collaborative, challenging as well as
empowering. Doerr and Tripp (1999) argue that conducive to learning are learning
environments that provide opportunities to express ideas ask questions, make
reasoned guesses and work with technology while engaging in problem situations that
elicit the development of a deep understanding of mathematics and significant
mathematical models.
1.3.4

Assessment of maths-anxiety
A number of researchers (e.g., Ainley & Hidi, 2002; Hickey, 1997; Jarvela &


Niemivirta, 1999; Pintrich, 2000) support the need for the development of
methodologies and measures that access the dynamics of students’ subjective
experiences or reactions whilst they are engaged in a learning activity. Ainley and
4


Hidi suggest that such methodologies and measures provide a new perspective from
which to consider the relation between what the person brings to the learning task and
what is generated by the task itself
To monitor emotions, a self-reporting instrument known as an On-line
Motivation Questionnaire (OMQ) that is administered before and after the specific
learning tasks has been found to be successful amongst primary and secondary
students in determining whether a learning situation is “an annoyer” or “a satisfier”
(Boekaerts, 2002). The development of the On-line Motivation Questionnaire was
guided by the theoretical model of adaptive learning (Boekaerts, 1992, 1996). This
theory according to Boekaerts (2002) predicts students’ appraisals (motivational
beliefs) of a learning situation and explains more variation in their learning intention,
emotional state, and effort than domain-specific measures.
1.3.5 Preservice mathematics education courses
Whilst some studies suggests that teacher education programs can assist in
changing the attitudes and mathematical self-concepts of preservice and in-service
primary school teachers to more positive ones (Bobis, & Cusworth, 1997; Philippou
& Christou, 1997), other studies imply that teachers maintain their negativity toward
mathematics and mathematics teaching after they begin to teach (Cockroft, 1982;
Freeman & Smith, 1997; Kanes & Nisbet, 1994; Pateman, 1989). To reverse this
negativity about mathematics, Carroll (1998) suggested the re-examination of teacher
education programs. She felt that there must be more focus on the development of
“confidence in the ideas of the teachers who must be encouraged to analyse and
critically evaluate their current knowledge, beliefs and attitudes and modify [these] to

include new ideas” (p.8).

1.4

Significance of the study
This project has both practical and theoretical outcomes for preservice

mathematics education and for research into computer supported collaborative
learning (CSCL).
In terms of practical outcomes, this study seeks to improve the quality of
teaching and learning in primary school mathematics by providing maths-anxious
preservice teachers with the means to combat their negative feelings about
mathematics through: a) the development of an understanding and awareness of their

5


learned negative feelings about mathematics, b) the development of repertoires of
mathematical content and pedagogical knowledge using CSCL that will allow for the
development of confidence in mathematics, and, c) identification of self and identity
(Brett, 2002).
In terms of theoretical outcomes, this study will extend Boekaerts (2002)
model of adaptive learning theory from its present context with primary and
secondary school students to contexts with self-identified maths-anxious preservice
student teachers. It will also advance the body of theoretical knowledge within the
field of CSCL especially with respect to its application within the field of teacher
education of maths-anxious preservice student teachers.

1.5


Chapter overview
Chapter 1 provides information on the background of the research. The

significance of the study is examined and an overview of relevant literature is presented.
Chapter 2 reviews the relevant literature and provides a foundation for the study
pertaining to what constitutes maths-anxiety, its origins and causes, consequences of
maths-anxiety on the individual, the student as well as the impact negative beliefs about
mathematics has on students’ numeracy outcomes. Chapter 3 outlines the exploratory
mixed-method design that was used in the study including the data collection and
analysis. A description of the data collection is given and a description of participants as
well as the criteria used in selecting these participants. In Chapter 4 the findings from the
research study are presented. Finally, Chapter 5 presents the discussion of the results, a
summary and conclusion in regards to the relevant literature as well as the implications
and limitations of the study for teacher preservice courses.

1.6

Summary
The aim of this research study was to investigate whether supporting sixteen

self-identified maths-anxious preservice student teachers (a) to develop mathematical
reasoning, (b) to reflect on their learning, (c) to challenge and then to modify negative
beliefs and attitudes about mathematics provided by a CSCL community would
reduce their negative beliefs and high levels of anxiety about mathematics. It is
argued that enhancing the preservice student teachers’ repertoires of mathematical
subject matter knowledge will lead to, reductions in their negative beliefs and
anxieties about mathematics and to enhancement of their sense of identity as future

6



primary mathematics teachers as well as valued members within their learning
community. Most importantly, the broader implications of the study relate to the
positive impact that these preservice student teachers will have on their future student
numeracy outcomes.

7


CHAPTER 2
LITERATURE REVIEW
2.1

Introduction
“Maths-anxiety is not just a simple nervous reaction, nor is it a harmless
myth: it is a debilitating affliction that restricts math performances among
both children and adults worldwide” (Martinez & Martinez, 1996, p. 9).

More than half of Australian primary teachers have negative feelings about
mathematics (Carroll, 1998). Research suggests that it is a teacher’s personal school
experiences that influence the developments of negative feelings about mathematics
(Brown, McNamara, Hanley & Jones, 1999; McLeod, 1994; Nicol, Gooya & Martin,
2002; Trujillo, & Hadfield, 1999; Williams, 1988). As a consequence of these
personal school experiences a considerable proportion of students entering primary
teacher education programs have been found to have negative feelings towards
mathematics (Carroll, 1998; Cohen & Green, 2002; Ingleton & O’Regan 1998;
Lacefield, 1996; Levine, 1996; Philippou & Christou, 1997). Negativity about
mathematics often manifests in what has long been identified as maths-anxiety
(Barnes 1984; Bessant, 1995: Blum-Anderson, 1994; Cemen, 1987; Fairbanks, 1992;
Hadfield, Martin & Wooden 1992; Ingleton & O’Regan, 1998; Martinez & Martinez,

1996; McCormick, 1993; Norwood, 1994; Richardson & Suinn, 1972; Tobias, 1993;
1978).

2.2

Maths-anxiety
An early definition of maths-anxiety suggests that it is “… feelings of tension

and anxiety that interfere with the manipulation of numbers and the solving of
mathematical problems in a wide variety of ordinary life and academic situations”
(Richardson & Suinn, 1972, p. 551). According to Cemen (1987), maths-anxiety can
be described as a state of anxiety which occurs in response to situations involving
mathematics which is perceived as threatening to self-esteem (Trujillo & Hadfield,.
1999). Such feelings of anxiety can lead to panic, tension, helplessness, fear, distress,
shame, inability to cope, sweaty palms, nervousness, stomach and breathing

8


difficulties and loss of ability to concentrate (Trujillo & Hadfield, 1999). Research
studies have found that maths-anxiety is related to test anxiety which means that it
surfaces most dramatically when the subject either perceives him or herself to be
under evaluation (Ikegulu, 1998; Tooke & Lindstrom, 1998; Wood, 1988). Although
early research suggests that the term maths-anxiety was rather an expression of
general anxiety and not a distinct phenomenon (Olson & Gillingham, 1980), more
recent research into maths-anxiety has recognized it not only to be more complex than
general anxiety but also more common than earlier suggested (Ingleton & O’Regan,
1998). It is because of its complexity that there is not a universal agreement as to what
constitutes maths-anxiety.
The origins of maths-anxiety and negative beliefs about mathematics can be

categorised into three areas: (a) environmental, (b) intellectual and (c) personality
factors (Hadfield & McNeil, 1994; Trujillo & Hadfield, 1999):
1. Environmental factors included negative experiences in the classroom,
parental pressure, insensitive teachers, mathematics being taught in a
traditional manner as rigid sets of rules, and non-participatory classrooms
(Trujillo & Hadfield, 1999; Stuart, 2000).
2. Intellectual factors including teaching being mismatched with learning styles,
student attitude and lack of persistence, self-doubt, lack of confidence in
mathematical ability and lack of perceived usefulness of mathematics (Trujillo
& Hadfield, 1999).
3. Personality factors included reluctance to ask questions due to shyness, low
self-esteem and, for females, viewing mathematics as a male domain (Levine,
1996; Trujillo & Hadfield, 1999).
From this it can then be seen that the origins of maths-anxiety are as diverse as
are the individuals experiencing maths-anxiety. For some, people maths-anxiety is
related to poor teaching, or humiliation and/ or belittlement whilst others may have
learnt maths-anxiety from the maths-anxious teachers, parents, siblings or peers, or
who may link their anxiety to numbers or to some operations generally (Martinez &
Martinez, 1996; Stuart, 2000). Thus, to understand maths-anxiety, it must be
recognized for its complexity. Maths-anxiety is not a discrete condition but rather it is
a “construct with multiple causes and multiple effects interacting in a tangle that

