5.  

Steffe, von Glasersfeld, Richard, and Cobb, 1983, p. 24.

6.  

Steffe, Cobb, and von Glasersfeld, 1988.

7.  

Steffe, 1994.

8.  

Gelman and Gallistel, 1978.

9.  

Gelman, Meck, and Merkin, 1986; Gelman, 1990, 1993.

10.  

Briars and Siegler, 1984; Frye, Braisby, Lowe, Maroudas, and Nicholls, 1989; Fuson, 1988; Fuson and Hall, 1983, Siegler, 1991, Sophian, 1988; Wynn, 1990.

11.  

Baroody, 1992a; Baroody and Ginsburg, 1986; Rittle-Johnson and Siegler, 1998.

12.  

Siegler, 1994.

13.  

Gelman and Meck, 1983.

14.  

Briars and Siegler, 1984.

15.  

Frye, Braisby, Lowe, Maroudas, and Nicholls, 1989; Miller, Smith, Zhu, and Zhang, 1995; Wynn, 1990.

16.  

Similar suggestions have been made by Baroody, 1992a, 1992b; Fuson, 1988, 1992; and Siegler, 1991.

17.  

Fuson, 1988, p. 73.

18.  

Miller, Smith, Zhu, and Zhang, 1995.

19.  

See Ifrah, 1985; and Menninger, 1969.

20.  

The so-called Hindu-Arabic numeration system is in some sense a misnomer because the Chinese numeration system has been a decimal one from the time of the earliest historical records. Because of the frequent contact between the Chinese and the Indians since the time of antiquity, there has always been some question of whether the Indians got their decimal system from the Chinese. Language has to be the product of its culture. So the fact that the names for numbers in Chinese, especially for the teens, reflect a base-10 system indicates that the decimal system has been in place in China all along. By contrast, the Hindu-Arabic system did not take root in the West until the sixteenth century, long after the names for numbers in the various Western languages had been set. The irregularities in the English and Spanish number names may perhaps be understood better in this light.

21.  

Menninger, 1969.

22.  

Miller, Smith, Zhu, and Zhang, 1995; Miller and Stigler, 1987.

23.  

Fuson, Richards, and Briars, 1982; Miller and Stigler, 1987; Siegler and Robinson, 1982.

24.  

Baroody, 1987a.

25.  

Fuson, Fraivillig, and Burghardt, 1992; Séron, Deloche, and Noël, 1992.

26.  

Miura, 1987; Miura, Kim, Chang, and Okamoto, 1988; Miura and Okamoto, 1989; Miura, Okamoto, Kim, Steere, and Fayol, 1993.

27.  

Miller, Smith, Zhu, and Zhang, 1995.

28.  

Huttenlocher, Jordan, and Levine, 1994.

29.  

Carpenter and Moser, 1984; Siegler, 1996; Siegler and Jenkins, 1989; Siegler and Robinson, 1982; see also Baroody, 1987b, 1989; and Fuson, 1992.

30.  

Siegler, 1987.

31.  

Siegler and Jenkins, 1989.



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement