lenges they face in doing so, it is important to understand the mathematics with which they are engaged. Because we have chosen to focus on proficiency with number, chapter 3 lays out the mathematics of number.

Notes

1.  

Robitaille, 1997; Stigler and Hiebert, 1999; U.S. Department of Education, 1998b, 1999a, 1999b.

2.  

Howson, 1995; Schmidt, McKnight, and Raizen, 1997.

3.  

An analysis of data from the Second International Mathematics Study (SIMS) examined features such as time for mathematics instruction, class size, and teacher preparation, and other instructional variables and concluded that none of them alone could explain differences in achievement across countries (McKnight, Crosswhite, Dossey, Kifer, Swafford, Travers, and Cooney, 1987).

4.  

National Council of Teachers of Mathematics, 1989.

5.  

National Council of Teachers of Mathematics, 1991.

6.  

National Council of Teachers of Mathematics, 1995.

7.  

National Council of Teachers of Mathematics, 2000.

8.  

See http://www.edc.org/mcc/currcula.htm for information on the 13 NSF projects.

9.  

See Jennings, 1998. In making the case for national standards and describing the background behind the movement, Ravitch, 1995, emphasizes that when the president and the governors established national education goals in 1990, mathematics was the only subject matter for which “educators were ready to say what children should learn and teachers should teach” (p. 121).

10.  

Elmore and Rothman, 1999, p. 1.

11.  

A Nation at Risk: National Commission on Excellence in Education, 1983; America 2000: U.S. Department of Education, 1991; Goals 2000: U.S. Department of Education, 1998a.

12.  

Blank, Manise, and Brathwaite, 2000, pp. viii–xi. See also Orlofsky and Olson, 2001.

13.  

See the individual state reports in Raimi and Braden, 1998.

14.  

Fordham Foundation, 1997–98; Gandal, 1997; Joftus and Berman, 1998; Raimi and Braden, 1998; for an analysis of the divergence across the three sets of ratings, see Camilli and Firestone, 1999.

15.  

Pimentel and Arsht, 1998.

16.  

Marzano, Kendall, and Gaddy, 1999.

17.  

Dossey, 1997, p. 40.

18.  

McKnight, Crosswhite, Dossey, Kifer, Swafford, Travers, and Cooney, 1987, p. 74; Suydam, 1985; Tyson and Woodward, 1989; Woodward and Elliott, 1990.

19.  

Council of Chief State School Officers, 1998.

20.  

Woodward and Elliot, 1990; Tyson and Woodward, 1989. The observations in this paragraph are based on a review by Grouws and Cebulla, 2000.

21.  

Fey, 1980.

22.  

Grouws and Smith, 2000.



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