9


defies simple diagnosis and simplistic remedies” (Martinez & Martinez, 1996, p.2). A
definition by Smith and Smith (1998) takes into consideration this intricacy by
encompassing both the affective and the cognitive domain of learning. Smith and
Smith state that maths-anxiety is a feeling of intense frustration or helplessness about
one’s ability to do mathematics. Maths-anxiety can be described as a learned

emotional response to participating in a mathematics class, listening to a lecture,
working through problems, and /or discussing mathematics to name but a few
examples (Hembree, 1990; Le Moyne College, 1999). This definition stipulates that
maths-anxiety is not exclusively a product of the affective domain but also of the
cognitive domain of learning.
According to Martinez and Martinez (1996), the cognitive domain of learning
can be described as the logical component of learning. For instance, logical thought
processes, information storage, and retrieval, aptitude for learning mathematics,
mathematics learning readiness and teaching strategies all belong to the cognitive
domain. Martinez and Martinez state that “the cognitive domain affects maths-anxiety
when there are gaps in knowledge, when information is incorrectly learnt, and when
the learning readiness and teaching strategies are mismatched” (pp. 5-6).
The affective domain of learning is the emotional component of learning
(Martinez & Martinez, 1996). This is the province of beliefs, attitudes and emotions
about learning mathematics, of memories of past failures and successes, of influences
from maths-anxious or maths-confident adults, of responses to specific learning
environment and teaching styles (Gellert, 2001; Martinez & Martinez, 1996;
Pehkonen & Pietila, 2003). The affective domain provides a context for learning
(Martinez & Martinez, 1996) and if the affective domain provides a positive context,
students can be motivated to learn, whatever their mathematical aptitude. However,
“if the affective domain provides a negative context, even students with superior
math-learning ability may develop maths-anxiety” argue Martinez and Martinez
(1996, p. 6).
Figure 2.1 demonstrates the interactions between the cognitive and affective
processes of solving mathematical problems. The figure shows a number of factors
involved in the mathematical problem-solving process. For example, the development
of confidence in contrast to anxiety is dependent on positive elements from the
affective (e.g., supportive environment, empathy, patience) and/or the cognitive
10



domains of the problem-solving process (e.g., development of conceptual
understanding of mathematics, relevance to real life, challenging). If however,
negative elements dominate the mathematical problem-solving process, “the byproduct will be anxiety” (Martinez & Martinez, 1996, p. 2). Hence the development
of confidence in mathematics is a critical emotion in the process of learning (Ingelton
& O’Regan, 1998).

This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library

Figure 2.1 The Process of Solving Mathematical Problems (Source: Martinez &
Martinez, 1996, p. 2).
Confidence is defined according to Barbalet (1998, p. 86) as “an emotion with
a subjective component of feelings, a physiological component of arousal and a motor
component of expressive gesture”. Confidence functions in opposition to shame,
shyness and modesty, which are described as emotion of self-attention or “thinking
what others think of us” (Barbalet, 1998, p. 86). Ingleton and O’Regan (1998) suggest
that confidence has its origins in particular experiences of social relationships, such as
“where a person receives acceptance and recognition in contrast to the onset of
anxiety and shame where a person is denied this acceptance or recognition” (p.3).

2.3

Consequences of maths-anxiety
Some of the consequences that result from being maths-anxious as opposed to

maths-confident include:

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1. The fear to perform tasks that are mathematically related to real life
incidents, such as sharing or dividing a restaurant bill amongst diners or
developing a household budget.
2. Avoidance of mathematics classes.
3. The belief that it is acceptable to fail/dislike mathematics.
4. Feelings of physical illness, faintness, fear or panic.
5. An inability to perform in a test or test-like situations.
6. Participation in tutorial sessions that provide little success (McCulloch
Vinson, Haynes, Sloan, & Gresham 1997).
Some commonly held beliefs associated with maths-anxiety and mathematics
avoidance identified by Kogelman and Warren (1978) still hold true today.
Specifically some of these are:
1. Inherited mathematical ability or some people have a mathematical mind
and some don’t.
2. Mathematics requires logic not intuition.
3. You must always know how you got the answer.
4. There is one best way to do a mathematical problem.
5. Men are better at mathematics than women.
6. It is always important to get the answer exactly right.
7. Mathematicians solve problems quickly in their heads.
8. Mathematics is not creative.
9. It is bad to count on your fingers. (Sam, 1999)
The implication of such negative beliefs and negative school mathematics
experiences on many primary teacher education students has resulted in the continuity
of the maths-anxiety phenomenon. Of concern is the persistent argument found in the
research literature for the transference of maths-anxiety from teacher to students
(Brett, et al., 2002; Cornell, 1999; Ingleton & O’Regan, 1998; Martinez & Martinez,
1996; McCormick, 1993; Norwood, 1994; Sovchik, 1996) and the difficulty in

bringing to an end its continuity.

