Content uploaded by Peter John Grootenboer
Author content
All content in this area was uploaded by Peter John Grootenboer
Content may be subject to copyright.
H. Forgasz, A. Barkatsas, A. Bishop, B. Clarke, S. Keast, W-T. Seah, P. Sullivan, & S. Willis (eds.),
Research in Mathematics Education in Australasia 2004-2007, xx-yy.
© 2008 Sense Publishers. All rights reserved.
PETER GROOTENBOER, GREGOR LOMAS, & NAOMI INGRAM
THE AFFECTIVE DOMAIN AND MATHEMATICS
EDUCATION
This chapter examines Australasian research in the affective domain. While
this domain during this review period has continued to be dominated by a
focus on beliefs, there is more research emerging in the areas of self-concept,
identity, motivation, and engagement. There remains however a lack of
theorising in aspects of the domain. Methodologically, while there has been
an increase in mixed methods studies, there has been little change since the
last review. With some exceptions, only a limited range of methodological
instruments has been used. Data is still primarily self-reported rather than
observational and this issue remains an aspect to be addressed in future
research.
Key words: affective domain, beliefs, attitudes, emotions, identity
This is the second chapter on affective issues to appear in MERGA reviews of
research in mathematics education and as such reflects the ongoing importance of
affective issues to the mathematics education research community. The first such
chapter (Schuck & Grootenboer, 2004) noted a continuing move away from studies
on attitudes to projects on beliefs and the consideration of a broader range of
affective aspects. This broadening of areas of interest in exploring affect in
mathematics education was reflective of worldwide trends. This is evidenced by
significant recent publications such as: the seminal book edited by Leder,
Pehkonen and Törner (2002) on beliefs in mathematics education; a special issue
of the Mathematics Education Research Journal (August, 2005) whose editorial
gave a brief overview of the previous 10 years of MERGA related research in the
affective domain; a chapter in the Handbook of Research in the Psychology of
Mathematics Education by Leder and Forgasz (2006) that discussed, among other
matters, developments in the use of different methodological approaches and the
potential of new technologies; and a Special Issue of Educational Studies in
Mathematics (October, 2006) where a series of papers employed six
complimentary theoretical frameworks to examine affective issues with a particular
emphasis on the place of emotion in the affective domain.
The evolution of interest in the affective domain in mathematics education from
considerations of attitudes and anxiety in the 1960s and 1970s, to a focus on the
relationship between affect and cognition in problem solving, and gender, in the
1980s, and to McLeod’s (1992) identification of the three affective concepts –
GROOTENBOER, LOMAS, & INGRAM
2
belief, attitudes and emotions – and the later addition of a fourth – values
(sometimes including ethics and morals), are discussed in Zan, Brown, Evans and
Hannula (2006). They state that arising from this history are two main trends in
current research on affect: the development of theoretical/conceptual frameworks
and of the development of new methodological instruments. In contrast to these
trends, Leder and Grootenboer (2005) noted the overall lack of theorising and the
limited range of methodological instruments used in Australasian research and
presented a theoretical model of the relationships between the four concepts (see
Figure 1) as a starting point in theorising the relationship between aspects of the
affective domain.
Figure 1. The affective domain (Leder & Grootenboer, 2005)
Parallelling the global situation reported by Zan, Brown, Evans and Hannula
(2006), Leder and Grootenboer (2005) reported a predominance of belief studies, a
diminishing number of studies on attitudes, a small number of studies on
‘emotions, feelings, attributions and motivation’ (p. 3) and a few on values.
Given the relative paucity of work in Australasia on clarifying concepts and the
development of theoretical frameworks, there has been little evolution of
definitions of the four key aspects of affect considered in the last review chapter
(Schuck & Grootenboer, 2004). While the positions taken there are used in this
chapter, Figure 1 captures a sense of a more holistic view of the affect domain as a
continuum (McLeod, 1992) and its inclusion of the cognitive while delineating the
four generally acknowledged concepts within affect – beliefs , attitudes, emotions
and values.
BELIEFS
VALUES
ATTITUDES
EMOTIONS OR
FEELINGS
Increased cognition and
stability, decreased affectivity
and intensity
Increased affectivity and
intensity, decreased
cognition and stability
THE AFFECTIVE DOMAIN
3
Beliefs are positions held by individuals that they feel to be true and their nature
cannot be directly observed but must be inferred from actions. Although there are a
variety of definitions of attitudes the common elements to these definitions are that
attitudes are learnt and are evident in responses to a situation or object, and are
seen as positive or negative. Emotions or feelings are described in terms of their
transitory and unstable nature arising as an affective response to particular
events/contexts whereas values are seen as criteria by which choices or
assessments, in terms of desired/desirable outcomes or behaviours, are made
(Schuck & Grootenboer, 2004). The first three of these will be discussed, as will be
self-concept/identity and engagement as in the previous review chapter. Following
this, certain methodological aspects will be considered.
The following sections consider Australasian mathematics education research on
the affective domain, except for work on values which is addressed in chapter
XXX of this book, as outlined above.
TOPICS/FINDINGS
In the broad area of affect in mathematics education, research has focussed on a
number of particular aspects, but about half of the studies have centred on beliefs.
Other affective aspects that have been prevalent include attitudes, emotions,
identity and engagement (and values).
Beliefs
The strong focus on beliefs is a continuing trend as was highlighted by Schuck and
Grootenboer (2004) in the previous MERGA review. The studies published in the
period 2004-2007 have again been mostly undertaken with teachers as their
participants with many exploring the relationship between beliefs and practice.
