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close this bookImproving Student Achievement in Mathematics (IAE - IBE - UNESCO, 2000, 48 p.)
View the document(introduction...)
View the documentThe International Academy of Education
View the documentPreface
View the documentIntroduction
View the document1. Opportunity to learn
View the document2. Focus on meaning
View the document3. Learning new concepts and skills while solving problems
View the document4. Opportunities for both invention and practice
View the document5. Openness to student solution methods and student interaction
View the document6. Small-group learning
View the document7. Whole-class discussion
View the document8. Number sense
View the document9. Concrete materials
View the document10. Students’ use of calculators
View the documentConclusions
View the documentAdditional resources
View the documentReferences
View the documentThe International Bureau of Education-IBE

10. Students’ use of calculators

Using calculators in the learning of mathematics can result in increased achievement and improved student attitudes.

Research findings

The impact of calculator use on student learning has been a popular research area in mathematics education. The many studies conducted have quite consistently shown that thoughtful use of calculators in mathematics classes improves student mathematics achievement and attitudes towards mathematics.

From a meta-analysis of seventy-nine non-graphing calculator studies, Hembree and Dessart concluded that the use of hand-held calculators improved student learning. In particular, they found improvement in students’ understanding of arithmetical concepts and in their problem-solving skills. Their analysis also showed that students using calculators tended to have better attitudes towards mathematics and much better self-concepts in mathematics than their counterparts who did not use calculators. They also found that there was no loss in student ability to perform paper-and-pencil computational skills when calculators were used as part of mathematics instruction.

Research on the use of scientific calculators with graphing capabilities has also shown positive effects on student achievement. Most studies have found positive effects on students’ graphing ability, conceptual understanding of graphs and their ability to relate graphical representations to other representations, such as tables and symbolic representations. Other content areas where improvement has been shown when these calculators have been used in instruction include function concepts and spatial visualization. Other studies have found that students are better problem solvers when using graphing calculators. In addition, students are more flexible in their thinking with regard to solution strategies, have greater perseverance and focus more on trying to understand the problem conceptually rather than simply focusing on computations. However, with increased use of graphing calculators, students are more likely to rely on graphical procedures than on other procedures such as algebraic methods. Most studies of graphing calculators have found no negative effect on basic skills, factual knowledge or computational skills.

In general, research has found that the use of calculators changes the content, methods and skill requirements in mathematics classrooms. Studies have shown that teachers ask more high-level questions when calculators are present, and students become more actively involved through asking questions, conjecturing and exploring when they use calculators.

In the classroom

Research strongly supports the call in Curriculum and evaluation standards for school mathematics, published by the National Council of Teachers of Mathematics, for the use of calculators at all levels of mathematics instruction. Using calculators in carefully planned ways can result in increases in student problem-solving ability and improved affective outcomes without a loss in basic skills.

One valuable use for calculators is as a tool for exploration and discovery in problem-solving situations and when introducing new mathematical content. By reducing computation time and providing immediate feedback, calculators help students focus on understanding their work and justifying their methods and results. The graphing calculator is particularly useful in helping to illustrate and develop graphical concepts and in making connections between algebraic and geometric ideas.

In order to accurately reflect their meaningful mathematics performance, students should probably be allowed to use their calculators in achievement tests. Not to do so is a major disruption in many students’ usual way of doing mathematics, and an unrealistic restriction because when they are away from the school setting, they will certainly use a calculator in their daily lives and in the workplace. Another factor that argues for calculator use is that students are already permitted to use them in some official tests. Furthermore, some examinations require the candidates to use a graphing calculator.

References:

Davis, 1990; Drijvers & Doorman, 1996; Dunham & Dick, 1994; Flores & McLeod, 1990; Giamati, 1991; Groves & Stacey, 1998; Harvey, 1993; Hembree & Dessart, 1986, 1992; Mullis, Jenkins & Johnson, 1994; National Council of Teachers of Mathematics, 1989; Penglase & Arnold, 1996; Rich, 1991; Ruthven, 1990; Slavit, 1996; Smith, 1996; Stacey & Groves, 1994; Wilson & Krapfl, 1994.