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FFJMy Experience with some Negative Consequences of Calculator Dependency in the United States
Ralph Kemphaus
University of Cincinnati
Cincinnati, Ohio USA
Abstract:
Mathematics education has encountered the technology revolution in the past 30 years I have experienced this clash as a secondary school teacher, as a district department head and currently as a university instructor. While technology has brought many positive changes there have been some negative consequences. This paper describes my
experience with and my thoughts on those consequences.
Will the use of technology in mathematics education contribute to an
undermining of the mathematics literacy at the student population? This
question has been the focus of my thoughts for the past five years.
Prior to that time I had experienced the technology revolution in
mathematics as a teacher and department head in a secondary school in
Ohio. My personality tends to make me a cautious adapter of new ideas and
new technologies. Our school under my direction followed the precept of
utilizing technology as a tool for speed and accuracy. The right to use
technology as a student had to be won. Once the student had demonstrated
competence in a mathematical concept or technique then he or she could use
the appropriate technology. This concept was applied throughout the
district from basic arithmetic through the evaluation of integrals.
In the United States another development in elementary and secondary
education began to have a profound impact on mathematics education.
Statewide Achievement Testing from grade one through grade twelve
became the primary means of evaluating schools and school districts.
Federal laws brought about by the No Child Left Behind initiative gave
the tests an even greater impact.
In time these tests began to drive school curriculum and the schools use of
technology. If the grade two achievement tests allowed the use of a
calculator then school administrators insisted that students have full access
to the calculator at all times. Mathematically gifted students still seemed to
be able to master the underlying concepts for which the calculators were
being used. Those, however who struggled somewhat with mastering the
basic arithmetic facts and techniques were told that mental mastery was of
minor importance. They were told to use the available technology for the
basics thus allowing more time and energy for higher order thinking.
The lobby for more and earlier technology use in mathematics education is
very strong in the United States. They cite many studies demonstrating that
it enhances mathematical understanding and make mathematics more
enjoyable and rewarding to the students.
I had neither the time nor money to undertake extensive studies, but by the
turn of the millennium I began to encounter many students, especially those
transferring from other districts, who could not multiply. Their knowledge
of fractions was extremely poor. Most of these had been using calculators
since at least the sixth grade.
In 2005 I ended 30 years at my school and began a career in developmental
mathematics at the University of Cincinnati. My new institution, like most
colleges and universities in the United States uses a placement test to guide
students into appropriate mathematics courses. These placement tests,
whether they are developed nationally or by the institution, are
predominantly an algebra test. Some allow limited use of technology while
others prohibit all technology. The tests themselves are designed to be done
without the aid of technology.
My initial courses teaching developmental mathematics were eye opening.
My students came from throughout the state of Ohio with about 10% outside
Ohio. Most had used calculators since grade four. The majority were
intelligent, conscientious students who had completed at least Algebra II in
high school. Very few could work accurately with fractions and more than
40% had not mastered their basic multiplication facts.
They had placed into developmental mathematics because of demonstrated
weakness in Algebra. This weakness most often derived from a lack of skills
in Arithmetic. Though we do not prohibit calculator use in Developmental
Algebra at the University of Cincinnati we do limit it somewhat. Many
courses in the mathematics department of our College of Arts and Science
such as College Algebra and Introductory Calculus do not allow the use of
any calculator. Students who had become calculator dependent since the
fourth grade are at a big disadvantage at the University of Cincinnati and
many other institutions.
Since 1974 there have been numerous studies, mostly confirming that the
use of calculators enhances rather than inhibits students skills and attitude
in mathematics. By nature I am experiential. I have found just the opposite
to be true within the realm of my experience. I am often skeptical of studies,
especially when the results can trigger expenditures of enormous sums of
money.
Most of my students in developmental mathematics were required to
purchase a graphing calculator at the time that they began to study Algebra I.
It is common practice now for schools or the state to provide every student
with at least a scientific calculator as early as the fourth grade.
I am not a non violent Theodore Kazinsky. I see much value in technology
in all phases of life and I believe it has a place in mathematics education. It
has been my experience however that the unlimited use of calculators in pre
college mathematics is having a detrimental effect on a large number of
students in the United States.
Whenever possible I have spoken with students, colleagues and friends who
have had their elementary and secondary education outside the United
States. I have gained a broad generalized perspective of international
mathematics education. In this conference I hope to expand that knowledge
significantly. I also welcome the opportunity to share my experiences
developed in 42 years as a mathematics teacher in a wide variety of settings.
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