My Life With ACHIEVE

“ACHIEVE” has a history; I can tell only part of it. (Also, I will in future reference merely call it Achieve, though it is an acronym.) It was formed in 1996 by a group of state governors, 13 of them, joined by some CEO's of corporations, and a couple of foundations, following a National Education Summit whose origins I don’t know about (One can read about this on Achieve’s home page, beginning at http://www.achieve.org.) Its projects include an occasional National Education Summit attended by governors and the like, but it mainly publishes Reports: educational advice and studies commissioned by individual member states. The Summits themselves do serve to announce educational priorities as seen at the governors’ levels, hence influencing the studies Achieve then undertakes, though Achieve mostly does things commissioned by the member states themselves.

In 1996 the priority endeavor was Standards, and many of the states involved had their Standards examined by panels of experts engaged by Achieve, and either commented on for improvement or compared with certain existing Standards as prototypes. Achieve itself has a minimal office staff in Washington, and forms its panels ad hoc, except for the editing that goes on in the central office. Some Achieve projects for individual states studied the alignment of their Standards with their statewide examinations. Achieve apparently sometimes does this sort of thing for non-members, too -- one of its Standards studies was done for Montgomery County (MD), but this might have been an exception. The financing of Achieve, according to its web page, comes from its member states and certain well-known foundations named there.

The current President of Achieve, since 2003, is Michael Cohen, a former Assistant Secretary of Education, who in 1997 was the “point man” for the National 8^th Grade mathematics examination bruited by the Clinton Administration’s Education Secretary Riley but shot down by Congress; however, the first President of Achieve (and Cohen’s only predecessor) was Robert Schwartz, a sometime professor at the Harvard school of education with credentials in English, and a man with administrative experience with the National Institute of Education (along with Chester E. Finn, Jr. there, among others) and the Pew Charitable Trust, which, while he was there, was financing the NCEE “New Standards” project.

With the presidency of Schwartz, Achieve began its own work, and many of its reports on the Standards and the examinations given by the States (and Montgomery County) can be found summarized on the web page. These reports are said there to have been the “consensus” of the experts engaged by Achieve for each of the several projects, but that is not how it works. I served on several of them, reviewing in detail the drafts or existing versions of state standards in mathematics, and while I would submit a document of dozens of pages, including line-by-line commentary sometimes but also answering the specific questions asked by the Achieve printed forms, I would be only one of perhaps four such experts, and the consensus spoken of by Achieve in its own reports to the states was strictly an in-house consensus, derived by Achieve staff from having read and digested the more detailed reports from the several reviewers. I never saw the reports of the other reviewers, nor a draft of the Achieve report itself, until it had been delivered and paid for, and posted on the Achieve web page. I have now read several of the Achieve reports in which I had had a part and was usually unable to find, or maybe recognize, evidence of my participation, apart from my name listed as one of the panel (and in one case they forgot to put that in, too, though they did pay me).

The Ohio math standards as of 1997, for example, had received a grade of A in the first (1998) Fordham report. The document then reviewed had been published back in 1990 and naturally showed no sign of NCTM influence. The second Fordham report (2000) remained A, since the 1990 Standards were still in effect in 1999, when the second Fordham review was written. In that year, too, coincidentally, Achieve commissioned a study “of Ohio’s school improvement efforts to provide the newly elected governor, new state superintendent, business leaders and other policymakers with a candid review of state education reform strengths and weaknesses … “ [etc.], and the summary report, though without much detail, is still found on the Achieve web site.

Though Diane Ravitch was one of the team engaged in the 1999 study, the report was largely uninformative. Sure and it urged Ohio to improve its Standards and examinations, though it did notice that the math standards, at least, were already rated “A” or “B+” by the only three national organizations then assessing Standards (Fordham, AFT, and CBE, I think, though the Report didn’t name them). The commission made no claim to have read those standards, and seemed (to me) to confine its recommendations to matters of governance and equity, i.e., things bigger than curriculum. It did note (ominously, in my opinion) that Ohio was currently (as of 1999) being assisted in improving its Standards by the Council for Basic Education (CBE), an organization older than Achieve but with similar announced purpose. So far as its attitude towards school mathematics is concerned, CBE avowedly takes the NCTM model as authoritative and definitive, or did in 1990.

