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					Icmepaper04 Effecting student resilience via the mathematics classroom: from
research to reality. Janet Hunter




 EFFECTING STUDENT RESILIENCE VIA THE MATHEMATICS
      CLASSROOM: FROM RESEARCH TO REALITY
                                     Janet Hunter
                          e-mail: janethunter@bigpond.com
                     Continuing Education, University of Sydney


As teachers, we know that the students in our care face many challenges other than
the academic mastery of mathematics. Society now is more complex, and violence,
drug-taking and depression are on the rise. Recent research in other fields such as
Psychology and Sociology suggests that if a student is more resilient then he or she
will be less inclined towards destructive, risk-taking behaviours. This paper discusses
the meaning of resilience and how it can be enhanced in students through the
learning of mathematics. Various factors of general classroom management,
relationships and behaviours have been identified as intrinsic to the development of
resilience. It can then be shown that mathematics by its nature is an ideal medium
through which to build resilience for life.

INTRODUCTION
This paper arose from a broader project called the Community Change Project, which
commenced in March 2003. A number of secondary schools are involved in this
project and it is funded by the New South Wales Drug Rehabilitation Centre in
Australia. The aim of the research is to determine explicitly what aspects of
classroom relationships and pedagogy enhance students‟ learning and psycho-social
development in the classroom. One of the participating schools is a metropolitan all
girls‟ school in a middle to upper middle class area of Sydney. The research in this
particular school began with a broad survey, including items relating to resilience.
Further research is now continuing into other aspects of school life although the
students‟ responses to the items on resilience prompted the school to focus on the
nature of resilience and, if possible, the aim of building resilience in students. While
the genesis of the project was not specifically related to the teaching and learning of
mathematics, the analysis of the results is useful in the light of what mathematics
teachers can learn about enhancing resilience in students.
The purpose of this paper is to:

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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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1. discuss indicators of resilience with reference to the results of a survey
administered to students in the school and
2. outline a set of proposals which address the responses to the survey, notably
practical ways in which the individual classroom teacher can help the student to
become more resilient through the learning of mathematics, in particular.

DEFINING RESILIENCE
There are various definitions of resilience although they all have a common theme.
Resilience could be defined as
  '….. relative resistance to psycho-social risk experiences.' (Rutter, 1999)
Risk experiences could include risk-taking behaviour on the part of the student such
as illicit drug-taking, delinquency, early sexual activity, attempting suicide and
alcohol abuse, but also externally imposed risk environments such as poverty, family
breakdown, abuse, or generally stressful times or situations.
The concept of resilience emerged through the study of children who were immune to
the factors that negatively affected others even though they were exposed to similar
circumstances. Key features of resilience are internal strengths of the individual and
external positive influences occurring within systems. One such system is a school
(Rutter, Maughan, Mortimore & Ouston, 1979).
Key concepts which manifest themselves in resilient children are characteristics such
as a sense of self-esteem, taking an active stance towards an obstacle, the ability to
see difficulties as something that can be overcome or worked through and resolved,
persistence, developing a range of strategies and skills to bear a problem and the
flexibility to do so.
The relevance of mathematics in building resilience can be seen through a comment
expressed by one staff member participating in the project, in regard to a learning
context:
  'resilience': I thought it meant emotional, but rather it (also) means: ability to cope with
  being gob-smacked by hard concepts and, because of a different belief re learning,
  keeping on to master it. (Nadge, 2003)
Mathematics by nature, pure or applied, is full of 'hard' concepts. Helping students in
the way they approach hard concepts in the mathematics classroom and how they
view themselves as learners is a worthwhile pursuit if it increases their resilience to
life‟s setbacks.
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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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THE ROLE OF THE CLASSROOM
One might ask the question, Why should teachers be worried about children's
psychosocial development? People might think that it is the concern and role of the
parents, family friends, friends or perhaps counsellors to worry about a child's sense
of self if there is a problem. Does it really fall within the realm of the classroom
teacher (especially in a subject like mathematics; maybe in health or personal
development subjects it is more relevant)?
A survey to determine the relative effects of various factors on learning and
performance in students was recently carried out for the Australian Council for
Educational Research. It found that the role of the teacher or what happened in the
classroom was indeed of much greater influence than previously realised.
  Class or teacher effect (eg 54.7%)…surpasse(s) the impact made by student background,
  school factors and administration factors. (Rowe & Rowe, 2000)
In fact, the older the students were, the greater the influence the role of the teacher
and classroom played, especially in the final years of schooling as the students were
preparing for their matriculation examinations which, to a large extent, will
determine whether they can enter university. It can then be deduced that whatever the
teacher can do in the classroom to enhance learning and well being in the students
should be done.

