MARKKU S. HANNULA
MOTIVATION IN MATHEMATICS: GOALS REFLECTED IN
EMOTIONS
ABSTRACT. Students in a mathematics classroom are motivated to do many things, not
only the ones we expect them to do. In order to understand student behaviour in classrooms
we need to increase our understanding of what motivation is and how it is regulated. Two
issues relevant to a critique of mainstream motivation research need consideration: (a) the
importance of the unconscious in motivation and (b) focusing on motivational states and
processes rather than traits. In the present paper, motivation is conceptualised as a potential
to direct behaviour through the mechanisms that control emotion. As a potential, motivation
cannot be directly observed. It is observable only as it manifests itself in affect and cognition,
for example as beliefs, values and emotional reactions. This potential is structured through
needs and goals. Based on this view of motivation and the author’s earlier studies, three
aspects of motivation regulation are discussed. Primarily, goals are derived from needs: in
learning situations, the psychological needs for autonomy, competence, and social belonging
are the most significant determinants of goal choices. As a second aspect, this view accepts
the influence of students’ beliefs about the accessibility of different goals. As a third aspect,
the influence of automatic emotional reactions for goal regulation will be discussed. The
case of Frank will be used 1) to illustrate how motivation can be inferred from different
kinds of data and 2) as an example of how conflicting goals lead to non-straightforward
self-regulation.
KEY WORDS: affect, emotion, goal, mathematics learning, motivation, needs,
self-regulation
1. INTRODUCTION
To understand student’s behaviour we need to know their motives. Motivation, in this paper, is seen as the inclination to do certain things and
avoid doing some others. In the literature (e.g. Ryan and Deci, 2000), one
important approach has been to distinguish between intrinsic and extrinsic motivation. Another approach to motivation has been to distinguish
(usually three) motivational orientations in educational settings: learning
(or mastery) orientation, performance (or self-enhancing) orientation, and
ego-defensive (avoidance) orientation (e.g. Lemos, 1999; Linnenbrink and
Pintrich, 2000). Murphy and Alexander (2000) also see interest (situational
vs. individual) and self-schema (agency, attribution, self-competence, and
self-efficacy) as important conceptualisations of motivation.
In mathematics education, motivation has not been a popular topic of
study lately. It has been discussed under the terms motivational orientation
Educational Studies in Mathematics (2006) 63: 165–178
DOI: 10.1007/s10649-005-9019-8
C
Springer 2006
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(Yates, 2000), interest (Bikner-Ahsbahs, 2003), and motivational beliefs
(Kloosterman, 2002). Also, Op ‘t Eynde, De Corte and Verschaffel (2002)
have integrated the issues of motivation into what they have called their
“socio-constructivist” perspective.
In my reading, all the above approaches fail to describe the quality of
the motivation in sufficient detail. This is perhaps inevitable, given that the
authors’ approaches aim to measure predefined aspects of motivation, not
to describe it. When motivation is conceptualised as a structure of needs,
goals and means (Shah and Kruglanski, 2000), we can see that these vary
a lot from person to person (Hannula, 2002b). The theoretical foundation
of motivation as a structure of needs and goals was further elaborated
in Hannula (2004b), where it was related to the theory of self-regulated
learning (SRL). The aim of this paper is to give an overview of ideas
elaborated more thoroughly in the aforementioned paper and then use that
framework in analyses of some case studies, one of these being the case of
Frank.
1.1. Motivation
Two issues relevant to a critique of mainstream motivation research need
consideration: acceptance of the importance of the unconscious in motivation and focusing on motivational states and processes rather than traits.
Murphy and Alexander (2000, p. 38) note that in contemporary motivation research “one assumption seemingly underlying a segment of this
research is that individuals’ motives, needs, or goals are explicit knowledge that can be reflected upon and communicated to others.” However,
the present view emphasises the importance of the unconscious in human
mind. Motivation, like much of our mind, is only partially accessible to
introspection.
Dweck (2002) claims that two motivational systems (traits and processes) are characteristics of the individual that are formed at an early
age. In contemporary research the focus has usually been on motivational
traits. Such research may help us predict future learning orientation and
success, but it will not help much in understanding why a particular student
is putting a lot of effort into some activities and not into some others, or
how to induce a desired motivational state in students.
