The following HTML text is provided to enhance online
readability. Many aspects of typography translate only awkwardly to HTML.
Please use the page image
as the authoritative form to ensure accuracy.
Adding + It Up: Helping Children Learn Mathematics
thinking. The term disposition should not be taken to imply a biological or inherited trait. As used here, it is more akin to a habit of thought, one that can be learned and, therefore, taught” (Resnick, 1987, p. 41).
See, for example, Stevenson and Stigler, 1992. Other researchers claim that Asian children are significantly more oriented toward ability than their U.S. peers and that in both groups attributing success to ability is connected with high achievement (Bempechat and Drago-Severson, 1999).
For evidence that U.S. students’ attitudes toward mathematics decline as they proceed through the grades, see Silver, Strutchens, and Zawojewski, 1997; Strutchens and Silver, 2000; Ansell and Doerr, 2000.
Cobb, Yackel, and Wood, 1989, 1995. For a more general discussion of classroom norms, see Cobb and Bauersfeld, 1995; and Fennema and Romberg, 1999.
National Research Council, 1989, p. 10.
Steele, 1997; and Steele and Aronson, 1995, show the effect of stereotype threat in regard to subsets of the GRE (Graduate Record Examination) verbal exam, and it seems this phenomenon may carry across disciplines.
Fuson 1992a, 1992b; Hiebert, 1986; Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Olivier, and Human, 1997. A recent synthesis by Rittle-Johnson and Siegler, 1998, on the relationship between conceptual and procedural knowledge in mathematics concludes that they are highly correlated and that the order of development depends upon the mathematical content and upon the students and their instructional experiences, particularly for multidigit arithmetic.
Hiebert and Wearne, 1996.
Ball and Bass, 2000.
The NAEP data reported on the five strands are drawn from chapters in Silver and Kenney, 2000.
Kouba and Wearne, 2000.
Wearne and Kouba, 2000.
Kouba, Carpenter, and Swafford, 1989, p. 83.
The NAEP long-term trend mathematics assessment “is more heavily weighted [than the main NAEP] toward students’ knowledge of basic facts and the ability to carry out numerical algorithms using paper and pencil, exhibit knowledge of basic measurement formulas as they are applied in geometric settings, and complete questions reflecting the direct application of mathematics to daily-living skills (such as those related to time and money)” (Campbell, Voelkl, and Donahue, 2000, p. 50).