Two Australian writers, who have regularly addressed this area both on their own,
and in conjunction with others, are Anderson (2005) and Beswick (2005a, 2005b,
2007).
Anderson (2005) (often with White & Sullivan, 2004, 2005) reported on her
work with primary school teachers in New South Wales where she explored the
relationship between the teachers’ problem solving teaching approaches and their
beliefs about the role of problem solving in mathematics. Significantly, Anderson,
Sullivan and White (2005) built on a range of earlier work to theorise and model
the relationship between teachers’ beliefs and practices for problem solving. After
collecting data through a range of methods they developed and refined their model
so that it included the significant influence of the social context. A particular
feature of Anderson, Sullivan and White’s report was the authors’ attention to
theorising, setting this report apart from many other, often largely descriptive,
reports on teachers’ beliefs.
Beswick is another author who has reported extensively and for an extended
period of time on beliefs (Beswick, 2005a, 2005b, 2007; Beswick, Watson, &
Brown, 2006), focussing primarily on secondary teachers. Amongst other findings,
GROOTENBOER, LOMAS, & INGRAM
4
she identified nine beliefs held by secondary teachers about the nature of
mathematics, mathematics learning and the role of the teacher. Furthermore,
Beswick noted some associations between particular clusters of beliefs and the
classroom environment, but also highlighted that these relationships were complex
and contextually bound. Other studies on teachers’ beliefs include: Barkatsas and
Malone’s (2005) exploration of the beliefs Greek mathematics teachers and the
relationship with their practice; McDonough and Clarke’s (2005) inquiry into
changes in the practices and beliefs of primary teachers involved with a numeracy
professional development program; Nisbet and Grimbeek’s (2004) quantitative
review of primary teachers’ beliefs about compulsory numeracy testing; Perry,
Way, Southwell, White and Pattison’s (2005) examination of the relationship
between preservice teachers’ beliefs and mathematical achievement; Prescott and
Cavanagh’s (2006) qualitative study into preservice secondary teachers beliefs
about effective mathematics teaching; and, Scott’s (2005) mixed method
investigation and modelling of preservice primary teachers beliefs and intentions
about mathematics education.
Studies into students’ beliefs about mathematics and mathematics learning have
been less frequent than ones on teachers’ beliefs, but nevertheless, there has been
some work done in this area. A focussed area for this study has been the University
of Waikato (New Zealand) where Taylor, Hawera and Young-Loveridge (2005),
Young-Loveridge and Taylor (2005), and Young-Loveridge, Taylor, Sharma and
Hawera (2006) have reported often on primary students’ beliefs about mathematics
learning, particularly in the context of the New Zealand Numeracy Project. Various
reports showed that many students had clear expectations about the teachers’ role
in teaching them mathematics and deep-seated views about mathematics, and these
influenced their learning.
In 2007 there were also reports from Anderson (2007), Grootenboer (2007), Ng
and Stillman (2007), Pierce, Stacey and Barkatsas (2007), and Sullivan and
McDonough (2007) on the development of theory-based quantitative instruments
to measure student’s affective responses to mathematics. While at this stage the
findings from the use of these instruments are limited, it is timely that some more
robust and rigorous scales are developed.
Attitudes and Emotions
In the period 2004 to 2007 there were only a few reports of research that focussed
specifically on attitudes and emotions. Pierce and Stacey (2006) reported on a
qualitative study that explored the improvement of students’ attitudes to
mathematics through association with simple pleasures from real world contexts.
They found that real world contexts appeared to lead to improved student attitudes
to mathematics, but they cautioned that this was due to superficial pleasures rather
than substantive mathematics. These authors also worked with Barkatsas (Pierce,
Stacey, & Barkatsas, 2007) to develop the Mathematics and Technology Attitudes
Scale (MTAS) that monitored students’ attitudes to learning mathematics with
technology. In this study they reported some small gender differences between the
THE AFFECTIVE DOMAIN
5
attitudes and confidence of the boys and girls related to learning mathematics with
technology.
In terms of students’ attitudes to learning a particular aspect of mathematics,
Norton and Irvin (2007) reported on a classroom intervention which was designed
to develop students’ positive perceptions of their ability to learn algebra. The six-
week intervention was based around a selection of activities designed to enable
students to make connections between materials, verbal language, and symbolic
language. The study found that the students valued the instructional discourse
much more than they did their normal mathematics learning experience and had an
increased confidence in their capacity to understand algebra.
Another attitudinal study focussed on secondary mathematics teachers’ attitudes
to a range of alternative assessment methods (Watt, 2005). In short, Watt found
that these teachers were generally satisfied with traditional tests as valid measures
of student achievement and they did not favour alternative assessments as they
were seen as too subjective.
Studies that centred particularly on emotional aspects of learning mathematics
were rather scarce. Hawera (2004) reported on a tertiary course designed to address
the feelings of some mathematically anxious preservice primary teachers. She
found that by creating a safe learning environment and by building the course
around social constructivist principles, the participants were able to go some way
to addressing their mathematical anxiety. Frankcom’s (2006) thesis examined
mathematics anxiety and self efficacy in preservice primary teachers and found, as
expected, that these were closely negatively correlated but that, unexpectedly,
success with mastery experiences in their mathematics education courses did not
reduce anxiety or increase self efficacy significantly. In Shannon’s (2004) case
study with one senior secondary school girl, she found that there were a range of
factors that were often not necessarily mathematical, that caused the student to
dislike and avoid participation in mathematics.
