Thank you, Joan, for the kind introduction.

As many of you know, Joan and Jim Leitzel were both members of Ohio State’s Department of Mathematics for 25 years.  They left Ohio State in 1990, but their influence on our math department and on the university is still felt in significant ways today. And Joan's leadership of the University of New Hampshire and, more generally, in higher education, is a tremendous source of pride for The Ohio State University.  I also want to thank Ron Rosier and the organizers of this conference for giving me the opportunity to address this important conference, with so many distinguished scholars in attendance. 

This “opportunity” is somewhat intimidating, however, considering how long it’s been since I was a working mathematician.  Shortly after accepting this invitation, my sense of elation over being asked to speak was replaced by a sense of panic not unlike that dream most of us had as students where we walked into class having forgotten that it is exam day.   I take great pride in my roots in mathematics, but what, I had to ask myself, could I possibly have to say that would interest a roomful of active, practicing professionals?  Despite my trepidation, after spending two decades in university administration and away from my discipline – and after living the past few years in Ohio – it’s certainly gratifying to be back in the Greater Washington area talking about mathematics.  To quote that noted philosopher, Yogi Berra, it’s almost déjà vu all over again.

And this is, indeed, a very appropriate place and time for us to hold a discussion about math education.  Earlier this year, right here in Fairfax County, parents, educators, and school board members divided up into opposing camps to wage one of the latest battles in what has been called the math wars.  Given that Fairfax County is one of the nation’s largest and best school districts and given that lines were drawn over a textbook contract estimated at more than $9 million, this had all the makings of a battle royal…and it was.  On the surface, things were fine.  Fairfax County has an outstanding school system, with strong parental support, solid math scores, and a wealth of high-achieving students.   About ten years ago, teachers in Fairfax began teaching mathematics from a more conceptual approach.  But this year, with a textbook contract up for bids, a strong group of parents and educators supporting more traditional math education rallied together and called themselves “Citizens for Better Math.”  There were contentious town meetings and memos condemning the meetings. Even the local Democratic and Republican parties chose up sides to support the so-called “nonpartisan” school board members on either side of the issue. 

Similar math wars are being fought all across this country – and they’ve even spread to Japan and Europe. They’re being fought on college campuses at a philosophical level by mathematics and education faculty. They’re being contested in state legislatures as more and more states start to formulate high stakes proficiency tests.  And, as happened here in Fairfax County, some of the most contentious fighting is in the trenches of the local school districts that must establish texts and curricula.  Wars have been fought over love.  Wars have been fought over taxes.  Wars have even been fought over soccer.  But over how we teach arithmetic! And we use to fret because people didn’t care enough about mathematics? 

The apparent catalyst for these math wars has been the poor math skills our students continue to demonstrate compared to their counterparts around the world.  In international math tests, our 4^th graders usually rank above average.  However, when they reach 8^th grade, they’ve slipped to about average.  And by the time they reach 12^th grade, they rank near the bottom. 

At the same time, good math skills and a solid grasp of mathematical problem-solving are now more important to our economy and our society than ever before.  We know that mathematics and mathematicians have played a crucial role in many of the phenomenal scientific and technological breakthroughs that have occurred over the past few decades.  But less noticeable – and just as important  – basic quantitative literacy has become absolutely essential for ordinary citizens to function successfully in their work, public, and personal lives.  For instance, to succeed in the business world, we have to manage spreadsheets, program computers, develop business plans, and solve complex problems – all requiring a firm grasp of mathematical concepts.  That’s true in businesses from computer chips to potato chips. And math literacy has become essential for us to understand vital public and personal issues – like weighing environmental risks and benefits, understanding statistics and surveys, seeing flawed or misleading logic, and developing a financial plan for retirement. 

Without a basic mathematical literacy, our democracy clearly will be in trouble in this technological age.  That was the theme behind the National Council on Education’s recent book, Mathematics and Democracy: The Case for Quantitative Literacy, in which the authors note:

“Quantitative literacy empowers people by giving them tools to think for themselves, to ask intelligent questions of experts, and to confront authority confidently.  These are skills required to thrive in the modern world.” 

Of course, for our students to develop these skills, they need to have good math teachers, especially in the early and middle grades.  Because of the cumulative way that we build up our math knowledge, all of you know well that if students get lost and fall behind early, they almost never catch up. 

That brings us to the real cause behind the math wars:  a severe shortage of good math teachers – and a lack of knowledge about the best ways to teach mathematics.  I’m sure many of you are familiar with the statistics about math educators: 

In other words, too many of  our teachers are living out Bertrand Russell’s whimsical definition of mathematics as “the subject in which we never know what we are talking about, nor whether what we are saying is true.”

Some of our Ohio State faculty members who work with school districts tell me about meeting K-12 math teachers who don’t know what integers are, teachers who can’t multiply or divide fractions – and many who, if they do know the rule for dividing fractions, can’t explain why it works.  A recent survey from California shows that more than 25 percent of California State University graduates of teacher programs believe they are ill prepared to teach math.  Obviously, if they don’t understand math, they aren’t going to be successful teaching it – and they certainly won’t inspire a passion for mathematics in their students. 

