CLES
An
instrument for monitoring the development
of
constructivist learning environments
Peter C Taylor,
Barry J Fraser & Loren R White
National Key Centre
for School Science and Mathematics
Curtin University,
Australia
Paper presented at
the annual meeting of the American Educational Research Association, New
Orleans, April 1994
abstract
A revised version of the Constructivist Learning
Environment Survey (CLES) has been developed for researchers who are interested
in the constructivist reform of high school science and mathematics.
Constructivist theory and critical theory have been combined to create a
powerful interpretive framework for examining science and mathematics teaching.
The cognitive focus of the earlier instrument has been broadened by including a
concern for the sociocultural forces that shape the rationality of traditional
science and mathematics classrooms. The revised CLES is concerned with the
extent of emphasis within a classroom environment on: (a) making science and
mathematics seem relevant to the world outside of school; (b) engaging students
in reflective negotiations with each other; (c) teachers inviting students to
share control of the design, management, and evaluation of their learning; (d)
students being empowered to express concern about the quality of teaching and
learning activities; and (e) students experiencing the uncertain nature of
scientific and mathematical knowledge. The revised CLES was trialled in an
innovative empiricallyoriented mathematics classroom. The results of the
study, which combined statistical analyses and interpretive inquiry, confirmed
the practical viability of the CLES and generated important insights into use
of learning environment questionnaires in classrooms undergoing constructivist
transformation.
Introduction
At AERA in 1991,
we presented a new learning environment instrument — the Constructivist Learning Environment Survey (CLES) — that we had
designed to enable teacherresearchers to monitor their development of
constructivist approaches to teaching (Taylor & Fraser, 1991). Our goal in
designing the original CLES was to provide teachers with an efficient means of
learning more about their students' perceptions of the extent to which the classroom
learning environment enabled them to reflect on their prior knowledge, develop
as autonomous learners, and negotiate their understandings with other students.
Although the original CLES was found to be
psychometrically sound with a sample of over 500 high school students in
science and mathematics classes, and was found to be very useful in a number of
studies (Roth & Bowen, in press; Roth & Roychoudury, 1993, 1994;
Watters & Ginns, 1994), we felt that its theoretical framework supported
only a weak program of constructivist reform. Our ongoing research program had
revealed major sociocultural constraints to the development of constructivist
teaching approaches (Taylor, 1992, 1993, 1994; Taylor & Williams, 1993). We
felt that a revised CLES should empower teachers to address these restraints.
Subsequently, in the revised CLES we incorporated a critical theory perspective on the sociocultural framework of the
classroom learning environment (Grundy, 1987; Habermas, 1972, 1984), and
developed a critical constructivist
theoretical framework.
The purpose of this paper is to present the rationale
of the revised CLES, especially its critical constructivist theoretical
framework, and to discuss what we learned as a result of our attempts to
determine the practical viability of the questionnaire. The redesign of the
CLES involves the trialling of the questionnaire in high school science and
mathematics classrooms. This paper focuses on the results of a collaborative research study (Kyle &
McCutcheon, 1984; Watt & Watt, 1982) that involved one of the authors
(Loren White) adopting the role of teacherresearcher
and introducing an innovatory empiricallyoriented mathematics project (The Egg
Project) into his Grade 8 mathematics classroom.
Following a brief overview of the field of classroom
learning environment, the second section of the paper presents the theoretical
framework of critical constructivism
that underpins the scales of the revised CLES. The third section discusses the
research design of the study which combines quantitative and qualitative
approaches to data generation and analysis. The fourth section presents the
results of the study which are organised as three interpretive research
assertions and evidence that warrants them. In the concluding section, we
reflect on the main results and consider their implications for future research
involving the use of the revised CLES for monitoring classroom learning
environments under transformation.
BACKGROUND: FIELD OF CLASSROOM ENVIRONMENT
Over the
previous two decades or so, considerable interest has been shown
internationally in the conceptualisation, assessment, and investigation of
perceptions of psychosocial characteristics of the learning environment of
classrooms at the elementary, secondary, and higher education levels (Chavez,
1984; Fraser, 1986, 1989, 1994; Fraser & Walberg, 1991; MacAuley,
1990). Classroom environment
instruments have been used as sources of both predictor and criterion variables
in a variety of research studies.
Use of
student perceptions of classroom environment as predictor variables in several
different countries has established consistent relationships between the nature
of the classroom environment and various student cognitive and affective
outcomes (Fraser, 1986; Haertel, Walberg & Haertel, 1981; McRobbie and
Fraser, 1993). For example, Fraser and
Fisher's (1982) study involving 116 Australian science classes established
sizeable associations between several inquiry skills and sciencerelated
attitudes and classroom environment dimensions measured by the Classroom Environment Scale and the Individualized Classroom Environment
Questionnaire. Furthermore,
research involving a personenvironment fit perspective has shown that students
achieve better where there is greater congruence between the actual classroom
environment and that preferred by students (Fraser & Fisher, 1983).
Studies
involving the use of classroom environment scales as criterion variables have
revealed that classroom psychosocial climate varies between Catholic and
government schools (Dorman, Fraser and McRobbie, 1994) and between
coeducational and singlesex schools (Trickett, Trickett, Castro &
Schaffner, 1982). Both researchers and
teachers have found it useful to employ classroom climate dimensions as process
criteria of effectiveness in curriculum evaluation because they have
differentiated revealingly between alternative curricula when student outcome
measures have shown little sensitivity (Fraser, 1981; Fraser, Williamson &
Tobin, 1987). Research in the USA
(Moos, 1979), Australia (Fraser, 1982), The Netherlands (Wubbels, Brekelmans
& Hooymayers, 1991), and Israel (Raviv, Raviv & Reisel, 1990) compared
students' and teachers' perceptions and found that, first, both students and teachers
preferred a more positive classroom environment than they perceived as being
actually present and, second, teachers tended to perceive the classroom
environment more positively than did their students in the same classrooms. In promising smallscale practical
applications, teachers have used assessments of their students' perceptions of
their actual and preferred classroom environment as a basis for identification
and discussion of actualpreferred discrepancies, followed by a systematic
attempt to improve classrooms (Fraser & Fisher, 1986).
Some of the
exciting recent lines of classroom environment research which are still in
progress involve: investigating the links between and the joint influence of
classroom, school, family, and other environments on students' outcomes (Moos,
1991); incorporating classroom environment as one factor in a multifactor
model of educational productivity (Fraser, Walberg, Welch & Hattie, 1987);
evaluating and investigating teacherstudent interpersonal relationships in the
classroom (Wubbels and Levy, 1993); exploring ways in which classroom
environment instruments can be used to advantage by school psychologists
(Burden & Fraser, in press); incorporating learning environment ideas into
teacher education (Fraser, 1993); investigating changes in classroom
environment during the transition from elementary to high school (Midgley,
Eccles & Feldlaufer, 1991); and incorporating the evaluation of classroom
environment in teacher assessment schemes (Heroman, Loup, Chauvin & Evans,
1991).
Critical
Constructivist Framework
The original version of the CLES was based on a theory
of constructivism that underpins recent research in science and mathematics
education that is concerned with developing teaching approaches that facilitate
students' conceptual development (Driver, 1988, 1990; Treagust, Duit, &
Fraser, in press). This conceptual change
research highlights: (1) the key role of students' prior knowledge in their development of new conceptual
understandings, especially the problematic role of students' alternative
conceptions; and (2) the reflective process of interpersonal negotiation of meaning within the
consensual domain of the classroom community.
However, our research on teachers' development of
constructivist pedagogies has shown how readily traditional teachercentred
classroom environments can assimilate conceptual change perspectives and remain
largely unchanged (Taylor, 1992, 1993, 1994). We have found that the
rationality of traditional teachercentred classrooms is dominated by two
cultural myths: (1) an objectivist view of the nature of scientific and
mathematical knowledge; and (2) a complementary technical controlling interest
that views the curriculum as a product to be delivered. If classroom
learning environments are to feature negotiation and meaningmaking, then
teachers need to be empowered to deconstruct these repressive myths.
Deconstructing Cultural Myths
From an objectivist (or Platonic) perspective,
scientific (or mathematical) knowledge seems to exist independently of our
minds, to be static and unchanging over time, and to be the embodiment of
universal Truths. If this foundationalist
perspective represents a true account of scientific and mathematical knowledge,
then teachers are entitled to adopt the role of experts whose task is to
transmit to their students accurate versions of the universal body of Truths.
However, during the second half of this century, the foundational view of knowledge has been challenged and largely
discredited by philosophers of science (Feyerabend, 1962; Kuhn, 1962; Polanyi,
1959; Toulmin, 1953) and philosophers of mathematics (Davies & Hersch,
1981; Hersch, 1986; Kitcher, 1984; Kline, 1953, 1980).
In the field of science education, Solomon
(1987, 1991) and Tobin (1990, 1993) have made accessible to science educators
an alternative view of the nature of scientific knowledge — social constructivism. Likewise, in
mathematics education, researchers such as Bauersfeld (1989, 1992) and Ernest
(1991, 1992) have developed social constructivist philosophies. The
interlinking of science and mathematics education by means of a constructivist
philosophy is evident in the work of Bauersfeld, Ernest and Tobin, all of whom
have built their theories by adapting von Glasersfeld's (1990, 1993) radical constructivism.
Of course, our scientific and mathematical knowledge
must be validated against community norms and, for Solomon (1987), who builds
on the sociology of knowledge of Berger and Luckman (1966), this intersubjectivity is achieved by means
of negotiating and consensus building, which are activities that are shaped by
the social and cultural frameworks within which they occur. For Solomon and
Cobb (1989), these activities are undertaken by both professional
scientists/mathematicians and students of science/mathematics, within their
respective communities.
From a social constructivist perspective, the roles of
teachers and students are dramatically transformed. Teachers become mediators of students' encounters with
their social and physical worlds and facilitators
of students' interpretations and reconceptualisations. A key role is to assist
students to problematise and reconstruct their existing conceptions and to
determine the viability of their new ideas in the social forums of the
classroom and the broader community (e.g., parents). However, the possibility
of teachers shaping classroom learning environments in accordance with a social
constructivist perspective is dependent on the prevailing curriculum and
assessment structure.
The Technical Interest
The philosopher, Jurgen Habermas (1972, 1984),
presents three fundamental human interests  technical, practical, emancipatory  that govern our ways of
knowing and acting towards one another. He argues that the technical interest, which underpins positivist views of the nature
of science, is associated with selfinterest, and the control and exploitation
of nature. Curriculum theorists who have adopted Habermas's epistemology argue
that a technical interest has prevailed as the dominant mythology of the West's
education professions for most of this century (Apple, 1979; Giroux, 1983;
Grundy, 1987; Schon, 1983). As a result, a professional culture has developed
that renders the concept of curriculum
in terms of the objectivist metaphor of
a container of immutable knowledge — curriculum as product — which the teacher is
obligated to deliver. Coupled with the traditional summative assessment policy,
a powerful cultural mythology has developed that holds the teacher accountable
for the delivery of knowledge to students. It is not surprising, therefore,
that in traditional science classrooms the locus of control of learning
activities is believed to lie with the teacher (who, in most Statecontrolled
curricula, serves as an agent for an external authority). In these classroom