THE CHALLENGE
The challenge at the school is to reach an equilibrium where the teachers‟ and
students‟ perceptions about teaching and learning beliefs are consonant, and to build
student resilience in the process. The role of the individual teacher is to engender an
atmosphere and implement strategies within the classroom to enable the students to
develop these outcomes. In order to meet this challenge we need to look at the
concepts about student learning and resilience, then determine how to apply them in
the mathematics classroom.

TWO USEFUL FIELDS OF PSYCHOLOGY RESEARCH
In trying to develop resilience in students, it is worthwhile to examine two fields of
research in Psychology which have defined factors influencing and attitudes held by
students which may impede or enhance resilience.



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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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Risk and Protection Theory
To shift the balance from vulnerability to resilience Rutter (1990) suggests that
intervention can take place in two ways: decreasing exposure to risk factors and
stressful life events, which is not always possible, or by increasing the number of
protective factors. He states, however that
  „…the search is not for broadly defined protective factors but rather for the
  developmental and situational mechanisms involved in protective processes.’ (Rutter,
  1990)
Werner and Smith (1982) suggest that positive relationships have a more profound
effect on a student‟s psycho-social state of mind than specific risk factors. While
resilience is regarded as a protective factor along with optimism, connectedness, self-
efficacy and motivation in the classroom, it appears that it is the synergistic effect of
the protective factors into a healthy state of mind which enables one to resist being
vulnerable to negative risk factors.
Goal Orientation
The notion of Goal Orientation as a frame of mind can impact on the way students
learn or, more importantly, fail to learn. Evidence suggests that students fall into two
groups according to how they react to difficulties when encountered. The first are
quick to give up in the face of perceived failure, whereas the second increase their
effort in the face of difficulty. Dweck (1998) describes these two groups in terms of
motivational patterns: the first are performance driven and believe that ability is a
given entity (entity theorists), static and unchangeable, whereas the second are more
task driven (incremental theorists), believing that ability is something that can be
developed and lead to mastery.

BUILDING RESILIENCE
The implications of these two theories suggest that we should be teaching, operating
and assessing in a classroom using various methods which enhance a positive attitude
towards learning. Let us consider some specific factors that previous research has
highlighted in building resilience.
    Resilience is not static but subject to change. Henderson and Milstein (1996)
     suggest that resilience can be built through
  …the provision of care and support through positive regard, setting and communicating
  high expectations and by providing opportunities for meaningful participation.

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    Students can change their beliefs: success is due to effort rather that innate
     ability. Dweck (1999) calls this „attribution retraining‟.
    Students need to become task driven, increasing effort rather than giving up in
     the face of difficulty (Simons, Dewitte & Lens, 2000).
    Talking about learning in the classroom, having time to discuss and think about
     responses to questions posed is conducive to believing that ability can be
     developed (McLaughlin, 2001; Perkins, 1992; Black & Wiliam, 1998).
    Resilience in students can be enhanced by the school they attend and by the
     particular subjects they study. Howard and Johnson (1998) suggest that
     language and mathematics are ideal media.
    Addressing the individual needs of students is an important factor in building
     resilience (McLaughlin, 2001a; Hunter, 2002).
    Formative rather than summative assessment is intrinsic to the perception that
     ability is not static (Black & Wiliam, 1998).
Having considered these resilience building aspects, we can now look at the
collection of data in the school to determine the current status of student resilience.
THE METHODOLOGY
The school has a population of approximately 60 teaching staff and 580 female
pupils, ranging in age from 12 years in Year 7 to 18 years in Year 12. The original
research was two-fold: a student survey, including an initial pilot group, and a
professional development session for staff.
An initial pilot group of 25 Year 10 students was randomly selected to complete the
student survey in order to refine it before administering to the larger sample. To get a
broad age selection for the larger student survey, it was decided to select half the
cohort in each of the years 7, 9 and 11. Alternating classes in the physical education
groupings were selected to gain a random selection within each year cohort. The
physical education classes are ungraded academically, so they gave a good cross-
section of student abilities.
The students were given a questionnaire containing ninety-three items, devised by a
committee of five staff volunteers. In the first ninety items the students could select
one of five responses ranging from „strongly agree‟ to „strongly disagree‟, and, in the
last three items, they could give an open-ended comment. The survey was divided
into topic headings:
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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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     „School and Me‟ – Questions 1-15
     „My teachers‟ – Questions 16-42
     „I am ready for the world in reference to‟ – Questions 43-55
     „In class, time is spent‟ – Questions 56-72
     „I learn well when‟ – Questions 73-90 and
     „Further comments‟ – Questions 91-93.
While not all items were of interest with regard to mathematics, twelve questions
related specifically to resilience, the analysis of which could lead to either a new
approach to the teaching of mathematics with a view to enhancing resilience or
confirmation that initiatives from other areas of research in mathematics education in
fact enhance student resilience, as well as student understanding of mathematics.
These twelve „resilience‟ questions were from the „My teachers‟ section and are
listed below:
My teachers
17. expect me to do my best                    31. show me how to reflect on my learning

