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## Adding It Up: Helping Children Learn Mathematics (2001) Center for Education (CFE)

### Citation Manager

. "4 The Strands of Mathematical Proficiency." Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press, 2001.

 Page 137

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Adding + It Up: Helping Children Learn Mathematics

The same is true for rational numbers. Only 35% of 13-year-olds correctly ordered three fractions, all in reduced form,56 and only 35%, asked for a number between .03 and .04, chose the correct response.57 These findings suggest that students may be calculating with numbers that they do not really understand.

#### Procedural Fluency

An overall picture of procedural fluency is provided by the NAEP long-term trend mathematics assessment,58 which indicates that U.S. students’ performance has remained quite steady over the past 25 years (see Box 4–4). A closer look reveals that the picture of procedural fluency is one of high levels of proficiency in the easiest contexts. Questions in which students are asked to add or subtract two- and three-digit whole numbers presented numerically in the standard format are answered correctly by about 90% of 13-year-olds, with almost as good performance among 9-year-olds.59 Performance is slightly lower among 13-year-olds for division.60

 Box 4–4 NAEP Scale Scores, Long-Term Trend Assessment, 1973–1999 SOURCE: Campbell, Hombo, and Mazzeo, 2000, p. 9. These scale scores include all content areas: number, geometry, algebra, and so on.
 Page 137
 Front Matter (R1-R20) Executive Summary (1-14) 1 Looking at Mathematics and Learning (15-30) 2 The State of School Mathematics in the United States (31-70) 3 Number: What Is There to Know? (71-114) 4 The Strands of Mathematical Proficiency (115-156) 5 The Mathematical Knowledge Children Bring to School (157-180) 6 Developing Proficiency with Whole Numbers (181-230) 7 Developing Proficiency with Other Numbers (231-254) 8 Developing Mathematical Proficiency Beyond Number (255-312) 9 Teaching for Mathematical Proficiency (313-368) 10 Developing Proficiency in Teaching Mathematics (369-406) 11 Conclusions and Recommendations (407-432) Biographical Sketches (433-440) Index (441-454)