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The affective dimension of learning and teaching mathematics and science


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Learning scientific and mathematics concepts is more than a cognitive process. Learning and teaching is highly charged with feeling. Nevertheless, in schools and universities, science and mathematics is for the most part portrayed as a rational, analytical, and non-emotive area of the curriculum, and teachers, texts and curricular documents commonly present images of science and mathematics that embody a sense of emotional aloofness. In the chapter, we review the most significant research on the affective domain in teaching and learning Science and Mathematics. We describe the research program carried out in the University of Extremadura (Spain) on the influence of emotions in primary pre-service teachers' process of learning to teach science and mathematics. We present the diagnostic studies that we conducted to determine the emotions that these primary pre-service teachers felt when they were learning science and mathematics in school, relating them to different variables (sex, education, topic, problem solving, etc.), and the emotions they feel when they are teaching science and mathematics during their practice teaching. Finally, we show the results of an intervention program for primary pre-service teachers which focuses on emotional control in solving mathematics problems in order to foster change in attitudes, beliefs, and emotions towards mathematics and its learning and teaching.
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In: Handbook of Lifelong Learning Developments ISBN: 978-1-60876-177-7
Editor: Margaret P. Caltone, pp. 265-287 © 2010 Nova Science Publishers, Inc.
Chapter 10
Lorenzo J. Blanco1, Eloisa Guerrero2, Ana Caballero1, María
Brígido1 and Vicente Mellado1
1Dept. Science and Mathematics Education, Faculty of Education, University of
Extremadura, Spain.
2Dept. Psychology and Anthropology, Faculty of Education, University of Extremadura,
Learning scientific and mathematics concepts is more than a cognitive process.
Learning and teaching is highly charged with feeling. Nevertheless, in schools and
universities, science and mathematics is for the most part portrayed as a rational,
analytical, and non-emotive area of the curriculum, and teachers, texts and curricular
documents commonly present images of science and mathematics that embody a sense of
emotional aloofness.
In the chapter, we review the most significant research on the affective domain in
teaching and learning Science and Mathematics. We describe the research program
carried out in the University of Extremadura (Spain) on the influence of emotions in
primary pre-service teachers' process of learning to teach science and mathematics. We
present the diagnostic studies that we conducted to determine the emotions that these
primary pre-service teachers felt when they were learning science and mathematics in
school, relating them to different variables (sex, education, topic, problem solving, etc.),
and the emotions they feel when they are teaching science and mathematics during their
practice teaching. Finally, we show the results of an intervention program for primary
pre-service teachers which focuses on emotional control in solving mathematics problems
in order to foster change in attitudes, beliefs, and emotions towards mathematics and its
learning and teaching.
Lorenzo J. Blanco, Eloisa Guerrero, Ana Caballero et al.
Learning and teaching science is more than a purely cognitive process and is highly
charged with feelings. Nevertheless, in schools and universities, for the most part science and
mathematics is portrayed as a rational, analytical, and non-emotive area of the curriculum.
Referring to research in mathematics education, De Bellis & Goldin (2006) and Furinghetti &
Morselli (2009) note that studies of students' performance and problem solving have
traditionally concentrated primarily on cognition, less on affect, and still less on cognitive
affective interactions.
In our work, we consider it to be a significant achievement in education that the affective
domain is accepted as a key aspect in teaching science and mathematics. Indeed, we believe
that recognizing the role of affect in the processes of knowing, thinking, acting, and
interacting is essential in the teachinglearning process. We concur with the definition of
McLeod (1989) that the affective domain in education covers a wide range of feelings
different from pure cognition, including attitudes, beliefs, and emotions as basic components.
Since the nineties, the study of affective processes has found a new conceptual
framework in the fields of neurobiology and the psychology of emotion. There were findings
that the intelligence quotient and psychometric tests are not predictors of professional and
personal success. An important contribution was the theory of multiple intelligences (Gardner,
1995) according to which cognitive skills are defined as a set of abilities. From this
perspective, intelligence is conceived of as an ability needed to solve problems. Gardner
identified seven different types of intelligence, including interpersonal and intrapersonal
In the classical models of school learning, the personal variables encompassed capacity
(intelligence and aptitude), motivation, personality, and the skills and strategies of learning.
This view has changed substantially with the recognition that the pupil's competence also
depends on such other factors as prior knowledge, styles of learning, attitudes, beliefs,
attributional styles, and emotional and affective factors. A study of the characteristics of
learners necessarily involves considering their individual differences in learning behaviour,
and this can be found very useful in adapting teaching to these differences.
School success depends on many social and emotional factors that have little to do with
the early development of intellectual capacities. Thus, emotional security, interest, self-
assurance, knowing what kind of conduct is expected of you, control of your impulses, and
the expression of your needs will be the catalyst of your establishment of relationships as a
learner with others, and of the effectiveness and quality of your academic, personal, affective,
and social development.
It is therefore advisable to distinguish between intelligence in its classical sense as an
aptitude, and the concept of emotional intelligence as a skill (Mayer & Salovey, 1995;
Shapiro, 1997; Goleman, 1995).
"Emotional intelligence" is defined as "that which involves the ability to monitor and
understand one's own and others' emotions, to discriminate among them, and to use this
information to guide one's thinking and actions" (Salovey & Mayer, 1990, 57). Goleman
(1998) elaborated on this idea, understanding emotional intelligence to be the capacity for
recognizing one's own and others' feelings, but also for self-motivation and the appropriate
handling of emotions. The origin of this new construct lay in the line of work begun by
The Affective Dimension of Learning and Teaching Mathematics and Science
psychologists in the seventies on the interaction between emotion and thought, with variables
that had not at first been suspected of being related (Anadón, 2006).
In recent years, cognitive neuroscience with the support of new brain imaging techniques
has contributed decisively to the development and modification of theories arguing that good
adaptation to the environment requires both declarative and affective information (Damasio
2005, 2006). Likewise, Bermejo (1996) and Pérez (2008) find a significant relationship
between variables relating to emotional intelligence and academic performance, and Páez &
Rigo (2008) relate the construct to the self-control of learning.
All this points to the need to study and to include emotional intelligence in the academic
and school contexts (Galindo, 2005; Salmurri 2004). In general, there is widespread
agreement about connecting the cognitive and the affective, since "emotions influence
knowledge, but [also] knowledge influences emotions" (Marina, 2004, 53). Indeed, recent
results have called into question the independence of the rational and the emotional since,
according to the theory of "affective cognitive moulds" of Hernández (2002), the cognitive
configures the affective and vice versa.
It is only a decade ago when the cognitive aspect still overshadowed the affective, and
LeDoux (1999) argued for the idea that emotion and cognition are best understood when
considered as separate but complementary mental functions. In recent years, the explanation
of the relationship between cognitive and affective variables has become oriented to
considering the cognitive and affective as mutually conditioning each other, as was put
forward in the aforementioned theory of affective cognitive moulds of Hernández (2002).
Research in science and mathematics education also recognizes the importance of
emotions in teaching and learning, and advocates the need to consider the cognitive and
affective dimensions (Gómez & Chacón 2001; Zan, Bronw, Evans & Hannula, 2006; Koballa
& Glynn, 2007; Furinghetti & Morselli, 2009).
Much of current research on the influence of the affective dimension on mathematics
teaching and learning has grown out of the work of McLeod (1986, 1989, 1992). This showed
how important it was to consider the basic descriptors of the affective domain beliefs,
attitudes, and emotions (McLeod, 1989). De Bellis & Goldin (2006) extended these
descriptors to a fourth subdomain of values / morals / ethics.
