Update on 9-14-07: Part 2 of the interview is now posted!
[The comments and reactions are beginning to pour in here and on others' blogs. SteveH's and mathmom's give-and-take in the Comments section is a must read -- it's a blog of its own! Part 2 of the interview will be coming on Fri and Mon.]
As reported a few days ago, Prof. Steen, one of the most highly respected voices in mathematics education, graciously accepted an invitation for an online interview at MathNotations. He has been a driving force for the reform of school mathematics for many years and was on the development team that produced NCTM's Curriculum and Evaluation Standards for School Mathematics. For the last few years, he has been involved in Achieve's commitment to developing world-class mathematics standards for K-8 and ADP's similar commitment to secondary mathematics. He will have much to say about these standards and the new Algebra II End-of-Course Exam that will be launched in the spring of 2008. He is a man of great integrity and towering commitment to quality education for all of our children .
A few days ago, I emailed Prof. Steen a set of 19 questions that I felt reflected many of the concerns of my readership and, even more, confronted some of the major issues in mathematics education today. He agreed to reply to all of these, asking only that I publish his remarks in full. My role here was purely reportorial. This is not a debate. Once the questions were composed I stepped back and allowed him free rein. Prof. Steen replied thoughtfully and candidly within 48 hours. MathNotations will publish the interview in 2-3 segments to allow readers to absorb his replies and comment. If you've stopped here by the side of the road, tell your friends and colleagues about it. I invite fellow bloggers to spread the word across the blogosphere as well.
Philosophically, Prof. Steen and I have much common ground, although we diverge on some key points. What I truly believe is that honest dialog is the only way we can move forward, end the Math Wars and reach a strong middle-ground position that best serves the interests of our children. Whatever your ideology may be, Prof. Steen's comments are profound and thought-provoking. Enjoy!
I'll begin with my note of appreciation to Prof. Steen:
Thank you Prof. Steen for your prompt yet thoughtful replies. This has
been a new and rewarding experience for me and I know my regular
readers (and perhaps new visitors) will read your comments with great
interest, regardless of where their ideologies lie. You and I share
many common views and yet we can respect our differences. In the end,
we both want what is best for all our children. There are no easy
answers to difficult questions, however I do believe, as you do, that
dialogs like this will ultimately move us in the right direction.
Thank you again for contributing to this process.
Math Notations Interview
Lynn Arthur Steen, St. Olaf College, September, 2007
1. Prof. Steen, your involvement in so many mathematics and science education projects is mind-boggling. At this time, what are your greatest concerns regarding mathematics education in the U.S.?
That in our stampede for higher standards we are trampling on the enthusiasms, aspirations, and potential contributions of many students for whom mathematics is best approached indirectly. There is plenty of interesting mathematics in areas such as medicine, technology, business, agriculture, government, music, and sports, but students don't get to see these until large percentages have already given up on mathematics. It is true that mathematics unlocks doors to future careers. But we also need to open more doors to the world of mathematics.
2. Over a dozen years ago, Professor Schmidt, Director of the U.S. participation in TIMSS, made his famous comment about our mathematics curriculum being ‘an inch deep and a mile wide’. He also stressed the importance of having a coherent vision of mathematics education. Since then, fifty states have independently developed sets of mathematics standards and assessments. Although similar in some respects, they lack overall coherence and consistency of high expectations of our children. What is currently being done nationally as you see it to remedy this situation?
Notwithstanding our constitutional tradition of federalism that leaves states responsible for education, some now suggest voluntary national standards as a cure for the incoherence and inconsistency that is evident in state standards. Indeed, Senator Dodd (D-CT) and Representative Ehlers (R-MI) have introduced just such a bill in the Congress. I rather doubt that there is sufficient political support for nationalizing education in this way. Nor do I think it would resolve the problem. It would simply shift the locus of inconsistency from written standards and assessments to teachers and students.
More promising are efforts such as the American Diploma Project Network which is an ad hoc coalition of states that decided to work together on a common education agenda. This is not a "national" effort, but it is more in keeping with the traditions of our nation. Public distribution of comparative data is another strategy for reducing unwarranted inconsistency. Recent studies such as Mapping 2005 State Proficiency Standards Onto the NAEP Scales (NCES, June 2007) that compare states to the common scale established by the National Assessment of Educational Progress lead naturally to improvement motivated by competition or, in some cases, by embarrassment.
Strategies that open more doors to mathematics are more likely to emerge in smaller jurisdictions, for the simple reason that innovation begins locally and the doors that need opening tend to have local roots. So I'm not terribly bothered by lack of coherence and consistency. I'd rather focus first on getting more students to learn more mathematics of whatever kind may interest them. What counts is that students gain sufficient experience with substantive mathematics—not just worksheets—to benefit from its power and, if possible, to appreciate its beauty.
3. What were some of the obstacles faced by Achieve’s Mathematics Advisory Panel, both at the K-8 level and for the secondary curriculum? Were many of the current conflicts in mathematics education (aka, the Math Wars) overcome by this Panel? If not, what issues remain?
This is not a simple question! First, Achieve's formal Mathematics Advisory Panel (MAP) was constituted to work only on the K-8 level and produced Foundations for Success, a report with outcome expectations and sample problems for the end of grade 8. When work moved into the secondary level, it became part of the American Diploma Project (ADP) and operated with an evolving set of advisors representing all levels of mathematics and mathematics education.
