Massachusetts Deputy Commissioner of Education Sandra Stotsky

For Her Support of Arithmetic

**Introduction**

In November, 1999, Hyman Bass, professor of mathematics at the University of Michigan and at that time incoming president of the American Mathematical Society, slandered Sandra Stotsky, the Deputy Commissioner for Academic Affairs and Planning for the State of Massachusetts in a nationally distributed e-mail message, and has consistently refused to retract and apologize for what he said despite a total lack of evidence to support his slanderous statements. In his message, he harshly criticized the Open Letter to U.S. Education Secretary Richard Riley that was endorsed by more than 200 mathematicians and other scholars, including Sandra Stotsky. Professor Bass' vitriolic letter was posted with his permission, on national list serves, and included the statement:

[Sandra Stotsky's] ideological and uninformed opposition to "constructivist ideas" has reached the incredible state where she is opposed to inclusion of discussion of "Classical Greek constructions" as being "constructivist pedagogy." Is this what serious mathematicians want to associate themselves with?

In a subsequent message, also circulated nationally with Professor Bass' permission, he quoted Professor Maurice Gilmore, the source for his accusation, as follows:

The State [of Massachusetts] has appointed a woman, Sandra Stotsky, who is so ignorant of mathematics that she debated for 30 minutes with us to remove "classical Greek constructions" from our document because it was "Constructivist pedagogy." There is much more, not surprisingly about algorithms. To her, algorithms are purely operative for the 4 arithmetic operations with integers, no more than that.

Professor Bass' accusations are completely fraudulent. Dr. Stotsky has given tapes and transcripts to Professor Bass which record the meeting in question. They prove that Bass' accusations are without any basis in reality. They are complete fabrications. Stotsky has consistently and strongly supported the inclusion of Euclidean geometry in the schools, and there is a paper trail to prove this. The term "classical Greek constructions" was never used by Dr. Stotsky nor by anyone at the meetings she attended, nor was any other phrase with any similar meaning ever uttered by her or anyone else at the one meeting with Professor Gilmore she ever had, as the tapes and transcripts of that meeting prove. Moreover the phrase does not appear in any of the draft versions of the Massachusetts Mathematics Framework.

Professor Bass' refusal to retract the false charges he disseminated about Sandra Stotsky have implicitly lent support to the campaign by former mathematics framework panelists Maurice Gilmore, Carol Greenes, Margaret Kenney, and Deborah Hughes-Hallett (and the other five members) to prevent the standard algorithms of arithmetic from being taught in Massachusetts elementary schools. Deputy Commissioner Stotsky insisted that knowledge of these standard algorithms of arithmetic be included as requirements in the Mathematics Framework. Her position in support of arithmetic, and her endorsement of the open letter to Secretary Riley make her a target for Hyman Bass.

In spite of a massive, concerted campaign by the mathematics framework panel and their allies to portray Deputy Commissioner Stotsky as someone who wanted simply to return to rote memorization of mathematical formulas and to prevent students from acquiring "deep mathematical understanding," she has proceeded with constructive revisions of the Massachusetts Mathematics Framework. Changes in the draft mathematics framework were made with assistance from Professor Wilfried Schmid of the Department of Mathematics at Harvard University. The revised Mathematics Framework now requires knowledge of the standard algorithms of arithmetic for elementary school students in Massachusetts and knowledge and understanding of the quadratic formula. The remaining changes are relatively minor, mostly to make the standards clearer and more specific. A recent op-ed in the Boston Globe by Stanley Spiegel, associate professor of mathematics at the University of Massachusetts at Lowell, summarizes the mathematical issues connected with the revisions of the framework.

Hyman Bass has been provided with the evidence we have described and upon which we elaborate below. In spite of repeated requests by Sandra Stotsky that he retract his inflammatory and false accusations, he has declined to do so.

Mathematically Correct supports Sandra Stotsky's efforts to promote sound mathematics education in Massachusetts, including her position in support of arithmetic in elementary school and algebra in eighth or ninth grade. Among the many proponents of "fuzzy math," Hyman Bass' circulated statements are being cited as "proof" that Deputy Commissioner Stotsky is a benighted fool. Bass' slander campaign is not only grossly unfair to Stotsky, it creates barriers to institutionalizing sound mathematics education policies in Massachusetts. It is therefore important to set the record straight on this matter.

