THE EFFECT OF PROBLEM POSING TASKS USED IN MATHEMATICS INSTRUCTION TO MATHEMATICS ACADEMIC ACHIEVEMENT AND ATTITUDES TOWARD MATHEMATICS

Abstract

The purpose of this research is to examine the effects of problem posing intervention on 8th grade students’ mathematics achievement and attitudes toward mathematics. Word problems were used in the research as a tool to observe the differences between experimental and control groups. We analyzed the effects of problem posing instruction by specially designed tests on pre and post activities. Meanwhile we sought student responses through individual meetings.This study has been conducted with 8th grade students at a Kazakh High School for gifted students during the second semester of 2010-2011 academic years. There were 54 students in total that were divided into two groups. One of the groups was experimental and the other was control group. There was equal number of students in each group with a number of 27. The research took two months in the same school.The research used a mixed methods design with quantitative and qualitative components. Data from quantitative component that was pre and post test which were analyzed by using SPSS computer package. Qualitative design included data through which students were compared from pre to post intervention opinions. We used the Mathematics Achievement Test in order to measure the students’ mathematics academic achievement. In order to measure students’ attitudes toward mathematics, we used Mathematics Attitude Scale .The reliability of the tests were measured by special techniques and the value of  Cronbach's Alpha constant was  calculated as 0.83 for achievement test and 0.90 for attitude scale. During the problem posing instruction with experimental group students we used the activities that were specially designed word problems in the light of problem posing stages. Traditional educational methods were used in the control group.  In addition, some questions were prepared for the students who got extreme scores from the activities. At the end of the research, data was evaluated by using paired sample t-test and the analyses of interview with students were conducted by using the descriptive methods.

Keywords: Problem posing, Mathematics academic achievement, Attitudes.

REFERENCES

National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. - Reston,Virginia. : National Council of   Teachers of Mathematics, 2000. - pp. 52-55.

National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. - Reston,Virginia. : National  Council  of Teachers of  Mathematics, 1989. - p.223

Stanic, G.A., Kilpatrick, J. 1988. Historical Perspectives on Problem Solving In the Mathematics Curriculum. International Journal of Educational Research.- Georgia Athens, GA 30602.: University of Georgia, 1992.-  pp.1-22. Cai, J. Hwang, S. Generalized and Generative Thinking in US and Chinese Students’ Mathematical Problem Solving and Problem Posing//Journal  of Mathematical Behavior. -2002. -No 21.-  pp 401-421

Lowrie,T.A. 2002.Designing a Framework for Problem posing:Young Children Generating Open Ended Tasks //Contemporary Issues in Early Childhood.-2002 .-No3 (3).-pp. 354-364.]

Brown,S.I. Walter ,M.I. (1993) The Art of Problem Posing.(2nd Edition).- Hillsdale,New.Jersey:Lawrance Earlbaum Associates,1993.-pp 16-27.]

Shoenfeld,A.H. Explorations of The Students’ Mathematical Beliefs and Behaviour//Journal for Research in Mathematics Education.-1989.-No20(4).-pp.338-355

Polya, G. How to Solve It:A New Aspect of Mathematical Method. .-New Jersey:Princeton University Press,1973.- pp 5-6.]  Silver, E.A.  On Mathematical Problem Posing//For The Learning of Mathematics.-1994.-No14.- pp 19-28

Philippou, G.N. Nicolaou, A.A. Efficacy Beliefs, Ability In Problem Posing and Mathematics Achievement // Proceedings of the 3rd International     Biennial Self Research Conference Berlin, Self-Concept,Motivation and Identity:Where to come from here .- 2004.-pp 177-188.

Cronbach, L. J. (1951). Coefficient Alpha and the Internal Structure of Tests //Psychometrika.-1951.-No 16.-pp. 297-334.

Fennema E. And Sherman J. ,1986)Fennema-Sherman Mathematics Attitudes Scales. Instruments Designed to measure attitudes towards the learning of mathematics by females and males.- Madison.: Wisconsin Center for Education Research School of Education, University of Wisconsin,1986-.

Rosnick,P.(1981) Some misconceptions concerning the concept of variable// Mathematics Teachers.-1981.-No 74.- pp.418-420

Stoyanova, E., Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.),Technology in Mathematics Education (518–525). Melbourne: Mathematics Education Research Group of Australasia.

Torrance, E. P. The Nature of Creativity as Manifest in its testing. – In R. J. Sternberg (Ed.): The Nature of Creativity: Contemporary   Psychological Perspectives. – New York.: Cambridge University Press, 1988.-pp. 43–75.

McLeod, B. D. Research on Affect and Mathematics Learning in the 1970 to the Present //Journal for Research in Mathematics Education.-1994.-No25 (6).-pp 637-647.

Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243-270.