Measuring Teachers- Beliefs about Mathematics: A Fuzzy Set Approach
This paper deals with the application of a fuzzy set in
measuring teachers- beliefs about mathematics. The vagueness of
beliefs was transformed into standard mathematical values using a
fuzzy preferences model. The study employed a fuzzy approach
questionnaire which consists of six attributes for measuring
mathematics teachers- beliefs about mathematics. The fuzzy conjoint
analysis approach based on fuzzy set theory was used to analyze the
data from twenty three mathematics teachers from four secondary
schools in Terengganu, Malaysia. Teachers- beliefs were recorded in
form of degrees of similarity and its levels of agreement. The
attribute 'Drills and practice is one of the best ways of learning
mathematics' scored the highest degree of similarity at 0. 79860 with
level of 'strongly agree'. The results showed that the teachers- beliefs
about mathematics were varied. This is shown by different levels of
agreement and degrees of similarity of the measured attributes.
[1] Curriculum Development Centre, Ministry of Education, Malaysia.
Integrated Curriculum for Secondary School, KualaLumpur:
Government Publication, 2001.
[2] P. Cobb. Contexts, goals, beliefs and learning mathematics. For the
Learning of Mathematics, Vol. 6, no. 2, pp. 2-9, 1986
[3] M.F. Pajeras, Teachers- beliefs and educational research: cleaning up a
messy construct. Review of Educational Research, Vol. 62, pp. 307-332,
1992.
[4] P. Ernest, The impact of beliefs on the teaching of mathematics, in
Bloomfield, A. and Harries, T. (Eds). Teaching and Learning in
Mathematics, Derby: Association of Teachers of Mathematics. 1994.
[5] A.G. Thompson. The relationship of teachers- conceptions of
mathematics and mathematics teaching to instructional practice,
Educational Studies in Mathematics, Vol.15, pp. 105-127, 1984.
[6] S. Lerman. Alternative perspectives of the nature of mathematics and
their influence on the teaching mathematics, British Educational
Research Journal, 16, 53-61. 1990
[7] A.G. Thompson. Teachers- beliefs and conceptions: a synthesis of the
research: In A.D Grouws (Ed.). Handbook of Research on Mathematics
Teaching and Learning, NY: Macmillan. 1992.
[8] B. Shealy. Conceptualizing the development of two first-year secondary
mathematics teachers- beliefs. Unpublished doctoral dissertation,
University of Georgia, Athens, 1994.
[9] L.A. Zadeh . Fuzzy Set, Information and Control, Vol. 8, pp. 338 -
353, 1965.
[10] L.A. Zadeh. The concept of a linguistic variable and its application to
approximate reasoning, Part 1 and 2, Information Sciences, Vol. 8, pp.
199- 249, pp. 301- 357, 1975
[11] H.J. Zimmerman. Fuzzy Sets Theory and its applications (2nd revised
ed.). Boston: Kluwer Academics Publishers, 1991.
[12] C.C. Ragin. Fuzzy Set Social Science. Chicago: Chicago Univ Press,
2000.
[13] K. Asai,. Fuzzy Systems for Management. Amsterdam: IOS Press,
1995.
[14] G.Bojadziev and ,M. Bojadziev. Fuzzy Logic for Business, Finance and
Management. Singapore; World Scientific, 1997.
[15] S. Weon, and J. Kim. Learning achievement evaluation strategy using
fuzzy membership function, 31st ASEE/IEEE Frontiers in Education
Conference, Reno: NV, 2001.
[16] P.E. Green, and V. Srinivasan. Conjoint analysis in market research:
New developments and directions, Journal of Marketing, Vol. 54, pp. 3-
19, 1990.
[17] I.B.Turksen, and I.A. Willson.. A fuzzy set preference model for
consumer choice. Fuzzy Sets and Systems, Vol. 68, pp. 253- 353, 1994.
[18] G. Carter, and K. S. Norwood, The relationship between teacher and
student beliefs about mathematics. School Science and Mathematics,
Vol. 97, no. 2, pp. 62-67, 1997.
