Feb 2002
From: W. Stephen Wilson, parent of Saul Wilson 4B
Today there is a passionate debate among K-12 mathematics
educators about how thoroughly a student needs to know
the basic algorithms and manipulative skills associated
with addition, subtraction, multiplication, division,
decimals, fractions and the similar operations with
polynomials in algebra. Unfortunately, the professors
who teach first year mathematics in college were not
invited to this debate. This, despite the fact that the
majority of high school graduates in the USA go on to
college and almost all Friends School graduates do.
At the request of a group of Friends School (of Baltimore)
parents, I did a quick poll of the few mathematicians I can
contact easily. I asked them if they agreed with the following
statement. Those who responded in agreement are listed (no
one responded who wasn't in agreement). I sent my request
to the moderator of the algebraic topology discussion group.
This email list is used mainly to announce conferences and
ask technical questions. It is a relatively small group of
mathematicians. They are a good cross section of
professors who teach first year mathematics in college. They
come from all kinds of universities and colleges and represent
all levels in those institutions. In particular, there were
several Deans who responded.
I fully expected at least one vociferously pro-calculator
response and was surprised that I did not get it. I did
not ask for comment but a number of people made powerful
compelling statements. I have put them at the end of the list.
I got 93 positive responses and no one disagreed. This
is particularly remarkable because if you ask this same
bunch what mathematics is, then no two of them will agree.
There are at least a couple of dozen who would normally
disagree just to be disagreeable.
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Statement:
In order to succeed at freshmen mathematics
at my college/university, it is important to have
knowledge of and facility with basic arithmetic
algorithms, e.g. multiplication, division, fractions,
decimals, and algebra, (without having to rely on
a calculator).
*****************************************************************
1.
Donald M. Davis
Professor of Mathematics
Lehigh University
2.
Thomas Hunter
Associate Professor
Swarthmore College
Department of Mathematics and Statistics
3.
Jim Turner
Associate Professor
Calvin College
4.
Steve Halperin, Dean
College of Computer, Mathematical and Physical Sciences
University of Maryland, College Park
5.
Felix Weinstein
Universitaet Bern,
Anatomisches Institut
6.
Kristine Bauer
Assistant Professor
Johns Hopkins University
7.
Jim Lin
Professor of Math
University of California at San Diego
8.
Clarence Wilkerson
Professor
Mathematics Department
Purdue University
9.
Vince Giambalvo
Professor of Mathematics
University of Connecticut
10.
Maria Basterra
Assistant Professor
University of New Hampshire
11.
Frank H. Bria
Adjunct Faculty
Weber State University
12.
Jack Morava
Professor of Mathematics
The Johns Hopkins University
13.
Albert T. Lundell
Professor of Mathematics
University of Colorado
14.
Mark W. Johnson
Assistant Professor of Mathematics
Syracuse University
15.
Jim McClure
Professor of Mathematics
Purdue University
16.
Walter D Neumann
Chair of Mathematics
Barnard College
17.
Robert R. Bruner
Professor
Wayne State University
18.
Ron Umble
Professor of Mathematics
Millersville University
19.
Hessam Tehrani,
Assistant Professor
Department of Mathemtaics and Computer Science
City University of New York
20.
David Hurtubise, Ph.D.
Assistant Professor of Mathematics
Department of Mathematics and Statistics
Penn State Altoona
21.
Stewart Priddy
Professor of Mathematics
Northwestern University
22.
Tom Goodwillie
Professor of Mathematics
Brown University
23.
Inga Johnson
Visiting Assistant Professor
University of Rochester
24.
Thomas Shimkus
Ph.D. Candidate; Lehigh University
Mathematics Instructor; DeSales University
25.
Ismar Volic
Graduate Student
Department of Mathematics
Brown University
26.
John McCleary
Department of Mathematics
Vassar College
27.
Laurence R. Taylor
Professor of Mathematics
University of Notre Dame
28.
Gerd Laures
Professor at Bonn University
Germany
29.
Richard Askey
John Bascom Professor of Mathematics
University of Wisconsin-Madison
30.
Jim Stasheff
Professor of Mathematics
University of North Carolina - Chapel Hill
31.
Hung-Hsi Wu
Professor of Mathematics
University of California at Berkeley
32.
