On Squares, Rectangles, and Square Roots - References / About the Authors / Acknowledgements

References

[1] Avital, S. History of Mathematics Can Help Improve Instruction and Learning, in F. Swetz, J. Fauvel, O. Bekken, B. Johansson, and V. Katz (eds.), Learn from the Masters, The Mathematical Association of America, Washington, 1995: 3-12.

[2] Brousseau, G. Les obstacles epistemologiques et la didactique des mathematiques, in N. Bednarz and C. Garnier (eds.), Construction des savoirs Obstacles et Conflits, CIRADE Les éditions Agence d'ARC Inc., Quebec, 1989: 41-63.

[3]  Dauben, J. W. Chinese Mathematics, in V. Katz (ed.), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press, 2007: 187-384.

[4] Duval, R. Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning, in Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1999.

[5] Fauvel, J. and van Maanen, J. (eds.) History in Mathematics Education: The ICMI Study, New ICMI Study Series, vol. 6. Kluwer, Dordrecht, 2000.

[6] Fried, M. Can Mathematics Education and History of Mathematics Coexist? Science and Education, 2001; 10: 391-408.

[7] Godino, J. D., Batanero, C., and Font, V. Fundamentos de la enseñanza y el aprendizaje de las matemáticas. In J. D. Godino, Didáctica de las matemáticas para maestros, Granada, 2004.

[8] Knuth, E. J., Stephens, A. C., McNeil, N. M., and Alibali, M. W. Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 2006: 297-312.

[9]  Li Yan and Du Shiran (trans. Crossley, J. N., and Lun, A. W.-C.), Chinese Mathematics: A Concise History, Oxford University Press, 1987.

[10] National Council of Teachers of Mathematics. Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000.

[11] Po-Hung, L. Do teachers need to incorporate the history of mathematics in their teaching? The Mathematics Teacher, 2001; 96(6): 416-421.

[12] Reimer, W. and Reimer, L. Historical connections in mathematics: Resources for using history of mathematics in the classroom, AIMS Education Foundation, Fresno, CA, 1995.

[13] Swetz, F. J. Learning Activities from the History of Mathematics, J. Weston Walch, Portland, ME, 1994.

About the Authors

María Burgos (ResearcherID: L-5265-2014, MR Author ID: 803300) is currently an assistant professor in the Department of Didactics of Mathematics at the University of Granada, Spain. She has a PhD in Mathematics and a Master's degree in Didactics of Mathematics. Her main research areas are functional analysis, mathematics education, instructional design, and teacher training.

Pablo Beltrán-Pellicer (ResearcherID: K-2196-2017) is an assistant professor in the Area of Didactics of Mathematics at the University of Zaragoza, Spain, and a secondary education teacher. He has a PhD in Didactics, and his research interests are analysis and design of educational sequences, use of specific resources (audiovisual, technological, etc.), and theory of mathematics education.

Acknowledgements

The first author is partially supported by FQM126 Research Group (Junta de Andalucía, Spain). The second author is supported by MINECO EDU2016-74848-P and S36-17D Research Group in Mathematics Education (Government of Aragón, European Social Fund). The authors would like to thank the students and teachers who made possible this rewarding experience. They would also like to acknowledge P. A. García-Sánchez and J. D. Godino for their valuable comments and suggestions, and Janet Beery for her support in the reviewing process.