### Effectiveness of problem posing and investigation in terms of problem solving abilities, motivation and achievement in mathematics

^{(1*)}, Dhoriva Urwatul Wutsqa

^{(2)},

(1) Universitas Negeri Yogyakarta

(2) Universitas Negeri Yogyakarta

(*) Corresponding Author

#### Abstract

The study aims at describing the comparison between the Problem-Posing Approach and the Investigation Approach in terms of effectiveness from the perspective of Mathematical Problem-Solving Skills, mathematical motivation and Mathematical Learning Achievements. The nature of the study is a quasi-experimental research. During the conduct of the study, the overall number of populations was 206 students from Grade VII of the State 2 Junior High School Gamping. The samples within the study were selected randomly from the population namely 32 students from Grade VII A and 34 students from Grade VII B. Then, the instrument that had been administered within the conduct of the study was the Mathematical Problem-Solving Skills Test, the Mathematical Learning Achievement Test and the Mathematical Learning Motivation Questionnaire. After the data had been gathered, the overall data were analysed by using the one-sample t-test, the T^{2} Hotteling’s Test and the independent sample t-test. The results of the study show that the learning process by means of Investigation Approach has been more effective in comparison to Problem-Posing Approach from the perspective of Mathematical Problem-Solving Skills and Mathematical Learning Achievement but, on the other hand, the results of the study also show that the learning process by means of Problem-Posing Approach has been more effective in comparison to Investigation Approach from the perspective of Mathematical Learning Motivation for the Grade VII students of the State 2 Junior High School Gamping.

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Abu, R., & El Sayed, E. (2000). Effectiveness of problem posing strategies on perspective mathematics teachers’ problem-solving performance. Journal of Science and Mathematics Education in S.E. Asia, 1, 56-69.

Adams, D., & Hamm, M. (2010). Demystify math, science, and technology: Creativity, innovation, and problem solving. Plymouth: Rowman & Littlefield Publisher, Inc.

Alderman, M. K. (2004). Motivation for achievement: Possibilities for teaching and learning. Mahwah, NJ: Lawrence Erlbaum Associates.

Ambrose, S. A., Bridges, M. W., & DiPietro, M. (2010). How learning work. San Fransisco: John Wiley & Sons, Inc.

Arends, R.I., & Kilcher, A. (2010). Teaching for student learning: Becoming an accomplished teacher. New York: Routledge.

Azwar, S. (2010). Sikap manusia: Teori dan pengukurannya. Yogyakarta: Pustaka Pelajar.

Bailey, J. (2007). Mathematical investigations: A primary teacher educator’s narrative journey of professional awareness. Dalam J. Watson & K. Beswick (Eds.), Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (MERGA): Mathematics: Essential research, essential practice (Vol. 1, pp.103-112).

Bonotto, C. (2010). Engaging student in mathematical modeling and problem posing activities. Journal of Mathematical Modelling and Application, 3, 18-32.

Brophy, J. (2010). Motivating students to learn. New York, NY: Routledge.

Brown, S.I., & Walter, M.I. (2005). The art of problem posing (3rd ed.). Mahwah: Lawrence Erlbaum Associates, Publishers.

Byrnes, J. P. (2008). Cognitive development and learning in instructional contexts (3rd ed.). New York: Pearson Education, Inc.

Carson, J. (2007). A problem with problem solving: Teaching thinking without teaching knowledge. Journal of The Mathematics Educator 2007, 2, 7-15.

Clark, A. (2009). Problem solving in Singapore Math. Diambil pada tanggal 18 Januari 2012, dari http://www.hmheducation.com/singaporemath/ pdf/MIFProbSolving. pdf.

Cohen, R.J., & Swedlik, M.E. (2009). Psychological testing and assesment: An introduction to tests and measurement (7th ed.). New York: McGraw Hill Published.

Cotton, T. (2010). Understanding and teaching primary mathematics. Harlow: Pearson Education.

Dembo, M. H. (2004). Motivation and learning strategies for college success: A self-management approach. Marwah, NJ: Lawrence Erlbaum Associates.