environments, students are required to comply unquestioningly with the
teacher's instructional prescriptions and with the prescribed social norms of
the classroom environment. At first glance, this curriculum straightjacket
seems to offer little prospect for social constructivist teaching approaches to
flourish.
The Practical Interest
However, recent developments in curriculum theory are
highly compatible with a social constructivist reform agenda in the science
classroom. The critical theory of the
Habermas (1972, 1984) provides a powerful conceptual framework for
understanding the rationality of social institutions, such as schools, and the
political interests that are served by traditional notions of curriculum. In
essence, Habermas argues that in order for a society to flourish the
traditional and predominant technical
selfinterest in control, prediction and manipulation (often associated
with economicallydriven exploitative practices) must be counterbalanced by a practical interest in the moral welfare
of others and an emancipatory interest
in becoming critically aware of cultural myths that distort our understandings
of self and others.
In the context of education, a practical interest is
associated with understanding and respecting the meaningperspectives of
others, and gives rise to opportunities for students to: (a) negotiate with the
teacher about the nature of their learning activities; (b) participate in the
determination of assessment criteria and undertake selfassessment and
peerassessment; (c) engage in collaborative and openended inquiry with fellow
students; and (d) participate in reconstructing the social norms of the
classroom. Many of these ideas have been embraced by constructivist mathematics
educators (Cobb, 1989). The practical interest might also be expressed in
classrooms by means of establishing an open
discourse, that is, communication
that promotes respect for participants, aims at understanding others'
understandings, and legitimates noncoercive actions and selfdisclosure of
goals, values, frustrations and beliefs (Taylor & Williams, 1993).
The Emancipatory Interest
However, we believe that the activation of a practical
interest constitutes only a part of the necessary reform agenda for traditional
science and mathematics classrooms. There is a need for an emancipatory
interest that gives rise to opportunities for teachers and students to become
critically aware of the influence of the repressive myths of objectivism and control
that govern the social reality of institutions and classrooms and that
constrain the development of open discourses.
We do not believe that it is desirable to try to
eliminate the technical interest. It constitutes one of the fundamental ways of
knowing and acting that underpin our society. Rather, we advocate the
achievement of a more harmonious rationality that is based on a balance between
the technical, practical and emancipatory interests. Therefore, in addition to an open discourse, we need to establish
a critical
discourse that serves to reveal and subject to critical scrutiny the
prevailing (invisible) myths that disempower teachers and students from
developing more harmonious classroom learning environments.
It was with these goals in mind that we redeveloped
the scales of the CLES and trialled it in a high school mathematics classroom.
SCALES OF THE CLES
The revised version of the CLES comprised five scales
each of which was designed to obtain measures of students' perceptions of key aspects
of their mathematics classroom learning environment. The CLES comprised 40
items arranged in traditional cyclic order.
Personal Relevance Scale
In revising the CLES, we were mindful of the need to
assist teachers who are interested in taking their first steps towards
developing constructivist pedagogies to develop teaching strategies that aim to
account for students' preconceptions.
However, we wanted teachers to broaden their pedagogical focus beyond students'
abilities to recall accurately previously learned formulae, rules, and laws,
and take account of the rich tapestry of experiences that students bring with
them from their outofschool worlds. Consequently, we developed the Personal
Relevance scale that is concerned with the perceived relevance of school
mathematics to students' outofschool experiences. We are interested in
teachers making use of students' everyday experiences as a meaningful context
for the development of students' mathematical knowledge.
Shared Control Scale
From a critical constructivist perspective, we are
concerned that students have opportunities to develop as autonomous learners.
We believe that this can be achieved partly by providing opportunities for
students to exercise a degree of control over their learning that extends
beyond the traditional practice of working 'independently' in class on sets of
prescribed problems. The Shared Control scale is concerned with students being
invited to share control with the teacher of the total learning environment,
including the design and management of learning activities, determining and
applying assessment criteria, and participating in the negotiation of the
social norms of the classroom. It seems to us that the rationale for this scale
fits well with the notion of a portfolio
culture (Duschl & Gitomar, 1991) that places a major emphasis on
students monitoring their own conceptual development.
Critical Voice Scale
Of course, we realise that many teachers will feel
constrained, at least in the shortterm, by their externallymandated interest
in delivering the curriculum and covering curriculum content. This
technical curriculum interest directs teachers' sense of accountability for
curriculum implementation away from the classroom and towards external
curriculum and assessment authorities. However, we believe that teachers also
should be accountable to their students for their pedagogical actions. From a
critical theory perspective, which promotes an interest in student empowerment,
we would like teachers to demonstrate willingly to the class their pedagogical
accountability by fostering students' critical attitudes towards the teaching
and learning activities. The Critical Voice scale assesses the extent to which
a social climate has been established in which students feel that it is
legitimate and beneficial to question the teacher's pedagogical plans and
methods, and to express concerns about any impediments to their learning.
Student Negotiation Scale
Although we recognise the importance of the teacherstudent negotiations set out in
the first three scales, we wish to emphasise in the CLES the importance of
developing instructional strategies that promote studentstudent negotiations
as a central classroom activity. The Student Negotiation scale focuses on whether
teachers' pedagogical attention extends beyond the traditional social activity
of students helping each other to work out the correct answer to a problem. The
scale assesses the extent to which opportunities exist for students to explain
and justify to other students their newly developing ideas, to understand other
students' ideas and reflect on their viability and, subsequently, to reflect on
the viability of their own ideas.
Uncertainty Scale
One of the major
constraints to constructivist pedagogical reform is the popular myth that
Western science and mathematics are universal, monocultural (or accultural)
endeavours that provide accurate and certain knowledge of objective reality.
The myth of certainty implies that mathematical and scientific knowledge exists
independently of collective human experience. By contrast, we want teachers to
provide opportunities for students to experience the inherent uncertainty and
limitations of scientific and mathematical knowledge. The Uncertainty Scale has
been designed to assess the extent to which opportunities are provided for
students to experience scientific and mathematical knowledge as arising from human experience and values, as
evolving and insecure, and as culturally and socially determined.
Items in Revised CLES Scales
As a result of
this study, the five scales of the revised CLES were refined and reduced to
seven items each. The final version of the revised CLES for use in mathematics
classes is provided in the Appendix.
The allocation of the 35 items to the 5 scales is shown in Table 1.
Table 1
Allocation of Items to CLES Scales
Scale Item
Numbers
Personal Relevance 1 7 13 19 25 30 37
Mathematical Uncertainty 2 8 14 20 26 31 38
Critical Voice 3 9 15 21 27 32 39
Shared Control 4 10 16 22 28 33 40
Student Negotiation 5 11 17 23 29 34 41
Items without their
item numbers underlined are scored 5, 4, 3, 2 and 1, respectively, for the
responses Almost Always, Often, Sometimes, Seldom and Almost Never. Items with their item numbers underlined are
scores in the reverse manner. Omitted
or invalid responses are scored 3.
Attitude scale
comprising Items 6, 12, 18, 24, 29, 35 and 42. These attitude items are scored in the same
way as the CLES items.
The final version
of the revised CLES for use in science classrooms has identical scales except
that a Scientific Uncertainty scale
replaces the Mathematical Uncertainty
scale
practical
viability of the cles
After redeveloping
the five scales of the CLES, we wanted to determine their practical viability.
That is, we were interested in finding an answer to the question about whether
they could be used to generate meaningful data about students' perceptions. In
order to assess the meaningfulness of the CLES data, we needed to generate data
from other sources and determine the extent to which the CLES data could be
combined with other data to generate a plausible account within a particular
context. This need gave rise to the following research question.
Research Question
The main research
question of the study was whether the CLES could be used to generate a plausible account of students'
perceptions in a constructivistoriented classroom? An interpretivist warrant for judging the efficacy of the
CLES was appropriate because our goal is to provide a means of enabling
teachers to understand better the perspectives of their students. The warrant
of plausibility recognises that the
inquirer's perspective is contextdependent and allows for multiple
interpretations to be made. In other words, by using this warrant, we are
claiming that multiple learning environments exist in the same physical space.
We were mindful,
therefore, of the need to avoid allowing only the traditional warrants of the
psychometric paradigm to prevail. We did not wish to fall victim to statistical determinism when evaluating
the efficacy of individual items. However, we also were mindful of the need for
an inclusive warrant that would enable us to combine qualitative and
quantitative data analyses. So, how did we define plausibility? We decided that
the warrant of plausibility would comprise the following criteria which allowed
us to make judgements about the educational significance of the results of the
trial.
• The
extent to which the CLES generated intelligible
and dependable responses from
students.
• The
extent to which student responses to groups of items (identified as scales)
aggregated in a coherent and meaningful way.
• The
extent to which the CLES data were consistent
with data from other sources.
Research Methodology
We adopted an interpretive
research approach (Erickson, 1986) that enabled us to conduct an indepth
investigation of a single high school mathematics classroom. The revised
version of the CLES was trialled in a Grade 8 mathematics class in a government
high school in the Perth metropolitan area. The purposes of the trial were to
determine the practical viability of the five scales and to reduce the 40item
CLES to a more economical 35 items (i.e., 7 items/scale). An interpretive
research approach framed the study and was used to investigate the implications
of statistical analyses. For each scale, we calculated: (1) wholeclass and
smallgroup mean scores and standard deviations; (2) a Cronbach alpha
reliability coefficient; and (3) itemscale correlation coefficients. For the
five scales, we calculated a scale intercorrelation matrix.
Major
methodological strategies that we attempted to employ for the purpose of
safeguarding our warrant of plausibility were drawn from the field of
interpretive research (Denzin, 1988; Eisenhart, 1988; Erickson, 1986; Mathison,
1988), and included:
(1) minimising
underdetermination of our theorising by employing triangulation in the form of multiple data sources, multiple
methods of generating data, and multiple investigators;
(2) avoiding
the predominance of our preconceptions by generating emergent research questions and assertions (i.e., grounded theory) and searching for disconfirming evidence;
(3) understanding
the context of participants' actions by immersing
ourselves in the field;
(4) establishing
a rapport with students so that interviews would be informal good conversations; and
(5) avoiding
unethical actions by maintaining our concern for safeguarding students'
learning opportunities and our guarantees of confidentiality and anonymity.
Nevertheless, we
experienced several problems in safeguarding our warrant. Given the time
constraints, it was not possible for the participantresearcher to attend all
lessons during the 10week project or to interview students on more than one
occasion.
The TeacherResearcher
We designed a collaborative research study (Kyle &
McCutcheon, 1984; Watt & Watt, 1982) in which one of us (Loren White)
adopted the role of teacherresearcher
in his own classroom. In this role, Loren was a member of the research team and
participated in both the ongoing generation and analysis of quantitative and
qualitative data. As a teacher, Loren was wellsuited to the study. One of his
first tasks was to appraise the appropriateness for high school students of the
language and content of a draft of the revised CLES. Loren tested the items for
sense and clarity with high school students in Grades 811 during private study