From the perspective of the "math wars," the original MAP panel was, for its time, a remarkably catholic forum. Strong voices from many different perspectives set forth conflicting views. Compromises were agreed to, and sometimes reversed after further discussion. Eventually a report emerged. No one was pleased with every detail, but I believe it is fair to say that everyone on the MAP committee agreed that as a whole it represented a good step forward.
We reached this point by agreeing to set aside issues of pedagogy and to concentrate only on content. We further agreed that lists of expectations were less capable of conveying our intent than were rich examples. That is why the final report had 8 pages of expectations and 130 pages of examples. It was far easier for the diverse MAP members—protagonists, witnesses, and victims of the math wars—to agree on the quality of a problem than on the wording of a standard.
We also choose to largely ignore the issue of calculators because it was one of the wedge issues on which we all knew that the panel could never agree. Some may view this as cowardice, and it may be that. However, it made possible the rest of the work and affirmed, in a sense, that issues such as this may best be left for local decisions.
Another wedge issue we faced head-on, namely the place of quadratic functions and quadratic equations. Here we compromised, setting an ambitious bar for end of eighth grade at completing the square with a deliberate mandate to not employ the quadratic formula until the next algebra course. The purpose, of course, was understanding rather than calculation, a goal that in this case everyone around the table could support.
Those on the panel with the most school experience worried that completing the square was much too ambitious. They were proved right in subsequent reviews from states who wanted to use the Foundations for Success as a guide for their own standards. Consequently, later Achieve documents dealing with the transition from elementary to secondary mathematics are much more realistic about just how much algebra can be expected for all students prior to ninth grade.
Secondary mathematics is part of Achieve's ADP effort; the benchmarks together with sample postsecondary tasks appear in Ready or Not: Creating a High School Diploma That Counts (Achieve, 2004). There the contentious issue concerned the quantity of mathematics, especially of algebra, that should be required of all students for a high school diploma. A compromise was reached in which certain benchmarks, marked with an asterisk, were described as recommended for all but only required for those "who plan to take calculus in college." Of course, this asterisk mildly undermines the nominal goal of the ADP enterprise, namely, to set a uniform standard for an American high school diploma.
These matters—the role of calculators, the amount of algebra—are but two of the issues that remain fundamentally unresolved both within the ADP networks and among individuals who care about school mathematics. Other sources of continuing disagreement concern the role of data analysis and statistics, the place of financial mathematics, the importance of arithmetic "automaticity" and a host of pedagogical issues that, as I noted, Achieve largely leaves to others.
4. I’ve expressed great concern on this blog about the lack of frontline teacher representation on these major panels, particularly the President’s National Mathematics Panel? I’ve reiterated my call for redressing this situation via numerous emails to the Panel and on this blog. To date, all such requests have been politely dismissed. How do you feel about the need for increased teacher representation on this and other panels? Was there more K-12 representation (current classroom educators) on the Mathematics Advisory Panel on which you served?
The names of all those who advised Achieve on its MAP and ADP projects are listed in the reports of these projects. Different individuals contribute different types of work: some meet in panels; some review drafts; some write standards or contribute problems. My impression is that quite a few of Achieve's mathematics advisors have taught K-12 mathematics, but relatively few were serving as "frontline teachers" at the same time as they were helping with the Achieve work. Frontline teaching doesn't leave that much spare time.
Generally, I find concerns about representation less important than those about relevant experience. Sometimes the complaint is about the lack of teachers, other times about the lack of mathematicians; often complaints are accompanied by qualifiers (e.g., "current classroom teachers," or "active research mathematicians") that appear to imply that those who do not meet the condition are somehow less capable. What matters is that a panel as a whole include individuals with a broad balance of experience, which for mathematics education certainly includes both mathematical practice and classroom teaching—but not necessarily all at the same time the panel is meeting.
5. Many critics of NCTM’s original 1989 Curriculum and Evaluation Standards for School Mathematics and the revision in 2000 have claimed there was not enough emphasis on the learning of basic arithmetic facts. In your opinion, is the issue primarily due to lack of clarity in the standards, or is there a real difference of position between NCTM and its critics on the importance of arithmetic facts?? What is your position on the relative importance of the automaticity of basic facts?
There is a range of opinion about the importance of arithmetic facts within NCTM, within the broader mathematical community, and within the public at large. I understood the 1989 Standards to acknowledge this fact. A chief insight of statistics is recognizing the importance of variation. Student and adult skills with arithmetic vary, so the goals of mathematics education must take this into account. Almost all disputes about NCTM's standards arose because the historic absolutes of mathematics were replaced by alternatives and variations. In this sense, the critics were right: the Standards made mathematics "fuzzy" by insisting that most problems can be solved in more than one way. In fact, they can be.
There is no dispute that knowing arithmetic facts is more desirable than not knowing them, and being quick ("automatic") is better than being slow. The issue is: how important is this difference in relation to other goals of education? It is a bit like spelling: being good at spelling is more desirable than its opposite, but there are plenty of high-performing adults—including college professors, deans, and presidents—who are bad spellers. They learn to cope, as do adults who don't instantly know whether 7 x 8 is larger or smaller than 6 x 9.
For what it's worth, my "position" is that every child should be taught to memorize single digit arithmetic facts because if they do so everything that follows in school will be so much easier. But failure to accomplish this goal should not be interpreted as a sign of mathematical incapacity. Indeed, both students who achieve this goal and those who do not should continue to be stimulated with equal vigor by other mathematical topics (e.g., fractions, decimals, geometry, measurement), just like both good and bad spellers continue to read the same literature and write the same assignments.
Part II is now published. I hope to hear from many of you!