Other Affective Aspects
Other studies related to the affective domain emerging amongst the MERGA
community focus on identity and engagement. Walshaw (2004a, 2004b) and Klein
(2004) focussed on the construction of identity with preservice teachers. They both
highlighted the complexity of identity development and the many discourses that
influence the process. A 2006 symposium at MERGA 2006 on researching identity
in mathematics education provided a general overview (Grootenboer, Smith, &
Lowrie, 2006), and then explored the topic from a range of perspectives including
Bourdieuian (Zevenbergen, 2006), Wenger’s social theory of learning (Smith,
2006), and feminist poststructuralism (Letts, 2006). The symposium was not
grounded in empirical research, but rather it gave some theoretical under-pinning
to work that may emerge in this area. Grootenboer and Zevenbergen (2007) and
Ingram (2007) have presented subsequent papers that further explore identity in
empirical studies on mathematical learning and secondary students’ affective
responses to mathematics respectively.
GROOTENBOER, LOMAS, & INGRAM
6
Motivation and engagement have been explored by Sullivan, McDonough and
their colleagues (Sullivan & McDonough, 2007; Sullivan, McDonough, & Turner
Harrison, 2004; Sullivan, Tobias, & McDonough, 2006). Their large scale and
continuing work has already produced a number of findings including the role peer
pressure and classroom culture can play in inhibiting students’ learning
opportunities in mathematics. Cretchley (2005) examined engagement through
lecture attendance in a tertiary context and found that there was a relationship
between participation and mathematics performance.
Critique of the Topics/Findings
In the preceding section we have provided a brief and concise summary of much of
the Australasian research that has been reported on the affective domain in
mathematics education in the period 2004-2007. While each report appears to have
individual merit, there are some themes and issues that are worth noting. This
critique is not so much about individual reports or studies, but rather about the
topics, findings and directions of the body of research in this area.
In the period 2004-2007 a significant proportion of the reports have focussed on
beliefs; a trend that has continued since the last review of research in this area
(Schuck & Grootenboer, 2004). There is a sense that some of the research has not
so much built on the previous work but is largely more of the same. Indeed, many
are largely descriptive studies of teachers’ beliefs, and lack any significant
theorising. It seems that in other parts of the world they are beginning to consider
the theoretical foundations of research into beliefs and other affective aspects (e.g.,
Zan, Brown, Evans, & Hannula, 2006), and it is time for a greater theorising about
the general findings that are, seemingly, being consistently reported in Australasia.
Many of the reports reviewed focus on a particular aspect of the affective
domain and this has given some illumination on these dimensions in mathematics
teaching and learning. However, due to the complex nature of the affective domain,
and the difficulties in clearly defining its various components, it would be valuable
to see affectivity explored in a more holistic manner. Similarly, there appears to be
only a few studies that look at the relationship between affectivity and cognition
and achievement (e.g., Watson, Beswick, Brown, & Callingham, 2007). That said,
Walshaw and Cabral (2005) contend that there are a number of studies into
affective and cognitive aspects of mathematics learning that are grounded in
theories of discursive practice, embodiment, somatic markers, neuroscience,
representation and situated practice, although these are largely undertaken outside
of Australasia (see Zan, Brown, Evans, & Hannula, 2006). Now that there appears
to be a greater understanding of the affective domain and its components, it is time
for a more focussed research agenda that examines these relationships. The
emerging focus on identity may well provide an avenue for such research.
THE AFFECTIVE DOMAIN
7
METHODOLOGICAL ISSUES
In this section we have focussed on methodological issues because of their
importance when researching the affective domain in mathematics education. As
understanding has grown of the complex nature of mathematics education, multiple
perspectives and new approaches to research methodologies and paradigms have
become valued. This is particularly true for the affective domain, which has unique
methodological issues and limitations because of its complexity as evidenced by
Bragg’s (2007) discussion of attempts to reconcile contradictory indicators arising
from quantitative and qualitative data. Also significant are the ethical issues
surrounding its highly personal nature and the high level of inference required. In
their review of affective literature, Leder and Forgasz (2006) stated “affect can not
be measured directly but needs to be inferred from the way an individual behaves
or responds to specifically designed instruments, cues, or situations” (p. 404). This
reliance on inference can limit affective research to “beliefs, attitudes and feelings
that participants are willing and able to share in either a verbal or written form”
(Schuck & Grootenboer, 2004, p. 12), creating a high proportion of self-reporting
data collection methods (Leder & Forgasz, 2006).
Anthony (2004) in her review of trends in mathematics education, commented
that grouping research papers by methodology was “fraught with difficulty” (p. 6)
because of a multiplicity of descriptors used by researchers. This was reflected in
the Australasian literature during the current review period. Philosophical
assumptions and methodological frameworks were sometimes absent and only the
methods and instruments used described. There are many reasons why this may be
the case including the limited space available in many contexts, but,
“metaphorically, unarticulated philosophical perspectives are like an unlighted
room … one is likely to stumble over objects and to misunderstand the nature of
the rooms within which one is stumbling around” (Maykut & Morehouse, 1994, p.
22).
