Testimony Before Math Panel

of Dr. James E. Schultz

Robert L. Morton Professor Emeritus of Mathematics Education

at Ohio University

June 29, 2006

INTRODUCTION

Thank you to Dolan Professor of Mathematics Ben Klein of Davidson
College for agreeing to read my testimony and to Jennifer Graban and the
organizers of this meeting for providing this opportunity. I wish the
distinguished panel well in this effort, so important to the future of
our nation and the millions of children who will be directly impacted.

My own experience includes five years of mathematics teaching in high
school, twenty-five years in departments of mathematics, and fourteen
years in colleges of education. It also includes short term teaching
mathematics at every level from Kindergarten through advanced calculus
and frequent observations in urban, rural, and suburban schools
throughout the world, as well as authoring or coauthoring eighteen
textbooks for three major publishers, refereed articles in eight major
journals, and the 1989 NCTM Curriculum and Evaluation Standards.

From this perspective I wish to share several observations and
recommendations.

OBSERVATIONS

1.  Collaborations like the work of this panel are exactly what is
    needed. While successful collaborations between mathematicians,
    mathematics educators, and classroom teachers are possible and do
    exist, energy is often wasted on nonproductive efforts, such as *ad
    hominem* attacks on those addressing the challenges of mathematics
    education.

2.  Polarization is a major impediment to developing a sound mathematics
    curriculum. Some programs seem to ignore the importance of basic
    skills, while others are obsessed with it. What we hear from some
    today, sounds too much like the opening of *Hard Times* where
    Dickens describes the classroom of 1854 in this way: "NOW, what I
    want is, Facts. Teach these boys and girls nothing but Facts. Facts
    alone are wanted in life. Plant nothing else, and root out
    everything else." Dickens aptly pointed out the negative
    consequences of this approach.

3.  With an emphasis on algebra, attention to probability and statistics
    is lacking. Even within algebra, exponential functions, with
    important applications in the everyday lives of *all* students are
    often neglected. Students who struggle for weeks to factor binomials
    too often are not introduced to the concepts of correlation and
    exponential functions which have major applications to their health
    and management of money.

4.  Though according to U. S. Census figures 25% of the population lives
    in rural areas, this segment of the population is often overlooked
    when educational changes are proposed.

5.  Technology which supports computation and enhances concept learning
    and provides new approaches to problem solving is now readily
    available. Just as it is now accepted that technology has changed
    the way we teach square roots, trigonometry, and logarithms,
    technology, which already exists in the form of hand-held computer
    algebra systems, should impact the way we teach students to
    manipulate algebraic expressions, solve equations and find
    derivatives.

6.  As an algebra teacher in high school, I saw the deficiencies in
    students emerging from middle school. As a calculus teacher in
    university mathematics departments, I saw the deficiencies in
    students emerging from high school. As a teacher of methods courses
    for prospective teachers in colleges of education, I saw the
    deficiencies in students emerging from the courses taught in
    departments of mathematics. Students are taught to manipulate
    symbols for fractions, algebraic expressions, and derivatives with
    virtually no understanding of the underlying concepts or how to
    apply them. Panel member Liping Ma has reported that in the case of
    dividing fractions this is true even for an astonishing number of
    American teachers!

RECOMMENDATIONS

1.  Avoid the negative impacts of a "nothing but the facts" approach to
    teaching.

2.  What is needed is a balanced \-- or better yet a "best of both" \--
    approach to skills vs. concepts and problem solving.

3.  Look to the future needs of students who will have increasing
    availability of technology so they know how to use it appropriately.
    Avoid the extremes of ignoring it or blindly depending upon it.

4.  Do not let the curriculum for college-bound students in science and
    engineering drive what is done for all students, including the
    non-college bound.

5.  Sound mathematics should prevail at all times, but not at the
    expense of ignoring individual differences or the varied cultures
    that impact learning. In particular, do not forget rural students.

6.  Endorse a broad curriculum including, in particular, exponential
    functions and probability and statistics, and be sure to call for a
    wide range of assessment practices that align with this curriculum.
    Build positively on the Panel's expertise in achieving mathematical
    power for all students in a technological society.

Respectfully submitted,

James E. Schultz

jamesschultz@charter.net