2.4

Teacher beliefs about mathematics
A review of the literature indicates that teachers’ beliefs have much influence

on their students’ attitudes and beliefs about mathematics. “A belief is the acceptance

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of the truth or actuality of anything without certain proof “, according to McGriff
Hare (1999, p. 42). Beliefs are one’s subjective knowledge including whatever one
considers as true knowledge, without the lack of convincing evidence to support these
beliefs (Pehkonen, 2001). Since beliefs are cognitive in nature and developed over a
relatively long period of time they seldom change dramatically without significant
intervention (Lappan, et al., 1988; McLeod, 1992). Schoenfeld (1985) suggests that
how one approaches mathematics and mathematical tasks greatly depends upon one’s
beliefs about how one has to approach a problem, which techniques will be used or
avoided, and how long and how hard one will one work on the mathematical task.
Research findings suggest that beliefs about the nature of mathematics affect
teachers’ conception of how mathematics should be presented (Ernest, 1988, 1991,
2000; Hersh, 1986). According to Hersh (1986, p.13):
One’s conception of what mathematics is affects one’s conception of
how it should be presented. One’s manner of presenting it is an
indication of what one believes to be most essential in it…The issue
then it is not, what is the best way to teach? But, what is mathematics
really about?
Indeed, it is because the two domains of teacher belief and knowledge are

intertwined and difficult to separate that makes them particularly of concern to teacher
education programs where this bottleneck should be addressed simultaneously.
A number of other studies have shown that teachers’ beliefs about
mathematics have a powerful impact on the practice of teaching (Charalambos,
Philippou & Kyriakides, 2002; Ernest, 1988, 2000; Golafshani, 2002; Putnam,
Heaton, Prawat, & Remillard, 1992; Teo, 1997). McLeod (1992) states that, "the role
of beliefs is central in the development of attitudinal and emotional responses to
mathematics" (p. 579).
Drawing on the philosophy of mathematics, Ernest (1991) distinguishes two
dominant epistemological perspectives of mathematics, namely the absolutist and the
fallibilist beliefs about the nature of mathematical knowledge. Absolutists believe that
mathematics consists of a set of absolute and unquestionable truths that is certain and
exact. This is where mathematical knowledge is believed to be objective, value free
and culture free. In contrast, fallibilists believe that “mathematical truth is fallible and
corrigible, and can never be regarded as beyond revision and correction” (Ernest,

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1991, p.18). In other words, mathematics can be seen as the outcome of social
processes and where mathematics knowledge is understood as fallible and always
open to revision. Rule-based ways of teaching are often associated with teachers with
absolutist beliefs about the nature of mathematics (Ernest, 2000). Some research
findings propose that maths-anxiety is often associated with teaching methods that are
conventional (absolutist and rule-bound) (Sloan, Daane & Giesen, 2002). It has been
noted that rule-based methods of instruction are commonly employed by primary
teachers who possess high levels of anxiety and negative attitudes toward
mathematics (Karp, 1991; Sloan et al., 2002) and thus the cycle is perpetuated.
Other researchers have provided other classification systems to describe the
different philosophies of teaching mathematics and their implications (Wiersma &

Weinstein, 2001). For example, Lerman (1990) identified the dualistic1 and relativist2
ways teachers depict when teaching mathematics. Teachers teaching from a dualistic
standpoint teach mathematics as a set of absolute and unquestionable truths. Teaching
from the relativist standpoint on the other hand is where mathematics is taught as a
“dynamic, problem-driven and continually expanding field of human creation and
invention, in which patterns are generated and then distilled into knowledge” (Ernest,
1996, p. 808). A review of the literature indicates that maths-anxiety is more likely to
emerge in classrooms where teachers employ absolutist/dualistic or content-focused
with emphasis on performance modes of teaching (Ernest, 2000).
A review of the research literature indicates that feelings of maths-anxiety in
preservice teachers are often associated with negative beliefs about mathematics and
the teaching of mathematics (Brett, et al., 2002; Cohen & Green, 2002; Karp, 1991;
Middleton & Spanias, 1999). It is suggested that teachers with negative beliefs about
mathematics influence a learned helplessness response from students this is a form of
a response where students seem to have lost the capacity to be accountable for their
own behavior and performance, because of repeated unfavorable past performances
(McInerney & McInerney, 1998). In contrast, the students of teachers with positive
beliefs about mathematics enjoy successful mathematical experiences that result in
their seeing mathematics as a discourse worthwhile of study (Karp, 1991). Thus, what
goes on in the mathematics classroom is directly related to the beliefs teachers hold
1
2