In this research period, excluding a small number of non-empirical position and
review papers, about a quarter of the studies were quantitative (26%) and there
were about equal numbers of qualitative (38%) and mixed method studies (36%);
the increase in mixed method studies reflecting general research trends (Creswell,
2003). Mixed method studies include a simultaneous or sequential collection of
elements of qualitative and quantitative methods in their design (Creswell, 2003;
Lankshear & Knobel, 2004). Research in this domain can perhaps be better seen as
lying on a continuum between qualitative and quantitative. There are a number of
studies in this research period that tend to be more qualitative. They are qualitative
in nature but have varying levels of simple numerical analysis, which help clarify
patterns or can be used for descriptive or illustrative purposes (Lundy Dobbert &
Kurth-Schai, 1992). McDonough and Clarke (2005), for example, in investigating
change in teachers’ beliefs and practice as a result of professional development in
the Early Numeracy Research Project in Victoria, used some quantification in
comparing the entry and exit questionnaires by using tables with frequencies of
themes and a simple t-test to show differences in beliefs about the nature of
mathematics, the role of the teacher, and attitude and confidence in teaching
GROOTENBOER, LOMAS, & INGRAM
8
mathematics. Barkatsas and Malone (2005) is an example of a mixed method
design that tends towards the quantitative. They used a sequential explanatory
strategy of inquiry when they initially investigated 465 Greek mathematics
teachers’ beliefs through a quantitative survey, and then explored the links between
these beliefs and classroom practice through a case study of one secondary school
mathematics teacher. The qualitative data from the teacher was integrated into the
overall analysis to help explain and interpret the findings of the larger quantitative
study.
The last four yearly review stated a need for more classroom-based research
using observational methods in primary and secondary classrooms (Schuck &
Grootenboer, 2004). While this review period indicates that a better balance in the
affective literature has been achieved with more studies researching, in particular,
secondary students, this research can not necessarily be considered classroom-
based. A large proportion of the student-centred studies were done through
interviews and surveys. The most frequent instruments were Likert-scale or open-
ended questionnaires and semi-structured interviews. Other methods used were
classroom observations (e.g., Seah, 2004), the collection of assessment information
(Cretchley, 2005; Seah, 2004), weekly conferences (Caswell & Nisbet, 2005),
journals (Hawera, 2004; Wilson & Thornton, 2005, 2006), task-related interviews
or teaching conversations (Sullivan, Tobias, & McDonough, 2006), and artefact
collection such as student work samples, written reflections, and enrolment
information (Brady, 2007; Parnell, 2005; Williams, 2006).
Smith (2006) explored the innovative methodology of self-study through
narrative inquiry using as a context a preservice mathematics curriculum subject of
which she was the teacher. She found narrative inquiry allowed her “identities as
classroom teacher, teacher educator, learner, and researcher to come together” (p.
477) enabling her to monitor her own journey, become a co-learner and therefore,
maximise generative learning. Later in the review period Bailey (2007) also
employed the use of narrative inquiry to pursue and change previously unknown
personal beliefs about learning mathematics. Anderson (2005) used a Personal
Journey Graph as an instrument in a case study that followed one teacher through
the implementation of the New Zealand Intermediate Numeracy Project. A
narrative framework was used and data gathered about changing attitudes and
beliefs, mathematical and pedagogical content knowledge, and knowledge of
student learning in numeracy. The Personal Journey Graph was drawn to reflect the
teacher’s “opinion of her ability to implement the approaches consistent with the
Numeracy Project in her mathematics classroom” (p. 98). The teacher was asked to
draw a curve that represented her implementation ability over time as low, medium
or high. She was given the opportunity to reflect on and make changes to her graph
at the end of the following year. The graph showed the teacher’s initial confidence
waning and then rapidly increasing in the latter half of the year allowing a unique
insight into the teacher’s reflections of her journey. This instrument was also being
used by Ingram (2007) to understand the affective development of secondary
school students through exploring their mathematical identities.
THE AFFECTIVE DOMAIN
9
Leder and Forgasz (2006) explored other methodological possibilities available
now with technological advances such as mobile phones and the conferencing
facilities of the internet. They outlined the Experience Sampling Method (ESM),
which allow self-reports of mental processes by using a signal as a trigger between
five and seven times per day (Leder & Forgasz, 2006). Participants chart their
activities, and their reactions to and beliefs about those activities allowing a less
intrusive way of capturing rich and comprehensive data. Forgasz and Leder (2006)
used ESM to collect contextualised information to explore the work patterns and
factors associated with stress in experienced and novice secondary mathematics
teachers. Over a one-week period, the daily lives of 14 teachers were tracked using
mobile phone text-messaging as a signal and data collected on their activities and
their reactions to those activities. Four of the teachers were then interviewed. The
study found that teachers’ work-related activities extended beyond work hours and,
while teaching mathematics was more likely to be the cause of stress for novice
teachers, experienced teachers experienced high engagement and pleasure in the
task of teaching mathematics, and were more likely to find administration work a
stressor.
The consistencies and inconsistencies between teachers’ professed and
attributed beliefs remains a major topic of study. However, there have been few
advances made to research designs, data collection, and data analysis methods.
Speer (2005) cautions that reported inconsistencies in this field of research may be
actually the consequence of methodological issues, specifically a lack of shared
understanding among researchers and teachers about what descriptive terms mean,
and a consequence of a lack of coordination between data on beliefs and practices.
Furthermore Speer (2005) contends “that it is inappropriate to classify any data on
beliefs as purely professed. All claims about teachers’ beliefs are, to greater or
lesser extents, attributed to teachers by researchers” (Speer, 2005, p. 362).
Anderson, Sullivan, and White (2004, 2005) go some way to addressing these
concerns. They investigated the problem-solving beliefs and practices of 162
primary teachers through a mixed method study using surveys, semi-structured
interviews, which used the survey responses as a starting point, and classroom
observations of two of the teachers. The authors recognised the possibilities of
misinterpretation in the survey questions and provided specific examples for the
teachers to illustrate the terminology.