Studies have shown that pupils' affects are key factors to understanding their behaviour in
relation to mathematics and science. Pupil's experiences in learning provoke in them feelings
and emotional reactions that influence the formation of their beliefs. Moreover, the beliefs
that they already hold have a direct bearing on their behaviour in situations of learning and on
their ability to learn (Gil, Blanco & Guerrero, 2006).
During their learning, pupils receive continuous stimuli associated with science and
mathematics problems, the teacher's actions, social messages, etc. These cause them a
certain tension to which they react emotionally either positively or negatively. If these
situations recur under similar conditions producing the same affective reactions, then the
activation of the emotional reaction (satisfaction, frustration, etc.) may become automated
Lorenzo J. Blanco, Eloisa Guerrero, Ana Caballero et al.
and "solidified" in a set of attitudes that influence the conformation of their beliefs. Thus,
their beliefs, being associated with their experiences, will condition their ideas about their
Following the classification that McLeod (1992) gave for mathematics education, one
could say that the learner generates beliefs about the discipline and its teaching and learning,
beliefs about him or herself as a learner of mathematics or science, and beliefs reflecting the
social context.
Beliefs are cognitive structures that allow individuals to organize and filter the
information they receive, and to progressively construct an understanding of reality, and a
form of organizing and viewing the world and of thinking (Gilbert, 1991). On the one hand,
beliefs are indispensable because they structure the meaning we give to things. But on the
other, they act as a filter with respect to new realities or certain problems, limiting the
possibilities for action and understanding (Blanco & Barrantes, 2006). For Schoenfeld (1992),
beliefs form a particular view of the world of mathematics, setting the perspective from which
each person approaches that world, and they can determine how a problem will be tackled,
the procedures that will be used or avoided, and the time and intensity of the effort that will
be put into the task.
It is therefore important to describe pupils' conceptions and beliefs about the discipline.
Many authors have pointed out that pupils conceive of mathematics as a difficult,
authoritarian, abstract, and rule-based subject, in which memorization and routine, and
algorithmic, algebraic, and analytical procedures predominate, with exercises having to be
solved that usually have little application in the real world (Mtewa & Garófalo, 1989; Flores,
1999; Schoenfeld, 1992). In this regard, according to Szydlik, Szydlik & Benson (2003)
research has shown that prospective teachers tend to "see mathematics as an authoritarian
discipline, and that they believe that doing mathematics means applying memorized formulas
and procedures to do textbook exercises" (Szydlik, Szydlik & Benson, 2003, 254).
All this leads pupils to regard mathematics as dispensable, and although they do not
doubt the true value of mathematical knowledge, they consider it to be external to their world
(Flores, 1999). These beliefs have a negative influence on mathematics activity, being a cause
of attitudes of wariness and mistrust.
Beliefs about oneself as a mathematics or science learner carry a strong affective load
with respect to confidence, self-image, and the causal attribution of success and failure in
class. Pupils who feel competent, who trust in their capabilities, and have expectations of self-
efficacy, involve themselves in the learning process. Moreover, learning is more satisfactory
if failures as well as successes are attributed to internal, variable, and controllable causes
(e.g., personal effort, perseverance, planning, …). It will be less satisfactory, however, if the
successes are attributed to external, uncontrollable causes (e.g., luck, easiness of the task,…)
and the failures to internal, stable, and uncontrollable causes (lack of ability) (Miras, 2001).
Confidence in the willingness and ability to want to learn mathematics plays an essential
role in pupils' achievements in mathematics (McLeod, 1992; Reyes, 1984).
For González-Pienda & Núñez (1997), subjects' active involvement in the learning
process is enhanced when they feel competent, i.e., when they trust in their own abilities and
have high expectations of self-efficacy, value the work they are set, and feel responsible.
Moreover, the beliefs of self-efficacy influence the activities in which they involve
themselves, the amount of effort they put in, their perseverance in the face of obstacles, their
capacity to overcome or adapt to adverse situations, the level of stress and anxiety they
The Affective Dimension of Learning and Teaching Mathematics and Science
experience when they are set some task to do, their expectations about the results, and the
process of self-regulation. They generally attribute success in mathematics to the teachers'
attitudes towards the pupils, and to greater commitment and effort in studying the subject, but
they reject the influence of luck. The conclusion is therefore that they attribute both success
and failure largely to internal, unstable, and controllable causes, an attribution that is
favourable for learning. These findings are similar to the conclusions drawn by Gil, Blanco &
Guerrero (2006).
Vanayan et al. (1997) and Kloosterman (2002) note that the beliefs that most influence
motivation and achievement in mathematics are pupils' perceptions about themselves in
relation to mathematics. Thus, self-confidence in mathematics is an important indicator of
learners' positive views of studying the subject, and hence of their active participation and
regulation in the learning process. Pupils who believe that mathematics is only for those with
mathematical talent, and is based on infallible and mechanical procedures of solution, have
less confidence in themselves in learning situations than those who do not think in this way.
We understand attitude to be an evaluative (positive or negative) predisposition which
determines personal intentions and influences behaviour (Hart, 1989), and which has four
components cognitive (knowledge), affective (feeling), intentional (intentions), and
behavioural (behaviour).
Pupils on the whole show rejection, denial, frustration in the learning process. Sarabia
(2006) observed that secondary education pupils exteriorize discontent, displeasure, and lack
of enjoyment, as well as little motivation or interest in learning mathematics.
In science education, affective aspects have been addressed only infrequently, and even
then generally relating them more to attitudes than specifically to emotions. In the first and
third handbooks on science education by Gable (1994) and Abell & Lederman (2007), there
are two extensive reviews of attitudes in science learning (in which the emotions are
included). These are the respective chapters of Simpson et al. (1994) and Koballa & Glynn
For Sanmartí & Tarín (1999), attitudes and science learning are not only strongly related,
but attitude is the starting point for any meaningful learning. However, pupils' attitudes can
not be conceived of as an isolated fact, but are correlated with a wide range of variables, both
internal and external to the classroom (Espinosa & Román, 1995). Several studies indicate
that interest and positive attitudes towards science and mathematics decrease with age,
especially during secondary education (Beauchamp & Parkinson, 2008; Murphy & Beggs,
2003; Osborne et al. 2003; Ramsden, 1998; Vázquez & Manassero, 2008; Yager & Penick,
1986). Boys usually have a more positive attitude to science than girls (Caleon &
Subramaniam, 2008; Koballa & Glynn, 2007). These last authors also note that the interest of
girls is far more focused on biology than physics.
This worrying attitudinal depression towards science and mathematics is attributed to
school science creating a negative image in pupils' minds over time, it being described as
authoritarian, boring, hard, or irrelevant for everyday life (Vázquez and Manassero, 2008).
The study of emotions is complex because we are all different, with different
personalities whose interactions between the cognitive and the affective-emotional form a
mosaic of individual factors and peculiarities. Nonetheless, it is a vital aspect of learning.
Studies of emotion have focused on the role of anxiety and frustration and their impact on
achievement in mathematics (Marshall, 1989; McLeod, 1989; De Bellis & Goldin, 1997,
2006). According to Ojeda et al. (2003), emotions take part in our learning because they block
Lorenzo J. Blanco, Eloisa Guerrero, Ana Caballero et al.
our intelligence and hinder success in life. Frustration is a very common emotion at the
secondary education level. This may be related to the belief systems that guide pupils'
behaviour and conditions the goals they set themselves to reach. Fear, emotional block, and
anxiety have often been confirmed as being able to influence the mental processes involved in
the development of mathematics skills (De Bellis & Goldin, 1997). For Richardson &
Woolfolk (1980), anxiety in mathematics consists of the feelings of tension, mental
disorganization, and helplessness that a pupil experiences when set mathematics problems to
solve. Anxiety leads to abandonment, avoidance of the task, and the pupils' protecting
themselves in some way (Guerrero, Blanco & Vicente, 2002).
