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Topic: Calculators - Elementary School
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Jerry P. Becker

Posts: 13,025
Registered: 12/3/04
Calculators - Elementary School
Posted: Aug 29, 1999 9:12 PM
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Here is some information about the use of calculators in the

curriculum in the elementary schools. Teachers at different levels

want to share this with teachers are other levels as well as
administrators and

parents. Teacher educators may find this useful too.


(1) The following is from one part of a chapter of the International
Handbook of Mathematics Education that Christoph Selter [Paedagogische
Hochschule Heidelberg, Heidelberg, Germany] and I wrote - it is
concerned with calculators and computers at the elementary school level
and is section 2.4 of that paper.

[International Handbook of Mathematics Education, Kluwer Academic
Publishers, Dordrecht, The Netherlands, Edited by Alan Bishop and
others -- two volumes: Can be ordered from Kluwer Academic
Publishers, Order Department, P.O. Box 358, Accord Station, Hingham,
Massachusetts, 02018-0358 (kluwer@wkap.com; fax at (617) 871-6528;
phone: (617) 871-6600)]

2.4 Calculators and Computers [Becker and Selter]

Of the most recent developments that have important implications for
mathematics education, probably none are more important, nor more
urgent or controversial, than technology; in particular, calculators
and computers (Fey 1989; Kaput 1992; Burkhardt & Fraser 1992; Bright,
Waxman & Williams 1994; NCTM 1987, 1991a; National Research Council
1990). Dealing with technology is

* urgent<italic>,</italic> because computers and calculators are so
ubiquitous in business and everyday life - and growingly more in
education - and will become even more so as greater numbers of children
and young people use them and as the prices go down;

*important<italic>,</italic> because the technology is available, in
use, and has potential to effect major changes in the teaching and
learning of mathematics (Cornu 1992), the curriculum (Ernest 1989), the
cognitive development of learners (Wachsmuth & Becker 1986) and thus,
the education of teachers; and

*controversial, because on the one hand, some people have the fear that
learning basic mathematics will be undermined (Shumway 1989, p. 15),
whereas on the other hand some people think that dealing with the
standard algorithms is a waste of time.

Let us deal with the calculator first. It offers many possibilities
(Clarke & Kelly 1989; Shuard et al. 1994, p. 192; Spiegel 1988). The
calculator´s full potential, however, cannot be realised without a
change in both teaching styles and teachers' conceptions about their
use (Groves & Cheeseman 1993). Apart from just checking answers, we see
their most important use in

* helping children to decrease computation time and effort in order to
concentrate on the core of a problem and to enable performance with
large and messy numbers,

* facilitating the exploration of numbers and operations with

* encouraging inquisitivesness and creativity through experimentation
(problem solving),

* developing estimation and mental computation skills by checking
reasonableness, and

exploring features of the calculator itself and the (dis)advantages of
its use in different situations.

Some elementary teachers as well as parents still seem skeptical about
the use of calculators because it appears to them that it may threaten
computational proficiency. But research findings point in a different
direction. Already in the late seventies, Bell et al. (1978) identified
a variety of elementary school teaching materials, activities and
children's responses that support the conclusion that calculators can
be used to enhance the learning of mathematical skills. Suydam (1983)
synthesized the research reported by the Working Group on Calculators
of the Second International Mathematics Study. While the evidence
accumulated at that time varies across the countries in the study, "the
overwhelming majority of the data - from both formal experiments and
information exploration - has supported the conclusion that the use of
calculators does not harm achievement scores" and that "the use of
calculators can promote computational achievement, as well as the
learning of other mathematical ideas" (p. 638). By the mid-eighties,
Hembree & Dessart (1986) did a meta-analysis of 79 calculator studies
and concluded that the use of calculators in instruction does not harm
computational skills and enhances problem solving skills and
development of concepts.

These findings are in harmony with the results of the Calculator-Aware
Number (CAN) project in England and Wales (Shuard et al. 1991) in which
children devised ingenious, nonstandard algorithms and knowledge of
large numbers, decimals and negative numbers much earlier than in the
traditional curriculum. The project was undertaken with six-year-olds
and emphasized mental computation - teachers in the project did not
teach the traditional algorithms. A test of understanding on a variety
of mathematical ideas provided evidence that project children performed
better than traditionally taught pupils with respect to understanding
and mental computation, and were also more enthusiastic and persistent
(Shuard 1992). Overall, the research findings advocate the use of
calculators in elementary school, but whether this should be the case
from the very beginning of formal schooling onwards is a question
requiring further long-term research. Especially, the training of the
basic arithmetical skills and abilities should not be replaced by a
premature use of the calculator.

In contrast to calculators, the public and the educational community
seem to be more open minded regarding computer use in schools (National
Research Council 1990; Ernest 1989). Nevertheless, there are several
constraints such as an insufficient number of high-performance
computers, limited access to high-quality software, and inadequate
preparation of teachers; in addition, most of the programs for
elementary school are simple drill-and-practice programs that restore
to life the ideas of behaviorism and programmed instruction in a new
<bold>'</bold>disguise<bold>'</bold> (Kaput 1992). Although there is a
place for such programs in the learning process, they should not be
used before a solid basis of understanding is established. On the one
hand, they may be more diversified and possibly more
<bold>'</bold>motivating<bold>'</bold> for the practicing of skills
than just doing pages of raw computation. On the other hand, we should
also recognize the disadvantages in their use and use great care to
evaluate software that might lead us to see education simply as
'entertainment,' as Postman (1985) once put it.