Anthony D. Elmendorf
Professor of Mathematics
Purdue University Calumet
33.
Philip Hirschhorn
Professor of Mathematics
Chairman, Department of Mathematics
Wellesley College
34.
Pascal Lambrechts
Professor
Universit de Louvain-la-Neuve
Belgium
35.
Carl F. Letsche
Assistant Professor
Department of Mathematics and Statistics
Altoona College
Penn State University
36.
Hal Sadofsky
Associate Professor
University of Oregon
37.
Ran Levi
Senior Lecturer
Department of Mathematical sciences
University of Aberdeen
Scotland, UK
38.
Yoram Sagher
Professor of Mathematics
University of Illinois, Chicago
39.
Steve Zelditch, Chair
Department of Mathematics
Johns Hopkins University
40.
W. Stephen Wilson (Chair 1993-96)
Professor of Mathematics
Johns Hopkins University
41.
Ken Monks
Professor of Mathematics
University of Scranton
42.
Norio Iwase
Associate Professor
Faculty of Mathematics
Kyushu University
Japan
43.
Kevin Iga
Assistant Professor, mathematics
Pepperdine University
44.
William Minicozzi
Professor of Mathematics
Johns Hopkins University
45.
Professor Larry Smith
Direktor
Mathematisches Institut
Universitaet Goettingen
Goettingen, Germany
46.
Juno Mukai
Professor
Shinshu University
Japan
47.
Kathryn Hess
Professor
Ecole Polytechnique Federale de Lausanne
Switzerland
48.
John Rognes
Professor
Department of Mathematics
University of Oslo
Norway
49.
Professor John Greenlees
Sheffield University
UK
50.
Sarah Whitehouse, Dr
Universite d'Artois
Lens, France
51.
Jose L. Rodriguez
Assistant Professor
University of Almeria
Spain
52.
John Hunton
Reader in Mathematics
Department of Mathematics and Computer Science
University of Leicester
U.K.
53.
William Browder
(past President of the American Mathematical Society)
Professor of Mathematics
Princeton University
54.
Scott Wolpert
Associate Dean for Undergraduate Education
College of Computer, Mathematical and Physical Sciences
University of Maryland, College Park
55.
J. Michael Boardman
Professor (Chair 1982-85)
Department of Mathematics
Johns Hopkins University
56.
Ayelet Lindenstrauss
Assistant Professor
Indiana University
57.
Hillel H. Gershenson
School of Mathematics
University of Minnesota
58.
Ralph Cohen
Professor of Mathematics
Stanford University
59.
Dev Sinha
Assistant Professor of Mathematics
University of Oregon
60.
Matthew Ando
Assistant Professor
Department of Mathematics
University of Illinois at Urbana-Champaign
61.
Daniel Davis
Graduate Student and Teaching Assistant
Northwestern University
62.
Slava Shokurov
Professor of Mathematics
Johns Hopkins University
63.
Dr. Yuli B. Rudyak
Department of Mathematics
University of Florida
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64.
Lowell Abrams
Assistant Professor
The George Washington University
I am shocked that there is any issue here. I absolutely agree with your
statement.
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65.
Anthony Bahri
Professor of Mathematics
Rider University
Lawrenceville, NJ 08468
At Rider University we require all students when admitted
to have a mastery of basic arithmetic calculation
and basic algebra. To ensure this, We administer a placement
test for which we do not allow the use of a calculator.
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66.
Jeanne Duflot
Professor
Department of Mathematics
Colorado State University
However, I should point out that Colorado State University does allow
some use of calculators in its introductory calculus courses. I am the
course coordinator for third semester calculus (mostly sophomores) and
no calculators are permitted to be used on any of my exams, nor on the
common final exam for that course.
By the way, it's not just your kid's school. Although my children
attended a private elementary school at which calculators were not used,
as soon as they began attending public school in junior high and high
school, calculators appeared.... I must say that sometimes I think they
are becoming crippled by too much reliance on calculators. Hopefully
they will not entirely forget that they once knew how to do those simple
calculations without calculators in elementary school...
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67.
Randy McCarthy
Associate Professor of Mathematics
University of Illinois
Yes--in fact calculators are often not allowed on exams.
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68.
