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					Calculators in Mathematics

             Carol Moule
M Ed, BSc, Dip Ed, Dip T, Grad Dip Ed Admin


        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:
Should primary school children use
• 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
• 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
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
• 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
• 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
   – 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
 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
• 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
• 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