The original version of this chapter was revised: The copyright line was incorrect. This has been
corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35615-0_52
D. Passey et al. (eds.), TelE-Learning
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the CL-Net project was to examine how knowledge construction and skill
building can be fostered in primary and secondary school pupils by immersing
them under the guidance of a teacher in computer-supported collaborative
learning networks (CLNs). CLNs can be characterised as powerful learning
environments in which technology-based cognitive tools are embedded as a
means and resources that can elicit and mediate in a community of networked
learners active and progressively more self-regulated processes of
collaborative knowledge acquisition, meaning construction, and problemsolving. The project combined the relevant expertise available in eight research
centres spread over five European countries. The shared expertise related to
such aspects as software development, teacher preparation for the
implementation of CLNs, design principles for technology-supported powerful
learning environments, and the construction of assessment instruments. In the
context of the CL-Net project these eight centres were working at different
levels of education in a variety of content areas, and with different software
tools that can support collaborative learning.
2.
THEORETICAL AND EMPIRICAL
BACKGROUND, AND HYPOTHESIS OF THE
STUDY
The part of the CL-Net project reported in this paper aimed at the design
and evaluation of a computer-supported learning environment that facilitates
the distributed learning of problem-solving and problem-posing skills in upper
primary school children. From that perspective two strands of theory and
research were combined and integrated.
A first line of enquiry relates to the (meta-)cognitive aspects of
collaborative learning supported by 'Knowledge Forum' (KF) and its
predecessor CSll..E (Computer-Supported Intentional Learning Environment)
(Scardamalia and Bereiter, 1992). KF was designed to foster a networked
"research team" approach to learning that supports knowledge building,
collaboration, and progressive enquiry. Key features in KF are a series of
cognitive tools for constructing and storing notes, for sharing notes and
exchanging comments on them, and for scaffolding students in their
acquisition of specific cognitive operations and particular concepts.
A second theoretical underpinning derived from a series of recent
intervention studies focusing on the development in pupils of a disposition
towards genuine mathematical problem-solving. The present investigation
drew especially upon a design experiment in which a technology-lean, but
innovative, constructivist learning environment aiming at the development of
Collaborative learning of mathematics
55
a mindful, strategic, and self-regulated approach towards mathematical
problem-solving, was created and successfully implemented in a number of
fifth-grade classes (Verschaffel, De Corte, Lasure, Van Vaerenbergh,
Bogaerts and Ratinckx, 1999).
Combining these two strands of theory and research has resulted in a
learning environment in which pupils, under the guidance of their teacher
and using KF, learned collaboratively to solve and pose mathematical
application problems, and to communicate about and reflect on their
problem-solving processes starting from the shared descriptions of, and on
mutual commenting about notes on their solution strategies. The basic
hypothesis of the study was that the technological enrichment of the earlier
learning environment (Verschaffel et al., 1999) by embedding in it the
cognitive technological tools that constitute a CLN, especially KF, would
lead to a significant improvement in the quality of upper primary school
pupils' problem-solving and communication skills, and, by doing so, would
result in greater learning effects than in Verschaffel et al.'s (1999) study. In
addition the study intended to explore and elaborate an effective strategy to
guide and support teachers in the embedded appropriate use of cognitive
technological tools in their teaching of mathematical problem-solving.
3.
AIMS AND BASIC FEATURES OF THE
NETWORKED COLLABORATIVE LEARNING
ENVIRONMENT
The overall aim of the learning environment was to guide and support upper
primary school children in becoming more motivated, strategic,
communicative, mindful, and self-regulated solvers and posers of mathematical
application problems. This general aim can be specified in terms of three subgoals:
1. Acquisition by pupils, guided by the teacher and supported by the cognitive
technological tools, of a five-step meta-cognitive strategy for solving and
posing mathematical problems in which heuristic methods are embedded;
2. Developing in pupils appropriate, positive beliefs and attitudes toward
(learning) mathematical problem-solving;
3. Acquisition by children of skills for collaboration and communication in
mathematical problem-solving, using thereby the technological tools
involved in 'Knowledge Forum'.
Key features of the learning environment were the following:
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Erik De Corte et al.
1. Use of a varied set of (non-traditional) complex, realistic, and challenging
word problems that elicit and enhance the application of heuristic and
meta-cognitive strategies;
2. Application of highly interactive and collaborative instructional techniques
(especially small-group activities and whole-class discussions) supported
byKF;
3. Creation of a fundamentally changed classroom culture and climate based
on new social and socio-mathematical norms;
4. Gradual removal (taking into account children's increasing mastery of the
problem-solving strategy as well as their skills in using KF) of the external
regulation by the teacher in the learning environment in favour of selfregulation by the pupils.
For the teachers the introduction of the CLN-approach amounted to the
adoption and implementation of a fundamentally new role and pedagogy based
on a technology-supported, collaborative, and self-regulated perspective on
learning. Taking this into account, substantial attention was paid to the
preparation of the teachers, taking as a starting point that the intended
fundamental change of the classroom environment and culture should be
undertaken in partnership between the researchers and the participating teachers
(De Corte, 2(00). From that perspective, a substantial part of the teacher
preparation was realised by simulating the new computer-supported approach
to leaming and teaching problem-solving in the format of an interaction
between the researchers and the teachers, both groups taking turns in acting as
teachers and as pupils.
4.
SPECIFICATION OF THE LEARNING
ENVIRONMENT IN A SERIES OF LESSONS
Starting from the aims and the basic features of the learning environment
a series of lessons was elaborated and implemented from January to May
1999. Each of the participating classes spent about two hours a week in the
learning environment over a period of 11 weeks. The series of lessons can be
divided into five phases.
Phase 1 (2 weeks): Introduction by the teacher and exploration by the
pupils of the five-step problem-solving strategy and the software tool
'Knowledge Forum' .
