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Adding + It Up: Helping Children Learn Mathematics
28.
Hiebert and Wearne, 1986.
29.
Bell, Fischbein, and Greer, 1984; Fischbein, Deri, Nello, and Marino, 1985.
30.
Hiebert and Wearne, 1985.
31.
Kieren, 1988, p. 178.
32.
Mack, 1990; Peck and Jencks, 1981; Wearne and Kouba, 2000.
33.
Peck and Jencks, 1981.
34.
Behr, Lest, Post, and Silver, 1983; Bezuk and Bieck, 1993; Bezuk and Cramer, 1989; Hiebert and Wearne, 1986; Kieren, 1988; Mack, 1990; Peck and Jencks, 1981; Streefland, 1991, 1993.
35.
Cramer, Behr, Post, and Lesh, 1997; Huinker, 1998; Lappan, Fey, Fitzgerald, Friel, and Phillips, 1996; Streefland, 1991.
36.
Huinker, 1998; Lappan and Bouck, 1998.
37.
Lesh, Post, and Behr, 1988.
38.
Tourniaire and Pulos, 1985.
39.
Behr, Harel, Post, and Lesh, 1992; Cramer, Behr, and Bezuk, 1989.
40.
Post, Behr, and Lesh, 1988.
41.
Lesh, Post, and Behr, 1988.
42.
Wearne and Kouba, 2000.
43.
Ahl, Moore, and Dixon, 1992; Dixon and Moore, 1996.
44.
Lamon, 1993, 1995.
45.
Lamon, 1993.
46.
Lamon, 1995.
47.
The term composite unit refers to thinking of 3 balloons (and hence $2) as a single entity. The related term compound unit is used in science to refer to units such as “miles/hour,” or in this case “dollars per balloon.”
48.
Lamon, 1993, 1994.
49.
Heller, Ahlgren, Post, Behr, and Lesh, 1989; Langrall and Swafford, 2000.
50.
Cramer, Post, and Currier, 1993; Kaput and West, 1994.
51.
Ben-Chaim, Fey, Fitzgerald, Benedetto, and Miller, 1998; Heller, Ahlgren, Post, Behr, and Lesh, 1989.
52.
Behr, Harel, Post, and Lesh, 1992; Karplus, Pulas, and Stage, 1983.
53.
Vergnaud, 1983.
54.
Hativa and Cohen, 1995.
55.
English, 1997. See also Crowley and Dunn, 1985.
56.
Fischbein, 1987, ch. 8.
57.
Duncan and Sanders, 1980; Moreno and Mayer, 1999; Thompson, 1988.
58.
Bruno, Espinel, Martinon, 1997; Kuchemann, 1980.
59.
Arcavi and Bruckheimer, 1981; Carson and Day, 1995; Davis, 1990; Liebeck, 1990; Human and Murray, 1987.
60.
Moreno and Mayer, 1999; Mukhopadhyay, Resnick, and Schauble, 1990.
61.
Duncan and Saunders, 1980; Thompson, 1988; Thompson and Dreyfus, 1988.