Zevenbergen (2004) cites various studies that indicate that prospective primary teachers
show "low levels of mathematics knowledge as well as considerable anxiety towards the
subject" (Zevenbergen, 2004, 5), even with respect to important aspects of the content that
they will have to teach in their future career (Brown & Borko, 1992). This lack of
mathematical knowledge is important since the ability to manage the class and the choice of
curriculum depend directly on the mastery of the content. Teachers with a low level of
knowledge of the subject they are to teach find it difficult to implement educational changes,
avoid teaching the topics they are unsure of, lack self-confidence, and reinforce the pupils'
conceptual mistakes (Mellado, Blanco & Ruiz, 1999). Conversely, when they acquire this
knowledge, they are more confident in their ability to teach (Manoucheri, 1998).
The same pattern of results is found in research on specific aspects of the curriculum
geometry and measurement (Baturo & Nason, 1996; Blanco 2001; Blanco & Barrantes,
2006), the use of new technologies in mathematics (Walen, Williams & Garner, 2003;
Wachira, Keengwe, & Onchwari, 2008), arithmetical aspects (Thipkong & Davis, 1991;
Tirosh & Graeber, 1989; Putt, 1995), etc.
In another sense, prospective primary teachers, as a consequence of their own learning
experiences in school, carry a baggage of conceptions and attitudes that are inconsistent with
today's curricular proposals and recommendations (Johnson, 2008). These conceptions and
attitudes almost always appear with strongly negative influences on the process of learning to
teach (Ernest, 2000). Student teachers use their conceptions, consciously or unconsciously, as
a kind of lens or screen to filter and occasionally block the mathematics teaching content of
their teacher education courses and interpolate their own educational process (Barrantes &
Blanco, 2006). Also, during the teaching they receive in their initial courses, they will feel no
need to express or reflect on their conceptions about the teaching of mathematics if they have
no practical references to compare with. And they typically show signs of "wishful thinking"
that teaching is easy and they will have no great difficulty in doing it (Flores, 1999).
To learn how to teach science and mathematics, prospective teachers need to understand
that the emotions they feel about learning are also related to those they feel about teaching. In
a study conducted at the University of Extremadura we identified the emotions aroused in a
sample of pre-service primary teachers during their period as secondary school pupils and
when doing their teaching practice in the Education Faculty regarding the subjects of Physics
/ Chemistry and Nature Sciences. The exploratory, descriptive study was conducted by means
The Affective Dimension of Learning and Teaching Mathematics and Science
of a survey presented to 63 students of primary education in the Faculty of Education at the
University of Extremadura during the academic year 2007/8. The instrument used was a
questionnaire in which the subjects noted from among those offered the emotions aroused in
them by the different subjects of science, both in their time as secondary school pupils and in
their teaching practice. The resulting data were subjected to the necessary processes of
checking, coding, and digital storage in order to proceed with their descriptive analysis using
SPSS (Statistical Product and Service Solutions) 13.0.
The results showed a great difference between the emotions related to the subjects of
Physics/Chemistry and Nature Sciences.
Their memory of the subjects of Physics or Chemistry at secondary school suggested
fundamentally negative emotions: nervousness, anxiety, tension, worry, or despair, and only
rarely positive emotions such as confidence or enthusiasm. During their practice teaching,
teaching topics related to physics or chemistry also suggested to them more negative than
positive emotions, but to a lesser extent than when they were at school.
Their memory of the subjects of Nature Sciences during their time in secondary school
suggested to them fundamentally positive emotions: fun, tranquillity, joy, satisfaction,
congeniality, capacity, etc. On teaching topics related to Nature Sciences during their teaching
practice, they also experienced positive feelings, even to a greater extent than when they were
at school. Figure 1 presents the percentage of each emotion chosen, both at school and in the
science teaching practice at the University. With regard to Nature Sciences, there was a high
correlation between their emotions when learning at school and as teachers during their
practice teaching.
Since conceptions influence attitudes, and both influence the teacher's behaviour (Ernest,
2000) and the pupils' learning (Georgiadou & Potari, 1999), in order to foster change in our
prospective teachers' views of teaching we will have to incorporate conceptions and attitudes
as part of a process of discussion and reflection in our initial teacher education programs
(Stacey, Brownlee, Reeves & Thorpe, 2005; Johnson, 2008).
Figure 1. Emotions aroused in topics related to Nature Sciences as school pupils and as teachers.
The above points suggest there is a need to consider in greater depth activities that
promote the critical analysis of prospective primary teachers' knowledge, conceptions, and
attitudes about mathematics and its learning and teaching. These activities should allow them
Lorenzo J. Blanco, Eloisa Guerrero, Ana Caballero et al.
to share, discuss, and negotiate the meanings that they generate, so that they will be able to
reinterpret their previous experiences and knowledge about the learning and teaching of
mathematics. This will enable them to develop metacognitive skills with which to analyze the
processes of their own learning as student teachers and of teachinglearning in primary
education. Their theorizing process will also give them a sound basis for their professional
knowledge and decisions. In this regard, it has to be noted that our students apply, consciously
or unconsciously, the models of teaching and learning that they themselves experienced at
school. For this reason, the reflection process has to be implemented explicitly, following
models that lead them to think about their own and the group's learning process, and about the
context in which this learning took place. They also need to be helped to verbalize and reflect
on the main variables in this process. And it has always to be borne in mind that the activities
must establish links between the students' cognitive and affective dimensions (Zevenbergen,
Mathematics Problem Solving and the Affective Domain
Since the 1980s (NCTM, 1980), the level of the presence and importance of problem
solving (PS) in curriculum proposals has been maintained and has even increased both
nationally and internationally (Castro, 2008). In these proposals, it is regarded as specific
content, as application of knowledge, and as a methodological approach (Schoenfeld, 1985;
Schroeder & Lester, 1989). Its importance is that it promotes analytical skills, comprehension,
reasoning, and application.
Recent international assessment reports (PISA, 2003; MEC, 2006) find poor levels of
performance in mathematics, and have again highlighted the importance of PS in school
Various studies have found that pupils see mathematics PS solving as a rote and
mechanical procedure, that they have few resources to represent and analyze problems, and
that they neither use different strategies or methods to find a solution nor do they make use of
the suggestions they are given to help them (Garofalo, 1989; Blanco, 2004; Córcoles and
Valls, 2006; Harskamp & Suhre, 2007; Santos 2008). Probably, "the prospective teachers'
relative ignorance of problem solving and the difficulties they manifest as solvers is also one
of the causes of their resistance to considering problem solving as a suitable context for
learning sciences" (Blanco & Otano, 1999, 295).
Also, it seems important to emphasize the lack of attention in textbooks to learning
heuristic problem solving strategies (Schoenfeld, 2007, Pino & Blanco, 2008).
The literature references given above that relate the affective domain to the teaching
learning of mathematics are also relevant to PS. Thus, McLeod (1986, 1992) shows that the
cognitive processes involved in PS are susceptible to the influence of the affective domain in
the three areas identified previously: beliefs, attitudes, and emotions. Thompson & Thompson
(1989) add that certain emotional states experienced by pupils during the PS process tend to
be regarded as undesirable affective states. Pupils make negative comments about
mathematics before starting to solve problems, which is construed as a signal of distress and a
The Affective Dimension of Learning and Teaching Mathematics and Science
revealing indicator of their negative attitude towards mathematics (Marshall, 1989).