[19] D.R. Wittink and P Cattin, Commercial use of conjoint analysis: An
update, Journal of Marketing, Vol. 53, pp. 91-96, 1989.
[20] R. Borasi, The invisible hand operating in mathematics instruction:
Students- Conceptions and Expectations. Teaching and Learning
Mathematics in the 1990s. Reston, VA: NCTM, 1990.
[21] C.S. Lim. A study on Malaysian Mathematician-s way of knowing.
Report on Short Term Research Grant, Penang: Universiti Sains
Malaysia Press, 2002.
[22] C.S. Lim. Public Images of Mathematics. Unpublished Ph.D thesis,
University of Exeter, UK, 1999.
[23] A.G. Thompson. Teachers- beliefs and conceptions: a synthesis of the
research, in A.D Grouws (Ed.). Handbook of Research on Mathematics
Teaching and Learning, NY: Macmillan, 1992.
[24] S. Perdikaris,. Mathematizing the Van Hiele levels: a fuzzy set approach,
International Journal of Mathematics Education and Science
Technology, Vol. 27, no. 1, pp. 41-47, 1996.
[25] C.S. Crowther, W.H. Batchelder, and X. Hu, Measurement -theoretic
analysis of fuzzy logic model of perception, Psychological Review, Vol.
102, no. 2, pp. 396-408, 1995.
[26] M. A. Lazim, Construction of conceptual knowledge of quadratic
functions in QFtica: A fuzzy approach and multiple representations.
Unpublished Ph.D thesis, University College of Science and
Technology, Malaysia, 2004.
[27] M.A. Lazim, W.A. Salihin, and M.T. Abu Osman, Fuzzy sets in the
social sciences: An overview of related research, Jurnal Teknologi,
Vol.41, no.E, pp.43-54, 2004.
[1] Curriculum Development Centre, Ministry of Education, Malaysia.
Integrated Curriculum for Secondary School, KualaLumpur:
Government Publication, 2001.
[2] P. Cobb. Contexts, goals, beliefs and learning mathematics. For the
Learning of Mathematics, Vol. 6, no. 2, pp. 2-9, 1986
[3] M.F. Pajeras, Teachers- beliefs and educational research: cleaning up a
messy construct. Review of Educational Research, Vol. 62, pp. 307-332,
1992.
[4] P. Ernest, The impact of beliefs on the teaching of mathematics, in
Bloomfield, A. and Harries, T. (Eds). Teaching and Learning in
Mathematics, Derby: Association of Teachers of Mathematics. 1994.
[5] A.G. Thompson. The relationship of teachers- conceptions of
mathematics and mathematics teaching to instructional practice,
Educational Studies in Mathematics, Vol.15, pp. 105-127, 1984.
[6] S. Lerman. Alternative perspectives of the nature of mathematics and
their influence on the teaching mathematics, British Educational
Research Journal, 16, 53-61. 1990
[7] A.G. Thompson. Teachers- beliefs and conceptions: a synthesis of the
research: In A.D Grouws (Ed.). Handbook of Research on Mathematics
Teaching and Learning, NY: Macmillan. 1992.
[8] B. Shealy. Conceptualizing the development of two first-year secondary
mathematics teachers- beliefs. Unpublished doctoral dissertation,
University of Georgia, Athens, 1994.
[9] L.A. Zadeh . Fuzzy Set, Information and Control, Vol. 8, pp. 338 -
353, 1965.
[10] L.A. Zadeh. The concept of a linguistic variable and its application to
approximate reasoning, Part 1 and 2, Information Sciences, Vol. 8, pp.
199- 249, pp. 301- 357, 1975
[11] H.J. Zimmerman. Fuzzy Sets Theory and its applications (2nd revised
ed.). Boston: Kluwer Academics Publishers, 1991.
[12] C.C. Ragin. Fuzzy Set Social Science. Chicago: Chicago Univ Press,
2000.