**The Story**

In early October, 1999, the U.S. Department of Education released a report to the nation's 16,000 school districts which designated 10 mathematics programs for K-12 as "exemplary" or "promising." The following month an open letter endorsed by more than 200 scholars and education leaders calling for the withdrawal of these recommendations was sent to Education Secretary Richard Riley. The letter was published as a full page ad in the November 18 edition of The Washington Post. Among the signatories are many of the nation's most accomplished scientists and mathematicians. Department heads at 16 universities including Caltech, Harvard, Stanford, and Yale, along with two former presidents of the Mathematical Association of America also added their names in support, as did seven Nobel laureates and winners of the Fields Medal, the highest award in mathematics. The open letter was covered by the leading newspapers in the United States and a congressional hearing was convened on account of it.

In addition to the many scientists and mathematicians, several prominent education leaders at the state and national levels added their names to the open letter. Among these was Sandra Stotsky, Deputy Commissioner of Academic Affairs for the state of Massachusetts. Dr. Stotsky was in the midst of coordinating changes to the Massachusetts Mathematics Framework when the open letter was released. Based upon the advice of many mathematicians and a report of the American Mathematical Society, she insisted that the standard algorithms of arithmetic (i.e. the standard procedures for addition, subtraction, multiplication, and division of numbers) be included in the elementary school grades, even though the Framework Panelists she "inherited" argued against them and supported child invented algorithms via discovery learning. These mathematics education advisors even went so far to deny the very existence of standard algorithms of arithmetic in direct contradiction to the American Mathematical Society report.

Shortly after the release of the Open Letter to Education Secretary Riley, Professor Hyman Bass circulated a long condemnation of it in which he defended the "exemplary" and "promising" curricula and denounced the authors of the letter and Mathematically Correct, as well as a member of the California State Board of Education. His concluding sentence was,

What appear to be very sensible reservations about what the Department of Education did, becomes in fact part of a veiled and systematic assault on the professional education community, in which Askey and Wu are perhaps inadvertently allied with people who have much more insidious political agendas.The "insidious political agendas" that two of the co-authors of the Open Letter, Professors Richard Askey and Hung-Hsi Wu, were being used for were never identified by Bass, but they presumably include the teaching of the standard algorithms of arithmetic to elementary school children.

In a subsequent message dated Sept. 24, 1999, that was nationally circulated with his permission, he added his condemnation of Deputy Commissioner Stotsky. Specifically, Bass wrote:

Mathematically Correct, an important agent in promoting this Open Letter, has been politically active around the country. In Massachusetts it is allied with efforts of the Deputy Commissioner of Education, Sandra Stotsky, to review proposed revisions to the State Framework. Her ideological and uninformed opposition to "constructivist ideas" has reached the incredible state where she is opposed to inclusion of discussion of "Classical Greek constructions" as being "constructivist pedagogy." Is this what serious mathematicians want to associate themselves with?

Hyman Bass had never spoken to or communicated in any way with Sandra Stotsky prior to spreading this attack on her. He did not even include her as a cc on his initial email message. When Dr. Stotsky learned of this message from Richard Askey, she wrote to back to him:

Absolutely bizarre. I have never said or written anything whatsoever regarding 'Classical Greek constructions.' I wouldn't have even known what was being referred to if you hadn't explained that it was related to geometry. Can't imagine what it could even be a distortion of. If anything, I have been concerned about the teaching of Euclidean geometry, wanting to be sure it's there in the curriculum.I sure would like to know Hy Bass's source for this bit of specious nonsense.

Askey asked Bass on November 25, 1999, for the basis of his condemnation of Deputy Commissioner Stotsky. His reply was:

Dear Dick,What I said was taken from a message from Maurice Gilmore. Let me quote below the relevant passages.