Nicolaidou and Philippou (2003) establish relationships between PS performance and beliefs
and attitudes. For Richardson & Woolfolk (1980), anxiety about mathematics comprises
feelings of tension, mental disorganization, and helplessness that a pupil experiences when set
PS tasks in mathematics, and that these arise in everyday and other school situations as well
as in PS.
Several recent studies have looked in greater depth into the problem (Gómez-Chacón,
2001; Gil, Blanco & Guerrero, 2006; Sarabia, 2006; Harskamp & Suhre, 2007). They reveal
the influence of the pupil's self-efficacy on performance (González-Pienda, Núñez & García,
1998; Hoffman & Spatariu, 2008). Hernández, Palarea & Socas (2001) and Caballero (2007)
note prospective primary teachers' lack of confidence in solving mathematics problems, and
that they do not consider themselves capable and skilled in this area. The great majority of
them experience insecurity, despair, and nervousness, which seriously hinders or even blocks
their performance of the task.
These literature references abound with observations on the need to relate cognition and
affect in PS. Specifically, there is seen to be a need for the affective and cognitive factors to
be developed simultaneously in teacher education programs (Furinghetti & Morselli, 2009).
"The role of teacher education is to develop beginning teachers into confident and competent
consumers and users of mathematics in order that they are better able to teach mathematics"
(Zevenbergen, 2004, 4).
Program of Intervention on PS and Emotional Control
The research discussed above has not yet led to the development of an integrating process
of teachinglearning that includes cognitive, emotional, and affective aspects. Knowledge and
learning are the products of the mental activity of the learner who perceives, evaluates, and
interprets the facts, the reality, the object, or the situation concerned. Similarly, we understand
that the learners themselves are key and active agents in managing their own knowledge,
since it is they who will generate new knowledge on the foundation of their previous
knowledge (Guerrero, 2006). The basis of school learning lies not in the amount of content
learnt, but in the degree of autonomy, how meaningful it is to the pupils, and the sense they
attribute to it.
Our current line of work is an integration of teachinglearning about PS and emotional
education. The latter is understood as a continuous and permanent educational process, aimed
at enhancing emotional development as an indispensable complement to cognitive
development, the two of which constitute the essential elements of the development of the
whole personality (Bisquerra, 2000).
We also believe that the development of problem-solving skills should be an attainable
goal given a suitable educational environment. Moreover, the approach to PS is very personal,
so that we shall have to help each student to discover his or her own style, capabilities, and
limitations. We must not only convey to them some given method or set of heuristic rules, but
the attitudes and emotions towards mathematics PS based on their own experiences. At the
same time, however, we recognize that attempts to teach PS strategies have failed
(Castro, 2008; Santos, 2008). We therefore considered it important to design a program of
Lorenzo J. Blanco, Eloisa Guerrero, Ana Caballero et al.
intervention on PS that integrates the above aspects into a process of action and
Oliveira & Hannula (2008) discuss three ideas for consideration in teacher education,
which we also consider in our model. The first is to challenge the prospective teachers'
beliefs, many of which are implicit. They therefore have to be made explicit and reflected
on, creating the opportunity for change. The second is to involve the stude nts actively as
learners of mathematics, usually in a constructivist setting. And the third, also aimed at
producing changes in belief structures, is to provide them with experiences of
mathematical discovery, which seems to have a profound and immediate transformative
effect on their beliefs regarding the nature of mathematics, as well as its teaching and
learning (Oliveira & Hannula, 2008).
González-Pienda, Núñez, Álvarez & Soler (2002) present a model that is a
combination of cognitive and constructivist paradigms. It is based on the following
assumptions: (a) learners bring frameworks of reference to the learning process as a result
of their previous experiences, their social context, interests, beliefs, and ways of thinking;
(b) they present major individual differences (abilities, learning styles, cognitive styles,
expectations, etc.); (c) learning is a constructive process that is facilitated when the
material to learn is meaningful, and when the learners are actively involved in creating
their own knowledge and understanding, connecting what they want to learn with their
prior knowledge and experiences; (d) learning is fostered by positive interpersonal
relationships and when the learner feels appreciated, valued, and recognized; and (e) the
teaching methods have to take the learners' goals, interests, and prior knowledge into
In our review of the literature, although though there were studies relating PS to the
affective domain, we found no research applied to the design and development of
programs of intervention that consider aspects of cognition and emotional control
conjointly, and that evaluate their effectiveness in the initial teacher education classroom.
Our aim is to describe the beliefs, attitudes, and emotions of prospe ctive primary
teachers, and to analyze how they confront them when they come to reflect on the
emotional states that accompany mathematical activity, given that their emotions will
affect their participation in the activities (Thompson & Thompson, 1989). Affects
towards mathematics exert a decisive influence on students' learning, on their perception
of the subject, and on their view of themselves as learners (which is a key element in
determining their behaviour). In this sense, affects play four roles: as a regulatory system
of learning in the classroom, as an effective indicator of the learning situation, as inertial
forces of resistance to or impulse in favour of activities and educational changes, and,
given their diagnostic nature, as a vehicle of knowledge (Gómez-Chacón, 2000).
We therefore wish to: "Provide prospective teachers with an educational tool that will
enable them to learn to solve mathematics problems, taking into account aspects of
cognition and emotional education."
The following specific objectives were considered within the overall program:
The Affective Dimension of Learning and Teaching Mathematics and Science
To assess attitudes, beliefs, affects, emotions, and attributional styles of the research
Training in emotional and cognitive skills related to the different steps in the process
of PS.
To provide resources for the management of the emotions, stress, and anxiety that
arise in the PS process.
To encourage the prospective teachers' self-esteem and professional self-efficacy in
relation to teaching about PS.
Methods and Population
The nature of the research suggested the use of qualitative and quantitative methods with
a focus on action-research, since the ultimate goal is to help the participants develop their
thoughts, modify attitudes, and find solutions to the "problem" that solving mathematical
problems represents for them.
Guerrero & Blanco (2004) proposed a theoretical model based on general models of PS
(Polya, 1957; Schoenfeld, 1985), on the cognitive-behavioural models of Zurilla & Goldfried
(1971) and Meichembaum (1974), and on the systemic model of De Shazer and the
Milwaukee group (De Shazer, 1985). Beginning with the 200607 academic year, we began a
research project that has enabled us to design an integrated model which forms the basis of
the study we are currently carrying out.
This study consists of a fifteen-session workshop divided into two distinct parts, which
was implemented in the 200708 and 200809 courses of prospective primary teachers in the
Faculty of Education, University of Extremadura. The first workshop had 55 participating
students, and the second 60.
In the first part, we work on knowledge, conceptions, attitudes, attributional styles,
expectations, and emotions on the basis of questionnaires and activities related to specific
The second consists of a process of experimentation and reflection based on the general
model, and structured in five steps: (i) accommodation / analysis / understanding / familiarity
with the situation; (ii) search for and design of one or more problem solving strategies; (iii)
execution of the strategy or strategies; (iv) analysis of the process and the solution; (v) How
do I feel? What have I learnt? In the first three steps, we consider two phases: control of the
situation (relaxation and instructing oneself), and the use of mathematical concepts and
processes based on heuristics specific to each case. In the fourth step, we evaluate the process
and its outcome in order to learn and to transfer knowledge to new situations. And finally in
the fifth step, we lay emphasis on the solver's situation to modify, in so far as possible, his or
her affects (conceptions, beliefs, attitudes, self-concept, etc.) regarding mathematics PS.
