this work indicates that we have begun the crucial journey into mathematical proficiency for all and that the principles of How People Learn can guide us on this journey.

NOTES

1.  

Holt, 1964, pp. 143-144.

2.  

National Research Council, 2001.

3.  

See Fuson, 1986a, 1986b, 1990; Fuson and Briars, 1990; Fuson and Burghardt, 1993, 1997; Fuson et al., 1994, 2000; Fuson and Smith, 1997; Fuson, Smith, and Lott, 1977; Fuson, Wearne et al., 1997; Fuson, Lo Cicero et al., 1997; Lo Cicero et al., 1999; Fuson et al., 2000; Ron, 1998.

4.  

Carey, 2001; Gelman, 1990; Starkey et al., 1990; Wynn, 1996; Canfield and Smith, 1996.

5.  

Case et al., 1999; Ginsburg, 1984; Saxe, 1982.

6.  

Carraher, 1986; Carraher et al., 1985.

7.  

Lave, 1988; Sternberg, 1999.

8.  

De la Rocha, 1986.

9.  

Ceci and Liker, 1986; Ceci, 1996.

10.  

National Council of Teachers of Mathematics, 2000.

11.  

National Research Council, 2001.

12.  

See, e.g., Hatano and Inagaki, 1996; Resnick, 1987; Stigler and Heibert, 1997.

13.  

Stigler and Heibert, 1999.

14.  

National Research Council, 2004.

15.  

See, e.g., Tobias, 1978.

16.  

Hufferd-Ackles et al., 2004.

17.  

Sherin, 2000a, 2002.

18.  

See, e.g., Bransford et al., 1989.

19.  

See, e.g., Schwartz and Moore, 1998.

20.  

Sherin, 2000b, 2001.

21.  

Lewis, 2002, p. 1.

22.  

Fernandez, 2002; Lewis, 2002; Stigler and Heibert, 1999.

23.  

Remillard, 1999, 2000.

24.  

Remillard and Geist, 2002.

25.  

Remillard, 2000.

REFERENCES

Anghileri, J. (1989). An investigation of young children’s understanding of multiplication. Educational Studies in Mathematics, 20, 367-385.

Ashlock, R.B. (1998). Error patterns in computation. Upper Saddle River, NJ: Prentice-Hall.


Baek, J.-M. (1998). Children’s invented algorithms for multidigit multiplication problems. In L.J. Morrow and M.J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics. Reston, VA: National Council of Teachers of Mathematics.



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