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Adding + It Up: Helping Children Learn Mathematics
7.
Berliner and Biddle, 1995. Opportunity to learn was also studied in what is now called the First International Mathematics Study (Husén, 1967), although there it was based on teachers’ perceptions of students’ opportunity to learn.
8.
McKnight, Crosswhite, Dossey, Kifer, Swafford, Travers, and Cooney, 1987.
9.
Knapp, Shields, and Turnbull, 1995; Mason, Schroeter, Combs, and Washington, 1992; Steele, 1992.
10.
Berliner, 1979.
11.
Stevenson and Stigler, 1992, p. 150.
12.
Freeman and Porter, 1989; Porter, 1993.
13.
See, for example, Campbell, 1996; Carpenter, Fennema, Peterson, Chiang, and Loef, 1989; Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Olivier, and Human, 1997; Knapp, 1995; Silver and Stein, 1996.
14.
Doyle, 1983, 1988; Stein, Grover, and Henningsen, 1996.
15.
Henningsen and Stein, 1997; Stein, Grover, and Henningsen, 1996.
16.
Clark and Yinger, 1979.
17.
Shavelson and Stern, 1981.
18.
Boaler, 1997.
19.
Good and Brophy, 2000.
20.
Good and Brophy, 2000.
21.
Smith, 1996.
22.
For example, Hatano, 1988, suggests that students are motivated to learn with understanding when they encounter novel problems regularly, are encouraged to seek comprehension over efficiency, and engage in dialogue.
23.
National Research Council, 1999b, pp. 29–38.
24.
Feather, 1982.
25.
Bandura, 1997; Bandura and Schunk, 1981; Dweck and Elliott, 1983.
26.
Good and Brophy, 2000.
27.
Brophy, 1998, Brophy and Kher, 1986; Good and Brophy, 2000.
28.
These principles and the discussion that follows are based largely on a synthesis by Baroody, 1999. For related research and syntheses, see also Baroody, 1987, 1996; Cawley, 1985; and Geary, 1993. For practical advice for teaching, see Thornton and Bley, 1994.
29.
Baroody, 1999.
30.
See Donlan, 1998, for example, for a discussion of students with speech deficiencies. See Nunes and Moreno, 1998, for a discussion of hearing impairment.
31.
Becker, 1981; Leder, 1987. See also Leder, 1992.
32.
Ladson-Billings, 1999.
33.
Foster, 1995.
34.
Steele, 1992.
35.
Knapp, 1995.
36.
Good and Brophy, 2000.
37.
See, for example, Ball and Bass, 2000; Cobb, Boufi, McClain, and Whitenack, 1997; Hiebert and Wearne, 1993; Lampert, 1990; Wood, 1999.
38.
Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Olivier, and Human, 1997.
