AASCIT - Journal - All Issues

ISSN Print: 2472-9450 ISSN Online: 2472-9469

International Journal of Psychology and Cognitive Science

The Journal

Manuscript Information

The Organizational Features of Good Mathematical Cognitive Structure Based on the Flop-Map Method

International Journal of Psychology and Cognitive Science
Vol.4 , No. 2, Publication Date: Jun. 1, 2018, Page: 67-74

644 Views Since June 1, 2018, 356 Downloads Since Jun. 1, 2018

Paper in PDF (278K)

Follow on

Authors

[1]	Zezhong Yang, The School of Mathematics and Statistics, Shandong Normal University, Jinan, China.
[2]	Zhaohua Qu, The School of Mathematics and Statistics, Shandong Normal University, Jinan, China.

Abstract

This study aims to find out the organizational features of mathematics knowledge in good mathematical cognitive structure (GMCS) based on the previous studies with the help of flop-map method. The results indicated the GMCS: (1) contained a relatively larger amount of more inclusive and abstract knowledge, such as propositions about connotation, domain, range, odd-even and monotone properties of the general function, as well as the relatively more knowledge about core concepts, such as propositions about connotation, domain, and range of function. (2) contained relatively more knowledge processed by higher-order conditional inferring and comparing and contrasting, as well as the radical defining, besides the majority processed by describing. (3) contained a larger amount of relatively more exact knowledge. (4) contained more connections and it was more compact and likely to be activated. (5) contained not any misconceptions about the connotation of the core concepts. (6) the connections contained in GMCS were the ones between parallel knowledge as well as between inclusive knowledge. These new findings undoubtedly enriched the existing results about GMCS and deepened the research about GMCS.

Keywords

Mathematics Proposition, Mathematical Cognitive Structure, Outstanding Students, Flop-Map

Reference

[01]	Zhang, Ch. W. (2003). The Psychological Meaning of Students’ Mathematical Cognitive Structure in Mathematics Teaching. Research of Mathematics Teaching-Learning, 12, 2-4.
[02]	Yu, P. (2004). Psychology of Mathematics Education. Nanning: Guangxi Education Publishing House.
[03]	Skemp, R. R. (1971). The psychology of learning mathematics. Penguin Books Limited.
[04]	Yang, Q. (1993). On the Influence of Cognitive Structure on Mathematics Learning -- One of the Explores about Psychological Factors that Have Influence on Mathematics Learning. Journal of Mathematics Education, 1, 66-70.
[05]	Zhang, M. L.(2007). How the Knowledge and Cognitive Structure Promote Each Other?. China Education Daily, 5, 11-23.
[06]	Zhang, Y. (2002). The Functions of Good Mathematical Cognitive structure. Proceedings of Conference on Psychology and Social Harmony. Wuhan: Wuhan University Scientific Research Publishing.
[07]	Wang, G. M. & Wang, Y. (2004). The Comparison of Top and Ordinary Students’ Mathematical Cognitive Structures in Senior High School, the Possible Reasons for difference, and Teaching Suggestions. Reference for Middle School Mathematical Education, 12, 1-4.
[08]	Han, B. & Wang, G. M. (2005). Role of Cognitive Structure and Reflections on It in the Process of Problem Solving. Educational Department of Journal of Junior Mathematics, 6, 5-7.
[09]	Jin, X. F. (2011). Again on the Construction of Students' Good Mathematical Cognitive Structure. New Curriculum Research, 209, 179-181.
[10]	Zhao, Ch. X. (2013). Optimizing and Perfecting Students' Mathematical Cognitive Structure in Inquiry Learning. Educational Practice and Research, 5, 53-55.
[11]	Sun, D. D., & Yang Z. Zh. (2015a). Research on Good Mathematical Cognitive Structure in Mainland China. Advances in Social and Behavioral Sciences: Proceeding of 2015 3rd Asian Conference on the Social Sciences, 15: 216-219.
[12]	Sun, D. D., & Yang Z. Zh. (2015b). Study on Content and Organization of Mathematical Cognitive Structure in Mainland China. Advances in Intelligent Systems Research, 283.
[13]	Maker, C. J. (1981). Curriculum Development for the Gifted. Aspen Publications.
[14]	NCTM (2000). Principles and Standard for School Mathematics, Reston, NJ.
[15]	Johnson, D. T. (2000). Teaching Mathematics to Gifted Students in a Mixed-Ability Classroom. Eric DIGEST E594, ERIC Publications.
[16]	Klein, F. (1989). Elementary Mathematics Under the High Viewpoint. Shijiazhuang: Hubei Education Publishing House.
[17]	Anderson, O. R. & Demetrius, O. J. (1993). A flow-map method of representing cognitive structure based on respondents' narrative using science content. Journal of Research in Science Teaching, 30, 953-969.
[18]	Zhang, J. W. & Chen, Q. (2000). Test Method of Cognitive Structure. Journal of Psychological Science, 6, 750-751.
[19]	Sofia M. V. C., Vitor G. L., Luis M. C. G., & Ricardo L. G. (2017). Evaluation of Changes in Cognitive Structures after the Learning Process in Mathematics. International Journal of Innovation in Science and Mathematics Education, 25 (2): 17-33.
[20]	Tsai, C. C. (2001). Probing Students’ Cognitive Structures in Science: the Use of a Flow Map Method Coupled with a Meta-Listening Technique. Studies in Educational Evaluation, 257-268.
[21]	Yang Z. Z., Zhu M., Qu Z. H., & Zhang Y. Q. (2018). Research on Organization of Mathematics Knowledge in Good Mathematical Cognitive Structure. Eurasia Journal of Mathematics, Science and Technology Education, 14 (1), 291-302.