Based on works by Nuttin (1984) and Buck (1999), motivation is defined
here as “a potential to direct behaviour that is built into the system that
controls emotion. This potential may be manifested in cognition, emotion
and/or behaviour” (Hannula, 2004b). For example, the motivation to solve
a mathematics task might be manifested in beliefs about the importance
of the task (cognition), but also in persistence (behaviour) or in sadness
MOTIVATION IN MATHEMATICS: GOALS REFLECTED IN EMOTIONS
167
or anger if failing (emotion). In cognition, the most pure manifestation of
motivation is the conscious desire for something, but the manifestation may
also take more subtle forms, such as a view of oneself as a good problem
solver. Emotions are the most direct link to motivation, being manifested
either in positive (joy, relief, interest) or negative (anger, sadness, frustration) emotions depending on whether the situation is in line with motivation
or not (for further elaboration, see Hannula, forthcoming). Emotions are
partially observable as facial expressions and body language, but part of
their nature is unobservable subjective experience (Buck, 1999; Hannula,
2004a). Although emotion and cognition are only partially observable and
even partially inaccessible to the person him/herself, behaviour is always
a dependable manifestation of motivation. Even when the person is unable to explain motives for own behaviour, inferences of the unconscious
and subconscious can be made from behaviour (see Evans, Morgan and
Tsatsaroni, this issue).
Needs are specified instances of the general ‘potential to direct behaviour’. In the existing literature, psychological needs that are often emphasised in educational settings are autonomy, competency, and social belonging (e.g. Boekaerts, 1999; Covington and Dray, 2002). The difference
between needs and goals is in their different levels of specificity (Nuttin,
1984). For example, in the context of mathematics education, a student
might realize a need for competency as a goal to solve tasks fluently or,
alternatively, as a goal to understand the topic taught. A social need might
be realised as a goal to contribute significantly to collaborative project work
and a need for autonomy as a goal to challenge the teacher’s authority.
This realization of needs as goals in the mathematics classroom is greatly
influenced by students’ beliefs of themselves, mathematics, and learning
as well as school context, the social and sociomathematical norms in the
class. Evans et al. (this issue), write about essentially the same thing when
they discuss the ‘positions’ that are available to the student in the specific
classroom. For example, in a teacher-centred mathematics classroom that
emphasises rules and routines and individual drilling, there is little room
to meet the students’ needs for autonomy or social belonging within the
context of mathematics learning. More student-centered classrooms with a
lot of teamwork going on, and where the emphasis is on meaning making,
there may be many opportunities to meet different needs; such approaches,
by definition, as it were, rely on students exhibiting their autonomy and
social interactions.
Goals are hierarchically arranged in a structure and one goal may be
inhibitory, necessary, or sufficient to reach another goal (Nuttin, 1984;
Power and Dalgleish, 1997; Shah and Kruglanski, 2000). The hierarchical
structure can be extended to means (Shah and Kruglanski, 2000), plans,
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and actions (Nuttin, 1984). Boekaerts (1999, p. 452) discusses how some
students may pursue multiple goals simultaneously, navigating elegantly
between them, while others approach their goals serially.
1.2. Self-regulation
Zimmerman and Campillo (2003) have characterised self-regulation as
“self-generated thoughts, feelings, and actions that are planned and cyclically adapted for the attainment of personal goals” (p. 238). When the role
of unconscious and automatic self-regulation is accepted, planning cannot
be seen as necessary for self-regulation, but otherwise the characterisation
is suitable.
Boekaerts (1999) outlined the three roots of research on self-regulation:
“(1) research on learning styles, (2) research on metacognition and regulation styles, and (3) theories of the self, including goal-directed behavior”
(p. 451). Based on these schools of thought, she presented a three-layer
model for self-regulation: the innermost layer pertains to regulation of the
processing modes through choice of cognitive strategies, the middle layer
represents regulation of the learning process through use of metacognitive
knowledge and skills and the outermost layer concerns regulation of the
self through choice of goals and resources.