sessions. Discussions with students resulted in several revisions and a modified
form of the 40item CLES (i.e., 5 scales each of 8 items) which was ready for
indepth evaluation with a mathematics class.
We were keen to
focus on a class where the teacher was involved in studentcentred practices
instead of mostly 'stand and deliver' practices. Loren believed that his Grade
8 mathematics classroom might have some of the characteristics of the learning
environment assessed by the scales of the CLES. He proposed that a special fiveweek mathematics activity that he
had been planning (that we came to call the 'Egg Project') would be an
appropriate context for our study.
The Egg Project
asked students to find a simple way to estimate the surface area of an egg.
From Loren's perspective, the pedagogy of this project was based on giving
students experience with openended problem solving and investigation. The
students were expected to make choices about processes including the
mathematics. As there were no known simple formulations to be 'found' easily in
books or to appear miraculously from somewhere, the challenge to students was
to be creative, and then validate their methods and results. Loren considered
that the project provided opportunities for students to engage in group work,
oral and written reports, and evaluation of peers. The project also was an
opportunity to give students experience with mathematical modelling, empirical
processes, multiple openended solutions to problems, and the uncertainty of
mathematics.
Framing the Egg
Project was Loren's pedagogical intention to integrate his students'
experiences in mathematics and science. Throughout the year, he had been
collaborating with the Grade 8 science teacher to emphasise the interdependence
of the two disciplines. Loren expected the students to use their science experiences
to observe, measure, collect and organise data, hypothesise, test, evaluate and
theorise. The fiveweek Egg Project provided his Grade 8 students with the
first extended opportunity to engage in these empirical activities in the
mathematics classroom.
Currently, Loren
is a PhD candidate at Curtin University. At the time of this study, he was
teaching parttime at the school in this study. He is an experienced teacher of
13 years, and has 10 years working experience in noneducational environments
prior to entering the teaching profession. Loren is aware of many forms of
constructivist theories and the associated pedagogical principles put forward
by constructivist educational theorists. He accepts the view that the Egg
Project meets much of the ideal discursive practices considered necessary by
constructivists to enhance learning in a classroom. However, he did not
consciously have particular key principles of constructivist theory in mind
when developing this project.
The Egg Project
evolved from a need to give the students, at this stage in their program of
study, an opportunity to synthesise many of their understandings of mathematics
and science. This was at the middle of the third term of a fourterm school
year. Loren's pedagogy comprises a constantly evolving set of ideals arising
from his life experiences. Foremost is his desire to consider students as
people first and teaching as a collaborative practice with students to help
them meet their expectations of school as tempered by the expectations of
others, such as parents and community. Constructivism, like many other isms is a useful framework for Loren for
rationalising many of his pedagogical principles and for reflecting on
classroom practices.
Key components of
the Egg Project were its empirical basis for justification, the ongoing
discourses between students and with the teacher, and redeemable assessment.
The last of these is a process of assessment where students are able to improve
their product in response to comments made by assessors, whether peer or
teacher. This can involve several rewrites or presentations, but grading is not
finalised until the students indicate the end of revision or until the end of
the course. The purposes of such assessment are to maintain a dialogue between
assessors and assessee over the criteria for judgment and, in so doing, keep
the mathematics and related concepts within the discourse of future activities.
Thus, a recursive aspect of learning becomes central to students' classroom
experience, enabling the benefits of reflection and the tyingin of later
experiences to enhance the sense making of earlier experiences for an
'improved' outcome or grade. This does not imply that the teacher or peers
'work' on students until they think in the same way. Rather, the goal is to
encourage students to be effective in presenting their theories.
The Students and ParticipantResearchers
The Grade 8
mathematics class in the study consisted of mathematically able students as
judged by the feeder elementary schools. (In Western Australia, Grades 17
comprise the elementary school, while Grades 812 make up the high school). The
mathematics courses chosen for these students assume that students are able to
continue the Grade 8 phase of the Statemandated K10 mathematics curriculum
without revision components. The Grade 8 course combined the topics of number, function, measurement, and space and inference, and included
investigations, problem solving, puzzle work, games and projects.
The other
researchers in the team had developed an earlier version of the CLES (Taylor
& Fraser, 1991) and were interested in utilising this study to trial the
new version. One of them adopted the role of participantobserver and visited
the class for the duration of the Egg Project. During lessons, he observed
wholeclass sessions and inquired into students' activities while they worked
in small groups both inside and outside the classroom. He recorded his
observations in the form of field notes, conducted afterlesson discussions
with the teacher, and interviewed selected groups of students on completion of
the project.
Attitude Scale
For purposes of
establishing the concurrent validity of the five CLES scales, we included a
sixth scale to assess students' attitudes towards their mathematics class. We
expected that favourable perceptions of the classroom learning environment
would be related to favourable attitudes towards the class. The Attitude scale
comprised items that asked students about their anticipation of the class,
their sense of the worthwhileness of the class, and the impact of the class on
their interest, enjoyment and understanding.
The attitude scale was based partly on items in the Test of Science Related Attitudes (TUSRA; Fraser, 1981).
Administration of the CLES
At the midpoint
of the fiveweek Egg Project (i.e., after completion of nine lessons), Loren
requested the class to complete the 40item revised version of the CLES. This
timing was chosen because it seemed that a relatively stable classroom
environment had been established. Loren explained to the class that the purpose
of the activity was to help us trial a questionnaire that we had designed to
assist teachers to obtain a better understanding of their students and,
consequently, develop more effective teaching approaches. In this way, we
attempted to make students feel that they were participating in a research
activity that aimed to improve the quality of teaching and learning.
Although we wanted
to identify individual student responses for the purpose of conducting
followup interviews, we were mindful of the need to ensure the integrity of
students' responses. To ensure that students felt free to express their genuine
opinions we offered them a choice of writing on the questionnaires either their
own name or a fictitious name of the group with which they had worked during
the project. As a result, eight groups were identified whose membership ranged
from two to six students, In addition,
there were two students who had appeared to work individually in class.
STATISTICAL ANALYSIS OF CLES
RESPONSES
In this section,
we discuss first the results of the initial statistical analysis of students'
responses to the CLES. On the basis of
these results, we selected students for interviews. The selection criteria and the interviewing process are
subsequently discussed.
The revised CLES
has a 5point Likerttype frequency response scale which comprises the
categories: almost always (5 points),
often (4), sometimes (3) seldom (2),
and almost never (1). Therefore, the
maximum possible mean score of each 8item scale was 40 and the minimum
possible scale mean score was 8 . This response scale was designed to enable
students to indicate their perceptions of the frequency of occurrence of a
range of salient phenomena (see earlier scale descriptions).
The student
responses (N=34) to the questionnaire were analysed statistically to obtain
mean scores and standard deviations. As well, estimates of the internal
consistency of scales were generated by calculating (1) Cronbach alpha
reliability coefficients, (2) itemscale correlation coefficients for each item
in relation to both its own scale and other scales, and (3) a scale
intercorrelation matrix. Tables 2 to 5 present descriptive scale statistics
which indicate, from a psychometric perspective, several problematic aspects of
the instrument.
In Table 2, the
relatively large standard deviation of most scale mean scores suggests a lack
of homogeneity amongst the perceptions of the class. The table shows also that
two scales have relatively low internal consistencies (Student Negotiation, a=0.68; Mathematical Uncertainty, a=0.54). The apparent lack of internal
inconsistency was a focus of our subsequent investigations.
Table 2
Descriptive Statistics for CLES (N=34)
CLES Scale Mean Standard Alpha
Deviation Coefficient
Personal Relevance 26.2 5.5 0.81
Student Negotiation 28.5 4.1 0.68
Shared Control 20.5 5.5 0.85
Critical Voice 29.9 5.3 0.79
Mathematical Uncertainty 24.3 3.7 0.54
Maximum possible score = 40;
Minimum possible score = 8
Table 3
CLES Items with Low or Negative ItemScale Correlation
Coefficients (N=34)
Scale Item
Wording ItemScale
(In
this class. . . ) Correlation
Coefficient
Student
I have no interest
in other students' ideas. 0.07
Negotiation
Critical
Voice I 'put up' with things
that prevent me 0.23
from
learning.
Mathematical
I learn that mathematics
provides 0.01
Uncertainty perfect answers to problems.
Mathematics
is about using rules to find 0.33
correct
answers.
Table 3 shows the
four (negativelyworded) items that appeared to make either little contribution
or a negative contribution to their respective scales.
We were interested
in exploring the relationship between students' attitudes towards the Egg Project
and their learning environment perceptions. Table 4 shows the results of calculating a scale intercorrelation matrix
. It is apparent that a positive relationship exists between students'
attitudes and their perceptions of the learning environment. This relationship
is strongest for the three scales of Personal Relevance (r=0.55), Student
Negotiation (r=0.49) and Shared Control (r=0.42). These relationships were
explored for each of the small groups of students and are discussed below. Table 4 shows also that, in this study,
several CLES scales have high degrees of intercorrelation: Personal Relevance
and Mathematical Uncertainty (r=0.53), Shared Control and Critical Voice
(r=0.63), and Student Negotiation and Critical Voice (r=0.48). Traditionally, learning
environment researchers have attempted to minimise the intercorrelation of
scales (by rejecting items with unsuitable itemscale correlation coefficients)
in order to ensure that each scale represents a relatively unique construct (or
factor).
Table 4
Intercorrelations Between Scores of CLES and Attitude Scales (N=34)
Correlation
Scale Student Shared Critical Mathematical Attitude
Negotiation Control Voice Uncertainty
Personal
Relevance 0.39 0.16 0.19 0.53 0.55
Student
Negotiation  0.38 0.48 0.09 0.49
Shared
Control   0.63 0.35 0.42
Critical
Voice    0.32 0.33
Mathematical
Uncertainty     0.26
We decided to
investigate the source of some of the main statistical problems that are
evident in Tables 2 to 4 by inquiring
qualitatively into students' responses to the CLES. But first we needed to
identify salient students.
We conducted a
further analysis of students' CLES responses by examining the scores of each
student. Table 5 shows the mean scores of each student group (A  J) for each
of the five scales of the CLES as well as for the additional attitude scale.
Also shown in Table 5 are the size and sex
of each group, and Loren's rating of the relative achievement of the
groups based on grades awarded to their interim project reports.
From Table 5, the
heterogeneity of classroom learning environment perceptions amongst the student
groups — a characteristic that usually is masked by analyses based on the whole
class — is evident. For example, for the Shared Control scale, the standard
deviation values amongst the 10 student groups cover a large range (Group A
SD=9.8; Group C SD=2.6). This result
implies that there was a heterogeneity of perceptions within small groups of students and that individual students,
therefore, were likely to have had experiences of the classroom that are
different from those of other students. Only by examining the perceptions of
individual students will researchers be able to understand the nature of this
diversity. This level of research was mostly beyond the scope of the study
presented in this paper. Apart from one of the students who seemed to work
individually, we investigated the perceptions of small groups. Also, it is
interesting to note the wide range of attitudes towards the project amongst the
class (see Attitude scale). Our
interpretive analyses of the interview data are reported and discussed in the
next section.
Table 5
Student Group Characteristics and
Descriptive Statistics (N=10)
Mean
Scale Score (Standard Deviation) 











