@article{5c91e6e9cae142178239fc4a6ee1fcf7,
title = "Students' performance in reasoning and proof in taiwan and germany: Results, paradoxes and open questions",
abstract = "In different international studies on mathematical achievement East Asian students outperformed the students from Western countries. A deeper analysis shows that this is not restricted to routine tasks but also affects students' performance for complex mathematical problem solving and proof tasks. This fact seems to be surprising since the mathematics instruction in most of the East Asian countries is described as examination driven and based on memorising rules and facts. In contrast, the mathematics classroom in western countries aims at a meaningful and individualised learning. In this article we discuss this {"}paradox{"} in detail for Taiwan and Germany as two typical countries from East Asia and Western Europe.",
author = "Aiso Heinze and Cheng, {Ying Hao} and Yang, {Kai Lin}",
note = "Funding Information: Leung, F. K. S. (2001): In search of an East Asian identity in mathematics education. Educational Studies in Mathematics 47, 35 – 51 Lin, F. L.; Chen, Y. J. (1999): A pilot study on proving and justifying of Taiwanese junior high school students. Dept. of Mathematics, National Taiwan Normal University, Taipei, Taiwan (in Chinese) Lin, F. L. et al. (2003): Development of Adolescents{\textquoteright} Compe-tence on Mathematical Argumentation. Technical Report of the NSC support project. Dep. of Mathematics, National Taiwan Normal University, Taipei, Taiwan Lin, F.-L.; Tsao, L.-C. (1999): Exam Maths Re-examined. In: C. Hoyles; C. Morgan; G. Woodhouse (Eds.), Rethinking the mathematics curriculum. London: Falmer, pp. 228 – 239 Marton, F.; Dall{\textquoteleft}Alba, D.; Tse, K.-T. (1996): Memorising and understanding: The keys to the paradox? In D. A. Watkins; J. B. Biggs (Eds.), The Chinese Learner: Cultural, psycho-logical, and contextual influences. Hong Kong: Comparative Education Research Centre, pp. 69 - 83 Mullis, I. V. S.; M. O. Martin; E. J. Gonzalez; K. D. Gregory; R. A. Garden; K. M. O{\textquoteright}Connor; S. J. Chrostowski; T. A. Smith (2000): TIMSS 1999 International Mathematics Report. IEA. Boston: International Study Center Lynch School of Education OECD (Ed.) (1999): Measuring student knowledge and skills. A new framework for assessment. Paris: OECD Reiss, K.; Hellmich, F.; Reiss, M. (2002): Reasoning and proof in geometry: Prerequisites of knowledge acquisition in secondary school students. In A. D. Cockburn; E. Nardi (Eds.), Proceedings of the 26th Conference of the Interna-tional Group for the Psychology of Mathematics Education. Volume IV. Norwich (Great Britain). University, pp. 113-120 Reiss, K.; Thomas, J. (2000): Wissenschaftliches Denken beim Beweisen in der Geometrie. Ergebnisse einer Studie mit Sch{\"u}lerinnen und Sch{\"u}lern der gymnasialen Oberstufe. mathematica didactica 23, pp. 96–112 Skemp, R. R. (1978): Relational understanding and instrumental understanding. Arithmetic Teacher 26 (3), pp. 9-15 Stevenson, H.W.; Stigler, J. W. (1992): The learning gap: Why our schools are failing and what we can learn from Japanese and Chinese education. New York: Summit Books Stigler, J.; Gonzales, P.; Kawanaka, T.; Knoll, S.; Serrano, A. (1999): The TIMSS videotape classroom study. U.S. Depart-ment of Education. National Center for Education Statistics, Washington, DC: Government Printing Office Voigt, J. (1984): Interaktionsmuster und Routinen im Mathe-matikunterricht. Theoretische Grundlagen und mikroethno-graphische Falluntersuchungen. Weinheim; Basel: Beltz Watkins, D. A.; Biggs, J. B. (Eds.) (1996): The Chinese Learner: Cultural, psychological, and contextual influences. Hong Kong: Comparative Education Research Centre ___________ Authors Heinze, Aiso, Dr., Lehrstuhl f{\"u}r Mathematikdidaktik, Universi-t{\"a}t Augsburg, Universit{\"a}tsstrasse 14, 86159 Augsburg, Germany Email: aiso.heinze@math.uni-augsburg.de Cheng, Ying-Hao, Prof. Dr., General Education Center, Chung Kuo Institute of Technology, No. 56, Sec. 3, Shinglung Rd., Wenshan Chiu, Taipei, Taiwan 116, Republic of China Email: yhjeng@mail.ckitc.edu.tw Yang, Kai-Lin, Prof. Dr., Center for Teacher Education, Chung Yuan Christian University, 22, Pu Jen, Chung Li 32023 Taiwan, Republic of China Email: kailinyang3@yahoo.com.tw",
year = "2004",
doi = "10.1007/BF02655668",
language = "English",
volume = "36",
pages = "162--171",
journal = "ZDM - International Journal on Mathematics Education",
issn = "1863-9690",
publisher = "Springer Verlag",
number = "5",
}