PaperState Mathematics Standards: An Appraisal of Math Standards in 46 States, the District of Columbia, and Japan
Every state is listed in the following table for the sake of completeness, though several of them are ungraded, marked "n" rather than with one of the numbers 0, 1, 2, 3, or 4, because (except for the special case of Tennessee) they do not have a standards document at all (Iowa) or because they have standards in process of revision, with no draft publicly available for comment (Minnesota, Nevada, and Wyoming). The StatebyState Notes (Section VIII) that follow the table of grades will explain the case of Tennessee, which has two sets of scores but with a single final (average) grade for its two documents. Giving grades to states differs somewhat from giving grades to students in school or college. In grading students, teachers are dealing with youngsters taking several courses, not all of which interest them greatly. The students are pressed for time on examinations, and during the week as well, and are sometimes fearful, ill, or troubled by personal problems. We wish to encourage students to improve, or reward them for performance we know about but which is not present in the written work they present. In consequence, we give many grades of "A" for less than exemplary performance. The world rather expects that 10% of a class (or 5%, or 15%) will receive grades of A (i.e., 4 grade points). A state publishing standards, however, is not an anxious youngster pressed for time. A state has time and money and the ability to secure expert advice. It can consult books and other states. It should be without psychological problems or learning disabilities. This particular "assignment," the writing of standards, is a professional responsibility, and any performance short of exemplary must be judged so, and announced so, even if the top grade were received by none of them. Thus, while we have used the scale 4, 3, 2, 1, 0 in more or less the usual way, "4" representing the best available and "0" representing the least useful, these figures must be seen simply as a ranking of value, five degrees of excellence being about as many as we can distinguish. It was only after tabulating all the numerical scores that we decided which total scores should accord with the more familiar scheme of A, B, C, D, Fgrades which are given as the right hand column of the chart. The grading for Negative Qualities might seem a bit curious, grades of 4 being awarded for the absence of False Doctrine, or of Inflation, and 0 for those states having the most; but, since a total score was needed for computing the final grade of A, B, C, D, or F, it seemed convenient to scale negations positively, in order to be able to use additions only to arrive at a total. Otherwise some states would have ended with negative scores. However, this method of scoring negative qualities would give a state publishing a standards document containing no words at all a grade of 4 points, because of its perfection in achieving the absence of inflation and false doctrine; and as it turned out this would have been just sufficient to earn a D. Thus, the 16 States that received a final evaluation of "F" would have scored better, or as well, in our final tally if they had turned in a blank paper. (With negative scores in part of the document, it seems, as in Minkowskian geometry, there is simply no way to avoid at least some anomaly.) General Impressions
The collapse of deductive reasoning as a desideratum in American school mathematics is the single most discouraging feature of the study of these documents. The second, strikingly evidenced by the paucity of grades of 4 at the Primary level for Content (Criterion II), and for False Doctrine (Criterion IV(B)), was the enthusiasm with which many states have embraced the recent doctrine that the algorithms for multiplication and division of fractions and decimals are obsolete and can be replaced by calculators. Indeed they are, for technicians who need the numerical answers for practical everyday purposes; but instructional purposes demand otherwise. We did not demerit the prescribing of technology per se, at the primary or any other level, but we did downgrade its prescription in places where its use obscures a mathematical lesson, or blunts a mathematical perception, that can only be conveyed in its absence. And there are many such places, from the decimal calculations of the 4th grade to the solution of linear systems in the 12th. Most failures found in these standards documents require more detail of presentation, and an effort is made in the Notes (Section VIII) to describe a representative selection of them. In addition to all the states we have named below, one other Standards is graded for comparative purposes: Japan, which appears at the end of the listing. The Japanese standards document is a translation of a publication of the Japanese Ministry of Education, and is listed in the Appendix, with information on its provenance. This document, while brief, is exemplary in most respects. Even so, it falls short of our maximum in the category of Reason (III), perhaps only due to deficiencies in the translation, or to a cultural difference that makes it seem unnecessary to the Japanese to mention the matter sufficiently often when describing content. We must judge only by what we can read, however. (See also the Note on Japan in Section VIII below.) There are nine scores (of 0 to 4) for each state, but for evaluation purposes there are but four Categories, I, II, III, and IV (as described above), for each of which an average is struck before the four averages are added for a total score for the state. That is, we are weighting equally each of the criteriaClarity, Content, Reason, and Negative Qualitieseven though some are split into more subheads than others. Thus, 16 is the highest possible total score.