Group ID Size 
Sex 
Relative Achvment 
Attitude 
Personal Relevance 
Student Negotiation 
Shared Control 
Critical Voice 
Mathematic Uncertainty 























A^{*} 
4 
F 
Hi 
21.5 (6.1) 
21.8 (3.8) 
28.3 (2.8) 
20.0 (9.8) 
30.0 (8.8) 
23.0 (2.6) 

B^{*} 
4 
F 
Hi 
27.8 (4.3) 
30.0 (4.8) 
28.3 (3.6) 
20.5 (3.9) 
31.8 (7.5) 
26.8 (1.3) 

C^{*} 
4 
M 
Av 
20.5 (5.1) 
20.5 (5.3) 
23.3 (2.6) 
19.3 (2.6) 
25.3 (5.1) 
23.0 (1.4) 

D^{*} 
3 
M 
Av 
33.0 (0.0) 
32.0 (2.0) 
32.7 (4.0) 
19.3 (6.0) 
30.3 (4.5) 
23.3 (6.7) 

E 
4 
 

29.3 (2.2) 
32.8 (2.9) 
29.5 (4.1) 
18.3 (4.1) 
29.3 (3.9) 
27.8 (2.6) 

F 
6 
 

29.5 (5.8) 
25.5 (5.2) 
31.2 (2.4) 
22.7 (7.3) 
32.2 (4.7) 
23.5 (5.3) 

G 
2 
 

33.5 (6.4) 
23.5 (0.7) 
31.0 (1.4) 
25.5 (0.71) 
28.0 (2.8) 
20.0 (0.0) 

H 
1 
 

39.0 (2.0) 
25.0 (0.0) 
27.0 (0.0) 
24.0 (0.0) 
35.0 (0.0) 
28.0 (0.0) 

I^{*} 
1 
M 
Hi 
34.0 (0.0) 
32.0 (0.0) 
32.0 (0.0) 
24.0 (0.0) 
34.0 (0.0) 
26.0 (0.0) 

J^{*} 
5 
F 
Low 
25.2 (2.4) 
23.6 (1.1) 
25.2 (3.9) 
18.4 (5.0) 
28.4 (2.7) 
24.0 (2.0) 