Hy

____________________________

Dear Hy,

Not that we know each other. But I am former Chair here at Northeastern University, .......I was an algebraic topolgist in the past. Now I work in secondary math reform in Boston. I was Andy Gleason's "replacement" on the Panel to revise the State Frameworks in Mathematics. Andy helped write the first version. Both he and I worked with math teachers at every level. Deb Hughes-Hallett was also on the panel I served on. I write because the process here is rapidly being politicized by Mathematically Correct from California.

The State has appointed a woman, Sandra Stotsky, who is so ignorant of mathematics that she debated for 30 minutes with us to remove "classical Greek constructions" from our document because it was "Constructivist pedagogy." There is much more, not surprisingly about algorithms. To her, algorithms are purely operative for the 4 arithmetic operations with integers, no more than that.

She is Deputy Commissioner and will be in charge of the review of our document. We are taking steps to have the review be a public review, as the current set-up is isomorphic tho the situation which occurred in California.

I am no "constructivist pedagog", I respect Connected Mathematics and work to implement it, along with extra work on both fractional and algebraic skill development, which the reform community here all are doing.

This extraordinary accusation is a complete fabrication. Sandra Stotsky met with Maurice Gilmore for the first time on July 27 and has not met with him since. Attending that July 27 meeting were David Driscoll, Commissioner of Education for Massachusetts, and the other math advisors serving on the Framework Panel, Carol Greenes and Deborah Hughes Hallett. The math advisors were fighting against the inclusion of the standard algorithms of arithmetic in the mathematics framework. Because of the official nature of this meeting, it was recorded and transcribed. Nothing resembling the phrase "classical Greek constructions" was uttered by anyone during the meeting and this can be verified by listening to the tapes or reading the transcript.

However, during this meeting and the following recorded dinner conversation, the math advisors explained several times that they had great mathematical expertise as they argued against the teaching of the standard arithmetic algorithms. They claimed that there is no such thing as standard arithmetic algorithms. At one point in the conversation, one of them claimed that the standard algorithm for adding numbers is mathematically incorrect! It was never explained by these allies of Hyman Bass how the standard procedure for adding two numbers could both be incorrect and not exist. Nor was it explained how a report of the American Mathematical Society could support the teaching of the standard algorithms if they don't exist. If the other two Framework Panelists present for that meeting had any reservations about these assertions of their colleague, they failed to express them.

A series of exchanges between Deputy Commissioner Stotsky, Professor Bass, and others occurred via email. There can be no doubt that Bass understood that his evidence against Stotsky had completely collapsed. Rather than admit that what he said was a mistake, he posted a message on a national education listserve. In response to information Stotsky sent him, he wrote,

Though this further information was very helpful to me in understanding her perspective on issues, I saw nothing in it that was inherently inconsistent with the possibility that she might have said what is cited above.A few days later, Bass sent Stotsky a copy of this message and he included some additional comments. He wrote:

I trust that you have seen the "clarification" message that I sent to Jerry Becker. In case you haven't I shall now forward it to you. It was sent to Becker on Nov 28, but it only appeared a couple of days ago, because of email backup. In that message I state that I still lacked confirming information about what happened in the review panel meetings. Since that time I have been able to speak to other panelists, and I am persuaded that the essentials of what I reported, as clarified, is correct. What I was told by the panelists, and what you yourself state in your memo, seem to be entirely consistent.

In his "clarification," Bass included Stotsky's June 10 Memo, which asserted her support of Euclidean geometry and also criticisms of constructivist approaches to mathematics education. Stotsky had previously sent an elaboration of her views on constructivism to Bass.

In the meantime, Bass' allies in Massachusetts were also busy. Carol Greenes, a Professor of Mathematics Education Boston University and a Framework Panelist opposed to teaching the standard arithmetic algorithms sent a letter dated December 13, 1999, with a long copy list, to Education Commissioner Driscoll criticizing Stotsky's position and objecting to the process of revisions. David Driscoll sent a letter of reply to Dr. Greenes with copies to the same list of recipients. In his letter, Commissioner Driscoll explained again the process for revising the Mathematics Framework by quoting procedures previously sent to Dr. Greenes. His letter explained that in accordance with policies of the Department of Education,

...we are pleased that Professor Wilfried Schmid of the Department of Mathematics at Harvard University has agreed to assist us in the preparation of the final draft with respect to the accuracy and adequacy of the mathematical content of the standards. Groups of teachers at different grade levels and from a variety of school districts will also be assisting us in deciding upon the right level at which to pitch the standards in K-8, an issue on which we have already received a wide range of comments.

