## The Trend NAEP

**Figure 1. Math Gains of U.S. Students**

The Arithmetic Gap

MAIN NAEP 1990–2003 | TREND NAEP 1990–1999 | |||||
---|---|---|---|---|---|---|

Scale Score Points | Standard Deviation Units | Years of Knowledge | Scale Score Points | Standard Deviation Units | Years of Knowledge | |

Grade 12/Age 17 | 7 | 019* | - | 3 | 0.10 | - |

Grade 8/Age 13 | 15 | 0.42 | 1.94 | 6 | 0.19 | 0.69 |

Grade 4/Age 9 | 22 | 0.69 | 1.76 | 2 | 0.06 | 0.20 |

*Source: Author's calculations based on NAEP data from NCES, 2003.*

## Basic Skills Achievement

## Why Does Arithmetic Matter?

Even if students can't compute very well, should we be concerned? We often hear statements reflecting apathy about students' declining arithmetic skills: My 9-year-old may not be able to divide 56 by 7 in his head, or figure out that 8 is one-third of 24, but the little guy has his own Web site and programs TiVo for me when I'm away at work. Besides, I was never a “math person,” and I turned out OK.

*Computation skills are necessary to advance in mathematics and the sciences*. Learning mathematics is an incremental process. Eighth graders who cannot do basic arithmetic with ease, who cannot find the right answer quickly and confidently without a calculator, will be hampered in their efforts to learn algebra and geometry in high school. Without some proficiency in algebra, students will have little grasp of calculus, physics, or chemistry and little chance of succeeding in college mathematics and science courses.

Computation skills are an increasingly important predictor of adult earnings. Learning basic computation skills is not just for our future brain surgeons and rocket scientists. In Murnane, Willett, and Levy's discussion of their landmark study on cognitive skills as a predictor of future earnings, they observe that a high school senior's mastery of skills taught in American schools no later than the 8th grade is an increasingly important determinant of subsequent wages. (1995, p. 264)

*Computation skills promote equity in math achievement*. Declining arithmetic achievement in the United States also raises concern about racial equity. The achievement gap in computation skills between black and white students narrowed in the 1980s but began to widen in the 1990s (Lee, 2002). From 1990 to 1999, for instance, white 9-year-olds' performance on division problems dropped one-tenth of a percentage point, whereas their black counterparts' performance fell by 6 percentage points. Thirteen-year-old white students fell 2.1 percentage points on fractions compared with a drop of 4 percentage points for black students. Most eye-opening is 17-year-olds' tumble in fractions. White students' performance fell nearly 18 percentage points, whereas that of black 17-year-olds decreased by 33.6 percentage points.

## How Did This Happen?

*Poor teacher preparation*. Recent survey data from the TIMSS suggests that U.S. math teachers are less prepared in their subject area than their more successful counterparts abroad: 78 percent of Singaporean students and 89 percent of Flemish Belgian 8th graders have teachers who majored in math, compared with only 41 percent of U.S. 8th graders. U.S. math teachers majored in education more than teachers in any other country (Loveless, 2001a; TIMSS, 2003). Richard Askey (1999), a math professor at the University of Wisconsin, notes the deficiencies in math education courses taken by elementary and middle school teachers. He derides time-wasting workshops and calls for an overhaul of professional development and a greater emphasis on deepening teachers' understanding of elementary mathematics.

*Use of calculators in elementary school classrooms*. On the NAEP, 4th graders who say that they use calculators every day on classwork have significantly lower math scores than students who never use them. The relationship reverses at 8th grade. Of course, correlation is not proof of causality. Generally speaking, research shows neither a positive nor a negative effect of calculator use on students' computation skills (Ellington, 2003), but most of the calculator studies have involved middle and high school students. Very few have focused on the elementary grades or on the long-term impact of calculators on students who are first learning arithmetic. Even less is known about whether calculators help or hinder students who are struggling to catch up with their peers in mathematics.

*Reformist math standards and curriculum*. The National Council of Teachers of Mathematics (NCTM) came up with the

*NCTM Standards*in 1989. The 24 drafters of the

*Standards*included faculty from teacher education schools and universities, as well as two K-12 teachers—but not a single mathematician. The vague standards suggest that K-4 students should devote more attention to “operation sense” and “cooperative work” while spending less time doing long division and using pencil and paper to compute fractions. An emphasis on using calculators at all ages runs through the entire document (Klein, 2002; Loveless, 1998; NCTM, 1989).