Claude Schochet
Professor
Wayne State University
In 1987-91 I served as associate dean of the College of Liberal Arts at
Wayne (at the time it consisted of 400 faculty in 23 departments in the
humanities, social sciences, and physical sciences.)
That it is even slightly in doubt is strong evidence of very distorted
curriculum decisions. I do not know even one university-level teacher of
mathematics who would disagree with it. I would be truly astonished to
meet a person who disagrees.
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69.
Peter D. Zvengrowski
Professor
University of Calgary
Canada
I couldn't agree more. Teaching arithmetic with calculators is like
saying we will do physical training by going for 20 km each day, then
driving the 20 km in a car daily.
I also recall a clever cartoon in a US newspaper about 10 years ago,
when George Bush Sr was President. Bush had announced a big initiative
in mathematics teaching, to "make the US number 1 in the world by 2000."
The cartoon showed two college students reading about Bush's initiative
and one remarking to the other "aw what's the difference, it's 7 of one
and a half dozen of the other." Clearly whatever Bush had in mind failed,
and I'm sure increased use of calculators has been a big part of the
problem.
Last winter at this time I was visiting Chennai (Madras), and one of
my talks was at a Jr H S (called a Secondary School there). I was amazed
to see the facility these young students had with arithmetic - of course
they never use calculators at all in school.
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70.
R. James Milgram
Professor of Mathematics
Stanford University
More exactly, what I know is this. Students cannot succeed
in any mathematics related course at the university level
unless they have completely internalized a real understanding
of the number system and the way the basic operations work.
It might be argued that we do not really require students to
fiercely add, subtract, multiply and divide in our university
courses - which is true. But we do require an automatic
understanding of these operations and why they work because
WE BUILD FROM THERE. It could be that there will be discovered,
in time, other ways to give students these prerequisites, but to now,
no better or more reliable way has been found than giving them
high level arithmetic skills. Unfortunately, programs that
in K - 8, substitute calculators for developing these skills have
produced students that do not succeed in our university courses.
Moreover, in every instance where people responsible for one of
these programs have pointed to specific students who have "succeeded"
in university courses one of three things has been found when we
actually checked.
(1) In the majority of cases, what was really said was that the
student in question was admitted to the university. When there
he or she typically took no mathematics at all
(2) The student actually did succeed. However, when we checked with
the student he or she explained that his or her parents made sure
that tutoring was available to fill in all the gaps.
(3) The student's parents had augmented the program, typically with
courses from EPGY at Stanford. Some of them had even withdrawn their
students from math at their respective schools. Many of these
students are currently still of high school age but are taking advanced
courses in their local universities.
[This last is what I urge that you consider.]
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71.
Dr. Kathryn Lesh
Department of Mathematics
Union College
Schenectady, NY 12308
In order to succeed at freshmen mathematics at Union College, it is
essential to have knowledge of and facility with basic arithmetic
algorithms, e.g. multiplication, division, fractions, decimals, and
algebra, (without having to rely on a calculator). Students without this
ability typically do not make it successfully through their introductory
calculus courses, and are often forced to repeat courses or to drop out of
engineering/science programs.
***********************************************************************
72.
Martin Tangora
Professor
University of Illinois, Chicago
Here is a new twist. My daughter got a terrible score
on her SAT II or whatever, because her calculator's
battery was dead, so she borrowed her brother's,
but it was set to give exact answers, and she didn't
know how to convert them to decimals, and she
was too stressed to figure it out, so she couldn't
do multiple-choice answers that required knowing
whether \pi or e (say) was closer to 3.
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73.
Professor David Rusin
Director of Undergraduate Studies
Department of Mathematical Sciences
Northern Illinois University
Hi Steve,
You probably don't remember me but ages ago I was in a Junior
Seminar you ran at Princeton. (We worked out of Wallace's
"Differential Topology".) I am sorry to see your talent wasted
on what I recognize as a battle over mathematical competence.
If I can be of help to you, let me know. We have fought with
campus groups over the use of calculators in the classroom
and over the definition of minimal mathematical competency.
In fact, much of our department's response has made it to
our web pages in an attempt to cut off these arguments before
they are presented to us. Here are the URLs :
http://www.math.niu.edu/programs/ugrad/gened.html
http://www.math.niu.edu/programs/ugrad/calculators.html
http://www.math.niu.edu/programs/ugrad/calc_rationale.html
These are directed at university bodies, and may not be
applicable to school districts, but they do give a hint of
what the _college-bound_ students must prepare for.