[13] K. Asai,. Fuzzy Systems for Management. Amsterdam: IOS Press,
1995.
[14] G.Bojadziev and ,M. Bojadziev. Fuzzy Logic for Business, Finance and
Management. Singapore; World Scientific, 1997.
[15] S. Weon, and J. Kim. Learning achievement evaluation strategy using
fuzzy membership function, 31st ASEE/IEEE Frontiers in Education
Conference, Reno: NV, 2001.
[16] P.E. Green, and V. Srinivasan. Conjoint analysis in market research:
New developments and directions, Journal of Marketing, Vol. 54, pp. 3-
19, 1990.
[17] I.B.Turksen, and I.A. Willson.. A fuzzy set preference model for
consumer choice. Fuzzy Sets and Systems, Vol. 68, pp. 253- 353, 1994.
[18] G. Carter, and K. S. Norwood, The relationship between teacher and
student beliefs about mathematics. School Science and Mathematics,
Vol. 97, no. 2, pp. 62-67, 1997.
[19] D.R. Wittink and P Cattin, Commercial use of conjoint analysis: An
update, Journal of Marketing, Vol. 53, pp. 91-96, 1989.
[20] R. Borasi, The invisible hand operating in mathematics instruction:
Students- Conceptions and Expectations. Teaching and Learning
Mathematics in the 1990s. Reston, VA: NCTM, 1990.
[21] C.S. Lim. A study on Malaysian Mathematician-s way of knowing.
Report on Short Term Research Grant, Penang: Universiti Sains
Malaysia Press, 2002.
[22] C.S. Lim. Public Images of Mathematics. Unpublished Ph.D thesis,
University of Exeter, UK, 1999.
[23] A.G. Thompson. Teachers- beliefs and conceptions: a synthesis of the
research, in A.D Grouws (Ed.). Handbook of Research on Mathematics
Teaching and Learning, NY: Macmillan, 1992.
[24] S. Perdikaris,. Mathematizing the Van Hiele levels: a fuzzy set approach,
International Journal of Mathematics Education and Science
Technology, Vol. 27, no. 1, pp. 41-47, 1996.
[25] C.S. Crowther, W.H. Batchelder, and X. Hu, Measurement -theoretic
analysis of fuzzy logic model of perception, Psychological Review, Vol.
102, no. 2, pp. 396-408, 1995.
[26] M. A. Lazim, Construction of conceptual knowledge of quadratic
functions in QFtica: A fuzzy approach and multiple representations.
Unpublished Ph.D thesis, University College of Science and
Technology, Malaysia, 2004.
[27] M.A. Lazim, W.A. Salihin, and M.T. Abu Osman, Fuzzy sets in the
social sciences: An overview of related research, Jurnal Teknologi,
Vol.41, no.E, pp.43-54, 2004.
@article{"International Journal of Business, Human and Social Sciences:62258", author = "M.A. Lazim and M.T.Abu Osman", title = "Measuring Teachers- Beliefs about Mathematics: A Fuzzy Set Approach", abstract = "This paper deals with the application of a fuzzy set in
measuring teachers- beliefs about mathematics. The vagueness of
beliefs was transformed into standard mathematical values using a
fuzzy preferences model. The study employed a fuzzy approach
questionnaire which consists of six attributes for measuring
mathematics teachers- beliefs about mathematics. The fuzzy conjoint
analysis approach based on fuzzy set theory was used to analyze the
data from twenty three mathematics teachers from four secondary
schools in Terengganu, Malaysia. Teachers- beliefs were recorded in
form of degrees of similarity and its levels of agreement. The
attribute 'Drills and practice is one of the best ways of learning
mathematics' scored the highest degree of similarity at 0. 79860 with
level of 'strongly agree'. The results showed that the teachers- beliefs
about mathematics were varied. This is shown by different levels of
agreement and degrees of similarity of the measured attributes.", keywords = "belief, membership function, degree of similarity, conjoint analysis", volume = "3", number = "9", pages = "1796-5", }