Professor Schmid made a number of improvements to the draft Framework, most of them minor. Commissioner Driscoll's letter also rebutted Professor Bass' invented scenario that portrayed Deputy Commissioner Stotsky as an idiot. The Commissioner wrote:

It is my hope that the revision process we have planned will be carried out without distractions. I regard as unfortunate the totally unfounded charge in an earlier letter from a member of the mathematics revision panel that one of my Deputy Commissioners supposedly "debated for 30 minutes" to remove the phrase "classical Greek constructions" from the draft of the mathematics document because she failed to understand that it referred to Euclidean geometry. Not only was there no such phrase in any of our mathematics documents, which several members of my staff have attested to, a tape recording of the meeting at which this "debate" supposedly took place provides unequivocal evidence that there was no discussion whatsoever about "classical Greek constructions" of any kind. Please note that the Department tape records some committee meetings for future reference, in the absence of a stenographer, with the explicit permission of those attending.

Stotsky sent a formal letter to Bass dated January 18, 2000. The letter once again asked Bass to act honorably and retract his previous damaging fabrications. Stotsky's letter once again reminded him that the only meeting that she and Professor Gilmore ever had was on July 27 and that meeting was recorded. A full transcript accompanied the January 18 letter. Nothing resembling what Bass had written had occurred.

Bass' response via email a few days later was as follows:

Dear Sandra,I just returned from some travel and found your letter accompanied by the transcript of the July 27, 1999 session of the Math Framework Review Panel. It is my understanding that the discussion of geometric constructions occurred in an earlier meeting, one not attended by Prof. Gilmore. He apparently reported on that exchange based on reports from others who had attended that session, which included Carol Greenes and Peg Kenney.

I can't be sure about the exact accuracy of this second hand reporting, but it would help me assess the situation further if you could supply a transcript of that meeting.

Best wishes,

Hyman

The meeting on June 10 that Bass obliquely refers to in this email note to Stotsky, was not recorded. It was an informal meeting in Stotsky's Office to discuss the June 10 memo that Bass included in his earlier December 1 letter to the education listserve. Department of Education staff members were present, however, and they have confirmed that no discussion of the kind Bass described had occurred. Gilmore was not present at that meeting. This contradicts Gilmore's original statement to Bass that was nationally circulated. Recall from above that Gilmore had written:

The State has appointed a woman, Sandra Stotsky, who is so ignorant of mathematics that she debated for 30 minutes with us to remove 'classical Greek constructions' from our document because it was "Constructivist pedagogy."The key word is "us." That means Gilmore was included and that forces the meeting to be July 27 since that is the only time Gilmore and Stotsky were ever together. Bass' December 1 letter included the following paragraph:

Prior to giving Jerry Becker permission to distribute my letters, Dick Askey had seen this and called it to the attention of Sandra Stotsky, who vehemently denied saying any such thing. Askey asked me for my evidence for this. I explained that it came in a message from a mathematician who was part of the Massachusetts Mathematics Framework Review Panel, and who was at the meeting where this was said to occur. I sent to Askey the relevant passages from that message.The key phrase here is "from a mathematician who was part of the Massachusetts Mathematics Framework Review Panel, and who was at the meeting where this was said to occur. "

Rather than admit his obvious error, Hyman Bass is now pretending that Sandra Stotsky committed the actions he invented on another occasion that was not recorded. Bass now expects Stotsky to jump through more hoops to try to convince Bass that she never did what he accuses her of with only Gilmore's discredited lie.

It is time that Professor Hyman Bass admits that he was wrong, apologizes to Sandra Stotsky, and fully retracts his fabrications.

