71.  

Bowers, Cobb, and McClain, 1999; Hiebert and Wearne, 1996; Kamii, 1989.

72.  

Carpenter, Franke, Jacobs, Fennema, and Empson, 1998; Fuson, 1986a; Fuson and Briars, 1990; Hiebert and Wearne, 1993, 1996; Kamii, 1989.

73.  

Fuson, 1986a; Fuson and Briars, 1990.

74.  

For example, Carroll and Porter, 1998; Kamii, 1994; Lampert, 1986a, 1986b.

75.  

Baek, 1998; Ambrose, Baek, and Carpenter, in press.

76.  

See, for example, the 1999 edition of Scott Foresman-Addison Wesley Math, Grade 4.

77.  

Lampert, 1992; Murray, Olivier, and Human, 1992.

78.  

See, for example, Scott Foresman’s Seeing Through Arithmetic, Grade 4 (Hartung, Van Engen, and Knowles, 1955).

79.  

For example, Bowers, Cobb, and McClain, 1999, and Carpenter, Franke, Jacobs, Fennema, and Empson, 1998; Fuson and Burghardt, in press; Hiebert and Wearne, 1996; Kamii, 1994. In a comparison study, Hiebert and Wearne, 1993, showed that students who spent more time on fewer problems and were asked to explain their procedures outperformed their more traditionally taught peers.

80.  

Fuson, 1986a; Fuson, Smith, Lo Cicero, 1997.

81.  

For example, VanLehn, 1986, and Fuson and Burghardt, in press.

82.  

For example, Bowers, Cobb, and McClain, 1999; Carpenter, Franke, Jacobs, Fennema, and Empson, 1998; Fuson, 1986a; Fuson and Burghardt, in press; Hiebert and Wearne, 1993, 1996; Kamii, 1994.

83.  

Beberman, 1959; Rathmell and Trafton, 1990. For a similar discussion about estimation, see Buchanan, 1978. Beishuizen, 1993, discusses students connecting mental arithmetic procedures to using base-10 blocks and hundreds squares.

84.  

Cohen, 1982.

85.  

Stigler, 1984; Hatano, 1988.

86.  

Sowder, 1992.

87.  

Hope and Sherrill, 1987.

88.  

Davis, 1984.

89.  

Markovits and Sowder, 1988.

90.  

Reys, Rybolt, Bestgen, and Wyatt, 1982.

91.  

Markovits and Sowder, 1994; Rubenstein, 1985.

92.  

Sowder and Wheeler, 1989.

References

Ambrose, R., Baek, J., & Carpenter, T.P. (in press). Children’s construction of multiplication and division algorithms. In A.J.Baroody & A.Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise. Mahwah, NJ: Erlbaum.

Armstrong, G.A. (1991). Use of the part-whole concept for teaching word problems to grade three children (Doctoral dissertation, National College of Education, 1990). Dissertation Abstracts International, 52(03), 833A.



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