Well, then; in Fordham’s third report on state standards (2005) based on Ohio Standards published in December of 2001, the math grade plummeted to D, but that wasn’t the result of any overt action of Achieve. Yet -- had Achieve’s helping team in 1999 urged Ohio to leave its math standards ALONE, and to buy out its contract with CBE, it would have earned its money. As it happened, Achieve did try to intervene in the creation of new, 2001, Ohio math standards, or appeared to try, for in my files I have the record of my participation in an Achieve study of an Ohio mathematics standards draft of 2001. But Achieve got to the effort too late: My own report, strongly criticizing most aspects of that new Standards draft, was contained in a letter dated 21 September, 2001, while the final version (still current now) of the Ohio Standards was published in December, only a few weeks later, without having taken account of my comments. It was unlikely, though possible, that my report had been blended at the Achieve offices in Washington into a “consensus” more favorable to the Draft than my own criticisms would indicate. Or, it was possible that the Achieve “consensus” report did in fact call for a substantial revision but was disregarded by the Ohio Department of Education. I don’t know, and at the time never thought to ask, though I was on friendly terms with the Achieve functionaries in charge of mathematical studies, Laura McGiffert and Ann Shannon. Curiously, there is no report on the Achieve web site of Ohio’s draft standards ever having been studied in 2001 at all. Probably the time table had rendered its recommendations, if any, moot, a fact sufficient to consign the entire study, of which I had been a part, to the memory hole.

Other Achieve studies are reported on the web site, and the experts engaged by Achieve are named in each case, but who was responsible for what cannot be deduced from the in-house condensations extruded by the Washington office for presentation to the states. The official authors of the reports are simmered down into the word “Achieve”. I believe this to be a mistake in policy, and that Achieve would be wise to send each state the unedited reports of each of its consultants (there are always several of them) along with the merged, Achieve, opinions. Yes, the Governor, and even the Commissioner of Education, of each state would not have time or inclination to read it all, but there are others in the bureaucracy whose business is to write these Standards, and examinations; they would be better served by having the frank evaluations to look upon, rough and non-consensual though they might be, than to have only the smooth commentary, mostly polite and non-threatening, that filters through from Achieve headquarters, containing only the most delicate suggestions for change (if warranted), though the latter might still be of some value to the Governor’s office and the newspapers.

At the present time the “American Diploma Project” seems to be the primary effort undertaken by Achieve, and 21 states have joined this project, whatever “join” means. That is, Achieve is developing a set of standards for the exams many states are giving to students as a minimal requirement for a high school diploma, and the intention apparently is to create, by some sort of cooperation between Achieve and each state, improved examinations for all the participating states, so that they can compare results with each other, and longitudinally as well. Maybe Achieve won’t go even this far, though the most reasonable thing to do with the results of their present activity would go farther, and create a truly common exam for comparison purposes. What Achieve has produced so far is an analysis of the “exit exams” for a number of states, showing that the demands in the fields of mathematics, at least, are quite minimal, and well below the demands of the marketplace, not to mention the academy. I myself know nothing about this project, except to say that it could be quite valuable if the participating states are serious about improvement. However, this rather preliminary study, unlike the MAP reports I will discuss below, was signed by a committee that included no mathematicians. Without them an Achieve-written common exam would have difficulty becoming an improvement on NAEP, or the New York Regents “A” examination of recent years, or the Michigan “MEAP”. (cf. highstake.html for examples)

One big project I did participate in, and maybe still do, was not at all at the State level, and was doubtless suggested to Robert Schwartz, then President of Achieve, by the aborted “National 8^th Grade Voluntary Mathematics Exam” of 1997.

It began with Achieve’s writing of the “MAP Expectations” for 8^th grade mathematics, (“MAP” for Mathematics Achievement Partnership), a sort of Standards for middle school math. The document was to outline in some detail what students ought to know by the end of the 8^th grade – more inclusive than what should be taught during that grade, but not listing everything back to kindergarten, either.