In the sciences, we have seen how inspiring teachers like Carl Sagan and Stephen Hawking can help raise the scientific literacy of a generation – and can inspire teachers and innovative teaching methods.  Where are the mathematics teachers to inspire today’s students?  Where are the teachers who can help our students understand why Carl Gauss called mathematics “the queen of the sciences.” 

Vartan Gregorian, the President of the Carnegie Corporation and the former President of Brown University, wrote in a recent issue of the Chronicle of Higher Education that teacher education must become a central preoccupation of colleges.  I think he is dead on, and there is probably no discipline where the need is greater than mathematics.  

Teacher preparation cannot be a peripheral assignment for our least engaged and inspiring faculty.  It must be a central mission of our math and education departments.  Mathematicians and math departments across our nation are doing vital research and making great breakthroughs that will have far-reaching impact in high-tech industries and in our knowledge of the universe. 

But it is my contention that today, one of the single most important contributions we can make to society will come from our breakthroughs in math education.  With advances in mathematics education, we can make an invaluable contribution to the economic, political, and social well-being of our nation.  And, at the same time, we can raise the understanding and appreciation of our entire profession. That would be good for students.  It would be good for the larger community.  And it would be good for mathematicians and math departments.  If the teaching and learning of mathematics really became a priority for university-level mathematics departments, just think about the possibilities. 

But to realize these possibilities, regrettably, we have a long way to go.

So, for the bulk of my remaining time with you, I’d like to focus on six strategies that I believe our mathematics and education departments must pursue as part of this central mission of teacher education. A couple of these strategies may be a little broad, but I wanted to limit my list to five or six items.  After all, Woodrow Wilson only needed 14 Points to end a world war.  And God Almighty got by with only 10 rules.  So, with my more modest assignment, I’ll stick with six.

First, we need to reshape and restructure the undergraduate curriculum – for prospective teachers and for all undergraduates.  We need to place greater emphasis on active learning at all instructional levels and on the connections mathematics has to other disciplines. Mathematics is important to all of our students, and today, we have to shift the mathematics department’s role from being an instructional filter to being an educational pump.  That’s especially true for prospective teachers. We need to reward those special faculty members who have a talent for sparking an interest in and understanding of math. In collaboration with colleges of education, we need to create departmental tracks to prepare K-12 teachers – and we need to create Ph.D. tracks in math education. Also, our math faculty should be modeling the pedagogical techniques that future teachers will use in the classroom. To help make that possible, one step we took recently at Ohio State was to limit some math classes for prospective teachers to no more than 20 to 30 students.  That simulates the size of classes they will teach, and it helps our own faculty use the same teaching methods that their students can use in their own classrooms. We also formed a University Teacher Education Council, which includes public school teachers and administrators, as well as representatives from the Arts and Sciences disciplines. This group is working to enhance the curriculum for prospective teachers in math, science, and many other fields. One of that group’s biggest efforts has been to completely restructure and strengthen our program for middle school math teachers.

The second strategy I want to talk about is improving diversity in our mathematics departments. In this era of rapidly expanding diversity throughout our nation, diversity is not being reflected in our math departments. Overwhelmingly, most of our math graduate students are male and are either white or foreign-born.  Among math graduate students, men currently outnumber women two to one. And African Americans now make up only about 5 percent of math graduate students.  As late as 1997, the total number of African Americans receiving a Ph.D. in math during the entire year was seven.  Yes, seven in the entire nation. Clearly, we must do a better job at improving the math education of under-represented students in their early years and inspiring them to continue their studies in mathematics. If we can encourage and attract a more diverse group of graduate students and faculty, we will certainly improve the diversity of our population of prospective math teachers. It’s not an impossible task.  In fact, the University of Nebraska has set an outstanding example for attracting women into its graduate mathematics program. During the 1980s, the University of Nebraska Mathematics Department did not award a single Ph.D. to a woman.  They had awarded only six in the school’s entire history.  The numbers were unacceptable to them, and they took action. About 10 years ago, Nebraska initiated a number of programs – ranging from math summer camps for high school girls, to weekly seminars on women in mathematics, to a decade of targeted recruiting and focused mentoring. The results: Nebraska now can boast about a math graduate student population that is about 50 percent female.  And in the past few years, about 40 percent of its math Ph.D.’s have gone to women.  The national average, by the way, is about 22 percent.  The University of Nebraska’s mathematics department even received a Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring in 1998 for this exceptional effort. My former department, the mathematics department at the University of Maryland, has had comparably dramatic success with African American graduate students.  Through an active recruitment effort, an individualized admissions process, and a highly effective mentoring program, they now boast some 25 African American graduate students in their Ph.D. program. For perspective, those 25 students represent almost 15 percent of all African American mathematics graduate students in the nation. Like the University of Nebraska, the University of Maryland is showing that we can create greater diversity in our nation’s mathematics departments, if it becomes a departmental priority to do so.  