The American Mathematical Society NCTM 2000 Association Resource Group's Second Report published in the Notices of the American Mathematical Society February 1998 contains the following passage:

Standard algorithms may be viewed analogously to spelling: to some degree they constitute a convention, and it is not essential that students operate with them from day one or even in their private thinking; but eventually, as a matter of mutual communication and understanding, it is highly desirable that everyone (that is, nearly everyone -- we recognize that there are always exceptional cases) learn a standard way of doing the four basic arithmetic operations. (The standard algorithms need not be absolutely unique, just as there are variant spellings between, say, the U.S. and England, but too much variation leads to difficulties.) We do not think it is wise for students to be left with untested private algorithms for arithmetic operations -- such algorithms may only be valid for some subclass of problems. The virtue of standard algorithms -- that they are guaranteed to work for all problems of the type they deal with -- deserves emphasis.We would like to emphasize that the standard algorithms of arithmetic are more than just "ways to get the answer" -- that is, they have theoretical as well as practical significance. For one thing, all the algorithms of arithmetic are preparatory for algebra, since there are (again, not by accident, but by virtue of the construction of the decimal system) strong analogies between arithmetic of ordinary numbers and arithmetic of polynomials. The division algorithm is also significant for later understanding of real numbers. For all its virtues, decimal notation suffers a significant drawback over, say, standard notation for fractions: decimal numbers (meaning decimal fractions with finitely many terms) do not allow division. This can be remedied at the cost of using infinite decimal expansions, but this is a big leap, and the general infinite decimal is not rational. To understand that rational numbers correspond to repeating decimals essentially means understanding the structure of division of decimals as embodied in the division algorithm. We do not see that naive use of calculators can be of much help here: the length of repeat of a decimal will typically be comparable to the size of the denominator, so that 7/23 or 5/29 will not reveal any repeating behavior on standard calculators.

David P. Driscoll

Commissioner of EducationDecember 17, 1999

Carole Greenes

Professor of Mathematics Education

Boston University

605 Commonwealth Avenue

Boston, MA 02215Dear Professor Greenes and Members of the Revision Panel:

Thank you for your letter of December 13 inquiring about the process to be used by the Department of Education in responding to the public comments on the draft of the Mathematics Curriculum Framework released to the public in September and in preparing the final version for the Board of Education's approval in February. I share your desire that your comments be considered. To that end, as the November 9 letter sent to all Panel members indicated:

After the period of public comment is over, the chair of the Curriculum Framework Revision Panel may wish to convene a meeting of Panel members to review all of the feedback. (This will not be an obligatory meeting.) The members of the Panel may then, singly or as a group, present their comments, inquiries, or suggestions to Dr. Sandra Stotsky, Deputy Commissioner for Academic Affairs and Planning, who will be in charge of the final revision, editing, and formatting of the document.The Department of Education will then determine the scope of the revisions to be made and the resources to be drawn upon, based on the Panel members' suggestions and on the Department's own review of the feedback. Outside experts may be drawn upon to assist in the preparation of the tentative final draft. Before this draft is presented to the Board of Education for formal approval, Panel members will be sent copies and given the opportunity for comment.

Once completed, copies of the tentative final draft will be sent to the Board of Education for its review and action.

This is the process the Department of Education will be following for the revision of the other curriculum frameworks being revised this year - science and technology/engineering, history and social science, and the English language arts. It is my intention to make sure that we present to the Board the very best Mathematics Curriculum Framework we can in February. To that end, we are pleased that Professor Wilfried Schmid of the Department of Mathematics at Harvard University has agreed to assist us in the preparation of the final draft with respect to the accuracy and adequacy of the mathematical content of the standards. Groups of teachers at different grade levels and from a variety of school districts will also be assisting us in deciding upon the right level at which to pitch the standards in K-8, an issue on which we have already received a wide range of comments.

It is my hope that the revision process we have planned will be carried out without distractions. I regard as unfortunate the totally unfounded charge in an earlier letter from a member of the mathematics revision panel that one of my Deputy Commissioners supposedly "debated for 30 minutes" to remove the phrase "classical Greek constructions" from the draft of the mathematics document because she failed to understand that it referred to Euclidean geometry. Not only was there no such phrase in any of our mathematics documents, which several members of my staff have attested to, a tape recording of the meeting at which this "debate" supposedly took place provides unequivocal evidence that there was no discussion whatsoever about "classical Greek constructions" of any kind. Please note that the Department tape records some committee meetings for future reference, in the absence of a stenographer, with the explicit permission of those attending.

