Using calculator in Mathematics in Elementary level:

1 .The 'battle' over calculator use

Some people say calculator enables children to concentrate on understanding and studying mathematical concepts instead of spending time on tedious calculations. They say calculator helps develop number sense, and makes students more confident about their math abilities

National Council of Teachers of Mathematics (1989) has recommended that long division and "practicing tedious pencil-and-paper computations" receive decreased attention in schools, and that calculators be available to all students at all times.

Others are against using calculator in lower level math teaching, saying that it makes children not to learn their basic facts, prevents students from discovering and understanding underlying mathematical concepts and instead encourages them to randomly try different operations without understanding what they're doing.

They say calculators keep students from benefiting from one of the most important reasons for learning math -- to train and discipline the mind and to promote logical reasoning.

2. Advantages using Calculator

In my opinion, calculator can be used in the teaching in a good way or a bad way - it all depends on the teacher's approach. Calculator in itself is not bad or good -- it is just a tool. It is used a lot in today's society, so students should learn to use it by the time they finish school.

At the same time, children SHOULD learn their basic facts, be able to do mental calculations, and master long division and other basic paper-pencil algorithms. Mathematics is a field of study that builds on previously established facts. A child that does not know basic multiplication (and division) facts will have hard time learning factoring, primes, fraction simplification and other fraction operations, distributive property, etc etc. Basic algorithms of arithmetic are a needful basis for understanding the corresponding operations with polynomials in algebra. Mastering long division precedes understanding how fractions correspond to the repeating infinite (non-terminating) decimals, which then paves way to understanding irrational numbers and real numbers. It all connects together!

For this reason, it is probably very wise to restrict the calculator use in the lower grades, until a child knows her basic facts and can add, subtract, multiply, and divide even large numbers with pencil & paper. THIS, in my opinion, can build number sense — as do mental calculations.

This does not mean that you couldn't use calculator occasionally in the elementary grades for special projects or when teaching specific concepts, or for some fun. It could be used for example in science or geography projects, or for exploring certain new concepts, or for some number games or checking homework. See below for some ideas.

The discussion here does not apply to graphical calculators in high school. I am strongly in favor of using graphical calculators or a graphing software when studying graphing of functions and calculus. Even there though, one certainly needs to learn the basis of how the graphing is done on paper.

3. Things to keep in mind when using calculator

When calculator is used more freely, one should pay attention to following points:

Calculator is a tool to do calculations. So is the human mind, and paper & pencil. Children should be taught when to use calculator, and when mental computing (or even paper & pencil) are more effective or appropriate. Choosing the right 'tool' is part of effective problem-solving process.

It is very important that students learn how to estimate the result before doing the calculation. It is so very easy to make mistakes when punching in the numbers and a student must not learn to 'rely' on the calculator without checking the reasonableness of the answer.

Calculator should not be used for a random trying out of all possible operations and seeing which one produces the right answer. It is crucial that the child understands the different mathematical operations so she knows WHEN to use which one - whether the actual calculation is done mentally, on paper, or with a calculator.

4. Ideas for calculator use in elementary grade math

If you use these ideas, make sure the kids don't get the idea that calculator takes away the need to learn mental math. It can serve as a tool to let children explore and observe, but afterwards the teacher should explain things, justify the math rules, and put it all together.

Let preschoolers or first graders explore numbers by adding 1 repeatedly (which can be done with first punching in 1 + 1 =, and then pressing the = button repeatedly) or subtracting 1 repeatedly. Observe their faces when they hit negative numbers! Or, let them investigate what happens to a number when you add zero to it.

Calculator pattern puzzles: An extension of the idea above, where first-third grade children add or subtract the same number repeatedly using a calculator. Children will observe patterns that emerge when you add 2 or 5 or 10 or 100 repeatedly, or will make their own "pattern puzzles" which are simply number sequences with a pattern where you omit some numbers, for example 7, 14, __, __, 35, __, 49. The activity can connect with the idea of multiplication very easily.

Place value activity with calculator: Students build numbers with the calculator, for example:

Make a three-digit number with a 6 in the tens place; OR Make a four-digit number larger than 3,500 with a four in the ones place; OR Make a four-digit number with a 3 in the tens and a 9 in the hundreds place; etc.

Write number one million on the board. Ask students to pick a number that they will add repeatedly with the calculator to reach one million within reasonable class time. If they pick small numbers like 68 or 125 they won't reach it! This can teach children about how vast and big the number one million is.