In addition to building a more diverse field of mathematicians and math teachers, we also need to increase and improve opportunities for change-of-career teachers.  That’s the third point I want to address. Here I am talking about those professionals who were working as scientists, engineers, and mathematicians in industry and government, but have decided they want to do something different.  Perhaps they are eligible for early retirement. At Ohio State, roughly 40 percent of the students enrolled in our master’s program to teach math and science are these second-career teachers. The way our system works now, they almost always have to quit their current job for 15 months to complete the M.Ed. and get a teaching license. Now, we’re exploring plans to develop a new program that would allow these professionals to take an intensive summer program of education classes and then get a job teaching half-time, while working with a paid mentor and taking additional classes for one year. After a second intensive summer of classes, they could acquire their teaching license and move full time into the classroom.  We’re very excited about the possibilities for such a program, and we think school districts will be eager to partner with us.

That leads to the fourth strategy I want to address:  increasing our involvement with school districts and math teachers. Not only do we need to better prepare the next generation of math teachers, but we also need to find innovative ways to help current teachers improve their professional development. For more than 40 years at Ohio State, we’ve conducted an 8-week summer program for outstanding high school math students.  It’s called the Ross Mathematics Program, and it’s been a tremendous training ground for aspiring mathematicians. Last year we initiated a Ross Mathematics Program for Teachers. High school math teachers from across the state can spend three weeks at the university becoming immersed in a world of mathematical discovery – and developing new techniques for learning and teaching. Then, the group meets twice more during the academic year to share ideas about teaching techniques that are working in their high school classes. Other universities across the country are also working more and more with public schools and teachers – and increasingly, they’re finding funds from NSF and other sources. For instance, the Lancaster, Pennsylvania school district and LaSalle University in Philadelphia recently received a $1.7 million NSF grant to improve math teaching throughout that district. And the U.S. Department of Education is helping to fund an effort by the University of Maryland and Anne Arundel County schools to develop a master’s degree program in elementary math education for teachers in that county. The National Science Foundation also announced two weeks ago a $100 million effort to create five new centers to improve science and math education.  

And that initiative relates directly to the fifth strategy:  We have to increase our research in math education. Our experts have generated some very good research lately on math education techniques. For instance, there is Liping Ma’s exceptional book, Knowing and Teaching Elementary Mathematics, which seems to be the one work claimed by both sides in the math wars. The new CBMS report, The Mathematical Education of Teachers, is another great contribution toward finding peace in the math wars. And just last month, the Association of American Publishers hosted a “Summit on Math Education” in Washington, D.C., in an effort to bring together both sides in those wars. We know the answer to the math wars.  It’s not emphasizing computational skills to the exclusion of conceptual understanding or vice versa.  It’s a balance of both that our students and teachers need. But the debate continues about where to place the fulcrum, and more research from the outstanding minds we have on our campuses will help us find the answers.  

This brings me to the final action I want to talk about.  It’s the concept of individualized faculty workloads. I think there is no area where universities are more subject to valid criticism than in the way we utilize our human resources.  I'm certain the situation has improved from when I was a chair – but surely not enough. In my day, we had a uniform teaching load regardless of whether faculty were actually engaged in research.  Indeed, we perpetuated a myth that everyone was involved in research.  God help the person who tried to take on some special assignment involving undergraduates.  Rumors would start to buzz in the hall.  “What’s wrong with old Joe?  His career must be on the skids.” Such attitudes were never justified, but with the issues facing our departments and universities, they can no longer be tolerated. We do need a new reward structure – one more in tune with current reality and current missions. Clearly, at research-intensive universities, we have every reason to expect that each candidate for tenure will demonstrate a research mastery of his or her field. In mathematics, this would almost certainly mean research published in major peer-reviewed journals. But, as Ernie Boyer pointed out in his brilliant book Scholarship Reconsidered, careers in academia are long, and few sustain an uninterrupted, 40-plus-year career of important research activity.  As we all know, this is especially true in mathematics. Let’s accept and take advantage of this fact. Let’s make it possible for faculty whose passion for research may be cooling to switch gears and focus on teaching, curriculum development, and outreach to the K-12 sector. And let’s make it possible for individuals to gain promotion from associate professor to full professor if they excel in scholarship related to the learning of mathematics. We need to accept and promote teacher education and the learning of mathematics as a central mission of the department and the university.

We’re at a moment of opportunity for our discipline, perhaps the single greatest moment of opportunity ever, to make a vital and long-lasting contribution to our students, to our profession, and to our nation’s social, political, and economic well-being.  We are making good strides with promising research, a growing number of programs with schools, and wit h gatherings like this that place math education at the forefront of our profession. And I am very pleased to say that I believe our Ph.D. recipients over the past several years tend to be better and more dedicated teachers of undergraduate mathematics than any generation I’ve seen. The key to our future success lies in our ability to form productive partnerships between:

With strong partnerships to address these six strategies I have mentioned, I’m confident that we can face the challenges ahead of us, take bold actions, and make math education not a casualty of the battlefield, but a strong foundation for the future of our discipline and our society.  

Thank you.