We look forward to producing a first-rate Mathematics Curriculum Framework for Massachusetts teachers and students but will be successful only if we focus on the issues that relate to the teaching and learning of mathematics for our students.

Sincerely yours,

David P. Driscoll

Commissioner of Educationc. Margaret Kennedy, Professor of Mathematics, Boston College

Maurice Gilmore, Professor of Mathematics, Northeastern University

Anne Collins, Principal Investigator for Partnerships Promoting Student Achievement in Mathematics

Deborah Hughes Hallett, Professor of Mathematics, University of Arizona

Victor Steinbok, Doctoral Candidate in Mathematics Education, Boston University

Barbara Haig, K-12 Curriculum Chair, Elementary Mathematics, Teacher, Northborough Public Schools

Gisele Zangari, Mathematics Instructor, Boston University Academy

Jacqueline Rivers, Director Math Power, Northeastern University

The Honorable Paul Cellucci, Governor, Commonwealth of Massachusetts

The Honorable Thomas Finneran, Speaker of the House, Commonwealth of Massachusetts

The Honorable Robert Antonioni, Senate Chair, Joint Committee on Education, Arts and Humanities

The Honorable David Donnelly, Representative Vice-Chair, Joint Committee on Education, Arts and Humanities

James A. Peyser, Chairman, Massachusetts Board of Education

Sandra Stotsky, Deputy Commissioner of Academic Affairs and Planning, Department of Education, Commonwealth of Massachusetts

Representative Paul Haley

Senator Cynthia Creem

Representative Ronny Sidney

Representative Ruth Balser

Representative Paul Demakis

Dr. Perry Davis, President, Massachusetts Association for Supervision and Curriculum Development

Lynn Ryan, President, Massachusetts Elementary School Principals' Association

Carol Woodbury, President, Massachusetts Parent Teacher Association

Dr. Russell E. Goyette, President, Massachusetts Secondary School Administrators' Association

January 18, 2000Professor Hyman Bass

Department of Mathematics

3864 East Hall

University of Michigan

Ann Arbor, MI 48109-1109Dear Professor Bass:

I am writing to you, again, to request that you provide your colleagues with an unambiguous explanation and retraction of the erroneous statement that you published, in which you attributed to me an "ideological and uninformed opposition to 'constructivist ideas' [that] has reached an incredible state where she is opposed to inclusion of discussion of "Classical Greek constructions' as being 'constructivist pedagogy.'" Your characterization is wrong, and it has no basis in fact.

As you indicated in an e-mail on November 25, 1999, you copied the statement from a personal e-mail that Professor Maurice Gilmore of Northeastern University sent to you sometime last fall. Professor Gilmore, whom I have met only once (at the July 27,1999 meeting of the Mathematics Framework Panel in Massachusetts) has since apologized to me for its tone. In fact, the transcript of the July 27, 1999 meeting of the Mathematics Panel, a copy of which I have enclosed for your review, clearly shows that there was no mention of "Classical Greek constructions" at that meeting (indeed, the phrase does not appear in any Department documents), and there was no discussion whatsoever of the content of Euclidean geometry. The words "constructivist" and "constructivism" do not even appear in the transcript. Further, contrary to what Professor Gilmore claims in his December 15 letter to me and contrary to what you claim in a personal December e-mail to me (based, you said, on conversations with other Panel members), there was no mention whatsoever (never mind a discussion) of geometric constructions created by a "straightedge" or "compass." These words do not appear at all in the transcript of the meeting. Nor have they ever been mentioned in any conversation about the mathematics standards in which I participated.

However you choose to word an explanation and retraction for your colleagues, it should be made clear that the transcript of that meeting proves conclusively that there is no basis to Professor Gilmore's charge, and that you made a grievous error in judgment (and interpretation) in broadcasting that mischaracterization of my views.

Sincerely yours,

Sandra Stotsky, Ed.D.

Deputy CommissionerC: Professor Maurice Gilmore