When introducing pi, have students measure the circumference and the diameter of several circular objects, and calculate their ratio with a calculator (which saves time and can help keep the focus on the concept).

Cheating in Mathematics subject:

Academic cheating is defined as representing someone else's work as your own. It can take many forms, including sharing another's work, purchasing a term paper or test questions in advance, paying another to do the work for you.

In the past it was the struggling student who was more likely to cheat just to get by. Today it is also the above-average elementary bound students who are cheating.

Cheating no longer carries the stigma that it used to. Less social disapproval coupled with increased competition for admission into universities and graduate schools has made students more willing to do whatever it takes to get the A.

Grades, rather than education, have become the major focus of many students. Many students feel that their individual honesty in academic endeavors will not affect anyone

else. Students who cheat often feel justified in what they are doing. They cheat because they see

others cheat and they think they will be unfairly disadvantaged. The cheaters are getting 100 on the exam, while the non-cheaters may only get 90's.

In most cases cheaters don't get caught. If caught, they seldom are punished severely, if at all. Cheating increases due to pressure for high grades Math and Science are the courses in which cheating most often occurs. Computers can make cheating easier than ever before. For example, students can download

term papers from the World Wide Web. Cheating may begin in elementary school when children break or bend the rules to win

competitive games against classmates. It peaks during high school when about 75% of students admit to some sort of academic misgivings.

Research about cheating among elementary age children has shown that: There are more opportunities and motivations to cheat than in preschool; Young children believe that it is wrong, but could be acceptable depending on the task; Do not believe that it is common; Hard to resist when others suggest breaking rules; Need for approval is related to cheating; Boys cheat more.

Research about cheating among middle school children (Ages 12-14) has shown that: There is increased motivation to cheat because there is more emphasis on grades; Even those students who say it is wrong, cheat; If the goal is to get a good grade, they will cheat.

Academic cheating begins to set in at the junior high level.

Cheating is seen by many students as a means to a profitable end. Cheating does not end at graduation. For example, resume fraud is a serious issue for

employers concerned about the level of integrity of new employees.

Best strategies for teaching elementary math:

Elementary math is a subject many students struggle to grasp. The material often requires extra attention and differs with each student. According to Best Evidence Encyclopedia, there is a large achievement gap between black, Hispanic and white elementary students. Here are some of the best and most effective methods of teaching math which may work to close the learning gap and help those who often experience learning hurdles in the classroom.

Visuals and graphicsTextbooks often include various visuals and graphics for students to learn from. They are crucial elements to accompany text and help get the concepts across to students. However, according to the National Council of Teachers of Mathematics, these graphics appeared to be much more effective when paired with specific practice or guidance. This guidance could be coming from the teacher or from another classroom tool.

Teachers are starting to implement computerized learning into the classroom for a more personalized learning approach. In fact, more than four in 10 teachers report the use of e-readers and tablet computers in their classrooms to complete assignments and assist in learning. With virtual math programs, children can not only see these graphics, but they can revisit concepts that were especially difficult. They are able to learn at their own pace and won't feel rushed to move onto a concept they are not yet ready to tackle.

Verbalized thinking The process of having students verbalize step-by-step how they got to the answer they did may help other students to learn basic procedures. As you may know, many students are hesitant to raise their hands in class to ask questions for fear of sounding unintelligent. If those in the class are required to explain how they got to that answer, they may be helping their classmates in the process. The act of students explaining their process may also help them to learn how to do a certain problem. This helps them to recognize the strategies they're using and potentially apply them to other areas of learning.

Specific feedback According to the Institute of Education Sciences, many students benefit from specific teacher feedback about what they did correctly and where and how they can improve next time. Teachers should also present their students with opportunities to correct their answers and see what errors they made. Instead of simply giving the correct answer and telling them where they went wrong, it helps for students to be guided in that direction so they can figure it out for themselves.

New Teacher?

Beginning your journey as a mathematics teacher? Empowering the Beginning Teacher of Mathematics in Elementary School has been created to help you reach your full potential as a mathematics educator. Resources cover professional growth, curriculum and instruction, classroom-level assessment, classroom management and organization, equity, and school and community.

Representation a Model for Understanding, Using, and Connecting Representations:

Teachers can reflect on their practice by examining a model for representation. Students’ thinking about problem solving as reflected in these representations may differ from their teachers’ thinking. The Representations Model provides a lens for making sense of students’ responses to tasks.