I have found that it helps a little in these kinds of battles to
yield a little when appropriate. As a rule of thumb, we allow
the students to use their security blankets in their terminal
math courses. So for example the arts and humanities students, who
need only one general-purpose math course, get to use calculators
at all times. But in exchange we insist on the right to require
students to work things out by hand whenever we are preparing
them for an additional later math course: the skills learned at
one level must be completely internalized before moving on to
the next level. (So, for example, our placement test for incoming
freshmen is taken WITHOUT calculators.) By this same reasoning,
the school districts should insist that all college-bound students be
able to show mastery of their subjects with hand calculations.
I can give you plenty of ammo if you like: I've already had to
prepare responses to many of the most common complaints about
our calculator policies, and I've taken the offensive a number
of times by trotting out long lists of errors calculators make.
One of my favorite attacks is that we are _helping_ the students
by insisting that they do things by hand because otherwise they
can waste a lot of time when the calculator would fail them.
(I regularly ask questions about y = (100-x)^3/10000 or
y=40 + log(x) - x/100 when I am forced to allow graphing
calculators on tests. Check out what the machines say some time...)
Some responses you'll need to prepare for: the NCTM standards call
for significant access to technology, and the devaluing of algorithmic
calculation; the SAT assumes access to calculators during the exam;
and there are studies which claim to show that calculators, _when
used appropriately_, enhance student learning. Watch out!
No doubt you are aware that the US educational system is releasing
increasing numbers of students who fail to meet even the minimal
standards imposed by state boards of review. I have had to become
well-versed in the matter for several reasons (e.g. we produce
many high-school math teachers here). It's a bad situation
and I'm glad you're standing up for a minimal competence.
You are welcome to quote any of this or our web pages and can quote
my titles:
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74.
H E A Eddy Campbell
Associate Dean, Faculty of Arts and Science,
Professor of Mathematics and Statistics,
Queen's University,
Kingston, ON, Canada
In order to succeed in our first-year mathematics courses at Queen's
University, it is important for students to have a knowledge of and a
facility with basic arithmetic algorithms, e.g. multiplication, division,
fractions, decimals, and algebra, without having to rely on a calculator.
Calculators are not forbidden in our courses, but our experience is clear:
if you are relying on them for basic arithmetic you will not be successful.
In my experience in this country, Canada, children are still expected to
acquire the basic arithmetic skills, and very often my own children come
home with strict instructions regarding which questions may be done with the
help of a calculator. Calculators are not provided for the junior grades.
My own university is proud to say that our students are by objective
measures the best in the country, and of the chief joys of teaching them in
first-year mathematics courses is their facility with these basic skills.
It makes an enormous difference to have students who can add fractions, for
example. This last skill is a key indicator of success - if you cannot add
fractions, you do not belong in university - we do not have the time nor the
resources to teach you that which you should already know on being accepted.
If you have graduated from high school without such skills, your high school
has cheated you.
In my view, the teaching of basic arithmetic skills is not an option for
schools, but rather an important part of their mandate. I'd be very unhappy
to send my children to a school that thought otherwise.
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75.
Prof A J Berrick
Department of Mathematics
National University of Singapore
SINGAPORE
At my university a stronger statement is true: without such facility
noone gets to enter the university!
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76.
Professor E Farjoun
Mathematics Department
Hebrew Univ
Jerusalem.
Israel.
This is a very minimal list of knowledge. In fact on top we demand
some facility with geometry, trigonometry, and some other subjects.
(Editors comment: I had a number of other comments like this but
didn't use them.)
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77.
Timothy Porter
Mathematics Division,
School of Informatics,
University of Wales Bangor
United Kingdom
In the UK we have had the same type of problem. Finally we have
persuaded the Government to include mental arithmetic type operations in
the junior school curriculum and to demand calculation without
calculators as a necessary skill. It will be years before the harm done
is undone (if ever) but there are some hopeful signs. If you need any
cross references there is a largish literature (including various
international reports) stressing the point you make.
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78.
Daniel T. Wilshire, Ph.D.
