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M. Khalid et al. Enhancing creativity and problem solving skills through creative problem...
mature closure and abstractness of titles in his figural test. Torrance saw creativity broadly
as the process of sensing a problem, searching for possible solutions,
drawing hypotheses,
testing and evaluating, and communicating the results to others. He added that the process
includes original ideas, a different point of view, breaking out of the mould, as well as recom-
bining ideas or seeing new relationships among ideas. However, this research chooses the
four components of creativity that Torrance (1971, p. 76) identified in his original creativ-
ity framework for mathematics problem solving in order to characterize the development
of students’ creative thinking. Creativity is believed to be an integral
part of mathematics
(Brunkalla, 2009) and has been proposed as one of the major components to be included
in mathematics education, since “the essence of mathematics is thinking creatively” (Mann,
2006, p. 239).
This study proposed creativity to be fostered through CPS. Whether problem solving is
creative or not depends on how it is taught and how it is learnt. Teachers’ pedagogical content
knowledge influences how mathematics will be taught. The problem context (environment –
whether it will be personal or social learning, teacher-centred or student-centred, interactive
etc.
) or the nature of tasks (problem type – whether open ended, static, dynamic, ill-defined)
determine the success of CPS. On the other hand, the process of learning (in
this case prob-
lem solving), is made up of the following sequence: exploring and understanding, represent-
ing and formulating, planning and executing, and finally monitoring and reflecting (OECD,
2014c) which is comparable to Polya (2004), a classic which was used in the framework of
this study (refer to Figure 1).
The middle part of the framework shows mutual relationship between CPS and creativ-
ity. The components of creativity that were examined in this study are the combination of
Torrance (1971) and Guilford (1967, pp. 10–11) model – fluency, flexibility, originality and
elaboration. Fluency is the ability to
generate quantities of ideas, flexibility is the ability to
create different categories of ideas from different points, originality is the ability to create
new and unique ideas and finally, elaboration is the ability to expand on an idea. Meanwhile,
three problem solving criteria were emphasized so that CPS could be generated. The first
criterion is the process of problem solving, where a 4-step process by Polya (2004, p. 41)
in guiding students to solve problems was adopted. The second and third criteria of CPS
are the learning context and nature of problem. The learning context here means students
setting which are characterized by student-centred and collaborative group-work learning,
where social interaction and negotiation of understanding with
others can help students to
construct knowledge.
Additionally, the nature of problems describes the kind of problems that were posed dur-
ing CPS which are open-ended, authentic and dynamic. Authentic problems provide realistic
contexts that provide for construction of knowledge. In order to generate creativity in prob-
lem solving, the problems created should be open-ended where multiple solutions (answers
and/or methods) is possible. Dynamic here means the problems created and posed should
create a lively environment where students would be discussing or debating their solutions.
Finally, lesson study will help the teachers to come up with criteria 2 and 3. However, this
paper will only report the middle part, which is on creativity and problem solving and the
relationship between them, and not the lesson study part.