Most research has focused on the two innermost layers and little effort
has been made to integrate motivation control, action control or emotion
control into theories of self-regulation (Boekaerts, 1999, p. 445). Boekaerts
and Niemivirta (2000) have proposed a broader view for self-regulation that
would accept a variety of different control systems, not only metacognition:
[Self-regulation] has been presented as a generic term used for a number of phenomena, each of which is captured by a different control system. In our judgment,
self-regulation is a system concept that refers to the overall management of one’s
behavior through interactive processes between these different control systems
(attention, metacognition, motivation, emotion, action, and volition control). . . .
In the past decade, researchers involved in educational research have concentrated
mainly on activity in one control system – the metacognitive control system – thus
ignoring the interplay between the metacognitive control system and other control
systems. (Boekaerts and Niemivirta, 2000, p. 445)
Although the scope of the present paper does not allow elaboration of all
the above mentioned control systems, the present view sees self-regulation
to be much more than mere metacognition. Most notably, the important role
of emotion is acknowledged (see Malmivuori, this issue, for an elaboration).
The focus of this paper, however, is the motivational system as a ‘lens’ to
look at mathematical behaviour.
MOTIVATION IN MATHEMATICS: GOALS REFLECTED IN EMOTIONS
2. SELF- REGULATION
OF MOTIVATION IN MATHEMATICS
OBSERVATIONS
–
169
SOME
2.1. Empirical background
The empirical background of this paper is a longitudinal (three years) qualitative study (Hannula, 2004a). The researcher interacted with students as
their mathematics teacher, and collected a lot of varied data (classroom
observations, individual and group interviews, interviews with parents and
teachers) on a small number of students (gradually decreasing to 10 focus
students). The main body of data consists of 68 interviews. In the analyses,
two basic approaches have been used. One approach has focused on one
particular student at a time to interpret and reconstruct their personal developing ways to perceive themselves and their experiences in the world.
Sometimes the results have been reported through the use of a model (e.g.
Hannula, 1998), and at other times through a narrative (e.g. Hannula, 2003a,
2003b). The other approach has been to focus on a certain phenomenon, and
to look at how that phenomenon manifests itself in the data (e.g. Hannula,
2002b, 2005). I will draw from these studies to illustrate how regulation
of motivation is unfolding in actual students’ lives. The two main topics in
the interviews that have contributed to the analyses of students’ motivation
were their views about the usefulness of mathematics in their future studies,
work, and life and their mathematics-related emotions.
2.2. Deriving goals from needs
The importance of needs is obvious when we think of physiological needs:
hungry or tired students cannot concentrate well on studying mathematics. Similarly, students may decide not to pursue learning goals when they
feel that one or more of their psychological needs are thwarted (Boekaerts,
1999). Some case studies suggest that different dominating needs lead to
adoption of different primary goals and to different behaviours in mathematical situations. In the comparative case study of Eva and Anna (Hannula,
1998, 2003a), social needs were dominating Eva’s goal choices, while competence was a more important need for Anna. In the specific social situation,
these different dominant needs led Anna to give priority to learning goals,
while Eva’s behaviour was determined by interpersonal relationship goals.
Of course, needs-goals relationships are mediated by personal beliefs.
One may perceive a single goal to satisfy multiple needs and a need to be
satisfied through multiple goals. One may also see goals as contradictory
to each other. For example, mastery and performance are usually seen as
competing motivational orientations (e.g. Linnenbring and Pintrich, 2000;
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Lemos, 1999). However, in my analyses of Maria and Laura (Hannula,
2002b), mastery and performance were goals that supported each other.
Maria was driven by her need for competence and mastery of mathematics
was her primary goal. However, performance in mathematics tests was
an important subgoal for her evaluation of reaching that goal. Laura, on
the other hand, was primarily driven by her desire to gain a high status
in the class ‘hierarchy’. Performance was her main goal, while mastery
of mathematics was an important subgoal. Also Dweck (2002, p. 73) has
pointed out that performance and mastery should not be seen as mutually
exclusive goals.
2.3. Perceived accessibility of goals
Students’ beliefs about accessibility of different goals form another aspect of regulation of motivation. This is usually discussed under the
term ‘self-efficacy beliefs’ (e.g. Philippou and Christou, 2002; see also
‘self-appraisal’, Malmivuori, this issue). The theory of self-regulation suggests that for a change in motivation to take place there must be a desired
goal and one’s beliefs (including efficacy beliefs) must support the change.