Topics that might have been taught in Grades 6 and 7 were frequently also included. Of such topics, we would include both those we could not be sure were ordinarily taught before Grade 8, and some we knew were ordinarily taught badly in those grades. Since a national 8^th grade examination appeared to be on the horizon whether or not the particular proposal of 1997 passed Congress, such a set of Expectations as we were writing would serve as a middle-school syllabus for at least all the States in Achieve, those important middle-school topics unmentioned being, one would hope, implicit. Even so, we included two Appendices to the finished document: one briefly naming what we considered necessary (K-5 or more) prerequisites to our Expectations, and the other briefly reviewing what we expected to follow in the high school continuation (9-12), if proceeding along the lines we imagined ourselves to be prefiguring.

Not only were Standards (i.e., the Expections) for that level projected, but a set of sample problems, solved problems, were to – and did, when it was done – accompany the text, to indicate the level of understanding expected of students. Those problems were to be more searching than “exam questions”, for they were directed to teachers – and perhaps authors of textbooks – and not to students. In addition, the MAP program was to continue (so said its opening manifesto) by ultimately composing sample questions for the 8^th grade examination. (We never got to this part, as will be explained below.) In all, it would be a national model for the middle schools, the middle school level being the one considered most in need of overhaul anyhow.

Schwartz put Bill Schmidt at the head of the project, and the list of participants included James Milgram and Hung–Hsi Wu along with myself, three firm opponents of NCTM doctrine. Others were less political, but certainly sufficiently proficient in mathematics, and while there was also a full complement of math education people and representatives of NCEE (the National Council on Education and the Economy, an organization that had published The New Standards, a rather soft document resembling the NCTM Standards) it did appear to me that good sense might make itself felt in the present project, which, apart from the California case of 1997, seems to have been the first time a more-than-token representation of mathematicians was part of a Standards composition team.. Schmidt led us off with a draft syllabus that was more ambitious than even the mathematicians thought wise, and the first meeting I attended had a long discussion of its provisions, line by line. I was very pleased by it all. The Achieve personnel divided our group into working parties (to communicate by email, mostly), as follows:

MAP Math Advisory Panel Working Groups

Number & Data Analysis, Leader: Bill Schmidt

Jim Milgram

Paul Sally

Chuck Allan

Norm Webb

Joan Ferrini-Mundy

Algebra , Leader: Dick Stanley

Hung-Hsi Wu

Wade Ellis

Diane Briars

Jim Lewis

Measurement & Geometry. Leader: Ann Shannon

Ralph Raimi

Marge Petit

Lynn Steen

Ed Silver

Not all of us participated equally (some of us not at all) in the writing, for after the first meetings certain ones of us were individually engaged and paid by the day for our work, which was done via email and telephone between each consultant and Achieve, but seldom with each other. All the text seemed to go through Ann Shannon, of NCEE originally, though apparently she had been seconded to Achieve for this project. Perhaps she was changing employers altogether; I never knew. (Her email address was and is at NCEE.) She did her best to be helpful, in particular to rewrite each draft from the “corrected and improved” preceding draft as it had been returned to her by the critic of the moment. Laura McGiffert, her superior at Achieve, was in administrative charge of the entire mathematics study and often took a direct hand, too. There were no “math wars” visible in this project, though we all did reflect our origins. We ended with a very good document, concise to a fault, since it avoided mentioning anything but the mathematics being prescribed. It was a set of standards, yes, but neither a curriculum nor yet a set of abbreviated lesson plans; it was a set of goals, definite, understandable, and usable by any good teacher or writer of examinations or textbooks. Its authors were in fact a rather small part of the group that had initially assembled in Washington, but this was as it should be, in view of the deserved reputation of documents written by committees. It concentrated on number, numerical operations, and algebra, a significant component in geometry and measurement, and a genuine downplay of “data analysis” compared to NCTM views.

The next task was to compose the illustrative problems, and here Shannon led off with a large collection she seemed to have downloaded from NCEE, most of them unacceptable. Over the next few months I composed some, while others, mainly Lynn Steen I think, composed others; but Ann Shannon herself and some of her indefatigable NCEE partners must have composed the rest. Then the process seemed to peter out. At least, Achieve was no longer using my work, while its mind seemed to be on other things. I did continue to get drafts to criticize or edit, but I didn’t like some of the problems.