At all times, we take into account the need to experiment and to reflect on the experience
as the basis for acquiring new knowledge and to provide specific activities to put into practice
in the primary classroom.
Lorenzo J. Blanco, Eloisa Guerrero, Ana Caballero et al.
Research Instruments
To verify the reliability of the research, we carried out a comprehensive and detailed data
collection process. The validity of the study was monitored using different data collection
instruments in order to relate, compare, and contrast different types of evidence. We used
various research tools to access the informants in depth. These were:
Questionnaires, both open and closed, which are analyzed qualitatively or
quantitatively depending on their structure:
Adaptation to mathematics PS of the BEEGC-20 Questionnaire (Battery of Scales of
Generalized Expectations of Control) of Palenzuela et al. (1997). This instrument
will allow us to determine the students' causal attributions in relation to mathematics
Adaptation to mathematics PS of the STAI (State-Trait Anxiety Inventory) of
Spielberger (1982).
Adaptation to mathematics PS of the questionnaires of Gil, Blanco & Guerrero
(2006), Sarabia (2006), and Caballero (2007) on the affective domain in
Re-elaboration of open questionnaires designed to extract from the participants the
sensations, feelings, attitudes, motives, reactions, etc., which they experience in the
different phases of solving a problem and at different stages during the workshop.
Observation of the behaviour in the classroom of both teacher and students,
videorecorded with two cameras, with subsequent transcription and analysis. These
recordings have a dual purpose: to be a source of data to analyze the evolution of the
participants' teaching strategies, and to constitute the fundamental material for
reflection with the students and teachers.
The Moodle Platform is a useful tool for the presentation of information and
communication. It allows information to be stored for later analysis (both qualitative
and quantitative), with the date and the subject contributing the information being
reliably logged. It allows one to evaluate the participation, and to see whether the
students have attained specific learning objectives, providing feedback as well as
motivation to the students (Rodríguez, 2005).
Diaries (Nichols, Tippins, and Wieseman, 1997; Volkmann & Anderson, 1998) kept
on the Moodle virtual platform. These allow the collection of observations,
sensations, reactions, interpretations, anecdotes, introspective remarks about feelings,
attitudes, motives, conclusions, etc.
Discussion Groups to facilitate debate (Watts & Ebbutt , 1987), since people who
share a common problem will be more willing to talk to others with the same
problem (Lederman, 1990). The prospective teachers require a group context and a
researcher for this information to emerge, be expressed, and deciphered in words
(Lederman, 1990). The discussion groups yield data of a type that would be hard to
obtain by other means since it corresponds to natural situations in which spontaneity
is possible, and in which, thanks to the tolerant atmosphere, there come to light
opinions, feelings, and personal desires that would not be expressed in rigidly
structured experimental situations (Gil, 1992-93).
The Affective Dimension of Learning and Teaching Mathematics and Science
For the data analysis, we used the program packages SPSS 15.00 program and Aguat for
the quantitative and qualitative methods, respectively, following the recommendations and
suggestions set out in various works, including those of Miles & Huberman (1984) Goezt &
Lecompte (1984), and Wittrock (1986).
Some Results
The data showed there to be a contradiction between the expectations, actions, and
reflections the participants make when solving problems. Thus, in the pre-workshop open
questionnaires they state that: "Maths is never learnt by memory, it must all be reasoned out",
"It is not enough to know all the formulas to apply". The questionnaire responses during and
after solving problems, however, implicitly considered it to be mechanical learning, as they
indicated that knowing how to do some school problems you can solve others by just
changing the data.
We also found contradictions between the attitudes they said they felt and those that they
manifested during the PS, and which we observed in the complementary videorecordings. For
example, they claim to look for different ways and methods to work on the problems, but in
reality there was evident abandonment in the face of difficulties in finding a solution. Their
statements show the relationship between mathematics PS and the emotions and beliefs
generated. "When I got it (solved the problem) I felt very satisfied", and "Solving problems
correctly also gives you more security and confidence". In the contrary sense: "When you do a
problem and it does not come out, you leave it, and you think that mathematics is very hard".
The findings derived from the questionnaires indicated that these prospective primary
teachers consider the results that occur in their lives will depend on their actions, i.e., they
have a great expectation of contingency or internality, pointing to effort, perseverance, and
patience as key aspects in mathematics PS. Hence they express such statements as: "With a lot
of effort and dedication I managed to get it out", and "Also, it is due to my own attitude".
However, despite their responses to the questionnaires declaring effort, perseverance, and
patience to be necessary factors in mathematics PS and saying that they persevere in that task,
the videorecordings at the beginning of the workshop showed that many of the participants
gave up easily in mathematics PS tasks. This attitude had improved, however, after the
As against this high locus of internal control, we observed a low locus of external control.
I.e., they attach little importance to the influence of external factors on the succession of
events or the attainment of their goals. There was a low score on helplessness (capacity for
control), which means again that they do not expect that the events or outcomes that may
happen to them will be independent of their actions. This was also the case, although to a
lesser extent, with the expectation or belief in luck. Thus, the degree to which they believe the
things that can happen to them in life will depend on chance and coincidence was practically
insignificant. They do not consider that the results achieved primarily derive from other
external sources excepting the teachers, to whom they assign a key role in the teaching and
learning of mathematics PS: "It depends on how they explained it to you", or "The attitude of
the teachers is decisive".
The prospective primary teachers do not feel very confident about their personal abilities
(expectations of self-efficacy). This confidence was favoured by tasks relating to everyday
Lorenzo J. Blanco, Eloisa Guerrero, Ana Caballero et al.
life, and disfavoured in situations of significant difficulty. Thus, they note that they lack
security and confidence in mathematics PS ("I have always been null with mathematics
problems"), but these factors increased with their working on the problems in groups. The
security and self-confidence improved after the workshop on solving mathematics problems,
as illustrated by the results of the STAI pre-test and post-test shown in Figures 2 and 3.
Figure 2. Security. (“I feel secured”)
The Affective Dimension of Learning and Teaching Mathematics and Science
Figure 3. Confidence. (“I have self-confidence”)
They have favourable expectations of success for goals of a general type, i.e., they expect
to get the desired results given the objectives we set them. However, when they are actually
faced with a mathematics problem, they show no such expectations of success, and their
confidence is lower. This again shows the discordance between what the subjects see as
Lorenzo J. Blanco, Eloisa Guerrero, Ana Caballero et al.
desirable and the reality, i.e., their responses to certain questionnaires not reflecting what they
really think or do, but what they believe to be the most positive, what is expected of them, or
what they would like their attitude to be like.
These results do show that the students are well predisposed to the learning situations.
The students state that they are calm when faced with mathematics problems. However,
when they get stuck or blocked with the solution, their insecurity and nervousness (anxiety)
increase. This could mean that it is the blocks in solving the problem rather than the problem
itself which provokes their anxiety, which would mean that there is a need to learn to
intervene when such blockages occur.
The workshop's evaluation conducted by means of questionnaires, discussions, and
specific PS activities showed that, in general terms, there was an increase in feelings of
security, satisfaction, and self-confidence.
Both at the beginning and at the end of the workshop, the subjects were asked to locate
themselves on a scale of 1 to 10 as problem solvers. The results are shown in Figures 4 and 5.
A Student's t-test for related samples showed there to exist statistically significant
differences between pre-test and post-test scores (p = 0.0000). This means that the prospective
primary teachers believed that they had significantly improved in their PS performance after
carrying out the workshop.
Figure 4. Problem solver.