18. set high standards for achievement         32. let me negotiate my learning
21. help me gain confidence in how to learn    33. empower me in my learning
24. know how I learn                           34. give me feedback that helps me learn

28. challenge me to do better                  39. help me set learning goals
30. help me to take risks in my learning       41. let me express my learning in different ways.


The responses to these questions would give an indication of the current state of
students‟ resilience. Other questions of interest relate to what goes on in the
classroom with the individual teacher. If we relate these to the research on what
builds resilience, we can see whether or not what we are doing is enhancing or
frustrating the building of resilience in students. We can then look specifically at the
activities in the mathematics classroom which could be utilized to increase resilience.
These questions were from two sections:



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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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In class, time is spent                       I am ready for the world in reference to
63. talking about learning                    48. my problem solving

65. reflecting on my own learning             49. my ability in mathematics
69. discussing my work with the teacher       51. making sound decisions
71. establishing learning goals               55. the way I evaluate my own work.

and


The pilot group was asked whether or not they agreed with the statement „I learn
from my reports‟. This was later omitted from the larger survey but the results are
worthy of mention.
During the staff professional development session, the staff was asked to „brainstorm‟
factors relating to student resilience. The results are discussed in the next section.
THE RESEARCH FINDINGS
A product of the professional development session was that teaching staff were able
to identify over ninety learning experiences which have the capacity to enhance
resilience in students. They contain one or more of the following six key elements
(Nadge, 2003):
       Empowerment
       Knowledge of self
       Goal setting
       Negotiation
       Risk taking
       Reflection
The student responses to the questions relating to resilience were analysed with the
following results.




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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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While there was strongest agreement that       There was weakest agreement that
   ‘…my teachers                                  ‘…my teachers
17. Expect me to do my best            (71%)   24. Know how I learn                    (15%)
18. Set high standards for achievement (47%)   30. Help me take risks in my learning   (22%)
28. Challenge me to do better          (35%)   31. Show me how to reflect on my learning (22%)
34. Give me feedback that helps me in my       32. Let me negotiate my learning        (18%)
learning                         (47%)’
                                               33. Empower me in my learning           (12%)
                                               39. Help set learning goals             (25%)


When asked about the frequency of learning processes in the classroom context, the
following were least frequent:
63. Talking about learning                                   25%
65. Reflecting on my own learning                            20%
69. Discussing my work with the teacher                      10%
71. Establishing learning goals                              19%
Students also felt that they were not „ready for the world’ in reference to „making
sound decisions (46%)’, the way I evaluate my own work (41%)’, my problem-solving
(38%)’, although they felt a little more confident with mathematics: „my ability in
mathematics (51%)’.
The pilot question „I learn from my reports‟ yielded only 36% agreement which
prompts one to wonder what is the value of the reports in their current summative
form.
Thus, while the teachers were able to identify key elements of learning which should
enhance resilience, the students did not perceive that the teachers were engaging
these elements in the day to day activities in the classroom. Further, the students did
not appear to display a number of characteristics of resilience.