My participation was not executive, though; like everyone else I simply did what I was told. Given a draft, I improved it; given some problems, I augmented them by what I though missing, in the categories assigned to me. The feeling we had had in our plenary sessions early in the project was no longer evident, each of us communicating with a hub rather than with each other. The answers to the problems, which took up more space in the final document that the rest put together, were not written by me, though I had submitted brief solutions when I first wrote them, to show what exactly the problems were illustrating. I believe Steen did many of them, but some of the solutions might have come via Ann Shannon from wherever she had found the questions. I found some of those answers confusingly verbose in their attempt to cover all the ground illustrated by the Problems, and in a couple of cases they seemed to miss the point the Problem was intended by its author to elucidate.

My memory is dim on how the whole project achieved closure, but it did, long after I stopped being part of it, even by the hour, though I continued to serve Achieve in other projects, mainly in the judging and improvement of certain state Standards. Yet something was going on concerning the Expectations, and sure enough, the Expectations, folded into a larger document called “Foundations for Success”, were printed and placed on the Achieve web page in 2002, and are still there, at

http://www.achieve.org/dstore.nsf/Lookup/Foundations/$file/Foundations.pdf.

This report was nicely printed -- the web page display is a photograph of the document -- but the hard-copy itself is out of print now. As a math syllabus for middle school through Grade 8 it is quite good, but it has some weaknesses, or, rather, uneven value or difficulty, among some of the problems that were supposed to be exemplary of the import of the Expectations. Despite the 130 pages devoted to the problems and solutions – as against 16 pages for the Expectations themselves – the document fails to have enough good ones to cover all its intentions; Achieve could have done a more systematic job commissioning such problems, but what they got is often, if not always, very good, and in many cases imaginative. The final version, though still called a “Consultation Draft”, included appendices (the work of Wu, Milgram, and Sally) outlining what the Expectations presupposed in the K-5 curriculum, and what it intended to lead to in 9-12, and an appendix on terminology and some common pitfalls of understanding.

These few pages were also good, but I was sorry to see that the Introduction to the “Foundations for Success”, as the document was now named, was written in language one would never expect from a mathematician. Unlike the Expectations and the Problems, the opening material, which reviewed Achieve’s purpose and the place of the present document in its plans, had not been circulated to the Mathematics Advisory Committee for comment or editing, and it was a surprise to me when I read it as part of the final text.

Maybe there is no harm in advertising mathematics, in the first line, by invoking the use of a Palm Pilot in managing a retirement portfolio as an example of how life in the 21^st Century “is drenched in data, dominated by computers and controlled by quantitative information” -- all this to justify the need for good schooling in middle schools. I think there is harm in such artificial puffery, for it then becomes material for further misunderstanding concerning the curriculum itself.

(Reading about the wonders of the Palm Pilot, some school systems are sure to spend a few million dollars on them for the classroom, machinery that then gets no use and turns obsolete and valueless three years later. This comment is more history than prediction, though it was computer network servers and not Palm Pilots that got bought and wasted in the case I have in mind.)

However, very little space in the Foundations for Success is given to this sort of talk, and the major part of the introductory material, which is in the form of Questions and Answers, is informative and well written, but nonetheless illustrates the difficulties facing mathematicians seeking to make their intentions plain. For example, Hung-His Wu had been asked to write a draft for an Introduction, and some of what he wrote did make it into the final version. But other lines were certainly not his, or even close. On page 12 of the ultimate Introduction, where a little review of the recent history of American mathematics education is given, the anonymous authors of the Foundations for Success wrote :

Fortunately, the United States does not have to look far to find a road map for improvement. In 1989, the National Council of Teachers of Mathematics (NCTM) initiated the drive toward higher standards in mathematics education by publishing K-12 standards that showed the breadth and depth of mathematics …

Well! Many of us considered the 1989 NCTM Standards as a milestone on the drive towards lower standards in mathematics education. But then, Achieve was only publishing, it thought, the “consensus”, not what I thought. In any case, it was never our purpose to either to praise or malign the NCTM, though our work was designed to correct and reverse what most of us saw as a current and baneful tendency in American mathematics education, wherever it came from. That I, as part-author, should be credited with what Achieve doubtless innocently saw as a simple courtesy to the leaders of the profession was galling, to me, anyhow. And the constant invocation of the dying metaphors of the Beltway are also galling: “roadmap”, for example, and “length and breadth”. When you see one of those you know the mathematicians have gone home and the front office is cleaning up the mess.