St. Dev.
Pretest. Solver
problem (before the
Postest. Solver
problem (after the
Figure 5. The mean scores as problem solvers.
The Affective Dimension of Learning and Teaching Mathematics and Science
As well as these results, we would note that the students valued the workshop positively,
emphasizing the importance of combining psychology and mathematics. The following are
some of their statements that together summarize the evaluations the students made of the
workshop: "It helps to see mathematics differently, not as a threat but as a challenge", "Now
we know how to look for different ways of solving problems", "I stop longer on the wording of
the problem to understand it better and I know how to analyze it better, before I faced it with
more nervousness, but now with these steps and with the strategies for relaxation I face it in
another way", and "The most important was the affect that you teachers had brought to the
workshop, by being understanding with the students, because you have given us more
keenness about learning".
The work that was carried out with prospective teachers, including their evaluation of the
workshop, reaffirms our conviction that there is a need for PS to be studied in greater depth,
considering cognitive and affective aspects as complementary. It is not easy to design and
implement a workshop on PS that includes in all of its sessions and activities specific aspects
of cognition and emotional education. Nonetheless, although difficult, we consider it
necessary because teachers in their actions in the classroom can not dissociate the two aspects
when they are dealing with some specific activity for pupils of a specific level.
It is true that some of the prospective teachers stated that they still lacked confidence as
problem solvers. But it is no less true that these same pupils showed more willingness to
tackle a problem that they were set than at the beginning of the workshop. This opens the way
to changes in their values concerning PS, and they will be better disposed to initiate changes
in this activity along the lines set out in the current curricular proposals.
The present study was funded by Research Projects SEJ2006-04175 of the Ministry of
Education and Science (Spain), and PRI08B034 of the Junta de Extremadura (Spain), and
European Regional Development Fund (ERDF).
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... Les émotions négatives affectent leur pratique car ces enseignants consacrent souvent moins de temps à l'enseignement des sciences, faute de confiance en eux (Jones & Carter, 2007). Enfin, il est souligné qu'il est important d'accompagner les enseignants en formation, comme les enseignants déjà titulaires à travers des programmes de soutien émotionnel, afin qu'ils développent le mieux possible cette compétence (Appleton, 2008 ;Blanco et al., 2010). ...
Cette thèse s’intéresse à la manière dont des enseignants de l’école maternelle en France s’approprient des dispositifs didactiques visant la construction d’un modèle précurseur sur les notions de lumière et d’ombre sous le prisme de l’optique géométrique. Disposant d’un tel modèle précurseur construit par des études antérieures, nous mettons en place une méthodologie spécifique pour observer et analyser dans quelle mesure des enseignants peuvent se l’approprier pour mener une éducation scientifique avec leurs élèves. Pour ce faire, nous avons constitué un groupe de quatre enseignants volontaires afin de mettre en place cette étude. Le groupe propose un scénario pédagogique, répondant à certaines contraintes en lien avec le modèle précurseur, qu’un membre met en oeuvre dans sa classe. Après avoir effectué une analyse critique sur sa pratique, cet enseignant propose un nouveau scénario. Basés sur la Théorie Anthropologique du Didactique de Chevallard, nous construisons une praxéologie de référence inspirée par le modèle précurseur, et des praxéologies didactiques du groupe et de l’enseignant. Nous effectuons une série d’actions afin de repérer des éléments de praxis et de logos, et nous identifions si les praxéologies des enseignants contiennent les éléments du modèle précurseur. L’analyse des données montre qu’une éventuelle appropriation du modèle est possible sous certaines conditions. Le groupe propose un scénario qui s’aligne avec le contenu du modèle précurseur mais la mise en oeuvre semble s’éloigner des principes du modèle en question. Cependant, notre méthodologie amène l’enseignant à prendre du recul sur sa pratique et à proposer un scénario respectant les contraintes du modèle précurseur.
... As part of the personal aspect, we consider it important to reflect on emotions, which can act as facilitators or obstacles to teaching and learning (Blanco et al., 2010;King et al., 2015). Indeed, the study of emotions plays a key role in PSTs (Schoffner, 2009) as they can minimise student tiredness, which is one means of engaging with the most relevant scientific content (Ritchie et al., 2011). ...
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Social constructivism is a learning approach in which students actively construct their own knowledge by way of experiences and interactions with others. As such, it is important to highlight both individual and group-based reflection practices in pre-service teacher training as a key aspect for improving teaching practice. This paper presents the results of the design and implementation of a training programme of 7 sessions (8.5 h of class participation plus 25 h of personal homework) for pre-service secondary school science teachers, who were asked to design a gamification resource and an e-rubric to evaluate it. Subsequent improvement of this e-rubric was enhanced by performing different reflection activities at key moments. The programme was carried out by 50 Spanish pre-service teachers from Málaga (Spain). Data collection centred on the e-rubrics designed, the emotions experienced and the possible transfer to real-life practice performed six months later. The impact of reflections on the evaluation was studied by analysing the evolution of the categories proposed by the participants for the e-rubric at different times, with marked changes being found during design and preparation of the gamification resource, and only very minor changes post-implementation. In addition, a group-based criteria consensus session favoured a more in-depth reflection. Interest was the main emotion experienced by pre-service teachers, especially during preparation and use of the resource. The programme also had a marked impact on transfer of the e-rubric into practice, as did the designed resource, although to a lesser extent.
... Also, the protective effects of exercise have been shown in cognitive deficits due to aging (Vanzella et al., 2017). Learning and teaching science is more than a purely cognitive process and is highly charged with feelings (Blanco, Guerrero, Caballero, Brígido, & Mellado, 2010). Cognitive and affective dimensions quite often are linked with behavior (Jackson, 2018;Rose, Gilbert, & Smith, 2013). ...
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Introduction: Resveratrol, a natural polyphenol abundant in grapes and red wine, has been reported to exert numerous beneficial health effects in the body. High-Intensity Interval Exercise (HIIT) is a form of interval training that provides improved athletic capacity and has a protective effect on health. The purpose of this study was to investigate the interactive effects of swimming HIIT and Resveratrol supplementation on behavioral function in Novel object recognition and open-field tests in aged rats. Methods: A total of 45 aged male Wistar rats with an age of 20 months were randomly assigned into five groups of control (C), swimming HIIT (SW-HIIT), swimming HIIT with Resveratrol supplementation (SW-HIIT-R), Resveratrol supplementation (R), and solvent of Resveratrol supplementation (SR). There was also another group that included young animals (2-month-old) and was used to compare with older animals. Swimming HIIT and Resveratrol supplementation groups performed the exercise and received Resveratrol (10 mg/kg/day, gavage) for six weeks. Novel object recognition and open-field tests were used for evaluating the behavioral functions in animals. Results: The results showed that HIIT and Resveratrol significantly improved recognition memory compared to old animals. Moreover, it seems that HIIT and Resveratrol partly could modulate anxiety-like behaviors compared to old animals in the open-field test.
... In order to measure anxiety, psychologists have mostly used questionnaires, while educators have no unique way of quantifying it. As in the case of attitudes, several authors (Blanco, Barona & Carrasco, 2013;Blanco et al., 2010;Jiménez et al., 2012;Di Martino & Zan, 2010; consider that it should be approached through essays or open-ended questions, as they argue that respondents to closed questionnaires are not sincere but are influenced by what they think they are expected to answer (Zan & Di Martino, 2008). On the other hand, studies with closed questionnaires are abundant (Arrebola & Lara, 2010;Cézar & Pérez, 2010;Palacios, Arias, & Arias, 2013;Seco & García, 1999). ...