^{ }
^{*}Groups selected for interview Maximum possible score = 40 Minimum possible score = 8
INTERPRETIVE ANALYSES:
RESULTS AND DISCUSSION
Because we wanted
to interview a diverse range of students, we chose groups for interview
according to a combination of three main criteria. The first was the group's
relative achievement in the Egg Project, as indicated by the interim grade
given to project reports; we wanted to interview both high and low achievers.
The second criterion was the group's attitude towards the project; we wanted to
interview students who had more favourable and less favourable attitudes. The
third criterion was the sex of the students; we wanted both sexes to be
represented. Table 5 summarises the characteristics of the six student groups
which participated in the interviews, and Figure 1 shows graphically the distribution
of the mean scale scores of their responses to the CLES.
The Interviews
Each group of
students was interviewed for about 30 minutes. A vacant classroom at the school
was used, and students sat in a semicircle with the interviewer. Their
approval for audiorecording was obtained after ensuring them of the
confidentiality of their responses (especially in relation to the teacher).
Transcripts of interviews were a major source of data for this paper.
A semistructured
interview was used which comprised the following threestep format. Firstly,
students' thinking was focussed on the Egg Project by asking them about its in
the context of the mathematics learning environment that they had experienced
throughout the year. Secondly, students were asked about their retrospective
perceptions of the Egg Project. In particular, they were asked to explain
apparent differences between their current responses (i.e., during the
interview) and their past responses to the CLES. To assist with the comparison,
each student was given the copy of the CLES that they had completed in class
several weeks previously. Thirdly, more detailed explanations were sought about
students' perceptions in relation to key issues by focussing them on specific
items in the CLES.
Fig 1. Distribution of scale mean scores of
interviewed groups & whole class (N=7)
Interpretive Data Analyses and Assertions
The following
results are based on data generated largely from student interviews, classroom
observations, and the administration of the CLES to a class of 34 students. The
results are presented in the form of three assertions
(Erickson, 1986) which constitute
emergent theory that has a sound empirical base.
1. ASSERTION 1. In the context of high school mathematics classrooms that are
undergoing a constructivist transformation, the five CLES scales — Personal
Relevance, Student Negotiation, Shared Control, Critical Voice, Uncertainty —
have the capacity to contribute to a plausible account of the classroom learning
environment.
2. ASSERTION 2. The capacity of the CLES to contribute to a plausible account of
a classroom learning environment might be optimised by careful design that: (1)
avoids conceptually asymmetric and
conceptually complex items, and (2) counters students' tendency to adopt
alternative experiential contexts as referents when responding to items.
3. ASSERTION 3. When determining the practical viability of learning environment
questionnaires, especially in the context of classroom learning environments
undergoing transformation, anomalies which arise from statistical analyses can be investigated profitably by
interpretive inquiry.
Evidence that
warrants the three assertions is presented in the following sections which
constitute an interpretive account of the statistical analyses of the revised
CLES .
Personal Relevance
According to the
CLES data, during the 9lesson period preceding the administration of the CLES,
the class as a whole perceived the Egg Project to be relevant to the world
outside of school only sometimes (see
Table 1, mean=26.2, SD=5.5). However,
group perceptions ranged from relevant often to relevant infrequently (see Table 4, 21.5<mean<39.0).
The data indicate also that students with more favourable attitudes tended to
perceive the project as being relevant more frequently than did students with
less favourable attitudes (see Table 3: r=0.55).
When we
interviewed students with the least favourable attitudes (Groups A, C), we
found that these students perceived the project to have no apparent relevance
during the early weeks:
S3(A) It seemed stupid to find the surface area of an egg. . . We were frustrated that it was an egg. . . The actual idea's still pretty silly.
S1(C) I thought it was a bit of a waste of time . . . The results weren't so beneficial for us. . . You just learned a bit of problem solving group work. . . . I don't know how we can turn this project into other things in life.
S2(C) [L]earning the surface area of an egg doesn't mean anything really.
Similarly,
students with slightly more favourable attitudes (Groups B, J) reported a lack
of awareness of the general relevance of the project:
S1(B) [W]e didn't know why we were doing it. . . . It was boring. . . . Who wants to know the surface area of an egg? Eat it, then chuck it away!
S2(B) It got really exciting towards the end, but it was boring at the beginning.
S1(J) I thought it was pretty well a waste of time. . . . In 7 or 8 years, I don't think it's really going to help us.
This is not a
surprising result in view of the Loren's stated goals of the project. According
to observational data, Loren had introduced the project to the class in the school mathematics context of work
previously completed on the concept of area
and use of scattergraphs for
representing data and identifying relationships between variables. He had
explained the purpose of the project as an empirical investigation of the
surface area of an egg that would make use of data to be pooled from all
groups. During the next 8 lessons, Loren's brief explanations to the class of
the goals of the project referred mostly to issues such as data collection and
analysis, "experimenting like science" (Field notes, Lesson 5), and
"real genuine mathematical thinking" (Field notes, Lesson 9), but
made little mention of the relevance of the project to the world outside of
school.
So, how can we
account for the CLES data that indicate high degrees of perceived relevance of
the project amongst some students (Figure 1: Groups I, D)? Interestingly, the
CLES data indicate also that these students had the most favourable attitudes
amongst the class. When we interviewed these students, we found that they
explained the relevance of the project to the world outside of school in terms
of their imagined future careers or the opportunity provided by the project to
learn how to work collaboratively and conduct investigations:
S1(D) [I]f we go into a job like engineering or something we need to know how to figure out things like this.
S3(D) [G]roup work. . . working together using all the brains that there were.
S1(I) [Y[You might have to do some investigative work. . . and the egg thing's just something to help you on the way.
Changing Experiential
Contexts
It therefore
seemed that when responding to the CLES items, a minority of students (with
more positive attitudes) seemed to transcend the immediate experiential context of the project (i.e., experiences of finding
the surface area of an egg) and referred to imagined experiential contexts
(e.g., future careers) in which the learning processes of the project (i.e.,
figuring things out, investigating, cooperating) had a high degree of perceived
relevance. By contrast, the majority of students (with less favourable
attitudes) tended to respond to the CLES items within the immediate
experiential context of the project. It seems that, in the absence of any
explicit indication by the teacher of the relevance of the project beyond its
stated school mathematics goals,
students' perceptions of the project's relevance were dependent on their a
priori beliefs, values and imaginations. The problem of changing experiential
contexts is explored in greater detail in relation to the results for the
Uncertainty scale.
We conclude that
the Personal Relevance scale of the CLES generated data about students'
perceptions that generally were congruent with data from observations and
interviews. The apparently anomalous higherthanexpected perceptions of
personal relevance indicated by a minority of students seem to have resulted
from an absence of direct instruction about the relevance of the project to the
world outside of school.
Recommendation 1
Future research is
necessary to determine the extent to which the Personal Relevance scale is able
to provide a plausible account of learning environments in which students have extensive opportunities to develop
understandings of the relevance of their mathematical activities to the world
outside of school.
Explanatory Teacher Note
The issue of
relevance of mathematics had been an ongoing part of discussions in the
classroom since the first lesson on the Egg Project. The students found much of
the mathematics was not relevant to their daily life activities, particularly
outside the school context of successfully completing studies. However, this
did not deter him from continuing to discuss the relevance issue although much
of the discussion regarding the relevance about finding surface areas of solids
occurred in earlier topics which dealt with surface areas of Euclidean shapes
such as cubes and spheres. There is not much to discuss. Even less so about the
need, in practice, to find the surface area of eggs, although he did draw an
analogy to some mathematical work that he had done for a friend. This work
aimed to establish a reasonable formula for finding the surface area and volume
of human testicles from ultrasound pictures for his research on male sterility.
So, Loren chose to tell the class his reasons for setting the project.
It appeared to
Loren that many students considered the large assessment component as giving
relevance to the project, especially as most students regarded the project as
an opportunity to get a high score. For other students, the project looked like
fun and therefore seemed relevant. The perceived relevance of the project is
also something that can be judged positively by the students at some future
time if the current experience proves to be useful. Choosing a project or
activity for students with this in mind is very much a part of teaching.
Student Negotiation
The CLES data
indicate that, during the early weeks of the Egg Project, the class as a whole
perceived that students negotiated with each other relatively frequently (see
Table 1, mean=28.5, sd=4.1). Group perceptions of the frequency with which they
negotiated with other students ranged from sometimes
to often (see Table 4,
23.3<mean<32.7). Figure 1 indicates that, with one exception, students
with more favourable attitudes tended to perceive themselves as negotiating
with other students more frequently than did students with less favourable
attitudes (see Table 3: r=0.49). The exceptional students belonged to Group A
(high achieving girls) who, despite their unfavourable attitudes, indicated
that they negotiated frequently within their group.
During classroom
observations, it was evident that, for most lessons, most students discussed
their work with other students in their group and, occasionally, with students
from other groups, especially during times when groups were seeking data from
other groups. However, we found it rather difficult to observe group
discussions for the purpose of determining the nature of their discourse. When
we approached groups, they tended to stop their discussions and direct their
attention to us. Nevertheless, brief observations indicated that students
seemed to be explaining their ideas to their group (e.g., about data collection
methods) and deciding which ideas were worth testing. When we interviewed
students with the strongest perceptions of negotiation (Groups D, A), they
explained that they had spent a considerable amount of time in class
considering each other's ideas carefully:
Intvr For how much of the time were you thinking seriously about the other person's ideas?
S1(A) Half the time.
S2(A) A lot of the time. What we do is just put in our ideas.
S3(A) We were talking a lot, but it was about the project.
S2(A) We were debating which ideas were good and which ideas, you know, we didn't need.
S1(D) A couple of times we had different methods of measuring, and we had to figure out which one to use and which one was the best.
S2(D) And we tried the ideas over and over with lots and lots of eggs. Then we just finally negotiated. . . what should be the best one. . . In group work, if you're working on a really tough problem like [the Egg Project], I think you need. . . coordination. . . because. . . you need a lot of people to help you, not just one person.
During classroom
observations, it also was evident that, within other groups, students were working
individually after having agreed about a division of labour in relation to a
range of complementary tasks (e.g., taking measurements, compiling tables of
data, report writing). Very little discussion of ideas was evident. Interviews
with students who perceived themselves as engaged in negotiations less
frequently confirmed these observations:
S1(C) We were pretty low on [negotiations].
S2(C) We each had a bit to do.
S1(C) Yes. We did our own job and that was probably it.
S1(J) Alice [pseudonym] did most of. . . the graphs.
S2(J) She wrote it all up.
S1(J) I wrote it all up. . . how we did it.
S2(J) I sort of did the graphs and that while she was writing.
Interestingly, the
CLES data of the high achieving male student who had been observed to be
working independently indicated a high degree of negotiation with other
students (Figure 1: Group I). This apparent anomaly puzzled us. However, during
the interview, the student explained that, although he rarely initiated
discussions with other students (probably because of his shyness), he often
listened carefully to other students' explanations and often explained his
ideas to other students when they consulted him. It seems, therefore, that
fruitful negotiation can occur amongst students who apparently are working
independently, especially if the classroom environment provides opportunities
for students to move around and consult one another.
Conceptual Complexity
Several items in
the Student Negotiation scale elicited inconsistent responses which resulted in
lessthansatisfactory itemscale correlation coefficients (see Table 2) and
contributed to a relatively low alpha reliability coefficient for the scale as
a whole (see Table 1, a=0.68).
Two of the items are negatively worded (Items 41, 47) which is a feature that
might have given rise to interpretation difficulties when students were
considering a suitable category from the frequency response scale. For example,
to choose seldom or almost never (as did a total of 25
students in this study) as a response to Item 41 (I have no interest in other students ideas), requires students to
think in terms of a conceptually complex double
negative statement that has a
greater likelihood of being interpreted inconsistently than do items that are
positively worded.
Recommendation 2
We feel that
learning environment questionnaires should avoid negativelyworded items that
are likely to be conceptually complex. Consequently, when refining the CLES
scales, we rejected Item 41, and changed Item 47 into a positivelyworded form:
Other students pay attention to my ideas.
In relation to the
Student Negotiation scale of the CLES , we concluded that the data generally
yielded a plausible account of the classroom learning environment that is
consistent with data from other sources.
Recommendation 3
However, because
students received little direct instruction on how to organise their groups to
optimise student negotiations, we feel that further research is needed to
determine the efficacy of this scale for generating plausible accounts of
classroom learning environments in which students have extensive opportunities
to engage in rich negotiations with one another.
Explanatory Teacher Note
It was intentional
on Loren's part not to organise and structure the groups and their roles. He
felt that it was not his role to guess the most appropriate configuration to
get the best results. Rather, he believed that this was part of the problem
solving aspect of the project.
Shared Control
The CLES data for
the Shared Control scale indicate that, as a whole, the class perceived that
relatively infrequently they shared control with the teacher of the management
of the classroom learning environment (see Table 1: mean=20.5, sd=5.5). In
general, students perceived that less than
sometimes were they able to help the teacher plan the learning activities
(Item 4), and have a say in deciding what activities to do and how much time to
spend on an activity (Items 40, 22, respectively).
During the
interviews, one of our chief concerns was to minimise the amount of lesson time
forfeited by students. We did this by focussing on the extent to which students
perceived that they had had a say, in a general sense, in what to do in
relation to their participation in the Egg Project. We found that, regardless
of their attitudes or levels of achievement, and with one exception, students
indicated that they had had very little say in shaping the project's
activities. Whereas most interviewed students acknowledged a degree of control
over their learning activities on a momentbymoment basis (e.g., negotiating
with each other about empirical methods), they seemed to believe that the locus
of control of the general management of the early part of the project lied
almost entirely with the teacher.
Intvr Do you reckon the teacher gave you much say in making decisions and deciding what to do?
S3(A) He gave us three sheets, and said what we had to do during the project.
S2(A) It was sort of really laid out, what we had to do.
S3(A) Yes, we had to do this, this and this. And we couldn't change that in any way. We had to do it THAT way and hand it in THAT way!
S1(B) [The teacher] told us what was asked of us. . . and that's all we did.