In truth, this misrepresentation of our debt to NCTM, and these clichés, didn’t matter much, since by the time of publication it had become clear that a focus on the 8^th grade was already out of date. New Federal legislation, it began to be seen, would mandate a whole string of tests, for each grade from perhaps third grade on up to high school, and so a syllabus such as ours, while of interest to people composing curricula for the education of children, would not be of much value to people composing test-prep materials for children in lower grades. The federal government, having lost in Congress its campaign for a national 8^th Grade math test (along with a national 4^th Grade test in Reading), was closing in on what turned out to be the No Child Left Behind (NCLB) legislation, which would mandate State testing, if not federal, at many more levels than just the 8^th Grade.

Therefore Achieve needed to attack a new problem, that of composing Standards (“Expectations” was still the preferred word) for each grade, and not just for the crucial way-station represented by the 8^th Grade.

Before discussing the Achieve K-8, grade-by-grade Expections that were then created, I must describe a reaction to the 2002 MAP Expectations that appeared in a publication of AMTE, the Association of Mathematics Teacher Educators. (A “teacher educator” is, I believe, a professor at a teachers college, a class of people that includes almost everyone who does research in mathematics education as well as those who teach teachers, or supervise those who do.) The document I refer to explained that AMTE had appointed a twenty person “task force” to report on the Achieve Expectations. The opening paragraphs of their report, which can be found at http://amte.sdsu.edu/resources/ACHIEV_Task_Force_Report.pdf, are as follows:

The purpose of Mathematics Achievement Partnership (MAP) is explained and is very extensive. The Foundations for Success document appears to be a first step in accomplishing the goals of MAP. In particular, it appears that the purpose of the document is to outline the content expectations for students to know by the end of 8th grade that are aligned with top performing countries. Given this as the purpose, two fundamental questions were raised:

(Interruption: Here we see already what comes of having Introductory material written by the staff at Achieve, and not the authors of the Expectations, who had it as no part of their purpose to imitate “top performing countries”, or even to mention them. Even the most innocuous boiler-plate can be misleading, even when it manages to avoid the deploring of the “export of jobs overseas”, or the mention of “the needs of the new century”.) In the present case (p.13), the relevant text from the Introduction to our Expectations had read:

“Foundations for Success offers guidelines and targets for states to provide mathematics education that is benchmarked to the best in the world.”

Guidelines? Targets? Benchmarked? These tired metaphors are no more a part of a mathematician’s prose than “roadmaps”. The AMTE “taskforce” – a lovely military image, that -- had, by just these words, that Achieve intended as a routine cliché, been given a convenient target for a flanking attack. AMTE goes on:)

1. What does this document offer that isn’t already offered through the many other recent publications about standards and expectations? The expectations are very similar to NCTM content standards and Mathematical Education of Teachers (MET) standards (Conference Board of the Mathematical Sciences (CBMS), 2001). Is another list of topics necessary? This document provides some sample tasks, but Principles and Standards and Navigations do this and in a more complete fashion.

