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provided. The problem posed is more complex than
the three other problems.
4 CONCLUSIONS
There are four categories of problems posed by
students, which contain one counting operation, two
counting operations, three counting operations, and
four counting operations. The characteristics of
problems that fall into category one are involving
one count operation, the absence of new quantitative
information and the low complexity of the question.
This shows that the source of ideas in posing
problems comes from the situation/information
provided. The characteristics of the problems
included in the second category involved two
counting operations, new quantitative information
and at least two steps in solving the problem. The
characteristics of the problems included in the third
category contain three counting operations, new
quantitative information and at least 3 steps to solve
the problem. The number of quantitative information
in the problem of third category is greater than the
categories in the second categories shows that the
students begin to develop out of the given situation.
The characteristics of the problems in the fourth
category involve four counting operations, the
presence of new quantitative information, at least 4
steps to solve the problem, and the development of
the form of the problem that was posed out of the
given situation. The development of the posed
problems in the fourth category can be seen with
more new quantitative information added and the
problems posed are more complex than the first,
second, and third categories.
REFERENCES
Bonotto, C., 2011. Engaging students in mathematical
modelling and problem posing activities. J. Math.
Model. Appl. 1, 18–32.
Cai, J., Hwang, S., 2002. Generalized and generative
thinking in US and Chinese students’ mathematical
problem solving and problem posing. J. Math. Behav.
21, 401–421.
Crespo, S., Sinclair, N., 2008. What makes a problem
mathematically interesting? Inviting prospective
teachers to pose better problems. J. Math. Teach.
Educ. 11, 395–415.
Haylock, D., 1997. Recognising mathematical creativity in
schoolchildren. ZDM 29, 68–74.
Kontorovich, I., Koichu, B., Leikin, R., Berman, A., 2011.
Indicators of creativity in mathematical problem
posing: How indicative are they, in: Proceedings of the
6th International Conference Creativity in
Mathematics Education and the Education of Gifted
Students. pp. 120–125.
Leung, S.S., Silver, E.A., 1997. The role of task format,
mathematics knowledge, and creative thinking on the
arithmetic problem posing of prospective elementary
school teachers. Math. Educ. Res. J. 9, 5–24.
Marhayati, M., Sa’dijah, C., 2018. Kemampuan berpikir
kreatif matematika siswa ditinjau dari aspek kefasihan,
fleksibilitas, dan kebaruan. Madrasah J. Pendidik dan
Pembelajaran Dasar 10, 111–117.
Pehkonen, E., 1997. The state-of-art in mathematical
creativity. ZDM 29, 63–67.
Shuk-kwan, S.L., 1997. On the role of creative thinking in
problem posing. ZDM 29, 81–85.
Silver, E.A., 1997. Fostering creativity through instruction
rich in mathematical problem solving and problem
posing. ZDM 29, 75–80.
Silver, E.A., 1994. On mathematical problem posing.
Learn. Math. 14, 19–28.
Silver, E.A., Cai, J., 1996. An analysis of arithmetic
problem posing by middle school students. J. Res.
Math. Educ. 521–539.
Singer, F.M., Ellerton, N., Cai, J., 2013. Problem-posing
research in mathematics education: New questions and
directions. Educ. Stud. Math. 83, 1–7.
Siswono, T.Y.E., 2010. Leveling students’ creative
thinking in solving and posing mathematical problem.
J. Math. Educ. 1, 17–40.
Stoyanova, E., Ellerton, N.F., 1996. A framework for
research into students’ problem posing in school
mathematics. Technol. Math. Educ. 518–525.
Van Harpen, X.Y., Sriraman, B., 2013. Creativity and
mathematical problem posing: an analysis of high
school students’ mathematical problem posing in
China and the USA. Educ. Stud. Math. 82, 201–221.
Xia, X., Lu, C., Wang, B., 2008. Research on mathematics
instruction experiment based problem posing. J. Math.
Educ. 1, 153–163.
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