question
Several calculators are now available that do computations in fractional form as well as in decimal form. Some of these automatically give results in the simplest terms. If you have access to such a calculator, discuss how it might be used in teaching fractions and especially fraction computation. If such calculators become commonplace, should we continue to teach fraction computation?
Answer
- Introduction
Some of the arguments for calculator use are based on the mistaken belief that they are essential for carrying out computations. For example, in a survey of pre-service teachers, Borg and Strachota (2002) claim that 55% of them rated the availability of technology such as calculators as an essential ingredient for the successful teaching of fraction concepts. Although the authors do not define what they mean by a successful teaching of fractions, it is certainly not necessary for the teacher or the students to have a calculator present in order to add, subtract, multiply, or divide fractions. In fact, it is often better for the teacher to be able to carry out these operations mentally or by using the board. It is well documented that children with poor basic arithmetic skills find it difficult to carry out fraction operations because they are unable to compute accurately with the numbers involved. Calculating with fractions has often been highlighted as a topic where the child’s development of arithmetic appears to come to a halt (Kieran, 1981). It has been suggested that the word problems which are often used to assess students’ understanding of fraction operations should be completely abandoned for this reason. It can be no coincidence that as traditional education methods in mathematics have been largely abandoned during recent years, the majority of standardized test scores across several countries have shown decline (Kjellstrom, 2002).
The use of calculators in education is a topic of much debate. There are concerns that students who grow up using calculators are less able to do mental arithmetic, are less adept at estimation and rounding, and are unable to decide whether their answers are reasonable. This is particularly a worry in the teaching of fractions where the concepts behind the operations are often more complex than with whole numbers. As hand-held calculators have become an inexpensive and convenient means of carrying out calculations, there has been increasing use of them in the teaching and learning of mathematics at all levels.
1.1 Benefits of using calculators in teaching fractions
Calculators allow pupils to concentrate on the processes of fractions rather than being preoccupied with the mechanics. For example, when asked to add 1/3 to 2/5 without a calculator, a pupil will generally have to spend a lot of time working out a common denominator after which he will add the two fractions and then try to reduce the answer to simplest form in order to be awarded full credit. Problems arise when the pupil is shaky on any of these processes leading to lack of success in achieving the final answer. The teacher is then left unsure of where the exact misconceptions lie and whether the mistakes were due to a lack of understanding of the actual processes of fractions involved and which formed the learning objectives of the lesson. Using a calculator, the pupil can add the two fractions, arriving at an exact answer and in turn sharpening the ever important skill of estimation. If using a CAS calculator he may even be able to see the unsimplified answer as an improper fraction allowing further discussion about when and when it is not appropriate to convert to mixed numbers. As any types of errors can be made and time is precious, the ideal scenario would be for the pupil to quickly check his exact answer by performing the operation on the calculator in simple mode and compare with his original mental calculation. Calculators provide the same benefits for all fraction operations allowing pupils to perform many calculations with the aim of hard wiring processes into memory. A foundation of a variously practiced skill set paves the way for higher level understanding of fractional concepts and a decreased dependency on procedures. Without a doubt, practice of pure computation is best achieved using calculators.
1.2 Potential drawbacks of relying solely on calculators
We will now look at the potential drawbacks of relying too heavily on calculators to teach fraction computation. As discussed in section 1.1, calculators can be very helpful for confirming that a particular algorithm is effective, or exploring various fractions with a view to developing a rule for a procedure. However, for the most part, obtaining answers to fraction problems by using a calculator is just the final “answer getting” stage of a computation. Relying solely on calculators to generate answers to fraction problems often means that understanding and skills work at other stages of the computation can deteriorate or fail to develop. This is particularly the case if a pupil’s skill in performing the operations involved is weak. Although it can be interesting and challenging to explore fraction problems in terms of the many higher level concepts and skills involved, various pupils may resort to using a calculator to obtain an answer, purely because it is the easiest way out. A simple problem such as dividing 3/4 by 5 can be posed in terms of sharing 3/4 of a cake between 5 people and asking how much each person gets. Now it is quite possible that a child with only a weak understanding of the concept of dividing by a fraction or of fraction equivalence, will punch 3/4 ÷ 5 into a calculator and accept the decimal answer as correct, without realizing that it should be expressed as a fraction and that this fraction should be smaller than the original 3/4. If the teacher is allowing calculator use and simply trying to develop understanding of the concepts involved through such problems, he or she will need to ensure that pupils can effectively communicate and explain what they are doing and why, and be prepared to discourage calculator use when it is apparent that less is being achieved than what one might hope. This will pose a significant teaching challenge in order to avoid discouraging pupils who may find the problems difficult!
- Understanding Fraction Computation
2.1 Introduction to fractions and their operations
2.2 Importance of learning fraction computation skills
- The Role of Calculators in Teaching Fractions
3.1 Using calculators as a tool for understanding fractions
3.2 Enhancing conceptual understanding through calculator use
3.3 Developing computational fluency with calculators
- Incorporating Calculators in Fraction Lessons
4.1 Introducing calculators as a supplementary tool
4.2 Providing guided practice with calculators
4.3 Using calculators for real-world fraction problems
- Potential Implications of Widespread Calculator Use
5.1 Examining the impact on students’ conceptual understanding
5.2 Considering the effects on computational skills development
5.3 Addressing the need for balanced instruction
- The Future of Teaching Fraction Computation
6.1 Evaluating the role of calculators in the classroom
6.2 Balancing calculator use with traditional instruction
6.3 Adapting teaching strategies to evolving technology