Nevertheless, computers have much more to offer than drill and
practice; in fact, they can be used in conjunction with all parts of
the constructive learning process, when embedded in a classroom culture
where there is communication and cooperation (Hoyles, Healy & Pozzi
1992). There are several ways in which computers can be used; for
example in the practicing of skills in a way that incorporates
understanding or in simulations that enhance concept building (Klep &
Gilissen 1989; Krauthausen 1995; van Galen 1995). At the moment, there
is no clear evidence about the role of Intelligent Tutoring Systems
(ITS) that aim at simulating an expert teacher who is able to perform a
sensitive and constantly retuned diagnosis of a pupil's thinking, and
on that basis give the right stimulations that may optimize the
learning process (De Corte, Greer & Verschaffel, in press, pp. 69-70).

Many computer based systems can provide children with new tools for
learning in an exploratory environment. The most popular is LOGO that
is widely used in some countries, but often limited to turtlegraphics
(Resnick 1988). Several studies have reported positive effects in the
use of LOGO (Watson 1993) that can provide a rich environment in which
pupils engage in collaborative mathematical activity (Hoyles &
Sutherland 1990). At the same time, it should be noted that Papert's
(1980) strongest claims for LOGO have not been confirmed (Hoyles & Noss
1992), the first and foremost of which was the 'cognitive-effects
hypothesis' that stated that experience with LOGO would achieve major
changes in general problem-solving skills (De Corte, Greer &
Verschaffel, in press, p. 71).

We know that children learn with computers and that they learn about
computers. Thus, learning how to make intelligent use of the computer
and its software seems to be an important goal in the coming years, and
this should begin in elementary school. In this respect, there is a
need to question how much emphasis should be placed on learning how to
program computers, since nowadays software is widely available and used
for many purposes

Overall, the potential of computers for enhancing learning in
mathematics has been demonstrated. Nevertheless, it remains a crucial
task for mathematics educators - in cooperation with experts from
several domains such as informatics, psychology, and pedagogy - to
develop significant software that is in harmony with constructivist
perspectives on learning and teaching. The standards of mathematics
education should be the guideline here, not the technical limitations
and possibilities of hard- and software.


(2) Some references:

Bell, A., Burkhardt, H., McIntosh, A. & Moore, G.: 1978, A Calculator
Experiment in a

Primary School, The Shell Centre for Mathematical Education,

Bright, G., Waxman, H. & Williams, S.: 1994, Impact of Calculators on

Instruction, University Press of America, New York.

Clarke, O. & Kelly, B.: 1989, 'Calculators in the Primary School - The
Time Has Come'

in B. Doig (ed.) Everyone Counts. Proceedings of the 27th Annual
Conference of the

Mathematical Association of Victoria, MAV, Melbourne, 27-30.

Fey, J.: 1989, Technology and mathematics education: A survey of recent
developments and important problems. Educational Studies in
Mathematics, 20, 237-272.

Groves, S. & Cheeseman, J.: 1993, 'Young Children´s Number Concepts -
The Effect of Calculator Use on Teacher Expectations.' in B. Atweh et
al. (eds.) Contexts in Mathematics Education. Proceedings of the 16th
Annual Conference of the Mathematics Eduaction Research Group of
Australasia, MERGA, Brisbane, 327-333.

Hembree, R. & Dessart, D.: 1986, 'Effects of Hand-held Calculators in
Precollege Mathematics Education: A Meta-analysis.' Journal for
Research in Mathematics Education 17 (2), 83-99. (**)

Kaput, J. J.: 1992, 'Technology and Mathematics Education' in D.
Grouws (ed.), Handbook of Research on Mathematics Teaching and
Learning, NCTM, Reston, VA, 515-556.

Shuard, H.: 1992, CAN: 'Calculator Use in the Primary Grades in England
and Wales''in J. Fey (ed.), Calculators in Mathematics Education, NCTM,
Reston, VA, 33-45.

Shuard, H. et al.: 1991, Calculators, Children, and Mathematics, Simon
& Schuster, Hemel Hempstead.

Shuard, H. et al.: 1994, 'The Impact of the Calculator on the
Elementary School Curriculum' in D. Robitaille, D. H. Wheeler & C.
Kieran (eds.), Selected Lectures from the 7th International Congress on
Mathematical Education, Les Presses de l´Université Laval, Sainte-Foy,

Shumway, R. J.: 1989, 'Technology, Mathematics and the International
Congress' in T. Cooney (ed.), American Perspectives on the Sixth
International Congress on Mathematical Education, NCTM, Reston, VA,

Suydam, M. N.: 1983, 'Calculators in the Pre-Secondary School' in M.
Zweng, T. Green, J. Kilpatrick, H. Pollak & M. Suydam (eds.),
Proceedings of the Fourth International Congress on Mathematical
Education, Birkhäuser, Boston, 637-640.

(**)Especially useful - it is a meta-analysis of many different studies
that have been done in the U.S. on calculator use.


(3) You should contact Gary Martin who heads the Research Section at
the NCTM

headquarters for further information - I am sure he can help you

gmartin@nctm.org or (703) 620-9840 X2191.


(4) You can get NCTM's position statements on calculators (#251) and
technology (#264)

by 'Fax on Demand' -- call (800) 220-8483 and follow the
instructions; alternately,

you can simply call NCTM at (703) 620-9840 and request a
hardcopy - it will be

sent to you.



Jerry P. Becker

Dept. of Curriculum & Instruction

Southern Illinois University

Carbondale, IL 62901-4610 USA

Fax: (618) 453-4244

Phone: (618) 453-4241 (office)

(618) 457-8903 (home)

E-mail: jbecker@siu.edu


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