MISCONCEPTIONS IN GEOMETRY AND SUGGESTED SOLUTIONS FOR SEVENTH GRADE STUDENTS
Abstract
The principal aim of this study is to find the weaknesses of secondary school students at geometry questions of measures , angles and shapes , transformations and construction and 3-D shapes. The year 7 curriculum contains 4 geometry topics out of 17 mathematics topics. In addition to this , this study aims to find out the mistakes, 28 , 7th grade students made in the last 4 exams including two midterms and two final exams.To collect data, students were tested on two midterms and two final exams using open–ended questions on geometry to analyze their problem solving skills and to test how much they acquired during the year.Frequency tables were used in data analysis.To fulfill this aim in the first midterm exam the subject measures were tested.In the first final exam which followed the first midterm exam in addition to measures and angles shapes skills were also tested. Following these tests , in the second midterm we tested the students on transformation and construction. A descriptive methodology and student interview were used in the study to analyze and interpret the results. The results from this study revealed that 7th grade secondary school students have a number of misconceptions, lack of background knowledge, reasoning and basic operation mistakes at the topics mentioned above.
Keywords: mathematics education, student difficulties, geometry questions, misconceptions, geometrical errors, teaching suggestions for geometry.
REFERENCES
Altun, M. (2008). ilkögretim ikinci Kademe (6, 7 ve 8. Sınıflarda) Matematik Ögretimi, 5. Baskı, Bursa: Aktüel Yayınları.
Archavsky and Goldenberg, 2005 N. Archavsky, P. Goldenberg Perceptions of a quadrilateral in a dynamic environment ,in: D. Carraher, R. Nemirovsky (Eds.), Medium and meaning: video papers in mathematics education research, Journal of Research in Mathematics Education Monograph XIII [CD-ROM], National Council of Teachers of Mathematics, Reston, VA (2005)
Baykul, Y. (1987). Matematik Ögretimi Yönünden Okullarımızdaki Durum, Hacettepe Üniversitesi Egitim Fakültesi Dergisi. 2, 154-168.
Ben-Hur, M. (2006). Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving, Association for Supervision
Baykul, Y. (2002). İlkögretimde Matematik Ögretimi 6.-8. Sınıflar için, Ankara: Pegem A Yayıncılık
Boekaerts, M. (1992). The adaptable learning process: Initiating and maintaining behavioral change. Journal of Applied Psychology: An international Review, 41, 377-397.
Boekaerts, M. (1995). The interface between intelligence and personality as determinants of classroom learning. In D.H. Saklofske & M. Zeidner (Eds.), Handbook of Personality and Intelligence (pp. 161-183). New York: Plenum Press.
Boekaerts, M. (1997). Capacity, inlination and sensitivity for mathematics. Anxiety, Stress, and Coping, 10, 5-33
Chazan, D. (1993). High school geometry students' justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24(4), 359-387.
Clements and Battista, 1992 D.H. Clements, M.T. Battista Geometry and spatial reasoning D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning, MacMillan, New York, NY (1992), pp. 420–464
Chiu, M., Robert M. Klassen R. M. (2008). Relations of mathematics self-concept and its calibration with mathematics achievement: Cultural differences among fifteenyear- olds in 34 countries, Science Direct Learning and Instruction Volume 20, Issue 1, Pages 2-17
Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the Teaching of Geometry for the 21st Century: An ICMI study (pp. 37-52), Dordrecht: Kluwer.
Erkus A. (2005). Bilimsel Arastırma Sarmalı, Seçkin Yayınları, Ankara.
Handal, B., Herrington, T. & Chinnappan, M. (2004). Measuring the adoption of graphic calculators by secondary mathematics teachers. Proceeding of the 2nd National Conference of Graphing Calculators, October 4-6, 2004, Penang, Malaysia, 29-43.
Healy, L. & Hoyles, C. (1998). Justifying and proving in school mathematics. Technical Report on the Nationwide Survey, London: Institute of Education, University of London.