Longitudinal studies are an important way of studying affect, allowing
understanding about what mathematical experiences the students have throughout
their education that led to the development of their affective views (Schuck &
Grootenboer, 2004). There were few studies in the review period, which were
explicitly called longitudinal. Lomas (2004) in his doctoral research examined the
perceptions of a primary preservice teacher cohort over the three year period of
their preservice teacher education degree. This tracked the level of alignment of a
‘reform’ agenda promoted by lecturers with its acceptance by the preservice
teachers. The findings show, over the three-year period of the study, high levels of
alignment with the pedagogical aspects of reform but significantly lower levels
with emancipatory aspects and only minor incremental change in students’
GROOTENBOER, LOMAS, & INGRAM
10
alignment in both aspects. Many of the longitudinal studies in the review period
(2004–2007) were reported in parts. The reasons for this are perhaps because
research is being published as it is being analysed particularly in longitudinal
studies relating to doctoral research or because of the space limitations in journal
and conference proceedings. This can lead to problems when the general and
methodological background for a paper is not fully presented due to their inclusion
in an earlier one so the paper does not completely stand-alone.
There is also a relative absence of action research or interventionist type
research in this period. The wealth of descriptive studies over the last decade have
provided a rich awareness of affective concerns in mathematics education, and it is
now time to undertake further studies that seek to not only report on, but also move
forward, on some of these concerns. As we continue to improve our knowledge
about the affective domain, this seems an important strategy for researchers to
adopt, literally putting knowledge into practice.
In the last review, Schuck and Grootenboer (2004) questioned the
disproportionate number of studies that involved preservice and inservice teachers,
and wondered if this was because these groups were more readily available to the
current field of researchers, often preservice teacher educators. This finding
appears to be different from Anthony’s (2004) review, which found that students
were the main focus, although it may be that preservice teachers were considered
here to be students. Anthony (2004) also remarked that there had been a noticeable
decrease in the proportion of papers that relate to the wider tertiary sector. In this
review period there have been several studies in the affective literature published
about tertiary students, in particular with a focus on technology (e.g., Berger &
Cretchley, 2005). However, there are still gaps in studies on tertiary mathematics
lecturers and a noticeable (now glaring) gap in any research in the early childhood
sector. There is also no research that concerns vocational education participants,
the community, or parents. This is consistent with the last review (Schuck &
Grootenboer, 2004) and also reflects Leder and Forgasz’s (2006) comment that
there has been little examination of general societal beliefs about mathematics or
the community’s concern with affectivity.
CONCLUDING COMMENTS
In the 2004 review a recommendation for a greater focus on school students’
affectivity was made. Over the last 4 years, although there has been an increase in
the number research reports dealing with school student perspectives, with a
predominance of secondary focussed studies, preservice teacher and classroom
teacher studies continue to dominate. This continues the trend reported by Leder
and Grootenboer (2005) and adds weight to their call for more work with primary
children and in early childhood.
While links between beliefs and practice continue to be a major area of interest,
few studies advance any theoretical considerations that might underpin causal
relationships between the two. Implications in studies are rarely developed beyond
a local frame of reference and indeed the testing or development of theoretical
THE AFFECTIVE DOMAIN
11
frameworks is largely absent. The need for theory development to underpin
research is apparent elsewhere in the world and needs to be a feature of
Australasian affect research in the near future.
Changes in methodological approaches have seen an increase in mixed method
studies with roughly equal numbers of qualitative, quantitative and mixed method
studies being represented. However, the actual extent of this change is difficult to
determine due to the ongoing reporting of some larger studies in small segments,
and with a variety of authors, which leads to multiple counts of some approaches.
This is further compounded by apparent variation in what is understood by mixed
methods; in some studies labelled mixed methods by the researchers, the reviewers
held a different view. Alongside this trend toward mixed methods studies with
multiple data sources has been the continued use of familiar data collection
methods. Indeed, the use of new types of instruments has been relatively limited.
The methods of data collection used remain predominantly that of self-reporting
via survey and interview, with classroom observation being largely absent. This
situation tends to restrict affect research to individual and group perceptions. If
belief/practice investigations are to move to more fertile ground then it is important
that observational data of teachers and students in classroom environments become
an integral part of research projects.
REFERENCES
Anderson, J. (2005). I didn't know what I didn't know: A case study of growth in teacher knowledge
within the Intermediate Numeracy Project. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A.
McDonough, R. Pierce & A. Roche (Eds.), Building connections: Research, theory and practice
(Proceedings of the 28th annual conference of the Mathematics Education Group of Australasia,
Melbourne, Vol. 1, pp. 97-104). Sydney: MERGA.
Anderson, J., Sullivan, P., & White, P. (2004). The influence of perceived constraints on teachers'
problem-solving beliefs and practices. In I. Putt, R. Faragher & M. McLean (Eds.), Mathematics
education for the third millennium: Towards 2010 (Proceedings of the 27th annual conference of the
Mathematics Education Research Group of Australasia, Townsville, Vol. 1, pp. 39-46). Sydney:
MERGA.
Anderson, J., Sullivan, P., & White, P. (2005). Using a schematic model to represent influences on, and
relationships between, teachers' problem-solving beliefs and practices. Mathematics Education
Research Journal, 17(2), 9-38.