UTILISING THE MATHEMATICS CLASSROOM TO FOSTER
RESILIENCE
While the Community Change Project did not set out to establish a link between
mathematics teaching and enhancing resilience in students, there could be a causal
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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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relationship between the two. Let us consider, in the light of the research findings
coupled with the theories discussed, what can be done in the mathematics classroom
to enhance resilience in students.
Rather than a fixed entity, resilience could be regarded as a dynamic quality, which
can be altered in the individual by environment, personal experiences and frame of
mind. This implies that resilience can be increased by exposing students to positive
resilience factors (Henderson and Milstein, 1996).
Perhaps we could start by considering our own beliefs about the way students learn.
Is it „entity‟ or „incremental‟? As teachers we need to have a positive regard for our
students in that we need to see them as incremental learners. For instance, how often
does a student say “I‟m no good at geometry proofs”, or “I can‟t do fractions”? We
need to challenge the „entity‟ learner in his belief that his ability is fixed. Teachers
can take a key role in „attribution retraining‟. (Dweck, 1999) We need to train
students to focus on effort rather than ability, as they will then begin to persist and
seek help. Failure becomes a different concept. Rather than regarding failure as a
reflection of self-worth, the student begins to see it as a result of insufficient effort or
technique. He or she will then tend to persevere more often. In this way we can
address the question of how to help students reflect on their learning (Q31).
Setting high expectations (Q17 & Q18) in terms of the mathematics classroom does
not necessarily mean communicating the aim that students must get all the questions
correct, in fact, quite the contrary. Referring back to Goal Orientation, research by
Simons, Dewitte and Lens (2000) suggests that those students who hold „performance
goals‟ will pass up learning opportunities that have a risk of error or failure. They
will only attempt questions with a known answer and concentrate on getting them
correct as fast as possible.
In order to help students to overcome this static belief, we need to engender the
alternative approach: to focus on learning and to develop a willingness to pursue
questions with ambiguous outcomes, i.e. taking greater risks in their learning (Q30).
For example, rather than saying “ok, do these questions and the first one to get them
all correct wins a chocolate”, perhaps the teacher could say “ok, let‟s try these
questions and there is a chocolate for anyone who can explain to the class how to go
about attempting the last question”. One could also say “I‟m not so much interested
in the answer but how you got it.” Another technique might be to give a set of
questions without the answers. Students in mathematics often like to have the
answers „to work back from‟. Having no answers forces them to concentrate on the

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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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process and skill acquisition rather than „getting the right answer‟. In this way they
will be “empowered” in their learning (Q33).
In order to facilitate opportunities for „meaningful participation‟ in the classroom, the
teacher needs to set and maintain a classroom climate which is conducive to dialogue,
not just about the subject matter, but about learning (McLaughlin, 2001b), i.e. talking
about learning (Q63) is of value in itself. Statistics collated by Perkins (1992)
suggest that only 5% of class time is spent on discussion and Black and Wiliam
(1998) found that the average time teachers waited before asking for a response to a
question was 0.9 seconds. We can see that this type of classroom climate reinforces
the entity concept, where students must be ready with an immediate response rather
than time to think or explore the nuances of the question.
Mathematics is often regarded by outsiders as „black and white‟, „right or wrong‟ and
perhaps this is an accurate observation of what happens in the classroom. We need to
promote cooperation before competition, mastery of skills and the setting of authentic
problem-solving. Mathematics students are forever asking, “when are we ever going
to use this?” Some „problem-solving‟ questions are often contrived in a pseudo-
context rather than reflecting anything real or utilizing valid skills of analysis. Open
questioning can be used to promote exploration of ideas, discussion of approaches to
find a solution and students describing their reasoning. Thus the students will be
discussing their work with the teacher (Q69).
Howard and Johnson (1998) suggest that schools can play a major role in fostering
resilience and that it should be through such subjects as language and mathematics.
By its abstract and analytical nature, mathematics, they believe, is such a crucial
subject that focusing on the teaching for mastery of mathematics will build resilience.
It encourages realistic problem-solving (rather than contrived) and provides the
opportunity for real achievement and the possibility of authentic success. This
emphasis on authenticity is not unintentional. We must be aware of the significant
impact that our responses can have on a student‟s reaction to success or failure.
Dweck (1999) notes that hollow or careless praise for finishing quickly can actually
be counterproductive as it reinforces mediocrity and easy success (the entity
approach) rather than a problem-solving approach. We must give feedback that helps
them in their learning (Q34) and ability to solve authentic problems (Q48). Teachers
need to be conscious of praising perseverance, effort and even finding errors rather
than „doing a good job‟.


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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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McLaughlin (2001a) notes the importance of the personalized approach in building
resilience or the development of a one-to-one relationship between the teacher and
student. In attempting to cater to the individual student‟s needs the teacher can tap
into Gardner‟s nine multiple intelligences to allow students to feel comfortable with
their learning. For instance, Hunter (2002) found that those with strengths in the
interpersonal intelligence preferred group activities or projects, whereas students with
the classical intelligences, such as verbal and logical, were happy with the traditional
modes of learning such as exercises and examinations. Teachers need to analyse each
student individually to determine his or her strengths and accommodate them with
appropriate activities. In this way, teachers will know how their students learn (Q24).
The way we assess mathematics can also build resilience if done in an appropriate
way. In the past, there has been much emphasis on „getting it right‟, as reflected in
the interminable „speed and accuracy‟ tests from the 1960s. While facility with
number is essential, recent research has found that formative rather than summative
assessment is more conducive to better learning and building resilience. The study by
Black and Wiliam (1998) found that the summative approach, which makes
comparisons with peers, is intrinsically competitive,
  In consequence, assessment feedback teaches pupils with low attainments that they lack
  ‘ability’, [the entity approach] so they are de-motivated, believing they are not able to
  learn.
Summative assessment is performance based, whereas the formative approach
focuses on the particular qualities of an individual student‟s work, without
comparison with the cohort. Formative assessment gives feedback on what the
student can do to improve the quality of his own work (Q39 & Q55). As mentioned
before, the historical nature of mathematics being „right or wrong‟ lends itself to
summative comparisons. By perhaps concentrating on open-ended tasks, without a
perceived solution, or by awarding marks for method, reasoning and approach,
students will benefit from a new perception that success is through acquired skills
rather than correct answers. The students may then find their reports more
meaningful and learn from them (addressing the problem arising in the pilot study
and Q65).

