• Inclusion of Students Who Use Testing Accomodations
• Implications of Information About Technology Use
• Conclusions

The Mathematics 2000 report provides an abundance of statistics and information. The National Assessment Governing Board (NAGB) and the National Center for Education Statistics (NCES) have worked diligently to make reports like this one more accessible and understandable to more people. Questions that beg to be asked and answered include the following: How does all the information presented in this report relate to the mathematics that students learn in school? How are students best taught this mathematics content? and Who should be conducting the mathematics instruction? I will be exploring and highlighting some of the implications not just for policymakers, but also for parents, schools, and teachers.

I believe that one of the most important findings emerges from comparing the two sets of results provided by this assessment: scores for students who were not permitted to use any testing accommodations and scores that include the performance of special-needs students who were provided with testing accommodations. In both 1996 and 2000, the NAEP mathematics assessment collected the two sets of results separately. At grades 4 and 8, there were no significant differences between the two sets in either 1996 or 2000. At grade 12, there was no significant difference between the two sets in 2000.

States, districts, and even schools are all grappling with the issue of including more special-needs students in assessments as well as in regular classrooms. Everyone knows this is a good idea, but the issue of accountability in assessing these students is complex. As NAEP continues to model inclusion and accommodation, perhaps this process will affirm the value of including special-needs students and dispel the uncertainty about how this inclusion will affect the reported results.

Many implications can be drawn from the information gained from questionnaires completed by students, teachers, and school administrators. "NAEP examines the relationship between selected contextual variables drawn from these questionnaires and students' average scores on the mathematics assessment. Readers are cautioned that a relationship between a contextual variable . . . and student mathematics performance is not necessarily causal." In other words, such a relationship may or may not indicate that a particular factor directly affects students' mathematics achievement. I would like to examine several relationships between questionnaire responses and student performance in the light of my experiences as an eighth-grade mathematics teacher. My focus will be on the use of technology.

As computers become more and more a part of our work and personal lives, questions arise as to how much computers should be used in school, in what ways computers should be used, and whether computer use has an impact on student learning. Certainly, computers are increasingly available in classrooms at each grade level. The Mathematics 2000 report states that the availability of computers in classrooms increased by at least 20 percentage points from 1996 to 2000, although the availability of computer labs did not change significantly during this period. Unfortunately, comparing the increase of computers in the classroom to student scores is not encouraging. There is not a direct relationship between the availability of computers in students' classrooms and increases in mathematics achievement.

I concur with these findings. Yes, I have two computers in my classroom, compared to none in 1996. But I have little mathematical software and relatively unreliable Internet access. Without a projector, it is almost impossible to effectively use two computers in a classroom with 30 students. Also, with only 44 minutes for each class, it is difficult to give students time to use the computer. Not surprisingly, teachers responding to the NAEP questionnaires quite often reported that computers were either not used at all or used primarily for math learning games or drill.

What are the implications? By themselves, computers in classrooms or labs are not going to make a difference in the amount or type of mathematics learned. Teachers need ongoing training and support in using the computer as an instructional tool. They need software and hardware, which unfortunately are often expensive, hard to find, and difficult to use. In this high-tech world, it is imperative to give students the opportunity to use computers in school. The issue is, how can computers be used to increase students' achievement in mathematics? I believe that access to and effective use of computers in schools is essential in closing the gap between those students who use technology efficiently and those students who are technologically deficient or deprived.

Regarding the issue of how calculator use in the classroom relates to student performance, the results of the 2000 mathematics assessment are more encouraging and clearer as to what works and what doesn't. The proper role of calculators in the K–12 mathematics curriculum has been and continues to be debated. Calculator-use policies vary across districts and schools; even within the same school, teachers have different opinions about how calculators should be integrated with instruction. States are also deciding if, how, and when calculators should be allowed on state assessments.

At grade 4, more frequent use of calculators for mathematics activities, as reported by students, was linked to lower scores. This information seems to confirm the need for caution in the use of calculators at grade 4. Since students in elementary school are still becoming fluent in computing whole numbers, calculators need to be used more for exploring and deepening the understanding of number sense.

At grades 8 and 12, the implications are much clearer. For example, using a calculator in the eighth grade appears to benefit mathematics achievement. At grade 8, daily calculator use for mathematics activities, as reported by both students and teachers, was associated with the highest scores. In fact, teachers who permitted unrestricted use of calculators and those who permitted calculator use on tests had eighth-graders with higher average scores. Even the type of calculator that students reported using was directly related to how they performed on the mathematics assessment. Eighth-graders who used a scientific calculator scored higher than their peers who did not use one, and the same was true of eighth-graders who used a graphing calculator compared to their peers who did not. Between 1996 and 2000, the percentages of eighth-graders who reported using scientific and graphing calculators increased. Many states do allow some calculator use on grade 8 state assessments. Again, it is important for teachers not only to have access to calculators, but also to have training in how to effectively use them. The key is teaching students to use calculators as a tool and giving students calculator tasks and assessments. I know that using graphing calculators with my eighth-grade students is extremely motivating and really works best for exploring patterns or making predictions.

At grade 12, daily use of calculators was again associated with the highest scores. The type of calculator used was important, with those twelfth-graders who reported using a graphing calculator scoring an average of 25 scale-score points higher than those who did not. Though it could be argued that twelfth-graders who use graphing calculators have higher scores because they have taken more advanced mathematics courses, I contend that being able to efficiently use a graphing calculator could make the advanced mathematics courses more accessible to all students.

There are a couple of implications regarding graphing calculators. Allowing or even requiring the use of graphing calculators on state assessments has a direct effect on the number of graphing calculators in the classroom and the amount of time that they are used in classroom instruction. I have seen this happen in Texas, where the state's end-of-course exam in Algebra I requires the use of graphing calculators. These calculators are expensive, however, and states or districts need to provide funding for purchasing these calculators and for training teachers to effectively use them.

In conclusion, there is much to be learned from the results of the NAEP 2000 Mathematics Assessment and from comparing these results to those of past assessments. Lots of people, especially local administrators and teachers, are not knowledgeable about NAEP. I believe that since districts and schools do not receive individual student scores, many educators conclude that the information is not relevant. I beg to differ. In addition to the implications that I have already discussed, the information in NAEP reports has many other important implications for state, district, and school policies. How much homework to assign, what types of mathematics courses to offer or require, and what courses teachers need for certification—these are all examples of policies for which NAEP could have implications. The results of the NAEP assessments can help educators and policy-makers make better decisions.

Using state-level results from 1990 or 1992 to 2000, states can track their own progress or look at other states that have shown dramatic increases in mathematics achievement. Mathematics learning and achievement can be affected by state policies on recommended textbooks, state curriculum guidelines, assessments, course requirements for students, and teacher certification requirements. Investigating a state's policies and the implementation of these policies over the past 8 to 10 years may provide insight about what it takes to improve mathematics achievement.