Earlier (Hannula, 2002a), in a case study of Rita, a radical change in beliefs
and behaviour included these two aspects. Using the terminology of goals,
we may say that Rita had ego-defensive goals dominating her behaviour
in the beginning (“You don’t need math in life”). However, this was later
replaced by performance goals (“I will raise my math mark”). Behind this
change, there was a new awareness of the importance of school success in
general (change in values) together with more positive self-efficacy beliefs
(success is possible). In the case of Anna and Eva (Hannula, 1998, 2003a),
we can also see these conditions for successful goal regulation. Both students see mastery of mathematics as a desirable goal that is not accessible
by simply listening to the teacher. However, only Anna has the confidence
to pursue this goal through studying harder.
2.4. Automated regulation
There are two fundamentally different ways in which an emotional state
may be changed (Power and Dalgleish, 1997). One way is the (possibly
unconscious) cognitive analysis of the situation with respect to one’s goals.
Another route is an automatic, preconscious emotional reaction from a relatively simple stimulus (e.g. a sound or a concept). Such automatic emotional
reactions are based on earlier experiences that have left an association (a
memory trace) between the emotion experienced in a situation and a specific
element of the situation. In the mathematics class, such a stimulus might
MOTIVATION IN MATHEMATICS: GOALS REFLECTED IN EMOTIONS
171
be, for example, the teacher’s tone of voice or the concept ‘fraction’. Such
emotional associations form the core of attitude as an emotional disposition (Hannula, 2002a). Although such associations allow shorter reaction
times to possible threats, they lack flexibility and are also an inertia force
against behavioural changes in mathematics. Malmivuori (this issue) and
Boekaerts and Niemivirta (2000) have distinguished between an automatic
and a more reflective self-regulation. In the case of Anna and Eva, one possible obstacle for Eva was her automatic emotional reaction-shame-when
she needed to ask for help.
Paradoxically, the automatic ‘inefficient regulation’ can be highly efficient when used in concert with more reflective self-regulation. Involvement is an example of such automatic (but productive) self-regulation, and
students may even consciously use different strategies to become involved
(Reed et al., 2002).
3. THE
CASE OF FRANK
The case of Frank with relevant data is presented elsewhere (Op ‘t Eynde
and Hannula, this issue). The data consists of Frank’s responses to a students’ Mathematics Related Beliefs Questionnaire (MRBQ), to an Online
Motivation Questionnaire (OMQ), an interview about student responses
to OMQ, observations of his behaviour during a problem solving episode
(obs.) and a Video Based Student Recall Interview (VBSRI). I had little
direct access to the data, but had to rely on summary scales (MBRQ) or the
interpretations made by Op ‘t Eynde.1
3.1. Beliefs
According to the present view, motivation is based on individualenvironment relationship categories (needs). Therefore, it is important to
get an understanding of Frank’s beliefs about the nature of mathematics
(environment) and his mathematical self (individual) before we can analyse
his motivation in mathematics.
According to Frank’s responses to MRBQ he sees mathematics as something that is developing, that there are still new things to be discovered. He
is also convinced that there is more than one correct way to solve a mathematical problem and that a lot of people use mathematics in everyday
life. His responses in OMQ further indicate that this specific task includes
elements of physics that he “is not too fond of”.
According to the MBRQ, he is very confident about his mathematical
competence. However, with this specific task he is less certain.
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M.S. HANNULA
3.2. Goals
Frank’s responses to the MRBQ and the OMQ show that he had the general
goal to do well in mathematics, and a specific goal to solve the problem at
hand. Furthermore, he wanted to work on the task up to the point where he
really understood it and had really learned something from it (OMQ). We
can also compare Frank’s beliefs about the nature of mathematics (above)
with the fact that he likes math and finds it very interesting (MRBQ), to get
further evidence for Frank having a mastery goal in mathematics. Frank’s
score on “mathematics as a domain of excellence” was also high, which
indicates that performance was an important goal for him as well. On this
scale, Frank also clearly scored higher than his average classmate (Op ‘t
Eynde and Hannula, this issue, Figure 1).