S1(C) He just basically told us what to do, and we just tried to do it. . . just [to] give him a result.
Nevertheless, the
stark contrast with earlier classroom experiences of working out of textbooks
was sufficient to cause the highest achieving student (Group I) to celebrate
the increase in control that he had experienced sometimes during the
project:
Intvr You think that the teacher doesn't give you much say in what to do in the class. Would that be true?
S1(I) Yes, I suppose, because. . . we do textbooks. You just learn out of it. You can't choose what you want to do.
Intvr And in the Egg Project, did you feel the same?
S1(I) Not really, because you can do it  get the information  however you like. . . . You had to do the Egg Project, but you could do it how you liked!
Observational data
were highly consistent with students' recorded perceptions. During the
ninelesson period prior to the administration of the CLES, we observed
students exercising a limited degree of autonomy with respect to their
participation in the management of the classroom learning environment.
Generally, students exercised most control over the practical problemsolving
component of their learning activities. During these activities, which occupied
most of the lesson time, students shared control with other students in their
group (i.e., designing data collection
methods, recording data). However, the overall goal of the project — "to
find a simple way to estimate the surface area of an egg" — was prescribed by Loren. As the lessons
proceeded, Loren prescribed also the data to be collected (i.e., which
variables to measure) and the types of analysis (i.e., which relationships
between variables were of interest). Because of the Loren's goal of pooling
group data and comparing the results of each group's data analyses, students
were given little opportunity to develop learning goals that differed from the
teacher's goals.
As well, the
nature of the formal assessment of the project was prescribed by the teacher.
Groups were directed to submit a single written report that addressed a set of
criteria determined by the teacher. The CLES data (for Items 10, 34, 46)
indicate that students perceived themselves as having infrequent opportunities
to participate with the teacher in assessing their learning. In general, data
from all sources confirmed that students were provided with limited
opportunities to share with the teacher control of their participation in the
project.
In this study, the
Shared Control scale had a satisfactory internal consistency (see Table 1: a=0.85). An analysis of individual items
indicated that only a single item (Item 28: I
have control over my learning) had a relatively small itemscale
correlation coefficient (r=0.36). The item elicited an overall response that
indicated that students perceived themselves to have frequent control over
their learning (i.e., more than sometimes). We attributed this anomalous result
to the less than precise nature of the term control
which might have been interpreted in relation to students' collaborative decision
making rather than in relation to sharing control with the teacher. Itemscale
correlations indicate that it had a strong positive association with three
other scales.
Recommendation 4
When designing an
item, care should be taken to avoid the use of terms that might give rise to a
range of interpretations at variance with the intention of its own scale. In
the case of Item 28, we rejected it from the instrument.
We concluded that
the Shared Control data yielded a plausible account of students' classroom
learning environment perceptions that was consistent with data from interviews,
classroom observations and documentation.
Recommendation 5
However, further
research is needed to determine the extent to which this scale generates a
plausible account of classroom learning environments that offer extensive
opportunities for students to exercise autonomy in relation to the design and
management of their own learning activities.
Explanatory Teacher Note
Constraints were
operating in the planning and execution of the Egg Project. For Loren, the
project's form had to be perceived by multiple audiences — colleagues,
students, parents and school administration — as 'fitting in' with the overall
curriculum. The topic choice and aspects of the implementation were
consequences of a demand to justify its presence in the course, and the
production of a suitable assessment product within a time limit for reporting
purposes. The students had strong views about what should happen in a
mathematics classroom, including the teacher doing a lot of the directing. The
students were very aware of what their colleagues were experiencing in other
classes covering the same mathematics course. There was not a lot of scope to
allow students to negotiate the project topic or initial guidelines. Furthermore, it was evident that, from the
start of the Egg Project, students treated the challenge differently. For some
students, it was a chance to take things easy and rely on other groups to set
the pace; some tried to get the answers from Loren; and some required regular
reassurance from him that they were capable of solving the problem. Often,
Loren felt that students were playing a game to shortcut the project and meet
their own goals, whatever they might have been. At the time, Loren was a little
frustrated with these games and, consequently, was blunt with students. However, he remained confident that they would
have more appreciation of the project as they made progress.
Critical Voice
Although students
shared with the teacher little control over their participation in the Egg
Project, they were not reluctant to express their opinions to the teacher about
issues of importance to them. The CLES data in Table 1 indicate that the class,
as a whole, believed that it was legitimate to exercise frequently a critical
voice about the quality of their learning activities (mean=29.9, sd=5.3).
Students' perceptions of the extent to which opportunities existed to question
the teacher's instructional plans and methods and express concerns about any
impediments to their learning ranged from sometimes
to more than often (see Table 4:
25.3<mean<35.0). Not surprisingly, perhaps, the highest achieving
students (Groups A, B, I) indicated that they felt most empowered in this
respect (see Figure 1).
The interview
focussed on the extent to which students experienced opportunities to be
critical, in a general sense, about the project. During interviews with
students who were amongst those who achieved the highest grades for their
project reports, it was apparent that students felt themselves to be
sufficiently empowered to approach the teacher with their complaints or felt
that they could do so if they wished. Most notable was the group of high
achieving female students which had had relatively unfavourable attitudes
during the initial 9lesson period (Group A):
Intvr Often you thought that you had a critical voice?
S1(A) Yes!
S3(A) Arguing!
S2(A) With Mr White. A lot!
Intvr Did you feel free to complain to Mr White?
S1(A) Yes. . . a lot.
S2(A) Definitely. . . . I think he got pretty high blood pressure from us.
S1(B) Yes. . . . We wouldn't be afraid to go up to Mr White and say "We don't like this", or "We don't understand this".
S2(B) Or "This doesn't look right, can you help us".
Intvr You felt that you had the opportunity to express your feelings, to complain if you wanted to, to say that you didn't like something?
S1(B) Or even if, like, he just said that "I'm not going to change it. Go back to your seat", we still wouldn't mind going up there.
S1(I) I just think that I can if I want to.
By contrast,
students who had achieved relatively low grades for their project reports (and
who had less favourable attitudes) seemed not to feel sufficiently empowered to
exercise a critical voice. There are indications in the following interview
excerpts that disempowerment was associated with students' awe of the teacher's
authority (Group C) and with students' chronic resignation that mathematics
seldom seemed to be of direct relevance to the world outside of school (Group
J):
Intvr You didn't express your opinion about the fact that you didn't like doing [the project] much?
S1(C) No. . . . Because it was the whole class that was doing [the project].
S2(C) No. He's the teacher, you know. . . . If he wants us to do a project we'll do the project. . . or else we'll get bad marks.
Intvr Did you let the teacher know that you didn't think that the project was particularly relevant?
S2(J) Yes, but not properly. . . not seriously.
Intvr You were just joking around with him, were you?
S1(J) Yes.
S2(J) Sort of like saying we don't want to do it.
Intvr OK. Why would you have not told him seriously?
S2(J) We didn't mind really, doing the project.
Intvr You didn't mind that it wasn't all that relevant to the outside world?
S1(J) No.
Intvr Is mathematics usually like that?
S1(J) Yes.
Classroom
observations indicated that students who exercised a critical voice with the
teacher did so largely in private, rather than during wholeclass interactions.
Explanatory Teacher Note
For one particular
student in this class (Group I), 20 weeks into the school year was the first
time when, in his view, he had actually challenged the teacher to argue for a
different outcome. After sevenandahalf years of schooling, this was a big
step for him, and he considered that he had exercised often a critical voice. Not so for one of the girls (Group A) who
challenged Loren's decisions almost every lesson.
Mathematical Uncertainty
The CLES data in
Table 1 indicate that, during the initial ninelesson period, the class as a
whole had experienced mathematics as a fallible human activity only some of the
time (mean=24.3, sd=3.7). A small correlation (see Table 3: r=0.26) between the
attitude and mathematical uncertainty scale scores indicates that, in this
study, students' attitudes were not
strongly related to their experiences of mathematical uncertainty.
Of great concern
to us were the statistical data in Table 2 that indicate the unsuitability of
several key items with unsatisfactory itemscale correlation coefficients (Item
38, r=0.01; Item 44, r=0.33). Normally, such items would be rejected in
favour of items that made a greater contribution to their scale (i.e.,
r>0.30). However, because of our interest in the educational significance of
the items, we were reluctant to abandon them on purely statistical grounds, and
decided to investigate students' responses to them. Our investigations yielded
valuable insights into the nature of a changing learning environment.
Changing Experiential
Contexts
First we focussed
on Item 38 — I learn that mathematics
provides perfect answers to problems. During interviews, we asked students
about their experiences of using mathematics to obtain a perfect answer to the
Egg Project goal of finding a rule for the surface area of an egg. Of the six
groups of students who were interviewed, Group B (one of the highest achieving
female groups with a favourable attitude towards the Egg Project) reported an
insightful experience of mathematical uncertainty.
Although they were
somewhat unsure of their ideas during the interview, there was a recognition
among them of the imperfect nature of the rule that they were trying to invent,
especially in contrast to the wellknown numerical rules (or axioms) that they
used in other contexts. They attributed this lack of mathematical certainty to
the irregularity (i.e., nonEuclidean nature) of the actual (real world) eggs
that they were using and to the consequent difficulty of modelling the shape
mathematically:
Intvr Was it possible to find a perfect answer in the Egg Project?
S3(B) I think . . . there probably would have been.
S1(B) I don't think. . . I don't know.
S2(B) I don't think there is an actual formula for the surface area of an egg. You could find the volume, probably, like with those [measuring] cylinders. And you could actually find the width [i.e., girth] with the Vernier callipers. But like you couldn't actually do the main question which was asked.
Intvr OK. Do you [inviting another student] think that was the case?
S3(B) Yes, because isn't the egg shaped, or something, inside the chicken . . . before it comes out? So, that way, the egg isn't an exact shape. I mean it could be a different type of shape.
Intvr But in other mathematics do you think you were able to find perfect answers?
S2(B) Well, in most things, like when it was like sums and that, we were given numbers and you had to get the perfect answer.
In contrast to
their stated frequent experience of mathematical uncertainty in relation to achieving
the main goal of the Egg Project, these students had indicated in their
responses to the CLES that they had only sometimes
or seldom learned that mathematics
provides perfect answers to problems. We wondered how this apparent anomaly
could be explained. The interview helped to provide a plausible explanation.
When responding to the CLES , these students acknowledged that they had changed
the context within which they were thinking about their mathematics learning
experiences. They had adopted as the main referent the context of their more
familiar learning experiences of mathematical certainty which tended to subsume
and to render much less significant the tentative experiences of mathematical
uncertainty that were occurring during the Egg Project. As a result, their CLES
responses understated the frequency of their experience of mathematical
uncertainty:
Intvr Item 38: I learned that maths provides perfect answers to problems. What have you got there?
S2(B) Sometimes.
S3(B) Seldom.
S1(B) Sometimes.
Intvr And during the Egg Project, did you have evidence that that was the case?
S2(B) No, we never had perfect answers. . . but in other maths there's always like a perfect answer.
S1(B) Yes, but in other maths you do. . . . So, I think that's probably why I put sometimes.
The tendency to
change experiential contexts when responding to CLES items was very evident in
the final comments of one of the students who had been reflecting on my
questions and who volunteered the explanation that, when responding to the CLES
items:
S1(B) I started off using the Egg Project. Then I, sort of, moved over to maths overall.
Intvr When you were answering the questionnaire?
S1(B) Yes. I sort of stopped and then went to maths overall.
In relation to our
second statistically problematic item (see Table 2: Item 44, r=0.33), there is
evidence that students had changed the context of their thinking when
responding to this negativelyworded item. Although student I (the high
achieving male student with the highly favourable attitude) claimed to have had
frequent experience of the activity of rule invention, when responding to Item
44 he seems to have used as the main referent his predominant experience of
using mathematical rules (this issue is developed further in the section on
conceptual asymmetry of negativelyworded items). As a result, his CLES
response understated his experience of mathematical uncertainty:
Intvr Item 44: Maths is about using rules to find correct answers. What did you have there?
S1(I) Almost always.
Intvr Do you think maths is about inventing rules, or using rules, or both?
S1(I) Both.
Intvr Were you doing any invention this year?
S1(I) No.
Intvr What about the Egg Project? Was that an invention exercise?
S1(I) Yes, you had to find a formula. So, that's inventing.
Intvr A formula that wasn't known before?
S1(I) Yes.
Another example of
students changing their experiential contexts when responding to this item, and
consequently understating their experiences of mathematical uncertainty, was
obtained from the Group B students:
Intvr Item 44: Maths is about using rules to find correct answers. What have you got for that?
S2(B) Often.
S3(B) Often.
Intvr When you answered the question were you thinking about the Egg Project, or were you thinking about maths outside of the Egg Project?
S3(B) Maths outside.
S2(B) I was thinking about maths outside, like 'length times width', or whatever.
What was the
influence on the Uncertainty scale statistics of students changing the contexts
of their thinking about their mathematics learning experiences when responding
to items? At this stage, it is impossible to give a comprehensive account
because we do not have sufficient data for all items on this emergent research question. However, in
relation to our two statistically problematic items (Items 38, 44), two
important consequences have been identified.
First, because
students understated the frequency of their experiences of mathematical
uncertainty during the Egg Project when responding to these items, the overall
scale mean score (see Table 1: mean=24.3) was depressed. Second, as a result of
averaging their experiences of
different learning environments, students tended to choose the midrange
response of sometimes. When analysed
statistically, the variance in the scores of students' responses was relatively
small, especially for Item 44 (sd=0.68). Consequently, the values of the
itemscale correlation coefficients of these items also were relatively
small.
So, why did
students change the context of their experiences when responding to items in
the Uncertainty scale? We believe that one of the main reasons concerns the
novelty of students' experiences of sustained mathematical uncertainty and
their tentativeness in accepting the authenticity of a counterintuitive
experience of a constructivist epistemology. The tendency amongst the class to
attribute greater authenticity to their familiar prior experiences of the
certainty of mathematics might have been strengthened by their perception that
mathematical uncertainty did not seem to be a legitimate learning goal.
Classroom observations indicate that, apart from stating the overall goal of
the project — to find a general formula for the surface area of an egg — Loren
made little attempt to establish mathematical uncertainty explicitly as a
learning goal for the class.
In a state of
intellectual and emotional uncertainty about the legitimacy of their new