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This article is integrated into a larger project, Attitudes towards Sciences and Mathematics, involving several Ibero-American countries. In this paper, we analyze the attitudes concerning anxiety in two samples of Spanish and Portuguese elementary pre-service teachers: the first sample is composed of Spanish pre-service teachers at the beginning of the Curricular Units of mathematics of their courses and Portuguese pre-service teachers at the beginning of professional master's degree courses; the second sample is composed of the same Spanish students and Portuguese pre-service teachers at entry into higher education. The studies adopted a quantitative methodology, delivering the Auzmendi questionnaire, and researched the association of anxiety with the factors gender, country and stage of education. The first study showed that there is association between anxiety and country: the Spanish pre-service teachers showed greater anxiety. The second study showed that there is no association between anxiety and the considered factors. It is concluded that students develop anxiety towards mathematics in their school pathway, before the attendance of higher education. During the attendance of higher education, after completing a 3 year degree in Basic Education, Portuguese prospective teachers reduced their level of anxiety.
... Si como señalan Bisquerra y Pérez (2007) los conocimientos académicos se aprenden mejor si los alumnos tienen competencias emocionales, es fundamental formar docentes emocionalmente competentes, que sepan diagnosticar y autorregular sus emociones a través de programas de intervención que incluyan tanto lo cognitivo como lo afectivo. En este sentido, diversos autores señalan la necesidad de la realización de programas de intervención durante la formación inicial del profesorado, donde los componentes cognitivos y afectivos deben desarrollarse simultáneamente (Blanco, Guerrero, Caballero, Brígido y Mellado, 2010;Efklides, 2009;Koballa y Glynn, 2007;Shoffner, 2009). Este tipo de programas suponen un proceso de reflexión sobre la propia experiencia personal como estudiante, pues es en la etapa escolar donde el futuro A. B. Borrachero, M. A. Dávila, E. Costillo y V. Mellado 20 docente ha ido acumulando experiencias afectivos que podrán incidir en su labor como profesional (Alsup, 2005). ...
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Literature indicates that future teachers, when they begin their teaching practices, carry with them a series of beliefs, attitudes and emotions, a result of the memory of their different years of schooling. Therefore, it is considered necessary that the teachers in formation reflect on the emotions that they experience towards the sciences. To this end, an intervention program is designed and developed for students of the Master's Degree in Teacher Training in Secondary Education, in the areas of Biology / Geology, Physics / Chemistry and Mathematics. The results show that at the end of the program, in general, the emotions that they experience are positive and there is an absence of negative emotions. In addition, their teaching self-efficacy has increased and they know how to use strategies to self-regulate.
... Las creencias que más influyen en la motivación y el rendimiento en matemáticas son la percepción de los estudiantes acerca de sí mismos en relación con las matemáticas (KLOOSTERMAN, 2002;SKAALVIK;SKAALVIK, 2011;HERNÁNDEZ;PALAREA;SOCAS, 2001;BLANCO et al., 2010) teniendo en cuenta que, generalmente, no se consideran capaces y calificados como resolutores de problemas, la mayoría de ellos se consideran a sí mismos incompetentes en la resolución de problemas. ...
This research project analyzed primary school teachers from 7th grade (second-cycle) enrolled in training through a Model of Professional Competences in Mathematics. The aim of the project was to develop and implement a teaching methodology that relates mathematics and pedagogical knowledge and teaching practice, with a view to updating mathematics teachers' content and pedagogical knowledge that fosters learning through problem-solving. The research used a quantitative, as well as a qualitative methodology. The research population were 47 teachers from 36 urban schools run by municipalities at Región de Los Lagos, in Chile. Results show that teachers improve when faced with didactic-mathematical tasks, reaching substantial improvements in their teaching performance and showing evidence of general and specific competences.
... Professional change has to go together with personal and social development (Bell & Gilbert, 1994;Proweller & Mitchener, 2004), taking affective aspects into account (Blanco et al., 2009;Brígido et al., 2009;Friedrichsen & Dana, 2005), reinforcing the teacher's self-esteem, encouraging constructive collaboration, strengthening the culture of the corresponding school, and building on the good practice that the teachers are already carrying out (Hargreaves, 1996). Social aspects are fundamental for science teachers' professional development. ...
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We describe the cases of Alicia and Mónica, two secondary education physics teachers in Cordoba (Argentina), who are participants in a program of professional development based on collaborative guided reflection. Alicia is a novice teacher, and Mónica an experienced teacher. We analyze the initial state and the evolution (over a period of 6 years or cycles for Alicia and 5 for Mónica) of their explicit educational and epistemological conceptions, of the theories they use and the underlying implicit theories, and of their educational models in the classroom. Initially, the declared conceptions of both teachers were far more advanced than their practice. But their educational changes were very different. For Alicia, the greatest change took place during the second cycle of the study in her behaviour associated with the pupils' construction of knowledge. For Mónica evolution was gradual, involving the resolution of conflicts between rival positions in her pupils' process of construction of knowledge, in her organization and management of the class, and in evaluation. At the end of the study, both secondary teachers showed considerable concordance between their explicit and implicit beliefs and their declared and actual educational models, both of which were close to an action-research–constructivist perspective. Nonetheless, the process of guided reflection affected the participating teachers very differently according to their teaching experience and particular school context. This implies that there is a need to individualize professional development according to the personal and social characteristics of the secondary teacher with whom one is collaborating
This is a quantitative-qualitative study that aims to determine the influence of heuristic or problem-solving strategies (PS) to the mathematics anxiety of 97 or 87% of the Bachelor of Elementary Education (BEEd) second-year students of Western Visayas College of Science and Technology enrolled in the subject Problem Solving during the second semester, SY 2014-2015. It also aims to find out the coping mechanisms and perceived causes of mathematics anxiety of the participants. For the quantitative data, a one-group pretest-posttest design was used. The Mathematics Anxiety-Apprehension Survey (MAAS) was administered before the start of the intervention and at the end of the intervention. For the qualitative data, the participants were asked to write a journal on the perceived causes of their math anxiety and their coping mechanism. Personal interviews were conducted to participants with high math anxiety regarding their coping mechanisms. The statistical tools used were the mean, standard deviation, Wilcoxon Signed Rank test, and Kruskal-Wallis Test. The test in the hypothesis was set at .05 alpha level. Results showed that, as an entire group, and when grouped according to sections, the participants have “moderate” mathematics anxiety. Likewise, the participants have “moderate” mathematics anxiety before and after learning heuristic strategies. There is no significant difference in the level of mathematics anxiety when the participants were grouped according to sections and before and after learning heuristic strategies. The perceived causes of mathematics anxiety of the participants were mostly attributed to their bad experience with their teachers in basic education such as “terror” teachers, physical or verbal punishment, as well as time pressure during math examinations/quizzes. Another identified factor was the quality of teaching like teachers spoke too fast or spoke with a low voice. Some of the common coping mechanisms of the participants were “studying harder”, “utilizing problem-solving strategies or heuristics”, “ asking help from peers”, “listening attentively during class “, and “developing positive attitude” in mathematics.