When we look at the data more closely, we can see some specific aspects
of the kind of mastery Frank is aiming at. First, he “always want[ed] to
do as much as possible without [the calculator].2 ” Second, he seemed to
want to know each step of a problem immediately and to proceed fluently
without breaks. This latter claim needs some closer analysis of the data.
First, the scale “mathematics as a domain of excellence” included an
item “Those who are good in mathematics can solve any problem in a few
minutes.” We know that Frank scored highly on this scale, and it would be
interesting to see his scoring on this specific item.
Second, there is more evidence on the goal of fluency in the qualitative
data. At the point when Frank had “forgotten how [. . .] to do it” (Turn 4.),
and was battling with himself whether to take the calculator or not, he
“panicked” (VBSRI). The observation data reveals emotional reactions.
Frank reflected on his feelings and causes for the feelings in the VBSRI. He
knew that if he would “stop and think for a moment, [he would] probably
know again what [. . .] to do”. But instead of doing it, he “panic[ked],
and then [. . .] immediately want[ed] to go to [his] calculator”, even if he
wanted “to do as much as possible without it” and did not “feel well” when
he needed to go to the calculator. My interpretation is that the problem was
with the lack of fluency in the process. Frank said that he “did not know
immediately how” to proceed (VBSRI). During his reflection, he twice
used the word “immediately” even if he also knew that to stop and think is
usually a productive strategy.
The nature of the emotional reactions of Frank suggests that there were
some ego goals at play as well. In true mastery orientation the emotional
reaction to not knowing the solution right away would more likely be interest, curiosity or bewilderment as in a positive affective pathway suggested
by DeBellis and Goldin (this issue). Experience of worry in the two first
subtasks and relief in the first subtask indicate that the basic emotion at play
MOTIVATION IN MATHEMATICS: GOALS REFLECTED IN EMOTIONS
173
was fear – Frank perceived an important goal to be at risk. Under threat
was probably either his identity or his desired social identity as being competent. However, as the process continued successfully, there was more
certainty and later obstacles were faced with frustration and anger, and the
final success induced happiness. This change of emotional reactions does
not necessarily indicate a mastery goal even at this later stage, but possibly
only difference in expectations to overcome the obstacles.
3.3. Needs
Based on the data, it is possible to make some educated guesses about
the needs that were the driving forces of Frank’s mathematical behaviour.
His view of mathematics, together with the goals described above, indicates
that competence was the primary need at play. He wanted to understand the
mathematics and learn from each task. This was also indicated in Frank’s
view of mathematics as important (MRBQ). Furthermore, Frank’s nervousness about possible failures indicates that for him nothing less than
perfection is satisfactory.
He preferred an active and regulating teacher who explains everything
very clearly, rather than one who leaves a lot of room for students to find
things out for themselves. He liked his teacher for being like that (MRBQ),
which indicates that need for autonomy was not high for Frank. The scales
also include some items3 that suggest that he had less need for social belonging with his classmates (MRBQ). We can relate these with evidence
of ego goals and assume that he had a social need to be approved by his
teacher.
3.4. Interpreting behaviour based on goals and needs
In this section analyses will be made in the opposite direction to above.
We accept the interpretations made in Sections 3.1–3.3 and see how the
needs and goals of Frank help us interpret and understand his mathematical behaviour. This is only an exercise, an illustration of how the present
framework can be applied. In ‘real’ research one needs different data for
making inferences about goals and for using goals to interpret behaviour –
otherwise one ends up with circular reasoning.
Frank had two basic needs that were at play in his mathematical behaviour, namely the need for competence and a social need to please his
teacher. The need for competence was realised in his goal to understand
the task and learn from solving it. The social need was realised in Frank’s
goal to be a good student in the eyes of his teacher. These two goals as
such are not in conflict with each other – quite the opposite. Yet, the means
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that Frank perceived to lead to these goals were in conflict. He mentioned
two different strategies he had found successful when trying to understand
difficult problems before. One was to stop and think for a moment if there
were stages where he did not know how to proceed. Another successful
strategy was to do numerical explorations. These strategies were both in
conflict with certain norms Frank perceived indicated good performance in
problem solving. A good solution had to be completed fluently and without
the use of calculator (Figure 1).
