Calculators in the Classroom: Is the Jury Still Out?
Jeffrey P. Smith
After nearly three decades of debate on the use of calculators in schools, is the education
community any closer to reaching consensus on how calculators affect children's understanding
of math and science? Regardless of philosophical, theoretical, or research-based arguments, both
advocates and opponents realize the importance of this debate, especially at a time when school
control has become such a hot issue.
At least three key factors seem to influence the technology policies of schools: (1) the
increasingly rapid development of new technologies; (2) the national outcry for today's student
(tomorrow's productive citizen) to be technologically literate; and (3) the rising comfort level of
adults who are using technology. With all of these forces at work, it becomes difficult to sort
through the logistics of using calculators in the classroom. What are the recommendations?
Recommendations for Curriculum Content
The National Council of Teachers of Mathematics and the National Science Teachers
Association have been strong proponents of using calculators in grades K through 12.
The draft document Principles and Standards for School Mathematics (online at
http://www.nctm.org/standards2000)
lists technology as one of the six guiding principles for mathematics instruction and
specifically discusses the use of calculators:
With calculators, students can have access to a wider range of complex problems, and they can
address these problems earlier in their school experience. Students at all levels should have
access to calculators and other technology as they solve problems. Research affirms the positive
impact of calculator use on the development of problem solving strategies and performance.
Furthermore, textbook publishers have recognized that calculators are now a mainstay in society.
Nearly all publishers include calculator-based instructions and exercises in their K-12 math
textbooks. They also supply teachers with resources for designing and implementing
calculator-friendly lessons. So at all grade levels in math and science, technology has created a
need to re-examine both the scope and sequence of curriculum content.
Recommendations for Instruction (Grades K-4)
| Counting With a Calculator |
|
Keystrokes |
Display |
| Counting On (by ones) |
3+1= = = |
4,5,6 |
| Counting Back (by ones) |
10-1= = = |
9,8,7 |
| Skip Counting (by fives) |
5+= = = |
5,10,15 |
| -Adapted from Mathematics and the Young Child
(National Council of Teachers of Mathematics, 1990). |
In the elementary grades, calculators are used to emphasize pattern generation and recognition
and to help children enhance their sense of numbers and develop mathematical intuition. For
example, technology helps children in kindergarten and grade 1 learn to count orally. Handheld
calculators with a constant function help those children count on, count back, and skip count (see
"Counting With a Calculator" to the right).
Calculators can also be used to reinforce computational skills. In the activity "What To Do With
a Broken Calculator?" (see the figure below), children are challenged to find a series of
keystrokes that will produce a specified, target answer. It sounds easy enough--until they're told
that some of the keys are off-limits.
| What To Do With a Broken Calculator? |
| Target |
Restrictions |
Possible Keystroke
Sequence |
Number of
Keystrokes* |
| 16 |
Using only 3,5,and all
arithmetic operations |
(5-3)x(5+3)= |
12 |
| 29 |
Using only 2,7,and all
arithmetic operations |
7x(2+2)+(2/2)= |
14 |
| 55 |
Using all numerals (except 0 and 1);
only addition and division |
54+(5/5)= |
9 |
| *For an added challenge, find the minimal
keystroke sequence that yields the target number.
-Adapted from Mathematics and the Young Child
(National Council of Teachers of Mathematics, 1990). |
Recommendations for Instruction (Grades 5-8)
Middle school students are encouraged to use technology to collect, sort, and analyze data. In
science classrooms, many teachers are designing activities that involve graphing calculators and
calculator-based lab (CBL) equipment. CBL probes can be used to collect data on phenomena
such as light, temperature, and motion.
By retrieving and analyzing real-time data in lab activities, children learn to apply scientific
principles in meaningful and relevant ways. The topic of periodic motion, once reserved for the
calculus classroom, now grounds itself in the middle grades--with calculators assisting in the
experimentation process.
Recommendations for Instruction (Grades 9-12)
In addition to recognizing the power of graphing calculators, educational technology specialists
believe the next big wave in handheld computing will come in the form of calculators that can
perform algebraic manipulations. With a few simple keystrokes, computer algebra systems
(CAS) calculators can do all the symbol pushing that used to require more time, patience, and
paper than many high school students were willing to sacrifice. Many problems, such as solving
the equation x3 - 27 = 0, become readily accessible to children, with the focus shifting away from
cumbersome algebraic manipulations and moving toward the meaning behind complex numbers
as solutions.
The use of CAS calculators, however, does not replace the need for children to learn to perform
algebraic manipulations fluently. Teachers should help children learn to use technology
appropriately as a tool for discovering more about math and science, not for covering up the
concepts or content.
Recommendations for Assessment
In the mid-1990s, standardized testing agencies recognized the importance of calculators in K-12
education and adopted policies allowing the use of handheld technology during exams. In fact,
today's high school student is encouraged to use a scientific or graphing calculator when taking
standardized exams, such as the ACT, SAT, or PSAT-NMSQT (although CAS calculators are
forbidden). Furthermore, even the College Board's Advanced Placement Calculus Exam permits
the use of graphing calculators on some sections of the test. This acceptance of calculators at the
national level has had a tremendous impact on teachers and students at the classroom level.
Many teachers are creating math and science tests that have three types of questions: (1) those
that require the use of calculators; (2) those that prohibit the use of calculators; and (3) those that
permit the use of calculators ("calculator-friendly" questions). Although it is easy and
philosophically pleasing to say that the best test incorporates problems of each type, little
research exists to support claims that children need to be evaluated at all three levels to
demonstrate understanding. When preparing assessments, teachers are therefore left to use their
best professional judgment to weigh the importance of each of the three question types on an
item-by-item basis.
Final Remarks
In an era when technology has become a hallmark of societal needs, the question of whether or
not children should be using calculators in math and science seems outdated. The
recommendations for curriculum, instruction, and assessment reflect widespread support for the
use of handheld technology in schools. The question, "Should kids be using calculators?" has
been replaced with, "In what ways should kids be using calculators?" The latter question will
certainly be a much more complex case to decide.
Reference
National Council of Teachers of Mathematics. 1990. Mathematics and the Young Child. Reston,
VA: Author.
| Jeffrey P. Smith is a Clinical Professor of Mathematics, Science, and Technology Education at
The Ohio State University in Columbus, Ohio. |
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This page was updated on Fri Nov 2 19:14:46 GMT 2001
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