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The use of calculators in primary schools is quite alarming. Students may be taught a

basic paper-and-pencil mathematical technique with simple values and are then instructed

to use calculators for larger values. For example, a student is asked to perform long

division by hand, let us say divide 76 by 3, but is then encouraged to use a calculator to

divide larger numbers, say 1024 by 72. The claim is that the students are still learning

the necessary basic skill of long division but not over exerting themselves in solving

more complex problems. However, Joe Garofalo, Hollylynne Stohl Drier, Suzanne

Harper, Maria A. Timmerman, and Tod Shockey claim in their article, Promoting

Appropriate Uses of Technology in Mathematics Teacher Preparation, that [] using

technology to perform tasks that are just as easily or even better carried out without

technology may actually be a hindrance to learning (71). What the grade school

students are missing is essential practice in order to firmly establish basic mathematical

concepts and much needed exercise in their problem-solving skills. In this way they may

also quickly lose sight of the underlying mathematical concept. Technology should not

be used [] in ways that can distract from the underlying mathematics (Garofalo 69).

The above approach also teaches students to depend on calculators to perform difficult

tasks, which is not exactly the best way to prepare them for higher education or the real

world. Also, it trains students to take calculator results on blind faith especially when

they unknowingly incorrectly enter the problem, but [] technology should not

influence students to take things at face value [] (Garofalo 69). Experience suggests

that calculator usage in primary school should be minimized, if not eliminated entirely.

Students should learn basic mathematical skills using the paper-and-pencil method,

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therefore building a strong mathematical foundation for higher-level mathematical

concepts. If the use of calculators is stressed, it should be for confirming results already

obtained by hand. Bert Waits and Franklin Demana suggest in their article, Calculators

in Mathematics Teaching and Learning: Past, Present, and Future, that appropriate use

of technology in the classroom includes the following strategy: Solve problems using

paper and pencil and then support the results using technology (9). In this way, grade

school students are prepared for the more difficult mathematics they will encounter in

high school and college, where calculators have their proper place in the mathematical

curriculum.

Mathematics presented at the high school and college level offer lots of

opportunities for proper calculator use in the classroom. In fact, at this level the use of

calculators can be most beneficial. Kenneth Ruthven and Sara Hennessy point out in

their article, Successful ICT Use in Secondary Mathematics A Teacher Perspective,

that a primary advantage to using calculators in the classroom is to [] bring variety to

classroom activity, and enhance its appeal (22). They found that the use of technology

[] could expedite and more broadly facilitate the more routine components

of classroom activity, increasing the productivity of pupils and improving the

quality of work they produced, allowing them to be carried out more quickly and

reliably, with greater ease, and to higher quality. (Ruthven 20-1)

Certainly the use of calculators in the classroom is advantageous to both teachers and

students. Considering the difficulties often encountered in motivating students in the

mathematical curriculum, the fact that calculators [] could make activities more

interesting, exciting and fun [] for students and teachers alike is certainly of interest

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(Ruthven 22). However, the same dangers lie in calculator use in higher-level

mathematics as in grade school math. Teachers still risk cultivating student dependence

on calculators and overlooking the building of important basic skills. This is especially

dangerous at the high school and college level since high schools and a number of

universities prohibit the use of graphing calculators when taking exams. Therefore, it is

all the more so important for students to learn basic skills using paper-and-pencil

techniques and exercise their problem-solving skills by performing more difficult tasks

without the aid of calculators. A balanced approach to calculator usage is strongly

advised to all math educators. Garofalo and his colleagues stress that teachers [] use

technology to enhance their students learning of mathematics (86). This enhancement

means to extend students knowledge and understanding of mathematics beyondhand

calculations, not replace them.

When used appropriately in conjunction with paper-and-pencil techniques, the

calculator, in particular the graphing calculator, can be quite valuable to extending

students understanding of mathematics beyond the basics. For instance, the calculator

offers an opportunity to solve many more problems than can be done by hand. As Waits

states, some new mathematics becomes possible (6). Also, students are able to focus

on more difficult concepts rather than on underlying basic calculations: Calculators

reduce the drudgery of applying arithmetic and algebraic procedures when those

procedures are not the focus of the lesson (Waits 6). Graphing calculators especially

make it easier for students to explore mathematical concepts that lead to a much better

understanding and potentially connect their knowledge to the real world. According to

Garofalo and his colleagues, [] technology facilitates this exploration by reducing the

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of calculators since they can make math more fun and speed up calculations in order to

focus on more important lessons. Even then the possibility arises for promoting student

over-dependency on calculators without really understanding the underlying

mathematical concepts. It is still important at the higher level to introduce concepts using

paper-and-pencil techniques and then incorporate calculators in the exploration and

extension of mathematical knowledge. In this way students see the value of mathematics,

gain the skills they need, and maintain a healthy respect for technology.

Reasons for Using Technology

In general, technology includes the various levels of available technology:calculators, CBLs, computers, and laptops. The particular technology changesdepending on resources and the level of coursework. There are a few guidingprinciples like computers should not be used as fancy calculators; primarily, thedetermination of the technology depends upon the material being taught and the

resources available. The strongest reason to use technology, of any sort, occursupon those occasions when it can drive the introduction/discovery of newmaterial.

The experience of mathematics educators lead us to believe that technologyhelps promote the following:

Understanding the concepts of function and functional behavior; Support of the development of algebraic concepts; Visualization of solutions and functions; Understanding estimation and its applications; Development of intuition and pattern recognition; Confirmation of algebraic solutions Understanding technologys failure to solve certain problems; Use of and appreciation of scientific notation; Evolution of a vision of mathematics as a laboratory science, which allows

student group projects, written reports, and an interdisciplinaryunderstanding of mathematics and other areas of study;

Consideration of more realistic problems; Attention to applications even when complicated algebraic computations

are involved

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Visual understanding of mathematics in general and functions inparticular;

Improvement in communication skills; Increased attention of students; Understanding of the reality of mathematics and the applications of

mathematics. Use of a broader selection of functions, less meaningless memorization,

and more emphasis on intellectual understanding.