Competence
Understand and
learn from the task
Stop and
think when
necessary
NEEDS
Social
(teacher)
GOALS
Be a good student
Do
numerical
explorations
Avoid
calculator
Solve
task
fluently
MEANS
Figure 1. A piece of the structure of Frank’s needs, goals and means.
As Frank was solving this task, the goals to understand and to impress
were active at the same time. As Frank then faced a moment in problem
solving when he did not know immediately what to do, he reacted emotionally (worry). He had two possible coping strategies, which were both in
conflict with his goal to impress the teacher. He reached for his calculator
to do numerical explorations, but that threatened his goal to avoid using his
calculator. This led to another emotional reaction (panic). He had to stop
and think, threatening the fluency of the process, and he was again reaching for his calculator but drew his hand back. The emotional pressure was
rising and Frank was frustrated and angry. When he was able to overcome
these obstacles and reach both his goals, he was happy.
4. DISCUSSION
In the theory of self-regulated learning, Boekaerts (1999) expressed the
need to increase our understanding of the regulation of motivation. She
argued that this least developed area of SRL is essential in understanding
student behaviour in classrooms:
MOTIVATION IN MATHEMATICS: GOALS REFLECTED IN EMOTIONS
175
information about . . . the goals [students] set for themselves . . . provides an indication of why students are prepared to do what they do and why they are not
inclined to do what is expected of them. (Boekaerts, 1999, p. 451)
The author has suggested a new definition for motivation: a potential to
direct behaviour through the mechanisms that control emotion. This potential is structured through needs and goals. Based on this view of motivation,
some observations were made on regulation of motivation. Three aspects
of motivation regulation were observed in empirical data: deriving goals
from needs, the influence of goal accessibility beliefs, and automated regulation of motivation. However, systematic qualitative research may point
to further important factors, as well as disregard some of the conclusions
made on the basis of this small number of case studies.
The field of affect in mathematics education is usually divided into
emotions, attitudes and beliefs (e.g. McLeod, 1992) and possibly including
a fourth element, values (DeBellis and Goldin, this issue). The present view
does not see motivation as another element of affect. Rather, motivation
offers a different perspective that illuminates new aspects of affect. As a
potential, motivation cannot be directly observed. It is observable only as it
manifests itself in affect, cognition and behaviour. How different elements
of affect (emotions, attitudes, values, and beliefs) and motivation relate
to each other and interact with each other is an issue that needs further
research.
The case of Frank illustrates how students may have multiple simultaneous goals and how choices between them are made. This fine balancing
between alternative goals suggests that Frank would have been sensitive to
changes in the setting. Had the teacher signalled that it is all right to stop and
think and do numerical explorations, Frank most likely would have done
that. Whether Frank’s worry and frustration actually impeded his problem
solving is hard to say, as the research indicates that ‘negative’ feelings
(e.g. anger) can both facilitate and impede problem solving (Schwarz and
Skrunik, 2003). However, his performance goal prevented him from doing
numerical explorations, which, in a different task, might have been crucial.
The present view of motivation is well aligned with some aspects of
the other frameworks presented in this issue. Goldin and DeBellis’ framework sees affect as a representational system. In a sense, we may say that
emotions, attitudes and values are representations of goals and needs or
at least they code important information about them. The position also
fully embraces Malmivuori’s view of affect as one self-regulative control
system, only taking a different focus into it. The concept of identity used
by Op ‘t Eynde et al. is closely related to motivation, the main difference
being in that identity encapsulates a whole system of needs and goals into a
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M.S. HANNULA
single ‘package’ – desired identity. Also ‘purposes’ as used by Brown and
Reid, can be seen as a specific instance of goals. The language of Evans
et al. is different from the language used here, yet both papers overlap in
their interest in ego (self) and desires as giving direction and impetus for
behaviour.
The specificity in the present approach is that it focuses on what the
subject wants to do and why. This difference becomes extremely important
when we wish to find implications for practice. Focusing on motivation
we may find ways to influence what the subjects want to do, not only how
they try to achieve it. The basic needs of autonomy, competence and social
belonging can all be met in a classroom that emphasises exploration, understanding and communication instead of rules, routines and rote learning.
