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.



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