CONCLUSION
Fostering resilience in students is a worthwhile pursuit as it can lead to better learning
and invulnerability to negative influences in life. As Howard and Johnson (1998)
noted:
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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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  Children in discordant and disadvantaged homes are more likely to demonstrate resilient
  characteristics if they attend schools that have good academic records and attentive,
  caring teachers….individual teachers can play an important role in resilient children’s
  lives.
The academic discipline of mathematics is an ideal medium through which to build
resilience due to its intrinsic abstract, problem-solving nature. It is full of „hard
concepts‟. We have seen that what we say and do in the classroom is imperative to
good learning and fostering resilience in students‟ lives. Simple acts such as listening
sympathetically, gaining trust and providing good advice can help to build self-
esteem. Real praise for real success promotes a willingness to persevere when a
solution is not clearly within reach. Although family and community also provide
protective processes, the school and individual teacher in the classroom can make a
positive contribution to a child‟s life. We can do this in the mathematics classroom,
using a number of strategies, by allowing students to become incremental learners,
who perceive success through effort rather than innate ability. Thus the individual
will be able to resist the impact of negative circumstances because he or she will see
the situation as transitory rather than a permanent blot on life.
The Community Change Project has identified a number of characteristics of
resilience which appear to be lacking in many of the surveyed students. These results,
while not specifically relating to the teaching and learning of mathematics, have
implications for mathematics teaching and teachers. Perhaps many resilience-
enhancing techniques are already utilized in mathematics classrooms, but on an
implicit level. The challenge is to raise the level of consciousness in teachers so that
these techniques become explicit.


References:
Black, P., & Wiliam, D. (1998). Inside The Black Box, British Educational Research Assocn, UK
Dweck, C. (1998). Motivation and Self Regulation Across the Lifespan, Cambridge: Cambridge
University Press.
Dweck, C. (1999). Self-Theories: Their Role in Motivation, Personality and Development, Essays
in Social Psychology. Philadelphia, PA: Psychology Press
Henderson, N., & Milstein, M. (1996). Resiliency in Schools. California: Corwin Press
Howard, S., & Johnson, B. (1998). Tracking Student Resilience, AARE Conference Proceedings,
Adelaide, Australia
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Icmepaper04 Effecting student resilience via the mathematics classroom: from
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Hunter, J. (2002). Utilising Multiple Intelligences to Enhance Teaching and Learning in
Mathematics, International Conference for the Teaching of Mathematics Conference Proceedings
93, Crete
McLaughlin, C. (2001a). The ARTE Project, University of Cambridge Faculty of Education
McLaughlin, C. (2001b) Care and Education – Centre or Periphery? Pastoral Care in Education, 19
(4) p3
Nadge, A. (2003). Community Change Project, Association of Independent Schools, NSW
Australia
Perkins, D. (1992). Smart Schools: Better Thinking and Learning for Every Child. New York: The
Free Press
Rowe, K. S., & Rowe, K. J. (2000). Report for Australian Council for Educational Research
Rutter, M. (1990). Psychosocial Resilience and Protective Mechanisms. Oxford Review of
Education, 25 (3)
Rutter, M. (1999). Resilience Concepts and Findings: Implications for Family Therapy, Journal of
Family Therapy 21, 119
Rutter, M., Maughan, B., Mortimore, P., & Ouston, J. (1979). Fifteen Thousand Hours, London:
Open Books
Simons, J., Dewitte, S., & Lens, W. (2000). Wanting to Have vs. Wanting to Be: The Effect of
Perceived Instrumentality on Goal Orientation. British Journal Of Psychology, 91, 335-351
Werner, E., & Smith, R. S. (1982). Vulnerable but Invincible: A Longitudinal Study of Resilient
Children and Youth. New York: McGraw Hill




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