However, this requires that all feel safe and perceive that they can contribute
to the process. A possible approach to meet all these conditions would be
the open approach (e.g. Nohda, 2000), and more generally focusing on
mathematical processes rather than products.
ACKNOWLEDGMENTS
Funding for the research has been provided by the Academy of Finland.
NOTES
1. The observation data describes only the changes in the brow region, which is not sufficient to discriminate all emotions. However, Op ‘t Eynde used the video data for the
interpretations, and, here, I assume these interpretations to be correct.
2. It would be interesting to know why Frank preferred to avoid the use of a calculator.
Was it a social norm in the class that it is more esteemed to solve problems without a
calculator? Was it something the teacher had stressed, or was it a criterion Frank had set
for himself?
3. e.g. “Group work facilitates the learning of mathematics” (with which Frank disagreed)
REFERENCES
Bikner-Ahsbahs, A.: 2003, ‘A social extension of a psychological interest theory’, in N.A.
Pateman, B.J. Dougherty and J. Zilliox (eds.), Proceedings of the 27th Conference of the
International Group for the Psychology of Mathematics Education, Vol. 2, Honolulu, pp.
97–104.
Boekaerts, M.: 1999, ‘Self-regulated learning: Where we are today’, International Journal
of Educational Research 31, 445–457.
Boekaerts, M. and Niemivirta, M.: 2000, ‘Self-regulated learning: Finding a balance between learning goals and ego-protective goals’, in M. Boekaerts, P.R. Pintrich and
MOTIVATION IN MATHEMATICS: GOALS REFLECTED IN EMOTIONS
177
M. Zeidner (eds.), Handbook of Self-Regulation, Academic Press, San Diego, CA, pp.
417–450.
Buck, R.: 1999, ‘The biological affects: A typology’, Psychological Review 106(2), 301–
336.
Covington, M.V. and Dray, E.: 2002, ‘The developmental course of achievement motivation: A need-based approach’, in A. Wigfield and J.S. Eccles (eds.), Development of
Achievement Motivation, Academic Press, London, pp. 33–56.
Dweck, C.S.: 2002, ‘The development of ability conceptions’, in A. Wigfield and J.S. Eccles
(eds.), Development of Achievement Motivation, Academic Press, London, pp. 57–88.
Hannula, M.: 1998, ‘Changes of beliefs and attitudes’, in E. Pehkonen and G. Törner (eds.),
The State-of-Art in Mathematics-Related Belief Research; Results of the MAVI Activities,
Research Report 184, University of Helsinki, Department of Teacher Education, pp.
198–222.
Hannula, M.S.: 2002a, ‘Attitude towards mathematics: Emotions, expectations and values’,
Educational Studies in Mathematics 49(1), 25–46.
Hannula, M.S.: 2002b, ‘Goal regulation: Needs, beliefs, and emotions’, in A.D. Cockburn
and E. Nardi (eds.), Proceedings of the 26th Conference of the International Group for
the Psychology of Mathematics Education, Vol. 4, Norwich, UK, pp. 73–80.
Hannula, M.S.: 2003a, ‘Affect towards mathematics: Narratives with attitude’, in M. A.
Mariotti (ed.), European Research in Mathematics Education III, Bellaria, Italy. Retrieved
October 25th 2005 from http://www.dm.unipi.it/∼didattica/CERME3/proceedings/
Hannula, M.S.: 2003b, ‘Fictionalising experiences – experiencing through fiction’, For the
Learning of Mathematics 23(3), 33–39.
Hannula, M.S.: 2004a, Affect in Mathematical Thinking and Learning, Doctoral Dissertation, University of Turku, Finland.
Hannula, M.S.: 2004b, ‘Regulating motivation in mathematics’. A paper presented at the
Topic Study Group 24 of ICME-10 conference. Retrieved September 15th 2005 from
http://www.icme-organisers.dk/tsg24/Documents/Hannula.doc
Hannula, M.S.: 2005. ‘Shared cognitive intimacy and self-defence – two socio-emotional
processes in problem solving’, Nordic Studies in Mathematics Education 10(1), 25–
40.
Hannula, M.S.: Forthcoming. ‘Understanding affect towards mathematics in practice’. To
appear in proceeding of the Norma05-conference.
