Impact Of Calculator Usage On Mathematics Learning In Schools

Significance of the Study

We live in an age of modern technology. Hence, we are memorizing multiplication facts or working calculation out as pencil and paper has become out of date and waste of time. Students learning of mathematical processes, concepts, operations and procedures are advanced as calculators are used for an instructive purpose that goes beyond drill, practice or checking work (Susskind, 2005).

Calculators have become an integral part of any student’s life. The students are given the permission to access calculators only after the 7^th grade. As majority of the tests taken have the form of multiple choice answering system, calculators are becoming less redundant as the closest answer to the calculations can be chosen as the answer. However, event test takers have taken a note of that and the options provided have close to each other. Calculators are a unique piece of technology, that when used appropriately can help in the calculations majorly (Etlinger, 1974). With the increasing tendency to use the calculators even when not needed, it has become a concern for the teachers as well parents.

It cannot be denied that using calculators save a lot of time that can be instead spent focusing on comprehending and producing a detailed solution (Koay, 2006). Besides, strategic utilization of calculators in the elementary grade students mathematically makes necessary connections across mathematical ideas and methods in real-life circumstances (Ellington, 2003).

This research investigates the issue of the usage of calculators in mathematics class by students and its impact. The statement of the problem is stated as – Use of calculator today permits students and teachers to expend more time increasing mathematical perception, reasoning, sense of number and its applicability by decreasing time that was used to spend on learning and performing monotonous paper and pencil work based on arithmetic operations and algebraic algorithm in the past. The statement of the research is established in accordance to the Act USI/CPMSA, 1997.

According to Suydam (1987), more than 100 studies conducted on this topic show that using calculators helps get work done faster with much greater accuracy. Using calculators also help increase the understanding of the subject matter as more time could be spent on comprehension of the subject (National Council of Teachers of Mathematics, 2008). However, over usage of calculator can reduce the ability to solve basic and easy sums. Students who use calculators on a usual foundation tend to be habituated with it and in the absence of calculators fail to solve relatively easier sums. Also, without appropriate knowledge of the theories of the subject, students tend to indulge in problems that include heavy calculations. It is necessary to have a thorough knowledge of the subject before quantitative analysis is carried out. The inherent mathematical concepts or theories are often missed out when using calculators to find the ultimate value.

Ultimately, all these give students a false impression of their ability to solve mathematical sums and provide a false sense of confidence in them. It is obvious that every piece of technology can be utilized in a good and bad way. It is up to the user either to use it for enhancing the quality of output or just to minimize efforts. On the other hand, using calculators take away many unnecessary efforts that could be tedious and boring (Deochand, Costello and Fuqua, 2015). Without any such hindrance, students can focus more on the conceptual part of the problem that in turn would help the student have better understanding of the subject matter. However, with such progress in technology and in calculators, scientific calculators provide a lot that could help students even cheat in exams. Formulas and values can be stored in the calculators which help cheat in exams. Thus, a proper policy regarding the usage of calculators by students should be implemented in the schools. This would help restrict the usage up to a certain level.  

The level of achievement, problem-solving skills and understanding of mathematical ideas mainly improve with the help of use of calculators in 8^th grade and afterwards.

This research signifies the usage of calculators by students in school and its corresponding impacts. Various prospects of positive and negative impacts on students have been discussed and analysed, which could help construct a guideline to restrict any such. With enhancement in the field of technology, students should be well aware of and acquainted with such. This study helps understand the need of the theoretical basis and the process of calculators makes it easy to have a better understanding of the subject.

Mathematics is always being a vibrant subject among the learners. The task of calculation becomes easy with the help of calculators. It might decrease the underlying mathematical calculations and ideas; but must inhibit students from observing the inherent patent in mathematical associations. The adoption of advanced technology in terms of calculators would help to solve day-to-day as well as exam mathematics during a high scale.

Calculators influence the motives of educational engagement of a student both positively and negatively. In the paper published by Wu et al., (2012) discusses the increase in usage of mobile devices for the betterment of education. The authors portrayed their objective as “The present study finds these factors represent the overall research trends and patterns in the field”.