Phase 2 (3 weeks): In the beginning of each week the children solved in
groups of three a problem presented in KF by a comic-strip character called
FIXIT. Initially they could use scaffolds provided by FIXIT in the form of
KF-notes with strategic help for solving the problem in a mindful way.
Taking turns they imported their solution but also their solution strategy in
Collaborative learning of mathematics
57
KF, on which the teacher (through FIXIT) made comments in KF before the
second lesson at the end of the week. During that lesson a whole-class
discussion was organised about the solution and solution strategies of the
different groups taking into account the teacher's comments (presented by
FIXIT), and about the role and use of KF in problem-solving.
Phase 3 (6 weeks): Pupils continued to work on complex application
problems (two weeks per problem) presented by FIXIT through KF.
However, in this phase the scaffolds were gradually withdrawn as the pupils
made progress, and they were encouraged to read the work of the other
groups and to comment on it in KF before the whole-class discussion at the
end of the second week.
Phase 4 (4 weeks): In the beginning of each of two two-week periods the
groups had to pose an interesting mathematics application problem
themselves which they imported into KF; also they had to solve at least one
problem posed by another group. Each group acted as 'coach' for the other
groups with respect to their own problem. The products of that work
(problems posed, solutions given by the groups, and possible comments, all
imported in KF) were again the object of whole-class discussion and
reflection at the end of the two-week period.
Phase 5 (2 weeks): All four participating classes got involved in an
international two-week exchange project with pupils from an elementary
school in Amsterdam, The Netherlands, during which pairs of Flemish and
Dutch groups of pupils exchanged problems and problem solutions in a
similar way as in Phase 4.
S.
IMPLEMENTATION AND EVALUATION OF THE
COLLABORATIVE LEARNING ENVIRONMENT
The designed learning environment was implemented in two fifth-grade
and two sixth-grade classes of a Flemish primary school. A computer was
available in each classroom; in addition, teachers and pupils had access to a
classroom with a large number of computers all networked to a common
server.
The preparation of the teaching materials and the interactions with the
pupils via KF (through FIXIT) was done by the researchers in consultation
with the teachers. However, the lessons were taught by the regular classroom
teachers, who were also responsible for the coaching of the pupils during the
small-group activities and for the leadership of the whole-class discussion.
A large variety of instruments - a word problem test, several
questionnaires, logfiles analysis, classroom observations using
videoregistration, and interviews with pupils and teachers - was used to
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Erik De Corte et al.
collect quantitative data before and after the intervention about the cognitive,
meta-cognitive, and affective effects of the learning environment on the
participating pupils, as well as qualitative data about its implemention and
about the changes in the pupils' and the teachers' mathematical thinking and
communication processes in reaction to the CLN-based environment.
6.
RESULTS
The cognitive, meta-cognitive, and affective effects of the CLNenvironment on the pupils were mixed. According to the results of the word
problem pre-test and post-test, the learning environment had a significant
positive effect on the problem-solving competency of the sixth graders, but
not of the fifth graders. Contrary to what was observed in the previous
technology-lean study (Verschaffel et aI., 1999), questionnaire data revealed
no significant positive impact of the intervention on children's pleasure and
persistence in solving mathematical application problems, nor on their
beliefs about and attitudes towards learning and teaching mathematical
problem-solving. However, the CLN-environment yielded a significant
positive influence on pupils' beliefs about and attitudes toward
(collaborative) learning in general. Finally, a significant effect of the i in
general and computer-supported learning in particular.
The study has shown that it is possible to create an innovative computersupported collaborative environment for teaching and learning mathematical
problem-solving in the upper primary school. From the data of the teacher
evaluation forms administered throughout the intervention and the answers
during the final interviews, we can derive that the teachers were very
enthusiastic about their participation and involvement in the investigation.
Their positive appreciation of the learning environment related to both the
approach to the teaching of problem-solving as well as to the use of KF as a
supporting tool for learning; for instance, they reported several positive
developments observed in their pupils such as a more mindful and reflective
approach to word problems. Furthermore the implementation profiles, based
on the analyses of videotaped lessons of the two sixth-grade teachers,
indicated a high degree of fidelity of implementation of the learning
environment.
Finally, the CLN-environment was also enthusiastically received by most
of the pupils. Throughout the lessons and in reaction to FIXIT's farewell
note at the end of the intervention, they expressed that they liked this way of
doing word problems much more than the traditional approach. Many of the
children also reported to have learned something new, both about
information technology and about mathematical problem-solving.
Collaborative learning of mathematics
59
REFERENCES
De Corte, E. (2000) Marrying theory building and the improvement of school practice: A
permanent challenge for instructional psychology. Learning and Instruction 2000, 10,249-
266
Scardamalia, M. and Bereiter, e. (1992) An architecture for collaborative knowledge
building. In E. De Corte, M.e. Linn, H. Mandl and L. Verschaffel, (eds.) Computer-based
learning environments and problem-solving (NATO-ASI Series F: Computer and System
Sciences, Vol. 84). Berlin: Springer-Verlag
Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H. and Ratinckx, E.
(1999) Learning to solve mathematical application problems: a design experiment with
fifth graders. Mathematical Thinking and Learning, I, 195-229
BIOGRAPHY
Erik De Corte is professor of educational psychology and director of the
Centre for Instructional Psychology and Technology at the University of
Leuven, Belgium. His major research interest is to contribute to the
development of theories of learning from instruction, focusing thereby on
learning, teaching, and assessment of thinking and problem-solving,
especially in mathematics and in computational environments. He is
currently president of the International Academy of Education (1998-2004).
In March 2000 he was conferred the doctorate honoris causa of the Rand
Afrikaans University, Johannesburg, South Africa.