Elementary Education Mathematics Is One

Elementary Education

Mathematics is one of the most complex fields of study within the sphere of Academia. At the elementary school level there has often been a debate as it pertains to the pedagogy of mathematics teaching. One of the primary concerns in mathematics at the elementary school level is the use of calculators (Lukas, 2005). The purpose of this discussion is to examine the various sentiments that exist as it pertains to the use of calculators in elementary school. The discussion will specifically focus on the pros and cons of using calculators in elementary school.

The use of calculators in elementary school mathematics

When discussing the use of calculators at the elementary school level it is important to explains that the use of calculators and other technological devices in the classroom has become quite common in recent years (Hoyles et al., 2004; Cavanagh, 2008). The decrease in the cost of calculators has perpetuated the use of calculators in classrooms at every grade level. According to Ellington (2003)

"The calculator is a technological force that has been a catalyst for lively debate within the mathematics education community during the last 30 years. In the

1970s, the educational relevance of the calculator was a controversial topic. More recently, calculators have become commonplace, and discussion has focused around ways to help students achieve maximum benefits from the use of this technology (Ellington 2003, 433-434)."

At the elementary school level, the use of calculators is particularly controversial because elementary school is a time in which students are learning foundational mathematic skills (Walen et al., 2003). Those that oppose the use of calculators assert that they are detrimental to a students ability to develop certain fundamental skills. On the other hand, proponents of calculator use in elementary school argue that it is actually beneficial to students because they are able to learn computational skills in a faster manner.

Cons: Opposition To Calculator use in Elementary School

Students become dependent upon calculators

The primary argument for minimizing or eliminating altogether the use of calculators in elementary school is that it prevents students from garnering a true understanding of mathematical computations (Chval & Hicks, 2009). According Golden (2000) "teachers' practices of frequently using calculators for mathematics instruction reduced students' ability to do well on computational problems on end-of-year tests where calculators were prohibited (Golden 2000)."

Indeed in some cases the use of calculators can become a dependency for students. Such a dependency is detrimental because some students have not mastered the foundational skills (Hoff, 2003). This lack of mastery makes them dependent upon calculators to solve simple computations. The lack of mastery is often seen at the end of the year tests when students are forced to solve problems without using calculators.

Klein (2005) calls the overuse of calculators debilitating to students. The author explains that

"One of the most debilitating trends in current state math standards is overemphasis of calculators. The majority of state standards documents call upon students to use calculators starting in the elementary grades, often beginning in Kindergarten and sometimes even in pre-Kindergarten. For example, the District

of Columbia requires that the pre-Kindergarten student "demonstrates familiarity with basic calculator keys (Klein (2005) ."

Klein (2005) contends that this is a major problem at the elementary school level because students do not have the opportunity to truly understand mathematics at the organic level. The use of technology at this level impedes upon the students' ability to properly understand mathematics.

The author further explains that while calculator use is feasible and needed at the high school level for complex math and science calculations, the overemphasis of calculator use at the elementary school level is problematic. The problem arises because elementary school students are still leaning arithmetic and the use of calculators can interfere with this process (Goya, 2006). The author points out that the primary purpose of mathematics in elementary school is to assist students in understanding numbers and arithmetic. However, calculators interfere with this process, because students can get answers without having to think about the process. In contrast pencil and paper calculations cause students to garner a true understanding of mathematical computation. The author also argues that pencil and paper calculations gives students a greater understanding of fractions and the decimal system.

Klein (2005) further explains that various state standards for the use of calculators in elementary school further complicate the issue. For instance, the author points out that in Alaska third-graders are permitted to use calculators to solve problems with sums up to fifty (Klein (2005). The author asserts that this type of use of calculators depletes the purpose of mathematics education.

In addition the author points out that several states permit the use of fraction calculators in elementary school (Klein (2005). The author insists that the use of fraction calculators can impair the ability of students understand rational number arithmetic which is a fundamental building block of understanding algebra (Klein (2005).

Understanding algebra is critical during the middle school and high school years (Royal, 2007). Students that have difficulty in algebra can not succeed in high levels of math that are required for college admissions. In this way it is evident that the use of calculators at the elementary school level can prove detrimental to students as it relates to future academic endeavours.

Still other states allow the use of calculators on standardized testing, but only when the questions are not measuring computational skills. This is true of Tennessee's TCAP tests. According to Tennessee's Department of Education

"Calculators and/or mathematics tables may be used for test items that do not measure the academic skill of computation (e.g., applied concepts and algebraic problems) and are permitted on all TCAP Achievement, EOC and Gateway Tests. Therefore, use of calculators and/or mathematics tables on items not measuring computation is not considered a Special Accommodation ("Allowable Accommodations")."

The article also asserts that many states seem to believe that children at the elementary school level need to be familiar with the use of calculators. As a result extremely young students are now using calculators (Klein 2005) . The problem with this is the simplicity of punching numbers into a machine causes many students to rely on the machine as opposed to actually figuring out the mathematics behind the answer. In other words the use of the calculator puts a greater emphasis on simply finding the answer to a math problem as opposed to putting the emphasis on the process of finding the answer.

Another negative effect of calculator use that is related in some ways to what has already been discussed is the proper implementation of calculator use for elementary students (McCauliff, 2004). Many educators are simply unaware of how best to implement the use of calculators into the classroom. In many cases this leads to overuse and children suffer because they never master mathematical process (McCauliff, 2004).

Another problem associated with the use of calculators is the effect of false progress. In many cases students and teachers may believe that a certain concept is understood but when the calculator is not available, students have trouble completing math problems. False progress also causes teachers to move forward with new skills when students haven't really mastered the old skills (McCauliff, 2004). When students move on to the next grade level they may be lost because they never really mastered the skills that they should have mastered (McCauliff, 2004).

