Madeleine Raven 31568146
5/7/2012

Using Technology: The Calculator
Since its invention over thirty years ago, the electronic calculator has evolved from a machine that could only perform simple four function operations (addition, subtraction, multiplication, division) into one that can now also execute highly-technical algebraic symbolic manipulations instantly and accurately. The
Calculators purpose is to allow students access to mathematical concepts and experiences from which they were previously limited with only pen and paper.
The technology that has helped me significantly in this unit and helped me to understand different mathematical concepts is the Scientific Calculator Casio FX-82. Calculators are vital components of a high-quality mathematics education because they make possible mathematical exploration, experimentation and enhancement of learning mathematical concepts. They allow students to reach a higher level of mathematical power and understanding.
2012
The Scientific Calculator has significantly helped my mathematics since year 10 when I received my first Casio FX-82. At first I thought the calculator would complete all of my work for me and all I would have to do was press a few buttons. This was not the case, I soon realised that to be able to press a few buttons I would have to understand what was being asked of me and know what the calculator was doing. An example of this is with the use of fractions; the conversion between 9/5 and 1 4/5 can be done with one button on the Scientific
Calculator Casio FX-82. However, you have to understand what the calculator is doing to see that it is showing that there are two different ways of thinking about the same fraction, but they both show the same number. To get this answer I needed to understand converting a mixed number to an improper fraction, so the answer did not mystify me at the end because I
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Using Technology: The Calculator would know the mathematics the calculator was doing. Calculators can help show connections between fractions, decimals and percentages, as well as numerical patterns. By reducing the time that, in the past, was spent on learning and performing tedious paper and pencil arithmetic and algebraic algorithms, I could spend more time developing mathematical understanding, reasoning, number sense, and applications. The scientific calculator provides learning tools that complement, but do not replace, mental and paper and pencil skills, and they expand student’s ability to solve problems by providing multiple solution techniques.
Being a student in the 21 st century, my level of engagement with the calculator is extremely
2012 high because mathematics today is more focused on developing mathematical understanding, reasoning, number sense and applications than mental and paper and pencil skills.
The calculator is helpful in the learning of mathematics because calculators are only as effective as the information the user enter into them. The calculator will never be able to replace the human mind when it comes to knowing how to read and understand a problem situation, writing an appropriate equation for the problem, choosing the operations to use to solve the problem, correctly interpret the solution displayed on the calculator, and determining the appropriateness of the answer. The calculator has supported and helped my mathematics learning by making me a better problem solver. Instead of wasting time
Calculators simplify tasks, but they do not do the real work for the student. It is still up to the student to read the problem, understand what is asked determine an appropriate mathematical model (e.g. an equation to solve), solve the equation using the appropriate method (mental, paper and paper or technology), interpret the answer in the problem situation to determine whether the answer makes sense.
I will now go through this calculator process with the algebraic equation 3.3 + 9 + 2.7r = 95 +
-11.
I have read the question, which is, 3.3 + 9 + 2.7r = 95 + -11.
It is asking me to find the variable which is r.
I will solve this equation with the use of the Solver Program in the Scientific Calculator Casio
FX-82.
With this process mathematics for me, became more about problem solving then performing long, monotonous computations. I wasn’t a student who could perform these manipulations
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Using Technology: The Calculator and computations quickly and accurately in my head so I wasn’t considered mathematically
2012 inclined; this turned me off mathematics. Calculator technology has enabled me to see and learn real mathematics and gain a higher level of understanding, rather than giving up. The appropriate use of calculators got me thinking and reasoning mathematically, so more people like myself will hopefully develop useful mathematical understanding and power.
The same equation in long hand would have frightened me to the point of giving up and not completing the equation. With the help of the above calculator process and the calculator program solver, I was able to see clearly that the question was asking me to find out the value of ‘r’. Even though the calculator gave me the correct answer, I could now go back and problem solve the equation and unravel the answer myself.
Simplifying
3.3r + 9 + 2.7r = 95 + -11
Reorder the terms:
9 + 3.3r + 2.7r = 95 + -11
Combine like terms: 3.3r + 2.7r = 6r
9 + 6r = 95 + -11
Combine like terms: 95 + -11 = 84
9 + 6r = 84
Solving
9 + 6r = 84
Move all terms containing r to the left, all other terms to the right.
Add '-9' to each side of the equation.
9 + -9 + 6r = 84 + -9
Combine like terms: 9 + -9 = 0
0 + 6r = 84 + -9
6r = 84 + -9
Combine like terms: 84 + -9 = 75
6r = 75
Divide each side by '6'. r = 12.5
Simplifying r = 12.5.
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Using Technology: The Calculator
It is still important for students to know how to do long hand work out, calculators help this process by quickening the time spent completing the equation so understanding the question and what is asked of them takes precedence. Calculators enable students to focus more on the
“whys” of the mathematics than on the “how’s.”
2012
Implementing calculators into the mathematics curriculum at the elementary level will allow students to learn more quickly and efficiently while keeping them engaged in what they are learning. The implementation of calculators has changed the nature of the problems that are important in mathematics and has opened doors for new methods of investigating those problems. Since calculators reduce the amount of time required to solve problems and learn certain skills, more applications can be considered. The National Council of Teachers of
Mathematics curriculum and Evaluation Standards recommends that all students use calculators to:

Explore and experiment with mathematical ideas such as patterns, numerical and algebraic properties, and functions.

Develop and reinforce skills such as estimation, computation, graphing and analysing data.

Focus on developing problem solving processes rather that the computations associated with the problems.

Perform tedious computations that often develop when working with real data in problem situations.

Gain access to mathematical ideas and experiences that go beyond those levels limited by traditional paper and pencil computation.
(NCTM, 1991)
Many people believe that primary school children should not be able to use calculators because it is lazy, they believe calculators eliminate half the work. I believe that if the technology is available, why not use it if it is the most appropriate way to solve the problem?
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Using Technology: The Calculator
Research has proven that using calculators does not harm student’s mathematical skills, however helps them to understand the mathematical concepts better than those who don’t.
2012
Technology is an essential tool for learning mathematics in the 21st century. Effective teachers maximize the potential of technology to develop students’ understanding, stimulate their interest, and increase their proficiency in mathematics. When technology is used strategically, it can provide access to mathematics for all students. The technology that has helped me significantly in this unit and considerably helped me to understand different mathematical concepts is the Scientific Calculator Casio FX-82. Calculators are vital components of a high-quality mathematics education. Being a student in the 21 st
century, my level of engagement with the calculator is extremely high because mathematics today is more focused on developing mathematical understanding, reasoning, number sense and applications than mental and paper and pencil skills. The calculator has supported and helped my mathematics learning by making me a better problem solver. It enabled me to focus more on the “whys” of the mathematics than on the “hows.” I believe calculators should be implemented in all primary schools because it is vital in secondary learning so why not start young and fully understand how to use a calculator and problem solve. The Scientific
Calculator Casio FX-82 has significantly helped me in understanding particular mathematical concepts in this course without this technology I would be clueless to how to problem solve the hard equations. The calculator gives me the tools and resources to get through any tough question and to not give up.
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Using Technology: The Calculator
References:
Campbell, Patricia F, & Stewart, Elsie L. (1993). “Calculators and Computers.” Early
Childhood Mathematics.
Ed. Robert Jensen. NCTM Research Interpretation
Project. New York: Macmillan Publishing Company, 251-268.
2012
Dunham, Penelope H. (1993). “Does Using Calculators Work? The Jury Is Almost In.” UME
Trends , 5 (2), 8-9.
National Council of Teachers of Mathematics Position Statement: Calculators and the
Education of Youth.
(1991). NCTM.
National Council of Teachers of Mathematics (2011) Illuminations: Algebra Equations .
Retrieved 12 January from http://illuminations.nctm.org/ActivityDetail.aspx?ID=80 .
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