Kloosterman, P.: 2002, ‘Beliefs about mathematics and mathematics learning in the
secondary school: Measurement and implications for motivation’, in G.C. Leder,
E. Pehkonen and G. Törner (eds.), Beliefs: A Hidden Variable in Mathematics Education,
Kluwer, Dordrecht, pp. 247–269.
Lemos, M.S.: 1999, ‘Students’ goals and self-regulation in the classroom’, International
Journal of Educational Research 31, 471–486.
Linnenbrink E.A. and Pintrich, P.R.: 2000, ‘Multiple pathways to learning and achievement:
The role of goal orientation in fostering adaptive motivation, affect, and cognition’,
in C. Sansone and J.M. Harackiewicz (eds.), Intrinsic and Extrinsic Motivation: The
search for Optimal Motivation and Performance, Academic Press, New York, pp. 195–
227.
McLeod, D.B.: 1992, ‘Research on affect in mathematics education: A reconceptualisation’,
in D.A. Grouws (ed.), Handbook of Research in Mathematics Education Teaching and
Learning, Macmillan, New York, pp. 575–596.
Murphy, P.K. and Alexander, P.A.: 2000, ‘A motivated exploration of motivation terminology’, Contemporary Educational Psychology 25, 3–53.
178
M.S. HANNULA
Nohda, N.: 2000, ‘Teaching by open approach methods in Japanese mathematics classroom’ in. T. Nakahara and M. Koyama (eds.), Proceedings of the 24th Conference of the
International Group for the Psychology of Mathematics Education, Vol. 1, Hiroshima,
pp. 39–53.
Nuttin, J.: 1984, Motivation, Planning, and Action: A Relational Theory of Behavior Dynamic, Leuven University Press, Leuven.
Op’t Eynde P., De Corte, E. and Verschaffel, L.: 2002, ‘Framing students’
mathematics-related beliefs: A quest for conceptual clarity and a comprehensive categorization’, in G.C. Leder, E. Pehkonen and G. Törner (eds.), Beliefs: A Hidden Variable
in Mathematics Education, Kluwer, Dordrecht, pp. 13–37.
Philippou, G. and Christou, C.: 2002, ‘A study of the mathematics teaching, efficacy beliefs
of primary teachers’, in G.C. Leder, E. Pehkonen and G. Törner (eds.), Beliefs: A Hidden
Variable in Mathematics Education, Kluwer, Dordrecht, pp. 211–232.
Power, M. and Dalgleish, T.: 1997, Cognition and Emotion: From order to disorder. Psychology Press, UK.
Reed, J.L.H., Schallert, D.L. and Deithloff, L.F.: 2002, ‘Investigating the interferance between self-regulation and involvement processes’, Educational Psychologist 37(1), 53–
57.
Ryan, R.M. and Deci, E.L.: 2000, ‘When rewards compete with nature: The undermining
of intrinsic motivation and self-regulation’, in C. Sansone and J.M. Harackiewicz (eds.),
Intrinsic and Extrinsic Motivation: The Search for Optimal Motivation and Performance,
Academic Press, New York, pp. 13–55.
Schwarz, N. and Skrunik, I.: 2003, ‘Feeling and thinking: Implications for problem solving’,
in J.E. Davidson and R.J. Sternberg (eds.), The Psychology of Problem Solving, University
Press, Cambridge, UK, pp. 263–290.
Shah, J.Y. and Kruglanski, A.W.: 2000, ‘The structure and substance of intrinsic motivation’,
in C. Sansone and J.M. Harackiewicz (eds.), Intrinsic and Extrinsic Motivation; The
Search for Optimal Motivation and Performance, Academic Press, New York, pp. 105–
129.
Yates, S.M.: 2000: ‘Student optimism, pessimism, motivation and achievement in mathematics: A longitudinal study’, in T. Nakahara and M. Koyama (eds.), Proceedings of the
24th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, Hiroshima, pp. 297–304.
Zimmerman, B.J. and Campillio, M.: 2003, ‘Motivating self-regulated problem solvers’, in
J.E. Davidson and R.J. Sternberg (eds.), The Psychology of Problem Solving, Cambridge
University Press, UK, pp. 233–262 Kluwer, Dordrecht.
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