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En el presente trabajo se presenta, en primer lugar, una detallada descripción de diferentes propuestas realizadas por diversos autores, tanto a nivel nacional como internacional, para la intervención en variables afectivas (creencias, actitudes, ansiedad…) hacia las matemáticas y la resolución de problemas matemáticos. En segundo lugar, se describe un programa concreto de control emocional en la resolución de problemas matemáticos para maestros en formación inicial así como el eje central del mismo: un Modelo Integrado de Resolución de Problemas Matemáticos (MIRPM). Igualmente se muestran algunos resultados que evidencian la eficacia de este programa, entre los que cabe destacar una disminución significativa de la ansiedad hacia la resolución de problemas matemáticos, un aumento de la autoconfianza y expectativas de éxito y una modificación de las creencias en torno a la resolución de problemas y su enseñanza y aprendizaje. Palabras clave: variables afectivas, matemáticas, resolución de problemas matemáticos, ansiedad matemática, programa de intervención. Abstract This paper shows, firstly, a detailed description of different proposals made by different authors, both nationally and internationally, for intervention in affective variables (beliefs, attitudes, anxiety...) towards mathematics and mathematics problem solving. Secondly, a concrete programme of emotional control in mathematical problems for teachers in initial training is described as well as its central axis: an integrated model for mathematics problem solving (MIRPS). Also shows some results that demonstrate the effectiveness of this program, which include a significant decrease of anxiety toward the mathematics problem solving, increased self-confidence and expectations of success and a change in beliefs around solving problems and its teaching and learning.
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We have performed a longitudinal study among BUP and COU students, from fourteen to eighteen years old, and their attitudes to Science. This attitude becomes neither linear nor more negative through successive years. On the contrary, we have observed a «saw tooth» profile.
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RESUMEN Los factores afectivos del profesorado tienen una gran influencia en los de los alumnos y en los logros de éstos. Además, pueden explicar gran parte de la atracción y rechazo hacia las matemáticas. En esta ponencia presentamos algunos de los resultados hallados en una investigación en curso acerca del dominio afectivo de los estudiantes para maestro de la Universidad de Extremadura hacia las matemáticas, describiendo por tanto las actitudes, creencias y emociones que manifiestan hacia dicha disciplina. Esta descripción parte de los datos obtenidos de la aplicación y posterior análisis de un cuestionario elaborado de acuerdo al fin propuesto. Palabras clave: matemáticas, dominio afectivo, actitudes, creencias, emociones, estudiantes para maestro. SUMMARY The affective factors of the teaching staff have a great influence in those of the students and in the profits of these. In addition, they can explain great part of the attraction and rejection towards the mathematics. In this communication we presented/displayed some of the results found in an investigation in course about the affective domain of the students for teacher of the University of Extremadura towards the mathematics, describing therefore the attitudes, beliefs and emotions that declare towards this discipline. This description leaves from the collected data of the application and later analysis of a questionnaire elaborated according to the proposed aim. Key words: mathematics, affective domain, attitudes, believes, emotions, students for teacher.
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The present work set out to analyze the beliefs, attitudes, and emotional reactions that students experience in the process of learning mathematics. The aim was to be able to demonstrate that the existence of positive attributes, beliefs, and attitudes about themselves as learners are a source of motivation and expectations of success in dealing with this subject. We used a sample of 346 students of the second cycle of Obligatory Secondary Education (ESO) of high schools in Badajoz. The participants responded to a questionnaire on beliefs and attitudes about mathematics. It was found that neither the students' gender nor their year of studies influenced their beliefs about their self-concept of mathematics.
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Guerrero, E.; Blanco, L.J. y Castro, F. (2001). Trastornos emocionales ante la educación matemática. En García, J.N. (Coor.), Aplicaciones de Intervención Psicopedagógica. Pirámide, 229-237 Introducción La educación matemática viene condicionada por múltiples factores que han sido considerados en mayor o menor medida en diferentes investigaciones. En los últimos años hemos constatado un aumento de publicaciones que relacionan la dimensión afectiva del individuo (creencias, actitudes y emociones) y la enseñanza/aprendizaje de las matemáticas. El dominio afectivo está adquiriendo tal protagonismo en la investigación en este campo, que nos lleva a mantener la hipótesis de que las actitudes, las creencias y las emociones influyen tanto en el éxito como en el fracaso de la enseñanza y en el aprendizaje las Matemáticas. Su importancia fue recogida en la propuesta curricular del MEC (1992), al señalar que “se considera indispensable que el profesorado sea consciente de la importancia de estos contenidos (actitudinales) como aprendizajes propiamente dichos y para la adquisición de otros de tipo conceptual y procedimental (p.82) ”. En este capítulo tratamos, en primer lugar, de los aspectos que relacionan las emociones negativas, las actitudes y las creencias con los comportamientos y la autoeficacia percibida del alumnado en relación a la actividad matemática. En segundo lugar, aportamos pautas de actuación, que en nuestra opinión, han de guiar el proceso de intervención psicopedagógica. Para ello, proponemos un programa de intervención y una metodología basada en la resolución de 3 problemas, en la responsabilidad del alumno y en el conocimiento de sus propios procesos cognitivos, emocionales y afectivos para superar las dificultades. Adjuntamos, también, instrumentos útiles. Creemos que las ideas aportadas pueden ser relevantes tanto en la formación del profesorado como en la del alumnado. Por un lado, al profesorado puede serle de utilidad en la instrucción, en la metodología a emplear y en la enseñanza de estrategias. Por otro lado, en el ámbito emocional y afectivo explicaría los rechazos y las atracciones que el alumnado siente hacia las Matemáticas, hacia el profesorado que la enseña, hacia la situación de aprendizaje en el que se desarrolla, y, en general, hacia la escuela, hacia los demás o hacia ellos mismos. La diversidad y la variedad emocional que tanto profesores como alumnos pueden experimentar influirán de manera decisiva sobre la salud física y/o emocional de ambos.
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Este artículo trata de mostrar la relación entre la dimensión afectiva y emocional y la influencia que ésta ejerce, fundamentalmente en el aprendizaje de las Matemáticas y en el éxito y/o fracaso de las mismas. Partiendo de la hipótesis de que las actitudes, las creencias, los pensamientos y las emociones explican una gran parte del resultado y rendimiento ante las Matemáticas, proponemos el diseño de un programa de intervención de corte psicopedagógico que se desarrollará en diez sesiones. Está inspirado en los modelos de Polya (1985) sobre resolución de problemas y el modelo de inoculación de estrés de Meichenbaum (1985), siendo sus principales objetivos resolver problemas de Matemáticas, adiestrar al alumno en el afrontamiento de situaciones ansiógenas y manejar las emociones. Se detallan algunos instrumentos útiles para la evaluación y se describe, sesión a sesión, cómo tendría que llevarse a cabo la implementación del programa de intervención. Palabras claves: intervención, resolución de problemas, estrés, emociones
examines the process of becoming a mathematics teacher, focusing on the individual and on changes he or she undergoes in assuming the role of a professional teacher / review the research related to becoming a mathematics teacher / discuss implications of this research both for mathematics teacher education as well as for future research reflects the three research traditions within which most research on becoming a teacher has been conducted: learning to teach, socialization, and adult development / within the learning-to-teach perspective, we include research on teacher knowledge, beliefs, thinking and actions, with major emphasis on research conducted within the discipline of psychology and grounded in the assumptions of cognitive psychology (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Although one may disagree with Shapiro and Ravenette’s evaluation of the various tests cited, their quote does sensitize us to the need to develop more explicit ways of assessing our client’s affects, cognitions, and volitions. The present chapter conveys some preliminary attempts at developing this assessment armamentarium, which follow from a cognitive-behavioral treatment approach. Specifically, the present chapter has two purposes. The first is to examine various assessment strategies that have been employed to study psychological deficits. This analysis indicates some shortcomings and an alternative, namely a cognitive-functional analysis approach. The second purpose of the chapter is to describe specific techniques that can be employed to assess more directly the client’s cognitions. Let’s begin with an examination of the current assessment and research strategies.