2. Is the vision of Foundations for Success intended to be a comprehensive vision for middle school mathematics? While it is very similar to the middle school section of Principles and Standards, it seems to be more traditional and narrow in focus, excluding processes, such as communication, representation, connections, problem solving, and reasoning. In addition, the focus of content seems to be more procedural than conceptual in nature. As one task force member stated, “the rationale for incorporating an expectation…is its inclusion in mathematics programs of high performing countries; a deeper rationale could be set out, one that includes …curricular integration and student understanding.” [my emphases]

The AMTE criticism so far “seems to be” (to employ a favorite AMTE phrase) that the Achieve Expectations had no real reason for having been written, since NCTM had covered that ground, only better, and that our text, in trying to imitate “high performing” foreign nations, implied a program too traditional and narrow. Narrow? AMTE didn’t notice, for example, that NCTM’s “PSSM” of 2000 had, unlike Achieve, advised against teaching middle school students how to divide fractions, which certainly is one way of avoiding a narrow concentration on arithmetic. (There was much else AMTE hadn’t noticed, in which our Expectations differed from NCTM advice.) Later in the AMTE report came this:

“While the content was in some cases more advanced than other published lists of skills and concepts, there were also omissions that were noted. These include:

• Work flexibly with fractions, decimals, and percents

• Relating number to place value (especially as it relates to expanded

notation)

• Develop, analyze, and explain methods for solving problems with

proportions

• Knowing everyday situations for using rational number operations

• Inverse proportion (simple rational functions are included)

• Reasoning about data is missing, instead small procedures are mentioned

• Formulating questions that can be addressed with data

• Develop and evaluate inferences and predictions that are based on data

• Randomness and samples

• Strategies for systematic counting

• Any geometry related to using visualization, spatial reasoning, and

geometric modeling to solve problems

• Transformations to two-dimensional figures

• Developing relationships among formulas for area and volume

• Estimation (in the number strand)

• Relative rate of growth of arithmetic, geometric, and exponential patterns

• Relationships between variables”

Here the criticism is that while Achieve calls for “advanced” material it has omitted 16 (count them) really impressive-sounding pieces of mathematics that NCTM’s Standards does include. But in fact some of these bulleted items are silly; some are things we intended to omit as time-wasting; and some (like fraction arithmetic) that were implicitly expected to have been taught partly in K-5, and included again by us again, at a deeper level, and in the Problems as well. And surely “relationships between variables” appears in our document everywhere functions are mentioned, which is often, though without the mystique of “variable” that so bedevils the education researchers. Moreover, the complaint that rational functions were omitted sits poorly with folks who refuse to teach children how to divide arithmetic fractions. Most disheartening is the AMTE notion that the relatively vacuous vocabulary items concerning “data” and “statistics”, and the bloated demands that cannot really be met at the K-8 level at all, such as the drawing of mathematically justified statistical inferences from data sets, should continue to clutter the middle school curriculum of the present day. In short, AMTE regretted that the Achieve Expectations were not a duplicate of the NCTM Standards, which the charge to the AMTE task force for this study had explicitly included as a criterion of value. The praise of NCTM in the Achieve Introduction hadn’t fooled them for a minute.

That alone should have given some satisfaction to us who worked to hard to create even the document we did. I ended with some questions in my mind about the adequacy of the Expectations, but reading this blast from the enemy is now reassuring. Yes, the Expectations are essentially what the mathematicians intended, and that the prose of the Introductions, Prefaces, and calls for a more glorious 21^st Century that the home office adjoined to those Expectations after sending us home had not really injured its essence.

Achieve should also be congratulated in having kept alive until now the 8^th Grade Expectations, albeit still in “discussion draft” form, and even though the occasion for writing them (a uniform 8^th Grade cumulative examination) was no longer in the works. Rather than jettison the Expectations, Achieve set about writing a full K-8 grade-by-grade curriculum outline paced in such a way as to include the earlier curricular demands by the end of Grade 8, but spreading them and their prerequisites in good logical sequence over the entire K-8 program. The process of doing this was called “back-mapping” from the Grade 8 Expectations.

This next project did not have the undivided attention of many of its participants. After some exploratory discussions, Steen was named “Editor”, Ann Shannon was named “Lead Author”, and Laura McGiffert was in charge of the project altogether. The rest of us, or some of the rest of us, were to be called on for writing tasks, or reviewing of drafts, as one of the three leaders needed us. I was on contract for the years 2003 and 2004, sending Achieve a bill for my services every time they came to a sufficient number of “days” to warrant payment to clear the books for the time being. At the beginning the mathematics team did work together, with a couple of conference calls, deciding how much of the resulting document should be devoted to each of Algebra, Number, Geometry, and Data, and other such generalities about pacing over the years K-8, as all of us had been asked early in the project. After that my major tasks were piecework, mostly by email transmission of my edited versions of partial drafts sent me by Ann Shannon or Lynn Steen, and in answer to a recurring demand for illustrative Problems, which were now needed in much greater numbers than for the 8^th Grade Expectations.