Anderson, V. (2007). An online survey to assess student anxiety and attitude response to six different
mathematical problems. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research,
essential practice (Proceedings of the 30th annual conference of the Mathematics Education
Research Group of Australasia, Tasmania, Vol. 1, pp. 93-102). Adelaide: MERGA.
Anthony, G. (2004). MERGA: A community of practice. In I. Putt, R. Faragher & M. McLean (Eds.),
Mathematics education for the third millennium: Towards 2010 (Proceedings of the 27th annual
conference of the Mathematics Education Research Group of Australasia, Townsville, Vol. 1, pp. 2-
15). Sydney: MERGA.
Bailey, J. (2007). Mathematical investigations: A primary teacher educator's narrative journey of
professional awareness. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research,
essential practice (Proceedings of the 30th annual conference of the Mathematics Education
Research Group of Australasia, Tasmania, Vol. 1, pp. 103-112). Adelaide: MERGA.
GROOTENBOER, LOMAS, & INGRAM
12
Barkatsas, A., & Malone, J. (2005). A typology of mathematics teachers' beliefs about teaching and
learning mathematics and instructional practices. Mathematics Education Research Journal, 17(2),
69-90.
Berger, M., & Cretchley, P. (2005). Technology and mathematics learning at university level: A South
African perspective. African Journal of Research in Mathematics, Science, and Technology
Education, 9(2), 97-108.
Beswick, K. (2005a). The beliefs/practice connection in broadly defined contexts. Mathematics
Education Research Journal, 17(2), 39-68.
Beswick, K. (2005b). It depends on the students: Influencing teachers' beliefs about the ends and means
of numeracy teaching. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce
& A. Roche (Eds.), Building connections: Research, theory and practice (Proceedings of the 28th
annual conference of the Mathematics Education Group of Australasia, Melbourne, Vol. 1, pp. 137-
144). Sydney: MERGA.
Beswick, K. (2007). Teachers' beliefs that matter in secondary mathematics classrooms. Educational
Studies in Mathematics, 65(1), 95-120.
Beswick, K., Watson, J., & Brown, L. (2006). Teachers' confidence and beliefs about the ends and
means of numeracy teaching. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.),
Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the
Mathematics Education Research Group of Australasia, Canberra, Vol. 1, pp. 68-83). Adelaide:
MERGA.
Brady, K. (2007). Imagined classrooms: Prospective primary teachers visualise their ideal mathematics
classroom. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice
(Proceedings of the 30th annual conference of the Mathematics Education Research Group of
Australasia, Tasmania, Vol. 1, pp. 143-152). Adelaide: MERGA.
Bragg, L. (2007). Students' conflicting attitudes towards games as a vehicle for learning mathematics: A
methodological dilemma. Mathematics Education Research Journal, 19(1), pages?.
Caswell, R., & Nisbet, S. (2005). Enhancing mathematical understanding through self-assessment and
self-regulation of learning: The value of meta-awareness. In P. Clarkson, A. Downton, D. Gronn, M.
Horne, A. McDonough, R. Pierce & A. Roche (Eds.), Building connections: Research, theory and
practice (Proceedings of the 28th annual conference of the Mathematics Education Group of
Australasia, Melbourne, Vol. 1, pp. 209-216). Sydney: MERGA.
Creswell, J. (2003). Research design: Qualitative, quantitative, and mixed method approaches (2nd
ed.). California: Sage Publications.
Cretchley, P. (2005). Mathematics and dumping lectures: Another perspective on the shift towards
learner pragmatism. In M. Bulmer, H. McGillivray & C. Varsavski (Eds.), Proceedings of the fifth
Southern Hemisphere conference on undergraduate mathematics and statistics teaching and
learning, Brisbane (Vol.?? pp.??). International Delta Steering Committee.
Forgasz, H., & Leder, G. (2006). Work patterns and stressors. Australian Mathematics Teacher, 62(3),
36-40.
Frankcom, G. (2006). Maths anxiety in third year pre-service primary student teachers: Fact or fiction?
Unpublished Masters thesis, University of Auckland.
Grootenboer, P. J. (2007). Measuring students' affective responses to mathematics and mathematics
education. In C. S. Lim, S. Fatimah, G. Munirah, S. Hajar, M. Y. Hashimah, W. L. Gan & T. Y.
Hwa (Eds.), Meeting challenges of developing quality mathematics education culture (Proceedings
of the 4th East Asia Regional Conference on Mathematics Education, pp. 273-280). Penang,
Malaysia: Universiti Sains Malaysia.
Grootenboer, P. J., Smith, T., & Lowrie, T. (2006). Researching identity in mathematics education: The
lay of the land. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and
learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research
Group of Australasia, Canberra, Vol. 2, pp. 612-615). Adelaide: MERGA.
Grootenboer, P. J., & Zevenbergen, R. (2007). Identity and mathematics: Towards a theory of agency in
coming to learn mathematics. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research,
THE AFFECTIVE DOMAIN
13
essential practice (Proceedings of the 30th annual conference of the Mathematics Education
Research Group of Australasia, Tasmania, Vol. 1, pp. 335-344). Adelaide: MERGA.
Hawera, N. (2004). Addressing the needs of mathematically anxious preservice primary teachers. In I.
Putt, R. Faragher & M. McLean (Eds.), Mathematics education for the third millennium: Towards
2010 (Proceedings of the 27th annual conference of the Mathematics Education Research Group of
Australasia, Townsville, Vol. 1, pp. 287-294). Sydney: MERGA.