This is very similar to Ernest’s (1991) classification of absolutist beliefs
This is very similar to Ernest’s (1991) classification of fallabilist beliefs

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about mathematics. Hence, teacher beliefs play a major role in their students’

achievement and in their formation of beliefs and attitudes towards mathematics
(Cooney, 1994; Emenaker, 1996; Kloosterman, et al., 1993; Roulet, 2000; Schofield,
1981).

2.5

Prior school experiences and the origins and the development of
negative maths-beliefs
As already discussed (see Section 2.2.), the developments of negative beliefs

about mathematics can be and, in many cases, are influenced by siblings and fellow
peers (Stuart, 2000). Negative beliefs about mathematics also have their origins in
prior school experiences such as the experience of being a mathematics student, the
influence of prior teachers and of teacher preparation programs (Borko, et al., 1992;
Brown & Borko, 1992), as well as prior teaching experience (Raymond, 1997). For
example, many negative beliefs held by teachers can be traced back to the frustration
and failure in learning mathematics caused by unsympathetic teachers who incorrectly
assumed that computational processes were simple and self-explanatory (Cornell,
1999). In their study Martinez and Martinez (1996) found that sixty percent of
student teachers tested using a Math Anxiety Self Quiz claimed to be highly mathsanxious, thirty percent claimed to be moderately maths-anxious and many attributed
their anxiety to hostile teaching strategies. These hostile teaching strategies (Martinez
& Martinez, 1996, p. 34) included:
1. Verbally abusing students for errors – being called math-dumb, bonehead,
knucklehead, and pea brain.
2. Punishing behaviour and deficiencies with math exercises.
3. Exposing students to public ridicule by assigning board problems and
badgering the un-prepared.
4. Isolating the learners – “Keep your eyes on the board. There will be no
talking, no exchanging of notes or papers and no questions for anyone but
the teacher”.

5. Ram-rodding information – “Listen up. I’m going to say this one time and
one time only”.

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6. Input/Output teaching – Without interacting with students, teacher inputs
information to them through lectures and study assignments; students
output information to teacher by doing homework and taking tests.
The consequences of these sorts of math-hostile teaching strategies ultimately
impact negatively on student behaviour as well as in their attitude towards
mathematics both in primary and secondary school and later in their deliberate
avoidance of careers that require extensive mathematical knowledge (Martinez &
Martinez, 1996; Tucker, et al., 2001).
There is an assumption amongst teachers that by controlling or hiding one’s
maths-anxiety behind well-planned and well-explained mathematics lessons that
students will not come to “learn the anxiety” of his or her teacher (Martinez &
Martinez, 1996, p.10). However, students and particularly young children do learn the
anxiety as they pick up on the covert signals displayed by the teacher, in other words
they tend to see the strain behind the smile or hear tension in a voice (Martinez &
Martinez, 1996). Thus, for a positive and successful teaching and learning experience
to occur “what the teacher says about math and what the teacher feels about math
must match” (Martinez & Martinez, 1996. p.11).

2.6

Overcoming maths-anxiety in preservice teachers
“Tell me mathematics and I forget, show me mathematics and I may
remember… involve me and I will understand. If I understand mathematics, I
will be less likely to have maths-anxiety. And if I become a teacher of

mathematics I can thus begin a cycle that will produce a generation of less
likely maths-anxious students for the generation to come” (Williams, 1988,
p.101)
Because of its complex nature encompassing both the affective and cognitive

domains of learning, interventions focusing on both elements are needed to overcome
maths-anxiety.
2.6.1

Beliefs
To overcome negative beliefs and anxiety about mathematics requires a

fundamental shift in a person’s system of beliefs and conceptions about the nature of
mathematics and mental models of teaching and learning mathematics (Levine, 1996).
Seligman (1991) believes that it is possible to successfully overcome maths-anxiety

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