We mathematicians had at least one and maybe two telephone conference calls during 2003, but all then retreated as I did to the back-and-forthing of documents, especially as Laura McGiffert sent at least one draft to a number of experienced school teachers (one of them now a staff member at TERC) of both elementary and higher grades, for comment. She then organized and listed the comments for us, for consideration in later drafts. Those comments “from the field” were mainly criticisms of the choices most of the mathematicians had made deliberately. Almost all of them were suggestions for modification of our program in the direction of NCTM doctrine. If we had done all that was suggested, there would have been no need for our project at all (a point AMTE had made most vigorously). Consensus was plainly not in the cards.

Since I was now privy to only part of the development of the final document I cannot detail the time table. Most of the work was done in 2003 but I know I reviewed a draft of part of it in early 2004 as well, just before hearing that McGiffert was sending our latest draft to “the state representatives.”

I have in my files a photocopy of that draft, of the Grades 6-8 portion of the expanded expectations, as I received from Lynn Steen in March of 2004, heavily annotated and corrected in red pencil by me just as I had then mailed to Achieve as part of my work on the k-8 document, so I know I was still on the team that late in the project. Even later, towards the end, Wu was, or thought he was, assigned to finish the document, and the work of assembling and organizing the drafts, corrections and objections being considerable, he spent a large number of real workdays on it, and I gave him a hand on some of it; but I believe it was clear by then that the successive corrections, whether from Wu or me, or compiled “from the field” by the Achieve staff, was not converging to any single result. Before Wu had finished what he considered his part, the completion of the document, at least as a DRAFT suitable for posting on the web for general comment, was assigned to Lynn Steen, who from the outset had been named Editor of the document, after all.

I do not know how much of the result is Wu’s and how much Steen’s, though clearly it was Steen who wrote a fine introduction to the result, an apologia in the first person, explaining why he had made some of the changes he did, and why he had done other things to the texts that had come to him, in particular stressing that he himself was not to be considered the ultimate author (though he didn’t put it in those words). This document, not intended as final, can be found at

http://www.achieve.org/dstore.nsf/Lookup/MAPK-8fullreport/$file/MAPK-8fullreport.pdf. where it is still called a “DRAFT” on every page.

For that matter, and since the earlier Expectations for Grade 8 is also still called a draft, albeit a “Consultation Draft”, whatever that is, I am not sure how Achieve intends to use what it has, or by what time-table, especially as the Achieve office is in possession of the Problems we had created up to that time, and Steen’s DRAFT omitted the Problems, without which the document really is not comprehensible. One change Steen made at the last minute was to omit some of the analysis of the quadratic functions, in particular “completing the square”, an omission suggested by some of the consultants from the education world who considered that to be developmentally inappropriate for the 8^th Grade. Steen himself merely says there was already too much other material in the 8^th Grade to make further analysis of quadratics possible to include. Many of us are disappointed that quadratics are deferred to the 9^th Grade in our recommendations, though an example concerning “completing the square” and graphing a quadratic function is still included among the Problems in the old Expections, an oversight perhaps. I, at least, am now surprised to find that linear inequalities and their graphing in the plane is part of the K-12 layout, though they had been omitted from the 2002 Expectations. Indeed, that might be better in the 8^th grade than the process of completing the square. Of course, all this is material for further discussion among the mathematicians if Achieve does intend to pursue this line further.

