Historical Development of Place Value
Author(s):
Deniz Mehmetlioglu (presenting / submitting)
Conference:
ECER 2012
Format:
Paper

Session Information

ERG SES C 12, Mathematics Education

Parallel Paper Session

Time:
2012-09-17
13:30-15:00
Room:
FCEE - Aula 4.4
Chair:

Contribution

Using history has a great importance in teaching mathematics subjects. In the history, there are many fundamental developments made by mathematicians, but most of them were ignored by later researchers. In fact, the difficulties met by children in historical development are similar to those done in today’s classroom (Avital, 1995). According to the National Council of Teachers of Mathematics (NCTM) (1991), students’ motivation may increase by the help of the using history in school curricula. In fact, the history of mathematics “creates a bridge from the past to the future” (Reimer & Reimer, as cited in Swetz, 1995, p. 14). However, some teachers may see mathematics as an abstract lesson and they try to teach by this way. A historical approach may help in understanding the mathematics is not an abstract field. Moreover, it may contribute to development of the society. 

Many studies (Kamii, 1986 ; Thompson & Bramald, 2002; MacDonald, 2008) indicate that several children get into difficulty while learning the concept of place value and the skills related to it. Therefore, there is a need for improving the main teaching abilities (Baroody, 1990).

Method

For this theoretical study, it is better to start with the history of the numbers because numbers may help teachers see the period of transition to place value. This number representation system is crucial to emerge of the place value concept. The history of numbers will be mentioned in three parts: The Ancient World, The Classical World, and China and India. In fact, historical process of numbers goes on respectively to Islamic World, The Middle Ages, Renaissance and Reformation, Early Modern Europe, The Eighteenth Century, The Nineteenth Century, The United States, and The Modern World. Hodgkin (2005) indicated that a place value system which was derived from India is used today to write our numbers. Therefore, the historical development of place value to the period of Indians will be inspected.

Expected Outcomes

In conclusion, examining the historical development of place value makes teachers aware of the period of transmission with some major contributions and their contributors. Moreover, the challenges the cultures met in the history show that how the place value is vital for not only mathematics but also society. Some implications and recommendations also could be proposed. This study offers new guidelines to teachers and program developers.

References

Avital, S. (1995). History of mathematics can help improve instruction and learning. In F. J. Swetz, J. Fauvel, O. Bekken, B. Johansson & V. Katz (Eds.), Learn from the masters! (pp. 3-12). Washington, DC: Mathematical Association of America. Baroody, A. J. (1990). How and when should place-value concepts and skills be taught? Journal for Research in Mathematics Education, 21(4), 281-286. Hodgkin, L. (2005). A history of mathematics from Mesopotamia to modernity. New York: Oxford University Press. Kamii, C. K. (1986). Place value: An explanation of its difficulty and educational implications for the primary grades. Journal of Research in Childhood Education, 1, 75-86. MacDonald, A. (2008). “But what about the oneths?” A year 7 student’s misconception about decimal place value. Australian Mathematics Teacher, 64(4), 12-16. National Council of Teachers of Education. (1991). Professional standards for teaching mathematics. Reston, VA: Author. Swetz, J. F. (1995). Mathematical pedagogy: A historical perspective. In V. Katz (2000), Using history to teach mathematics: An international perspective (pp. 11‐16). Washington, DC: Mathematical Association of America. Thompson, I. & Bramald, R. (2002). An Investigation of the Relationship between Young Children’s Understanding of the Concept of Place Value and Their Competence at Mental Addition. Report for the Nuffield Foundation, Department of Education, University of Newcastle upon Tyne.

Author Information

Deniz Mehmetlioglu (presenting / submitting)
Middle East Technical University
Elementary
Ankara

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