Ingram, N. (2007). A story of a student fulfilling a role in the mathematics classroom. In J. Watson &
K. Beswick (Eds.), Mathematics: Essential research, essential practice (Proceedings of the 30th
annual conference of the Mathematics Education Research Group of Australasia, Tasmania, pp. 450-
459). Adelaide: MERGA.
Klein, M. (2004). Preservice teacher education in mathematics: Thinking innovatively about innovation.
In I. Putt, R. Faragher & M. McLean (Eds.), Mathematics education for the third millennium:
Towards 2010 (Proceedings of the 27th annual conference of the Mathematics Education Research
Group of Australasia, Townsville, pp. 328-335). Sydney: MERGA.
Lankshear, C., & Knobel, M. (2004). A handbook for teacher research: From design to implementation.
England: Open University Press.
Leder, G., & Forgasz, H. J. (2006). Affect and mathematics education. In A. Gutiérrez & P. Boero
(Eds.), Handbook of research on the psychology of mathematics education: Past, present and future
(pp. 403-427). Rotterdam, The Netherlands: Sense Publishers.
Leder, G., & Grootenboer, P. (2005). Affect and mathematics education. Mathematics Education
Research Journal, 17(2), 1-8.
Leder, G., Pehkonen, E., & Törner, G. (2002). Beliefs: A hidden variable in mathematics education?
Dordrecht, The Netherlands: Kluwer Academic.
Letts, W. (2006). Bringing feminist poststructuralism to bear on [mathematics] teacher education. In P.
Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and learning spaces
(Proceedings of the 29th annual conference of the Mathematics Education Research Group of
Australasia, Canberra, pp. 623-627). Adelaide: MERGA.
Lomas, G. (2004). The relationship between mathematics educators' beliefs and their teaching
practices. Unpublished Doctoral Thesis, Curtain University of Technology, Perth.
Lundy Dobbert, M., & Kurth-Schai, R. (1992). Systematic ethnography: Towards an evolutionary
science of education and culture. In The handbook of qualitative research in education. California:
Academic Press, Inc.
Maykut, P., & Morehouse, R. (1994). Beginning qualitative research: A philosophic and practical
guide. London: The Falmer Press.
McDonough, A., & Clarke, B. (2005). Professional development as a catalyst for changes in beliefs and
practice: Perspectives from the Early Numeracy Research Project. In P. Clarkson, A. Downton, D.
Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche (Eds.), Building connections: Research,
theory and practice (Proceedings of the 28th annual conference of the Mathematics Education
Group of Australasia, Melbourne, pp. 521-528). Sydney: MERGA.
McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualisation. In D.
Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575-596). New
York: NCTM and Macmillan.
Ng, K. E. D., & Stillman, G. (2007). Interdisciplinary learning: Development of mathematical
confidence, value, and the interconnectedness of mathematics scales. In J. Watson & K. Beswick
(Eds.), Mathematics: Essential research, essential practice (Proceedings of the 30th annual
conference of the Mathematics Education Research Group of Australasia, Tasmania, pp. 533-542).
Adelaide: MERGA.
Nisbet, S., & Grimbeek, P. (2004). Primary teachers' beliefs and practices with respect to compulsory
numeracy testing. In I. Putt, R. Faragher & M. McLean (Eds.), Mathematics education for the third
millennium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics
Education Research Group of Australasia, Townsville, pp. 406-413). Sydney: MERGA.
GROOTENBOER, LOMAS, & INGRAM
14
Norton, S., & Irvin, J. (2007). Developing positive attitudes towards algebra. In J. Watson & K.
Beswick (Eds.), Mathematics: Essential research, essential practice (Proceedings of the 30th annual
conference of the Mathematics Education Research Group of Australasia, Tasmania, pp. 561-570).
Adelaide: MERGA.
Parnell, S. M. (2005). Do student reflections increase undergraduate mathematics learning? In M.
Bulmer, H. MacGillivray & C. Varsavsky (Eds.), Proceedings of Kingfisher Delta '05, World
Heritage Fraser Island, Queensland, Australia (pp. 95-102). Place published?? Publisher??
Perry, B., Way, J., Southwell, B., White, A. L., & Pattison, J. (2005). Mathematical beliefs and
achievement of pre-service primary teachers. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A.
McDonough, R. Pierce & A. Roche (Eds.), Building connections: Research, theory and practice
(Proceedings of the 28th annual conference of the Mathematics Education Group of Australasia,
Melbourne, pp. 625-632). Sydney: MERGA.
Pierce, R., & Stacey, K. (2006). Enhancing the image of mathematics by association with simple
pleasures from real world contexts. Zentralblatt fur Didaktik der Mathematik, 38(3), 214-225.
Pierce, R., Stacey, K., & Barkatsas, A. (2007). A scale for monitoring students' attitudes to learning
mathematics with technology. Computers in Education, 48(2), 285-300.
Prescott, A., & Cavanagh, M. (2006). An investigation of pre-service secondary mathematics teachers'
beliefs as they begin their teacher training. In P. Grootenboer, R. Zevenbergen & M. Chinnappan
(Eds.), Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the
Mathematics Education Research Group of Australasia, Canberra, pp. 424-431). Adelaide: MERGA.
Schuck, S., & Grootenboer, P. (2004). Affective issues in mathematics education. In B. Perry, C.
Diezmann & G. Anthony (Eds.), Review of mathematics education in Australasia 2000-2003 (pp.
53-74). Sydney: MERGA.
