Comparison of 6th-8th graders’ efficiencies, strategies and representations regarding generalization patterns
Tipo de documento
Autores
Lista de autores
Akkan, Yasar
Resumen
The study aims to compare and determine 6th-8th graders’ efficiencies, strategies and representations of student from different grades (from 6th to 8th) when dealing with problems related to linear and quadratic patterns. Research data was obtained from tests applied to 246 students and clinical interviews implemented with 18 students. It was shown that when grade increases students’ efficiencies of generalizing pattern improve in a positive way in all levels. Besides this, as learning levels of 6th and 8th grade students increase, the variety in pattern generalization strategies changed at least in all types of patterns. While students at different learning levels generally used recursive strategy to solve all the problems, the number of the students using explicit strategies is relatively low. The students of high levels use many types of representation in generalization; in contrast, the weak level students prefer mostly numerical representations.
Fecha
2013
Tipo de fecha
Estado publicación
Términos clave
Comparativo | Estrategias de solución | Patrones numéricos | Representaciones
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Volumen
27
Número
47
Rango páginas (artículo)
703-732
ISSN
19804415
Referencias
AMIT, M.; NERIA, D. Rising to the challenge: Using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM Mathematics Education, v.40, n.1,p.111-129, Jan.2008. ARMSTRONG, B. E. Teaching patterns, relationships and multiplication as worthwhile mathematical tasks. Teaching Children Mathematics, Reston, v.1, n.7, p.446-450, Mar. 1995. BECKER, J. R.; RIVERA, F.An investigation of beginning algebra students’ ability to generalize linear patterns. In: HOINS, M. J.; FUGLESTAD, A. B. (Ed.).Conference of the International Group for the Psychology of Mathematics Education.28th, 2004, Norway. Proceedings… Bergen, Norway: Bergen University College, 2004.v.1, p.286. BECKER, J.R.; RIVERA, F. Generalization strategies of beginning high school algebra students. In: CHICK, H.L.; VINCENT, J.L. (Eds.).2005, Melbourne. Conference of the International Group for the Psychology of Mathematics Education, 29th, 2005.Proceedings… Melbourne, Australia: University of Melbourne, 2005, v.4, p.121- 128. BISHOP, J. W. Linear geometric number patterns: Middle school students’ strategies.Mathematics Education Research Journal, v.12, n.2, p.107-126, Sep.2000. BREITEIG, T.; GREVHOLM, B. The transition from arithmetic to algebra: To reason, explain, argue, generalize and justify. In: NOVOTNA, I.J.; MORAOVÁ, H.; KRÁTKÁ, M.; STEHLIKOVÁ N. (Ed.).Conference of the International Group of Mathematics Education.30th, 2006,Prague.Proceedings…Prague: Charles University, 2006, v.2, p.225– 232. EBERSBACH, M.; WILKENING, F. Children’s intuitive mathematics: The development of knowledge about nonlinear growth. Children Development. v.78,n.1, p.296-308, Jan.-Feb. 2007. ENGLISH, L.D.; WARREN, E. A. Introducing the variable through pattern exploration.Mathematics Teacher, v.91, n.2, p.166-170, Feb.1998. FEIFEI, Y. Diagnostic assessment of urban middle school student learning of pre- algebra patterns.Doctoral Dissertation, Ohio State University, USA,2005. GARCIA-CRUZ, J.A.; MARTINON, A. Actions and invariant schemata in linear generalizing problems. In: PEHKONEN E. (Ed.). Conference of the International Group for the Psychology of Mathematics Education.21th, 1997, Helsinki. Proceedings… Helsinki,University of Helsinki, 1997, v.2, p.289-296. KENNEY, P.A; SILVER, E.A. Probing the foundations of algebra: Grade 4 pattern items in NAEP. Teaching Children Mathematics, v.3, n.6, p.268-274, Feb.1997. KREBS, A.S. Middle grade students’ algebraic understanding in a reform curriculum.School Science and Mathematics, v.103, n.5, p.233-243, May.2003. LANNIN, J. K. Developing algebraic reasoning through generalization. Mathematics Teaching in the Middle School, v.8, n.7, p.342-348, Mar. 2003. LANNIN, J.K. Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning. v.7, n.3, p.231-258, Jul.2005. LEE, L. An initiation into algebraic culture through generalization activities. In:BEDNARZ, N.; KIERAN, C.; LEE, L. (Ed.). Approaches to algebra: Perspectives for research and teaching.Kluwer: Academic Publishers, 1996, p.87-106. LEY, A. F. A cross- sectional investigation of elementary school students’ ability to work with linear generalizing patterns: The impact of format and age on accuracy and strategy choice. Master Dissertation, Toronto University, Toronto: Canada,2005. NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS (NCTM).Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM, 2000. Available at: http://www.nctm.org/standards.htm>. Access in: 07.03. 2007. ORTON, A.; ORTON, J. Pattern and the approach to algebra. In: ORTON, A. (Ed.).Pattern in the teaching and learning of mathematics. Cassell: London, 1999, p.104 - 120. ORTON, J.; ORTON, A.; ROPER, T. Pictorial and practical contexts and the perception of pattern. In: ORTON, A. (Ed.). Pattern in the teaching and learning of mathematics. Cassell: London, 1999, p.121-136. RIVERA, F.; BECKER, J.R. Figural and numerical modes of generalizing in algebra.Mathematics Teaching in the Middle School, v.11, n.4, p.198-203, Nov.2005. RIVERA, F. Visualizing as a mathematical way of knowing: Understanding figural generalization. Mathematics Teacher, v.101, n.1, p.69-75, Aug. 2007. SMITH, E. Stasis and change: Integrating patterns, functions, and algebra throughout the K-12 curriculum. In: KILPATRICK, J.; MARTIN, W.G.; SCHIFTER, D.(Ed.). A research companion to principles and standards for school mathematics. Reston, VA: NCTM, 2003, p. 136-150. STACEY, K. Finding and using patterns in linear generalizing problems.Educational Studies in Mathematics, Dordrecht, v.20, n.2,p.147–164, May.1989. SWAFFORD, J. O.; LANGRALL, C. W. Grade 6 students’ pre-instructional use of equations to describe and represent problem situations. Journal for Research in Mathematics Education. v.31, n.1, p.89-112, Jan. 2000. THOMPSON, A.G.; THOMPSON, P. W.A Cognitive perspective on the mathematical preparation of teachers: The case of algebra. In:LACAMPAGNE, C.B.; BLAIR, W.; KAPUT, J. (Ed.). The algebra initiative colloquium. Washington, DC: US Dep. of Education, 1995. p.95-116. TURKISH MINISTRY OF EDUCATION (TME).6th-8th grade mathematics curriculum. Ankara: MEB, 2005, p. 95-96. ZAZKIS, R.; LILJEDAHL, P. Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, Dordrecht, v.49, n.3, p.379-402, Mar.2002.