Depdiknas. (2006). Peraturan Menteri Pendidikan Nasional RI Nomor 22, Tahun 2006, tentang Standar Isi untuk Satuan Pendidikan Dasar Dan Menengah.

Diezmann, C. M., Watters, J. J., & English, L. D. (2001). Implementing mathematical investigations with young children. Proceedings 24th Annual Conference of the Mathematics Education Research Group of Australasia, pp 170-177, Sydney.

Elliot, S. N., et al. (2002). Educational psychology: Effective teaching, effective learning (3rd ed.). Boston: McGraw Hill.

Gorman, R.M. (1974). The psychology of classroom learning: An inductive approach. Columbus: Meril Publishing Company.

Grimison, L. & Dawe, L. (2000). Report Supporting for the Advanced and Intermediate Courses of the NSW Mathematics Years 9–10 Syllabus. Dalam Literature Review: Report on Investigational Tasks in Mathematics in Years 9–10 for Advanced and Intermediate Students. New South Wales: University of New South Wales.

Guvercin, S., Cilavdaroglu, A. K., & Savas, A. C. (2014). The effect of problem posing instruction on 9th grade students’ mathematics academic achievement and retention. International Journal of Contemporary and Applied Study of Man, 17, 129-136.

Haylock, D., & Thangata, F. (2007). Key concepts in teaching primary mathematics. London: SAGE Publications.

Hawkins, K. B., Florian, L., & Rouse, M. (2007). Achievement and inclusion in schools. New York, NY: Routledge.

Jaworski, B. (2003). Investigating mathematics teaching: A constructivist enquiry. London: Falmer Press.

Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis (6th ed.). New Jersey: Pearson Prentice Hall.

Kirkley, J. (2003). Principles for teaching problem solving. Indiana University. Downloaded on March 20th, 2012, from www.d55.k12.id.us/plato/I.../principlesforteachingproblemsolving.pdf.

Lavy, I., & Shriki, A. (2007). Problem posing as a model means for developing mathematical knowledge of prospective teachers. Emek Yezreel Academic College. PME-31.

NCTM. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

Ormrod, J. E. (2003). Educational psychology: Developing learners (4th ed.). New Jersey, NJ: Merril Prentice Hall.

Pearson, R. W. (2010). Statistical persuasion. Thousand Oaks: SAGE.

Polya, G. (1973). How to solve it: A new aspect of mathematical method. Princeton: Princeton University Press.

Ponte, J. (2001). Investigating in mathematics and in learning to teach mathematics. In F. L. Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp.53-72). Dordrecht: Kluwer.

Rencher, A. C. (1998). Multivariate statistical inference and applications. New York: John Wiley & Sons, Inc.

Royer, J. M. (Ed.). (2003). Mathematical cognition. Greenwich, Connecticut: Age Publishing, Inc.

Santrock, J. W. (2011). Educational psychology (5th ed.). New York: McGrow-Hill Companies.

Shumway, R. J. (Eds.). (1980). Research in mathematics education. Reston: NCTM.

Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students [Versi Elektronik]. Journal for Research in Mathematics Education, 5, 521-539.

Silver, E. A., et al. (1996). Posing mathematical problems: An exploratory study [Versi Elektronik]. Journal for Research in Mathematics Education, 27(3), 293-309.

Slavin, R. E. (2006). Educational psychology: Theory and practice (8th ed.). Boston, MA: Pearson Education.

Stevens, J. P. (2009). Applied multivariate statistics for the social sciences (5th ed.). New York: Routledge.

Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.). Boston: Allyn & Bacon.

Walpole, R. E. (1997). Pengantar Statistika (Edisi ke-3). Jakarta: Gramedia Pustaka Utama.

Williams, K. C., & Williams, C. C. (2010). Five key ingredients for improving student motivation. Research in Higher Education Journal. Downloaded on November 20th, 2013, from http://www.aabari.com/manuscripts/11834.pdf

Woody, R. H., Lavoie, J. C., Epps, S. (1992). School psychology: A development and social system approach. New York: Allyn & Bacon.

Woolfolk, A. E. (2005). Educational psychology (9th ed.). Boston: Allyn and Bacon.

DOI: http://dx.doi.org/10.33292/amm.v1i2.27

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