EDCURRIC 714 Exploring Mathematical Thinking taught by Gail Ledger at the University of Auckland is a great paper for learning about how humanity has thought about how number systems work and how the place value system came about. The practical values come in understanding where to start developing the concept of "one" or a single unit and building that into the concept of place value among other mathematical concepts.
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| Follow this link to the University of Auckland calendar website. |
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| Ancient Egyptian numbers. Source: Grauberg, Eva (see below). |
Now, time for the obligatory declaring of evidence that I have done some reading on the topic and not just pulled these ideas out of thin air. There are many texts on place value and ancient number systems, but here are a few (no, I'm not using any particular format e.g. APA).
Place Value:
- Elementary mathematics and language difficulties; a book for teachers, therapists and parents (1998). Grauberg, Eva.
- Children's Developing Understanding of Place Value: Semiotic Aspects. Maria Varelas and Joe Becker. Cognition and Instruction, Vol. 15, No. 2 (1997), pp. 265-286
- Numbers through the ages (1989), Written Numbers pp. 76--130. Flegg, Graham.
- The Beginnings of Arithmetic, The Mathematical Gazette, Vol. 12, No. 177 (Jul., 1925), pp. 401-414. L. N. G. Filon
- Ancient Egyptian - see above sources
- Chinese -
- Joseph, G. (2011). The crest of the peacock: non-European roots of mathematics (3rd ed.). Princeton: Princeton University Press
- Pellatt, V. (2007). Numbers and numeracy in Chinese culture, language, and education : the social substratum of the development of mathematical thinking.