experiences during the Egg Project students, therefore, might have responded to
items of the Uncertainty scale by using as a referent their rich experiences in
more traditional learning environments whose legitimacy was beyond doubt.
Recommendation 6
In order to
determine the extent to which items in the Uncertainty scale can elicit
dependable responses, it is necessary to trial the CLES in a classroom learning
environment that provides rich and sustained experiences of mathematical
uncertainty whose legitimacy as a learning goal has been affirmed by the
teacher.
Explanatory Teacher Note
From the first day
of the school year, Loren had endeavoured to have uncertainty of mathematics as
part of the classroom discourse. Counting, symbols, conventions, concepts and
ideals had been discussed in terms of subjective decisions being made on the
bases of other beliefs, preferences, and desires such as uniformity,
simplification, universalism or religion (e.g., positive indicated to the
right, negative to the left). Nonroutine puzzles and problems had been part of
the class program leading up to the Egg Project. Many problems provided
multiple solutions and needed negotiation for a best answer. The difference with the Egg Project related more to
the size of the project, the need for measurements to be made, the negotiation
of plausible methods and answers, and assessment. It is not clear to Loren what
should be presented to students as demonstrating mathematical uncertainty,
other than to give them opportunities to experience framing of problems. That
is, to provide opportunities to experience the social construction of mathematics
by sorting out information to see if there is a problem and whether the problem
can be mathematised, and making a choice of models in which to redescribe the
problem. Can a teacher tell a student what uncertainty is, or is it a sense or
feeling embodied in experience?
We believe that a
contributing factor in students' practice of changing their experiential
contexts when responding to items in the Uncertainty scale concerns the nature
of the prompt in the CLES. This
prompt, which takes the form of In this
class. . . and precedes each group
of three items, was designed to focus students' thinking on the learning
environment in their current class.
However, in the case of this study, where a changing and unstable
classroom learning environment existed, it seems that the prompt failed to
maintain students' new experiences as a referent for responding to items. In
the absence of rich experiences
amongst students of mathematical uncertainty during the Egg Project, students
changed the context of their thinking to their prior learning experiences in this class.
Recommendation 7
In the context of
a changing learning environment, questionnaire prompts should be designed to
maintain students' thinking on the appropriate set of experiences. For example,
in this study an appropriate prompt might have been: During the Egg Project.
Explanatory Teacher Note
Although the CLES
was administered during the Egg Project, it did not ask students to confine
their considerations to this project. It seems that the students were more
likely to respond to each question according to what contexts the questions
suggested as being most meaningful. The result could be an aggregate of
meanings related to at least the whole year's experiences in Loren's class,
rather than to experiences at only the specific point in time when the CLES was
administered. Furthermore, although any student can give what appear to be
contradictory answers, such contradictions might not exist for the student.
Researchers and teachers tend to give more primacy to consistency and logic
of student answers, and have a fear of contradictory answers. They tend
to regard the context of classroom learning environments as universal, timeless
and unchanging, and tend to think that, when students make sense of a new
experience in a different way, they update automatically all other related
meanings such that contradictions are ironed
out.
Conceptual Asymmetry
Our investigation
into the statistically problematic Item 44
— Mathematics is about using rules
to find correct answers — provided
another explanation for its apparently negative contribution to the Uncertainty
scale (Table 2: r=0.33).
During the Egg
Project, students made use of their prior mathematical knowledge, especially
their knowledge of mathematical rules, to enable them to mathematise the
problem of finding a rule for the surface area of an egg. They devised
mathematical models of their eggs (e.g., hemispheres, triangular nets), measured various linear
dimensions (e.g., width, circumference, girth), and calculated other dimensions
(e.g., volume, mass) in order to obtain approximations of the surface areas of
their eggs. After pooling their results, the various groups set about the
complex task of ordering the data and looking for patterns that might be
expressible in the form of a general rule for the surface area of an egg.
Clearly, the Egg Project comprised much use of alreadyknown mathematical rules
during the process of inventive problemsolving.
The student
interview data indicate that most students recognised that the Egg Project was
an activity in which they used
wellknown mathematical rules (e.g.,
surface area of triangular and spherical shapes; rules of multiplication
and addition) in their overall attempts to invent a general mathematical rule
for the surface area of an egg.
Intvr Is maths about using rules, or is it about inventing rules? Think about the Egg Project.
S1(A) I think we invented. . .
S2(A) We used [rules] more. We used the 'sphere theory'.
S1(D) I've got "sometimes" because. . . for area and surface area [Euclidean shapes] you can have rules. But for other areas [nonEuclidean shapes] you can't because they just don't work.
Intvr Item 44: Maths is about using rules to find correct answers. Did that apply in the Egg Project?
S1(C) Yes, we used a couple of rules. Like how to find the volume.
S2(C) I used rules like working out the volume by putting it in water.
Intvr And you were saying before that you were trying to invent a new rule. Is that right?
S1(C) Yes, we used a bit of both.
Although students
claimed that, in hindsight, they had both
used and invented mathematical rules during the Egg Project, when responding to
Item 44 of the CLES the more familiar (momentbymoment) experience of using mathematical rules seems to have
dominated their thinking. Only three of the total of 34 students chose a
response category (i.e., seldom)
that, when reversescored, made a positive contribution to the internal
consistency of the Uncertainty scale. Students' experience of using rules seems
to have overshadowed their experience of inventing a rule. What might be the
reason for this outcome?
At the time of
responding to the CLES, the experience of having invented a mathematical rule
was unfamiliar to the class. Classroom observations revealed that none of the
class had achieved the main goal of the project, that is, to invent a general
rule for finding the surface area of an egg. Instead of having invented a
general rule students were engaged in openended processes of invention that
did not necessarily guarantee the existence of a general rule. Interviews
indicated that: (1) students with unfavourable attitudes towards the project
expressed doubts about the existence of a general rule; and (2) the majority of
the class seemed to have experienced little sense of personal relevance in
relation to the main goal of the project (see Personal Relevance scale). It is
not surprising, therefore, that students' responses to Item 44 reflected their
dominant experience of using, rather than inventing, mathematical rules.
However, we
believe that there is another, more important, issue associated with the
problematic nature of Item 44 (using
rules). This negativelyworded item was designed on the assumption that,
when reversescored, it was equivalent to the concept of inventing mathematical rules. That is, we had assumed, somewhat
naively, that in a constructivist learning environment students would be
engaged to a much greater extent in inventiontype activities than in
ruleusingtype activities. What we learned from the Egg Project was that the
two activities are complementary rather than antithetical. In order to invent
new mathematical knowledge students must utilise their extant mathematical
knowledge, much of which is expressible in the form of rules. What
characterises an emergent constructivist learning environment, therefore, is
not the abandonment of ruleusing activity but a new instructional emphasis on
students use of knownrules for the purpose of experiencing mathematical knowledge
as an uncertain product of human endeavour. In other words, students would
experience not only the usefulness of using mathematical rules to invent models
of problematic aspects of their everyday worlds, but also they would experience
the inherent uncertainty of the mathematical knowledge that they construct
during this process.
As a result of our
investigation of Item 44, we concluded that a conceptual asymmetry exists
between the item and the Uncertainty scale, and that the item does not serve as
a legitimate negativelyworded item. We have realised the importance of not
assuming that conceptual symmetry can be achieved readily between a scale and a
negativelyworded item, especially where the negativelyworded item addresses
experiences that might have a legitimate role in various learning environments
including an emergent constructivist environment. Our experience in previous
research confirms this concern. For example, in an earlier version of the CLES,
an Autonomy scale was designed to
obtain measures of the exeunt to which students experienced opportunities to
exercise selfcontrol and independence from the teacher. The scale contained a
few items that referred to the role of the teacher as an agent of control. It
was assumed that, when reversescored, these items would be conceptually
equivalent to the positivelyworded items that referred to the role of students
as agents of control. However, factor analysis of responses to these items
indicated that they were distinct factors, a result that suggested that the
assumption of conceptual equivalence was invalid.
We concluded that,
if the CLES is to be of use to teachers in monitoring emergent constructivist
learning environments, then it should aim to provide measures of the presence
of desired attributes rather than the absence of undesirable or complementary
attributes that might characterise alternative learning environments.
Recommendation 8
When designing
negativelyworded items, care should be taken to avoid conceptual asymmetry between
items and their scales resulting from the inappropriate use of nonequivalent
concepts. Therefore, (1) Item 44 should be reworded in the form: I learn that mathematics is about inventing
rules, and (2) Item 38 should be
reworded in the form: I learn that
mathematics cannot provide perfect answers.
Conclusion
This paper
presents an analysis of the results of a trial of the revised Constructivist
Learning Environment Survey (CLES) that was conducted in a single high school
mathematics classroom during 1993. We had chosen that particular classroom
because we wanted to assess the efficacy of the CLES in generating a plausible
account of a classroom learning environment that was characterised by the
presence, rather than absence, of key attributes that were compatible with the critical constructivist perspective
underpinning the five CLES scales.
What might have
been considered, from a purely psychometric perspective, to be a relatively
straightforward task of generating statistical data and refining the CLES
scales by abandoning or modifying problematic items became, instead, an
intriguing inquiry into the complex nature of a changing classroom learning
environment. During this process, we found ourselves supplementing psychometric
warrants (e.g., reliability) associated with traditional learning environment
questionnaires. We were able to do this by adopting an interpretive research framework within which we studied in detail
the complex array of perceptions held by the teacher and students. The statistical
analyses, especially problematic results (such as negative itemscale
correlation coefficients) became starting points, rather than end points, of
our investigation. We sought to generate plausible explanations for anomalies
that were apparent in both quantitative and qualitative analyses.
The richness of
our investigation was enhanced by the establishment of a dialogical
relationship between the teacherresearcher and one of the
participantresearchers. The teacherresearcher was able to express his own
critical voice about the significance of both the data that were generated in
the study and the participantresearchers' interpretations. His voice appears
in two ways throughout the paper. The first is his influence (by means of
continuous negotiations during the study) on the participantresearchers'
interpretations that are presented in the discussion of the results. The
second, which is in a more explicit form, is by means of the Explanatory Teacher Notes which are
appended to, and provide alternative interpretations of, the
participantresearchers' analyses.
One of the
outcomes of the study was our realisation of the difficulty faced by teachers
who wish to transform their classroom learning environments in accordance with
a constructivist philosophy. The process of change might not be a simple
transition from state A (e.g., high degrees of teacher control and mathematical
certainty) to state B (e.g., high degrees of student autonomy and mathematical
uncertainty). Rather, the process might be a complex transformation that
involves the partial coexistence of both states, especially where shared
attributes are involved. For example, in this study, we came to understand
that, whereas state A is concerned mostly with the use of mathematical rules, in
state B students both use and invent mathematical rules. In a transformative
situation, in which state B is being introduced, a student is likely to hold
conflicting beliefs about the nature of his/her experiences, and can tend to
use his/her more familiar and secure experiences (e.g., of state A) as a
referent when responding to items in a learning environment questionnaire,
thereby underreporting experiences of state B. In this paper, we refer to this
practice as students changing their experiential contexts. We suggest that this
problem might be minimised by careful design of items (e.g., avoid conceptually asymmetric items) and by
careful design of prompts that
constrain students' thinking within an appropriate experiential context.
Another important outcome
of the study was our realisation of the difficulty facing learning environment
researchers who wish to promote the adoption by teachers of the role of teacherresearcher for the purpose of
undertaking pedagogical change of a constructivist nature. The CLES comprises
five scales that, for many teachers, could represent five radical
transformations of their current learning environments. We are sufficiently
realistic that we would not wish teachers to undertake more than one or two of
these transformations at any one time. In that case, it would not be
appropriate to make use of all five scales when monitoring students' learning
environment perceptions. There is no point in monitoring the absence of
attributes of state B, especially if anomalous and misleading results are
likely to be generated.
A similar problem
is likely to occur if CLES scales are used too early in the monitoring of
transformations to classroom learning environments (e.g., in the manner of a
pretest). In the absence of desired attributes of state B, students' responses
to CLES items might be inconsistent. For example, when considering the
immediate relevance of the Egg Project to the world outside of school (which,
by most accounts, seemed to lack this type of relevance) some students (with
highly favourable attitudes) overreported perceptions of relevance as a result
of transcending their immediate experiential contexts and referring to imagined
future careers. We therefore caution researchers to take care when adopting
research designs that involve the use of the CLES to obtain measures of change
in students' perceptions.
Finally, the trial
of the CLES scales made us aware of a major problem associated with the use of
negativelyworded items. We believe that some negativelyworded items yielded
inconsistent responses from students partly because of the conceptual
complexity that occurs when students consider the item in relation to
negativelyworded categories (i.e., seldom,
almost never) of the frequency response scale. Of course, this problem is
exacerbated by the use of conceptually asymmetric items which, when
reversescored, are assumed to contribute to a particular scale.
In this study, we
encountered a classroom in which the learning environment was in a state of
flux. Environments such as this pose challenges for learning environment
researchers, and give rise to several important questions. First, can learning
environment questionnaires stand alone as indicators of learning environments
under transformation? Second, to what extent do the warrants of psychometric
research (e.g., validity, homogeneity) provide adequate criteria for
understanding the nature of a transforming learning environment? Third, what
types of research design are best for teacherresearchers
who wish to use learning environment questionnaires to transform their
classroom learning environments?
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APPENDIX
mathematics CLASSROOM
LEARNING ENVIRONMENT SURVEY
STUDENT PERCEPTIONS
directions
1. This questionnaire asks you to describe this classroom which you are in right now. There are no right or wrong answers. This is not a test. Your opinion is what is wanted.
2. Do not write your name. Your answers are confidential and anonymous.
3. On the next few pages you will find 48 sentences. For each sentence, circle one number corresponding to your answer.
For example:


Almost Always 

Sometimes 

Almost Never 
In this class . . . 







the teacher asks me questions. 
5 
4 
3 
2 
1 
• If you think this teacher almost always asks you questions, circle the 5.
• If you think this teacher almost never asks you questions, circle the 1.
• Or you can choose the number 2, 3 or 4 if this seems like a more accurate answer.
4. If you want to change your answer, cross it out and circle a new number, e.g.:




3 
2 
1 
5. Please provide details in the box below:
a. School: 
b. Teacher's Name: 
c. Subject: 
d. Grade/Level: 
e. Your Sex (please circle): Male or Female 
6. Now turn the page and please give an answer for every question.



Almost Always 

Sometimes 

Almost Never 

In this class . . . 



1 
I learn about the world outside of school. 

5 
4 
3 
2 
1 

2 
I learn that mathematics cannot provide perfect answers. 

5 
4 
3 
2 
1 

3 
It's OK to ask the teacher "why do we have to learn this?" 

5 
4 
3 
2 
1 

In this class . . . 







4 
I help the teacher to plan what I'm going to learn. 

5 
4 
3 
2 
1 

5 
I get the chance to talk to other students. 

5 
4 
3 
2 
1 

6 
I look forward to the learning activities. 

5 
4 
3 
2 
1 

In this class . . . 







7 
New learning starts with problems about the world outside of school. 

5 
4 
3 
2 
1 

8 
I learn how mathematics has changed over time. 

5 
4 
3 
2 
1 

9 
I feel free to question the way I'm being taught. 

5 
4 
3 
2 
1 




Almost Always 

Sometimes 

Almost Never 

In this class . . . 







10 
I help the teacher decide how well my learning is going. 

5 
4 
3 
2 
1 

11 
I talk with other students about how to solve problems. 

5 
4 
3 
2 
1 

12 
The activities are among the most interesting at this school. 

5 
4 
3 
2 
1 

In this class . . . 







13 
I learn how mathematics can be part of my outofschool life. 

5 
4 
3 
2 
1 

14 
I learn how the rules of mathematics were invented. 

5 
4 
3 
2 
1 

15 
It's OK to complain about activities that are confusing. 

5 
4 
3 
2 
1 

In this class . . . 







16 
I have a say in deciding the rules for classroom discussion. 

5 
4 
3 
2 
1 

17 
I try to make sense of other students' ideas. 

5 
4 
3 
2 
1 

18 
The activities make me interested in mathematics. 

5 
4 
3 
2 
1 




Almost Always 

Sometimes 

Almost Never 




Almost Always 

Sometimes 

Almost Never 

In this class . . . 







19 
I get a better understanding of the world outside of school. 

5 
4 
3 
2 
1 

20 
I learn about the different mathematics used by people in other cultures. 

5 
4 
3 
2 
1 

21 
It's OK to complain about anything that stops me from learning. 

5 
4 
3 
2 
1 

In this class . . . 







22 
I have a say in deciding how much time I spend on an activity. 

5 
4 
3 
2 
1 

23 
I ask other students to explain their ideas. 

5 
4 
3 
2 
1 

24 
I enjoy the learning activities. 

5 
4 
3 
2 
1 

In this class . . . 



25 
I learn interesting things about the world outside of school. 

5 
4 
3 
2 
1 

26 
I learn that mathematics is just one of many ways of understanding the world. 

5 
4 
3 
2 
1 

27 
I'm free to express my opinion. 

5 
4 
3 
2 
1 




Almost Always 

Sometimes 

Almost Never 

In this class . . . 







28 
Other students ask me to explain my ideas. 

5 
4 
3 
2 
1 

29 
I feel confused. 

5 
4 
3 
2 
1 

30 
What I learn has nothing to do with my outofschool life. 

5 
4 
3 
2 
1 

In this class . . . 







31 
I learn that today's mathematics is different from the mathematics of long ago. 

5 
4 
3 
2 
1 

32 
It's OK to speak up for your rights. 

5 
4 
3 
2 
1 

33 
I have a say in deciding what will be on the test. 

5 
4 
3 
2 
1 

In this class . . . 







34 
Other students explain their ideas to me. 

5 
4 
3 
2 
1 

35 
The learning activities are a waste of time. 

5 
4 
3 
2 
1 

36 
I have a say in deciding what activities I do. 

5 
4 
3 
2 
1 




Almost Always 

Sometimes 

Almost Never 



Almost Always 

Sometimes 

Almost Never 

In this class . . . 







37 
What I learn has nothing to do with the world outside of school. 

5 
4 
3 
2 
1 
38 
I learn that mathematics is about inventing rules. 

5 
4 
3 
2 
1 
39 
I feel unable to complain about anything. 

5 
4 
3 
2 
1 
In this class . . . 







40 
I have a say in deciding how my learning is assessed. 

5 
4 
3 
2 
1 
41 
Other students pay attention to my ideas. 

5 
4 
3 
2 
1 
42 
I feel tense. 

5 
4 
3 
2 
1 



Almost Always 

Sometimes 

Almost Never 