The vast debate over the use of calculator in mathematics classroom specifically in elementary school would probably never be resolved. In case of calculative and problem-solving skills, Hembree and Dessart (1986) alienated the studies dependent upon the method of investing and analysed every group individually. As per their study, while calculators were component of the assessment method, the calculative and problem-solving skills of students enhanced.

The outcomes were cheering for the function of calculators in classroom study of mathematics. Mainly two types of skills (1. Operational, computational and conceptual 2. General problem-solving skills) are attempted as the outcome of having access to a calculator at the time of direction and the capability to choose the proper strategy of problem-solving (Chen and Lai, 2016). This analysis helps to reveal the role of calculator in the development of attitude of students towards mathematics. According to the journals of Dye (1981), Lloyd (1991) and Lawrance & Dorans (1994), the usage of calculator enhances the performance on computational items. Besides, it looks that graphing calculators were more expected to be linked with increment of scores and it had little influence on the speed with which student accomplished the test.  

Starting from the initial phase learning to the high school, calculators are erasing the inclemency regarding big multiplication or division (Milou, 1999). From the previous exam, teachers felt that calculator has helped students to perform subsequent tests on multiplicative factors. According to Pearson (2010), if the use of calculator is allowed, then examinees should depend on their skills at the time of imputing arithmetic and geometric problems in the calculator for answering the items properly.

With the growth of mathematics in past few decades, the availability of technological tools to help the students has evolved rapidly as well. Mathematics has emerged to be a subject of paramount importance (National Council of Teachers of Mathematics, 2014). It is vital for the students to cultivate a thorough and proper understanding of the subject and to develop a logical assessment temperament (Ansley, Spratt and Forsyth, 1989). Introduction of scientific calculators and hand-held graphing calculators contribute to the progress in the subject field over all. These are considered useful and powerful mathematical tools that enable students to conduct an in-depth analysis on the topic at hand. Using calculators also decrease the time to solve any sum to a great length. Rohrabaugh & Cooper (2016) presented the following benefits of using calculators in their study. Suydam (1985) stated that when students use graphical calculators, they are being more involved in problem solving techniques that enlarge their achievement.

In the statement of Colton and Gao (1997), outcomes of the research were unstable concerning the ability to the student with a couple of studies proposing a discrepant usefulness favouring the students of lesser capability.

According to the authors,

• Calculator helps save time for the students/educator because it gets rid of tedious steps in certain problems, such as three-digit multiplication.
• Usage of calculator brings an engaging aspectinto mathematics classrooms.
• If the answers of both students do not line up, students can go back and re-check their work to observe where they may have gone wrong (Bridgeman, Harvey and Braswell, 1995).
• Calculators are valuable for validating work. Students should learn the use of calculators that is a helpful tool delivering help and fast answers.
• Calculators help to explore and discover the elementary operationof the classroom (Rakes et al., 2011).
• Instead of long and tedious calculation by hand, students could see the patterns quicklywith a calculator.
• Additionally, students focus on the concept and new ideas of computationby calculators (Kutzler, 2000).
• Helpful and effectiveuse of calculators can easily avoid careless mistakes.
• Basic computationsby calculators provide a good understanding of estimation.
• Mathematics could be tough, but, calculators might make it enjoyable.

According to Dunham and Dick (1994), technology in terms of calculators can motivate students to learn mathematics. It is a known fact that use of calculators is widespread, and technology improved classrooms is more prevalent.

Handheld graphing calculators were introduced in 1990’s and have been in practice since. Teaching methods were modified to incorporate the usage of these as it received positive feedbacks (Math et al., 2018). The main objective behind invention of such a tool was to enrich the student’s perceptive of the subject by confronting the problems with the help of a visual representation. Although in general such calculators are used to solve mathematical problems, it is also used in fields of engineering or statistics as well. Usually students of higher grades tend to use the graphing calculators. It can even produce graphs of mathematical functions. According to Rohrabaugh & Cooper (2016), “By having access to these graphs, students can see different transformations of parent functions, find the intercepts, asymptotes, and are even provided with a table”.