Assistant Professor of Mathematics
Coordinator / Adjunct Math Faculty
Having taught 20 years in public school mathematics and now 16 years at
Penn State Altoona in the Mathematics Dept. I heartily agree that public
school students must learn the basic arithmetic algorithms to be successful
in college mathematics courses. Calculators are a good thing and are being
used extensively in my engineering math classes, but successful students
know the basics without a calculator.
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79.
James R. Martino
Director of Undergraduate Studies in Mathematics
Department of Mathematics
Johns Hopkins University
We do not use calculators of any kind in any of our
courses. As a result, our placement tests for Calculus I and Calculus II
require that the students be able to work without a calculator.
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80.
Jay A. Wood, Chair
Department of Mathematics
Western Michigan University
My department houses mathematics educators as well as mathematicians.
While there is much that these two groups disagree about, everyone
agrees that all students must have the ability to perform basic
"mental mathematics," i.e., perform basic arithmetic operations
without the assistance of a calculator.
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81.
Carl Rupert
Penn State Altoona 2001/2
NC Central University 1989 - indefinite
After more than a decade of full time college/university level teaching, I
agree with the following statement and believe that a failure to
understand, and an inability to do simple hand arithmetic, prevents many
students from mastering the hand calculation skills necessary for success
in college algebra and subsequent higher level classes:
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82.
Lynn Dover
Department of Mathematical and Statistical Sciences
University of Alberta
I am a candidate for a Ph.D degree in mathematics and a
graduate TA (which means that I run tutorial sessions and
grade assignments for first and second year mathematics.)
RE: your posting to the algebraic topology mailing list.
If you can't divide numbers, how on earth are you going to
divide polynomials? I could keep coming up with examples all day.
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83.
William Singer
Professor of Mathematics
Fordham University
I more than agree with your statement about the need for
children to learn arithmetic; and the necessity of being
able to do simple arithmetic without a calculator.
Yes, these skills are necessary to succeed in freshman
mathematics at my university.
I see many students who, when confronted with an expression
like (64)^(-2/3) will hit their calculators to find out the
value; but, because they have been raised with the calculator,
have no idea what the expression means; how it has been defined;
what are the algebraic properties of exponents.
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84.
Michael Spertus
Chairman and Chief Technology Officer
Geodesic Systems
I am not at a college or university currently, but I am the Chief
Technology Officer of a software company. I suppose this may actually
count for more than being a university professor with your son's school.
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85.
Dagmar M. Meyer
Research Assistant (PhD)
University of Goettingen
Germany
What a question: the answer is of course "yes, obviously"!!!
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86.
Hans-Werner Henn
Professor of Mathematics
Univesite Louis Pasteur
Strasbourg, France
I completely agree with your statement which is repeated below.
It is sad that such things which ought to be completely obvious
are controversial!
I'd like to add that in my first year courses calculators are usually not
authorized in exams. Of course, calculators are (extremely) useful but
manipulting them has very little to do with mathematics.
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Below are respondents who wrote in after my artificial cutoff.
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87.
Dan Christensen
Assistant Professor
University of Western Ontario
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88.
Paul Yiu
Professor of Mathematics
Florida Atlantic University
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89.
Norihiko Minami
Professor
Department of Mathematics
Nagoya Institute of Technology
I thought it was a joke for you to have asked our
opinion about such a self-evident truth, but I am
afraid I was wrong. I am very sorry that you had
to do this.
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90.
Younggi Choi
Dapartment of Mathematics Education
Seoul National University
I am surprized at hearing what happened in that school.
How can they do not teach math until the middle school?
I can not believe it and can not imagine such a
situation in Korea.
But in these days even in Korea there is some trend of
thoughts lowering the standard of math ability. In fact,
the eduactional system of America have been giving a great
influence on that of Korea. So I am very afraid of
that situation.
If I were in your place, I would consider seriously
having my son transferred to another school in which
my son can do math and can make preparation for the future.
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90.
Martin Bendersky
Professor
Hunter College
City University of New York
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91.
Jean-Pierre Meyer
(Chair 1985-90)
Department of Mathematics
Johns Hopkins University
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92.
David C. Johnson
Professor of Mathematics
University of Kentucky
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93.
Kojun Abe
Professor
Department of Mathematical Sciences,
Shinshu University, Matsumoto,
390-8621 Japan.
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