Scott, A. L. (2005). Preservice teachers' intentions to provide good examples and help children replicate
them. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche
(Eds.), Building connections: Research, theory and practice (Proceedings of the 28th annual
conference of the Mathematics Education Group of Australasia, Melbourne, pp. 656-663). Sydney:
MERGA.
Seah, W. T. (2004). Shifting the lens of inquiry into the socialisation of mathematics teachers: Nature of
value differences. In I. Putt, R. Faragher & M. McLean (Eds.), Mathematics education for the third
millennium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics
Education Research Group of Australasia, Townsville, pp. 501-508). Sydney: MERGA.
Shannon, F. (2004). Classics counts over calculus: A case study. In I. Putt, R. Faragher & M. McLean
(Eds.), Mathematics education for the third millennium: Towards 2010 (Proceedings of the 27th
annual conference of the Mathematics Education Research Group of Australasia, Townsville, pp.
509-516). Sydney: MERGA.
Smith, T. (2006). Self-study through narrative inquiry: Fostering identity in mathematics teacher
education. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and
learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research
Group of Australasia, Canberra, pp. 471-478). Adelaide: MERGA.
Speer, N. M. (2005). Issues of methods and theory in the study of mathematics teachers' professed and
attributed beliefs. Educational Studies in Mathematics, 58, 361-291.
Sullivan, P., & McDonough, A. (2007). Eliciting positive student motivation for learning mathematics.
In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Proceedings
of the 30th annual conference of the Mathematics Education Research Group of Australasia,
Tasmania, pp. 698-707). Adelaide: MERGA.
Sullivan, P., McDonough, A., & Turner Harrison, R. (2004). Students' perceptions of factors
contributing to successful participation in mathematics. In M. Johnsen Hoines & A. Berit Fugelstad
(Eds.), 28th conference of the International Group for the Psychology of Mathematics Education
(Vol. 3, pp. 289-296). Bergen, Norway: Bergen University College.
Sullivan, P., Tobias, S., & McDonough, A. (2006). Perhaps the decision of some students not to engage
in learning mathematics in school is deliberate. Educational Studies in Mathematics, 62(1), 81-99.
THE AFFECTIVE DOMAIN
15
Taylor, M., Hawera, N., & Young-Loveridge. (2005). Children's views of their teacher's role in helping
them learn mathematics. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R.
Pierce & A. Roche (Eds.), Building connections: Research, theory and practice (Proceedings of the
28th annual conference of the Mathematics Education Group of Australasia, Melbourne, pp. 728-
734). Sydney: MERGA.
Walshaw, M. (2004a). Becoming knowledgeable in practice: The constitution of secondary teaching
identity. In I. Putt, R. Faragher & M. McLean (Eds.), Mathematics education for the third
millennium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics
Education Research Group of Australasia, Townsville, pp. 557-564). Sydney: MERGA, Inc.
Walshaw, M. (2004b). Pre-service mathematics teaching in the context of schools: An exploration into
the constitution of identity. Journal of Mathematics Teacher Education, 7, 63-86.
Watson, J., Beswick, K., Brown, N., & Callingham, R. (2007). Student change associated with teachers'
professional learning. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential
practice (Proceedings of the 30th annual conference of the Mathematics Education Research Group
of Australasia, Tasmania, pp. 785-795). Adelaide: MERGA.
Watt, H. M. G. (2005). Attitudes to the use of alternative assessment methods in mathematics: A study
with secondary mathematics teachers in Sydney, Australia. Educational Studies in Mathematics, 58,
21-44.
Williams, G. (2006). Autonomous looking-in to support creative mathematical thinking: Capitilising on
activity in Australian LPS classrooms. In D. Clarke, C. Kietel & Shimizu (Eds.), Mathematics
classrooms in twelve countries: The insider's perspective (pp. 221-236). Rotterdam, The
Netherlands: Sense.
Wilson, S., & Thornton, S. (2005). 'I am really not alone in this anxiety': Bibliotheraphy and pre-service
primary teachers' self-image as mathematicians. In P. Clarkson, A. Downton, D. Gronn, M. Horne,
A. McDonough, R. Pierce & A. Roche (Eds.), Building connections: Research, theory and practice
(Proceedings of the 28th annual conference of the Mathematics Education Group of Australasia,
Melbourne, pp. 791-798). Sydney: MERGA.
Wilson, S., & Thornton, S. (2006). To heal and enthuse: Developmental bibliotherapy and pre-service
primary teachers' reflections on learning and teaching mathematics. In P. Grootenboer, R.
Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the
29th annual conference of the Mathematics Education Research Group of Australasia, Canberra, pp.
36-44). Adelaide: MERGA.
Young-Loveridge, J., & Taylor, M. (2005). Children's views about mathematics learning after
participation in a numeracy initiative. Research in Education, 74, 83-90.
Young-Loveridge, J., Taylor, M., Sharma, S., & Hawera, N. (2006). Students' perspectives on the nature
of mathematics. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, cultures
and learning spaces (Proceedings of the 29th annual conference of the Mathematics Education
Research Group of Australasia, Canberra, pp. 583-590). Adelaide: MERGA.
Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An
introduction. Educational Studies in Mathematics, 63(2), 113-121.
Zevenbergen, R. (2006). Teacher identity from a bourdieuian perspective. In P. Grootenboer, R.
Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the
29th annual conference of the Mathematics Education Research Group of Australasia, Canberra, pp.
616-618). Adelaide: MERGA.
AFFILIATIONS
Peter Grootenboer
Gregor Lomas
GROOTENBOER, LOMAS, & INGRAM
16
Naomi Ingram