Overall it seems that the major con of calculator use at the elementary school level is that it can become a crutch. The research asserts that students can't really understand or learn arithmetic processes if they are given too much access to calculators. There is no mastery of simple computational skill sets when greater emphasis is not placed on paper and pencil computation. In addition, it is evident that the habits that children develop in elementary school can affect their future academic progress. Students that do not wholly understand or grasp fundamental mathematical concepts have difficulty with the higher levels of math that they encounter in high school and beyond. The research also seems to suggest that calculators use does not have to be completely eradicated but they must be used carefully and there should be careful monitoring of their use.

Pros: Proponents of Calculator use at the elementary school level

Although there are some obvious disadvantages associated with the use of calculators there are also some advantages. Those who believe in the use of calculators at the elementary school level assert that there use enhances students' fundamental knowledge of arithmetic. In fact the National Council of teachers of Mathematics have developed a philosophy that favours the use of calculators even at the elementary school level.

Seely et al. (2005) assert that the use of calculators at the elementary school level is necessary. The authors argue that students must be exposed to a balance approach to solving math problems. This balanced approach should include pencil-and-paper skills and the ability to use of calculators. The balanced approach to teaching mathematics is the official position of the National Council of teachers of Mathematics (NCTM) The authors also explain that

"Research studies have shown that students who use calculators are better at understanding mathematical concepts and solving problems…The same studies confirm that calculator use does not interfere with students' development of computational skills, and in many of these studies, student's pencil-and-paper skills also increased when they had the opportunity to use calculators (Seely et al.,

2005, 2)."

The article asserts that students benefit greatly from the use of calculators at the elementary school level. The research also explains that calculator use should be used in addition to traditional techniques from problem solving.

McAuliffe (2004) reiterates the aforementioned belief that the use of calculators at the elementary school level can be quite beneficial. The authors asserts that the majority of research has found that there are not any harmful effects that occur as a result of early calculator use. The author explains that the use of calculators simply serves as an enhancement to elementary school mathematics curriculum, when they are properly used. The author insists that this enhancement can be seen in the fact that students have more time to solve problems on a conceptual level. McAuliffe (2004) expounds upon this idea stating

"a simple four-function calculator will allow students to use whatever operation is appropriate in a problem, regardless of whether they are confident of their own skill at carrying out that operation." Here, the students experience a computational advantage and become more secure in their abilities. Computation is important specifically because it is necessary to solve many mathematical problems. The particular method used, however, whether it involves mental math, paper and pencil, or a calculator, is just one part of the computation process (McAuliffe

2004, 3) ."

The author goes on to explain that the other aspect of the computational process necessitates that students fully and have the capacity to determine the right numbers to use while completing computations. The author explains that really understanding mathematics requires proficiency in using different strategies to solve mathematic problems. As such the use of calculators permits students to think of mathematics in more abstract terms. That is "It allows children to solve problems whose solutions are within theoretical, but not computational, grasp (McAuliffe 2004, 3)."

Discovery is also seen as another benefit associated with the use of calculators in the classroom. In many cases students are introduced to aspects of mathematics that they never knew before. For instance, an article entitled "Clearing up the Confusion over Calculator Use in Grades K-5" explains that in the classroom setting some elementary students have discovered such things as negative numbers. The author explains.

"One student entered 6-8 and was curious about the displayed result, which was -2. The teacher used the opportunity to model negative numbers by extending the number line to .the left of 0 ("Clearing up the Confusion over Calculator Use in Grades K-5)." In this instance, the teacher was able to introduce students to a totally new concept. This concept would not have been discovered without the presence of a calculator.

There are also arguments for the use of calculators for very young students. This argument asserts that young students benefit greatly from the use of calculators because it allows them to recognize numbers in a new way. According to de Walle (2003) in small children "The calculator is a good instructional tool for numeral recognition. In addition to helping children with numerals, early activities can help develop familiarity with the calculator so that more complex activities are possible (de Walle 2003, 3) ." This particular author contends that calculators are beneficial to small children when they are beginning to learn about numbers and numerical recognition.

Overall the pros of using calculators in elementary school are inclusive of a knowledge of calculator usage, increased ability to solve mathematics problems, discovery, higher levels of abstract reasoning, and recognition of numbers. The research indicates that elementary school students that use calculators in combination with traditional forms of math instruction have higher levels of proficiency in math than those that rely on traditional instruction alone. The overall consensus seems to be that the use of calculators is beneficial when properly implemented in the elementary school curriculum.

The Middle

In addition to those that advocate or oppose the use of calculators in elementary school, there are also those that believe that calculators should only be used in certain elementary school grades. That is they believe in the use of calculators in elementary school but they disagree that children as young as kindergartners should be allowed to use calculators.

These individuals believe that students should learn the fundamental facts of math before they are allowed to use calculators. In treating the use of calculators in elementary school in this manner, there is exposure to calculators but students also understand the processes behind mathematical computation. As it relates to this particular argument it is asserted that the emphasis should be on traditional practices as it pertains to mathematics education. However, once a fundamental understanding of numbers and basic mathematical processes are developed calculators can and should be introduced (Varol F. & Farran, 2007). A study conducted by Vanderbilt university found that "it is important children first learn how to calculate answers on their own, but after that initial phase, using calculators is a fine thing to do, even for basic multiplication facts (Vanderbilt University)." The study also found that students; fundamental understanding of mathematics was the key indicator in determining whether or not they were harmed or hurt by the use of calculators in mathematics. This particular study insists that the use of calculators is only harmful if the student has knot established how to find answers without the use of a calculator. That is the calculator simply enhances understanding, it is not responsible for gaining the understanding.