Healy, L. & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428.
Gal and Linchevski, 2010 H. Gal, L. Linchevski To see or not to see: Analyzing difficulties in geometry from the perspective of visual perception Education Studies in Mathematics, 74 (2010), pp. 163–183
Fischbein and Nachlieli, 1998 E. Fischbein, T. Nachlieli Concepts and figures in geometrical reasoning International Journal of Science Education, 20 (10) (1998), pp. 1193–1211
Indradevi, N. N. (1998). An investigation of the teaching methods using ICT to promote higher order thinking skills.
Unpublished Master Thesis, University Malaya, Kuala Lumpu
Inzunza, S. (2006). Students’ Errors and Difficulties for Solving Problems of Sampling Distributions by Means of Computer Simulation, ICOTS-7.
Jeavans, A. C,why dynamic geometry software is such an effective tool in mathematics education, Chichester,U.K.
Klein, A.S. (1998). Flexibilization of mental arithmetic strategies on a different knowledge base. Utrecht: Freudenthal Institute
Lim, C. S., & Hwa, T. Y. (2007). Promoting mathematical thinking in the Malaysian classroom: issues and challenges. Center for Research on International Cooperation in Educational Development (CRICED), University of Tsukuba
Montague,M.Applegate,B.& Marguard,K.(1993).Cognitive strategy instruction and mathematical problem solving performance of students with learning disabilities.
National Council of Teachers of Mathematics (NCTM) (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics (NCTM). (2004). Teaching children mathematics. Retrieved Oct. 16, 2004, from http://my.nctm.org/eresources/article_summary.asp?URI=TCM2005-04-3a&from=B.
National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and Evaluation Standarts for School mathematics, Reston, VA: Author.
National Council of Teachers of Mathematics (NCTM). (1991). Curriculum and Evaluation Standarts for School mathematics, Reston, VA: Author.
Porter,A.(1989).A curriculum out of balance:The case of elementary school mathematics.Educational Researcher,18(5),9-15.
Pumadevi, S. (2004). Distributed cognition and the use of graphing calculators in the learning of mathematics. Proceeding of the 2nd National Conference of Graphing Calculators, October 4-6, 2004, Penang, p. 93-103 Rosch, 1973 E.H. Rosch Natural categories Cognitive Psychology, 4 (1973), pp. 328–350
Schoenfeld, A. (1992). Learning to think mathematically: problem solving, metacognition and sense making in mathematics. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 189-215). New York: Macmillan
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning, Cognitive Science, 12, 257-285
Senemoglu, N., (2000). Gelisim Ögrenme ve Ögretim, Ankara, Gazi Kitapevi.
Simon, M. A., Tzur, R., Heinz, K., Kinzel, M. (2004). Explicating a Mechanism for Conceptual Learning: Elaborating the Construct of Reflective Abstraction. Journal for Research in Mathematics Education, 35(5), 305-329.
Stacey,K., MacGregor, M. (1997). Ideas About Symbolism That Students Bring to algebra, The Mathematics Teacher, Vol: 90, no:2.
Tall, D., Razali, M., R. (1993). Diagnosing Students’ Difficulties in Learning Mathematics, International Journal of Mathematics Education in Science &Technology Vol:24 pp:209-202.
Thompson, P. (1994). The Development of the Concept of Speed and its Relationship to Concepts or Rate, In G. Harel, J.Confrey (Eds.), The Development of multiplicative reasoning in the learning of mathematics (pp. 179-234). New York, Albany: New York Press.
Van Hiele, P. M. (1959/1986). The child's thought and geometry. In D. Fuys, D. Geddes, & R. Tishchler (Eds.), English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele (pp. 243–252).
Vermeer, H.J. (1997). Sixth-grade students' mathematical problem-solving behavior: Motivational variables and gender differences. Doctoral Dissertation. The Netherlands: Leiden University
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