Comments to the
National Voluntary Mathematics Test Committee

We applaud the goal of introducing a national grade 8 mathematics exam as a way to stimulate improvement in mathematics education. In developing such a national mathematics test, it is critical to get the details correct lest the goals be lost. We are seriously concerned that the development of the national mathematics test is flawed and in need of correction.

It is clear that the authors of the exam are working under the assumption that there is, or will be, a national consensus regarding mathematics education that roughly mirrors the 1989 Standards of the National Council of Teachers of Mathematics (NCTM). This is not true. Troublesome issues about the NCTM model are now being raised by committees of various mathematics professional associations and by parent groups.

The exam itself, at least as represented in the examination plan, is not at all adequate. To be truly informative, the exam should be comprehensive and cover those topics that are important to the future of America.

Specifically:

• There is an intentional effort to avoid testing basic computational skills under the assumption that all students will know these things. Unfortunately, this is not true, as anyone who deals regularly with 8th graders can tell you. If we do not test basic skills we will hide from ourselves the extent and range of our weaknesses at the lowest levels. Hopefully, this is not the intention of your committee.
• The exam must be sure to reflect the President's claim that all 8th graders will learn Algebra. This is an important goal for our country. We cannot monitor our progress toward that goal if it is not measured. In spite of calling 25% of the test "Algebra," the content addressed is not algebra at all -- it is not even pre-algebra. This country will not be fooled into believing a claim that algebra is included, or that scores on such an examination would indicate that American students have learned algebra. By ignoring the demanding content of algebra, the design will fail to measure success at the level of our international competition. The test will also fail as a vehicle to promote greater mathematics achievement.
• Under the guise of allowing multiple solutions strategies, an effort is being made to design test items that promote guessing rather than more powerful and general analytical methods. This works against the goal of promoting accuracy, clear thinking and careful work.
• If one compares the sample problems with those used for 12-year-olds in Japan, it becomes immediately obvious that the sample problems developed by the committee are not on a level that will be competitive internationally.
• Numerous issues concerning individual sample items have been raised by several others and need not be repeated here. Suffice it to say that these issues need to be addressed as well and that even sample problems must be carefully written.
• Extreme limitation of the number of hand-scored items is to be encouraged as these are the items that are most likely to suffer from low reliability and subjective grading. Because of the current high fraction of points dedicated to hand scored items, because of the dangers of subjective grading and because of differences in scoring between individual graders, it is highly likely that hand scored questions will have a substantial, and artifactual, contribution to the variance between scores. Such items also contribute to a significant increase in the cost to administer the test and vastly slow the rate with which results can be returned to the concerned parties. For these reasons we urge a drastic decrease in the number of hand scored items and in the fraction of total points allotted to hand scored items.
• The notion that the examination can and should be modified over time is a serious mistake. The only way we will have to track progress over the years is if equivalent forms addressing the same achievements are used year after year. The intention of the committee to use changes to the examination as a scheme to increase the use of calculators in the face of public opinion to the contrary is both an insult and inappropriate if we are to progress as a nation.

As representatives of concerned parents throughout the country, we implore you to take every effort to address these issues. Please realize that our need for a well-structured national assessment device far outweighs the importance of promoting the so-called "reform" agenda in mathematics education.