The final, i.e. Steen’s, text was accomplished with more success than I expected, though both Wu and I have some quarrels remaining. And there are some misprints and so on. Achieve, however, has not asked us for a last round of criticism – it has to stop somewhere, one supposes. From some of our colleagues, not members of the Achieve team, the major criticism is that the earlier grades give entirely too much attention to “data and statistics”, taking up space and time we had deliberately intended to have filled with more about number and arithmetic, in preparation for (say) the quadratics that therefore didn’t find space in the syllabus. I would agree if this were so, but inspection of the actual document put together by Steen shows a minimum of the time-wasting “data” that is so popular these days, and a good portion of attention to elementary probability and – if read rightly, something that the inclusion of Problems would make more clear – combinatorics. Yes, the definitions of “quartile” and “bar graph” are present, but in a genuine curriculum these things are rightly incidental to exercises in arithmetic, at no cost of time at all unless the teacher is unreasonably fussy about vocabulary tests. And the words are an unfortunate necessity for nationwide exam purposes. Ten minutes and a few homework problems would suffice, and the text of the K-8 back-mapping indicates as much. I’m quite sure that AMTE will consider it shamefully deficient, when they put their task forces to work on it..

This Achieve K-8 document, for all its faults, and once it has passed from Draft to Policy, can when completed serve as a syllabus for member states to use in composing their grade-level exams as required by NCLB, and indeed the “final” exam they are all working on for the high school diploma project. Before it can do this, however, it needs a great effort in producing exemplary Problems. This was a big job for the original, Middle School only, Expectations; and wasn’t entirely successful. I have not yet heard that Achieve has begun this part of the process; maybe after the American Diploma Project it will. The Problems already in place for the 8^th Grade level are a start, though even they need improving. To make the K-8 unrolling of the 8^th Grade Expectations a success will require a considerable effort, and necessarily via the enthusiastic participation of more than a couple of mathematicians, but the off-again on-again conduct of the enterprise so far has disaffected some of them, who are tired of working for Achieve if their efforts languish half-baked on some obscure web site.

And – would the result actually get used by the states that make up Achieve, if the “reports from the field” represent what the member states’ Departments of Education will in the event tolerate? I have my doubts that Achieve will be able to assemble a group as spirited, skilled and dedicated as they had at our first meeting for the Expectations, though they should try.

The problem is complicated by politics. Every state now has Standards for math and other necessary subjects, from K to 12, for college-intending students and for those who don’t so intend; and most have, or have in prospect, school-leaving exams for high school diplomas. At this time, most of those Standards are weak, undemanding, or obscure – anything to permit giving examinations everyone should pass. (See, for an unhappy analysis of the present-day state math standards, http://www.edexcellence.net/doc/mathstandards05FINAL.pdf.) Even so, the statewide examinations I know about don’t even come close to those weak standards on the books today. And despite all efforts, the failure rate has been appalling, and the “racial gap” doesn’t seem to close.

The attempted cure up to now has been to dumb down the exams, and this includes NAEP, since observing NCTM priorities has that tendency, and NAEP has over recent years paid increasing attention to what the schools are actually teaching (or permitting students to discover). I don’t believe this will work; the only cure is to teach mathematics right. Weakening the exams maps back to a weakening of instruction, and so on in a vicious cycle, of which we have experienced several turns since the NCTM 1989 Standards. What Achieve is on the way to doing is in the right direction, for all that present-day politics makes it impossible for most states to follow in that direction.

Until this political and cultural climate changes I don't believe the Achieve K-8 standards will end up having the use it intends, which is to be a guide to grade-by-grade examinations – at least, not soon. There is no incentive. Today’s states are not observing their own written standards in composing their own state’s exams, for while the law might say they should, there is no court and no police force to compel compliance. They are avoiding it by all means necessary. New York, though not an Achieve state, is a perfect example, which I cannot take time here to describe.

Just the same, having a good Standards gives critics and defenders alike something in print to shoot for, or at. A good debate, at least, could be the effect of the Achieve K-8 document, once it is completed with the projected Problems, within its own member states. It might take a generation or two for them to reach Achieve standards in all seriousness, but since a state is eternal this might actually come about. It will certainly not come about in the absence of a model, and propaganda in favor of that model. On a national scale there have been up to now only weak voices, or few, opposing NCTM doctrine. If Achieve can, even with its guidelines, targets, benchmarks and roadmaps, add volume to those voices, it can only be for the good.

Ralph A. Raimi

25 September 2005