Calculators in Mathematics

Carol MouleM Ed, BSc, Dip Ed, Dip T, Grad Dip Ed Admin

Email cemoule@internode.on.net

Mobile phone 0419695061

Calculators need not be a crutch – they can be an outstanding learning tool.

Where are calculators useful and which one would I choose?

Making a difference:

A SPECIAL EDUCATION EXPO 2009

Should primary school children use calculators?

• Using calculators in primary school should not be an either or situation.

• Children should be proficient in all sorts of calculating – mental, written, and technology assisted.

• To be able to be good at mathematics users need to master all of these methods and be discerning about when to use each appropriately.

• Aversion to using calculators in schools contrasts with their general acceptance in the work place and the daily life of adults.

• Calculators are ubiquitous in the work world and as important for employees as voice mail and word processing.

• Word processing is an analogous skill. We do not require that students check all spelling with a dictionary rather than by the computer's spell check program. Instead, we expect students to be able to gauge the reasonableness of a spell check message using their own experiences drawn from reading, writing, and dictionary use.

Because there is much more to mathematics than right-answer reliable calculating, it is important to access the broad scope of math abilities and not judge intelligence or understanding by observing only weak lower level skills.

Often a delicate balance must be struck in working with learning disabled math students which include:

• Acknowledging their computational weaknesses

• Maintaining persistent effort at strengthening inconsistent skills;

• Sharing a partnership with the student to develop self-monitoring systems and ingenious compensations; and at the same time, providing the full, enriched scope of math teaching.

Students with learning difficulties may already have an external locus of control i.e. they believe they can’t improve their mathematical capacities.

It is when they feel confident to have a go, make mistakes, discuss and question, that engagement and achievement will occur.

• In the same way, young students can learn to compare the calculator's messages to the reasonable answers they have learned to expect from their evolving understanding of arithmetic.

• The issue is not should students use calculators in the classroom but how calculators should be used.

• When students do not have to worry about computation mistakes, they can focus on reasoning and problem solving.

• Teachers can help students see patterns, check estimates against reality, and solve complex problems, like those encountered in daily life, through the structured use of calculators.

• Children introduced to the calculator when they are young will find it easy and effective to use.

• Calculators should be used in the classroom for many reasons: – Calculators help students at all levels learn mathematically

complicated material. – Even young children can use calculators to focus on the ideas

behind computation rather than on the act of calculating. – Rather than hampering mathematical ability, calculator use can

actually improve student achievement in mathematics, according to research.

– Many of the senior classes for older students now allow students to use calculators during testing, as do many in exams.

– Students who have not been comfortable with calculators from a young age may be at a disadvantage on these tests.

• In the recent Third International Mathematics and Science Study (TIMSS) fourth and eight graders in the US who used calculators almost every day performed at higher levels than did those who never used one or only used it once or twice a month.

• There is research done over the last 20 years which shows that

Children who use calculators on tests have higher scores in both basic computation skills and problem solving.

Students who use calculators within a mix of instructional styles do not lose their paper and pencil skills.

Calculator use in the classroom improves the paper and pencil skills of students regardless of their ability levels.

Those who use calculators in class have better attitudes toward mathematics than children who do not use them.

• Too often schools approach calculator use casually and uncritically. While people understand the need for a strategic plan to incorporate computers into the curriculum, often they do not see a similar need for a systematic calculator strategy.

Some strategies for effective classroom use follow: Have students decide on the reasonableness of

calculator answers by estimating before they do the calculation.

Use questions and discussion to help students think actively about the processes used to arrive at answers.

Incorporate open-ended problems or projects with several possible solutions (or no solutions) into classroom instruction.

Mix in problems that are easier to solve by hand or that become unwieldy on the calculator so students will become discriminating in calculator use.

Teach mathematics as an integrated discipline rather than as disconnected processes.

• In secondary school, calculators can help students develop their understanding of algebra and other advanced mathematics. Students will have an easier time learning advanced mathematical procedures if the foundation for complex calculator use is laid in the elementary grades.

• 'The calculator is a tool to help people with their tasks and their thinking but never a substitute for thinking.'

Three types of calculators are generally used in schools:

• Arithmetic calculators cost little and have a numeric keypad with the four basic arithmetic operations, although some may also have percentage and square root keys. A single line of characters displays up to eight digits. CAUTION!!

• Scientific calculators have a broader range of functions and cost around $20. Some statistical abilities, a more extensive keypad with more than one function for certain keys, and scientific and engineering notation are common.

• Graphing calculators have an extensive range of operations, a larger screen, more characters on the line, and the ability to move between displays and use alphabetic characters. They can graph data and symbolic expressions, cost close to $200, and are generally only appropriate in the higher grades.

Are students losing skills?

• Many are- but does it matter? There are skills we really do not all need any more…. But there are others that are just as important as ever! The trick is to identify them and ensure that students have them for life.

• eg Students still need to know their number facts and multiplication tables.

• By freeing students from time-consuming arithmetical calculations, more time in the classroom can be devoted to learning more mathematics. Lots more mathematics.

• While some students do become too reliant on the use of calculators, their use should not be prohibited. Calculators, if used correctly, can enable a student who struggles with basic facts to learn more advanced skills without the worry of making a simple mathematical mistake.

• Today's calculators are a very powerful and effective tool if used correctly. Teachers need to focus their efforts on getting the calculators to be used as a learning tool, not a computational crutch.

• It is important to note that most research supports the use of calculators, but also cautions that responsibility must lie with the teacher.

• “Technology should not be used as a replacement for basic understandings and intuitions; rather, it can and should be used to foster those understandings and intuitions.”

• In order for this technology to have a positive impact on students’ learning of mathematics, teachers must be educated as to how to put the calculator into practice. The calculator should be used as a supplement to learning, not as a replacement for learning computational algorithms.