Hembree and Desart (1986) showed in their articles that along with traditional instruments like pen and paper, support of calculator is enhancing the ability levels of the students. A related study of Barton (2001) indicates that usage of calculators had considerably higher accomplishment in mathematics and substantial deviation in the qualities and attitudes of the students. A referential study of Waits and Demana (200) proposed an approach of paper and pencil as well as calculators for the joint learning and teaching methods of mathematics.

While calculators provide a wide range of benefits for mathematical calculations, it does however have some barriers to its usage as well. Baker, Lusk & Neuhauser, (2012) conducted a research on the use of electronic devices in classroom by surveying faculty and students. It is mentioned in the study that over reliance on these technologies cannot guarantee an improved learning, instead possesses the risk of distracting the student and consequently lower the student’s engagement with the subject. It depends on the student and teacher and even the classroom environment where as the student will develop a tendency to overuse calculators (Andrews and Brown, 2015). The possibility of students becoming familiar with calculators cannot be disregarded. From the student’s perspective, he or she might think it is the easier or familiar method of solving problems and thus indulge in doing so without realizing the possible consequences. Thus, strict policies regarding the use of calculators should be implemented in schools and colleges to restrict the students from develop an overreliance on calculators.

Some people consider that there should be no place for calculator in the classroom especially in primary and high school (National Council of Teachers of Mathematics, 2015). It may be needed only in case of post matriculation study. The main reason behind this suggestion is that it could hamper the practice of “mental math” (Powell, 2015). Pupils might receive an unreal realization about the lack of confidence about their ability in mathematics. Students fail to show their interest in complicated mathematics as calculator had an actual negative use.  Calculators that can perform a variety of things put immense bad effect on the habit of students. Therefore, a calculator policy can only justify at what limit of calculators could be allowed to the students (Quesada, 1996). A general concern relating the use of calculator on assessment of large scale permits the use of calculator of the scores that examinees obtain.

Calculator math and non-calculator math are tough things to balance. Therefore, a look at some terms, contexts and definitions with using calculator in the classroom and exam is required.

Calculator: A calculator is an electronic device, which performs operations on numbers. The simplest calculators allowed for students can do addition, subtraction, multiplication and division.

Graphical Calculator: The calculator that has four-function, graphing techniques and other complex scientific features like CAS is known as graphical calculator (Doerr and Zangor, 2000).  

Mathematical Accuracy: Mathematical accuracy is a measure that increases when number of errors decrease in mathematics. Calculators are fast and accurate that makes students many complementary features for students (Simmt, 1997).  

Based on the literature review presented in this study, the relevant issues that should be explored are as follows -

1. What are the effects of using calculators on students during mathematical assessment tests?
2. Does the use of calculators help students understand the basic theoretical concepts that are been taught in class better?
3. What is the appropriate timing and conditions to use calculators for maximum need (Wheatley, 1980)?
4. Is it of utmost importance to keep a track of whether the students’ learning of core mathematical skills is being hindered using calculators or is it actually being enhanced?

To present a research study that yields accurate and specific results, relevant analytical tools and procedures must be utilized. Quantitative research with proper statistical analysis ensures the authenticity of the study. In this chapter, the relevant methods and procedures have been discussed.

Research design is a blue print of the procedures that enable the research to test hypothesis by reaching valid conclusions about the association between dependent and independent variables. It is a structurally and strategically research design for obtaining answer to research question for controlling variances. The scheme of paradigm is the operation of variables. Research design is the overall operational pattern of the project that stipulates information of procedures.

The three most popular types of conducting research are quantitative, qualitative and mixed method. There has been a lot of debate regarding the appropriate and best methodology; however, it depends on the requirements of the topic at hand. Various researchers prefer various processes deepening on the respective research work. After careful consideration of the three methodologies, the selected methodology for this study is that of quantitative method. This research revolves around the impacts of using calculators in class. Its primary focus is to comprehend the effect calculators have on students in math classes and tests. The study is important to provide information about the impact of calculators. Three different types of skills as well as obtained score is determined depending on the fact that calculators were used or not. Outcome of scores helps to show the use of impacts to the total score.

Detailed statistical analysis is executed to find the necessary explanations. Initially after constructing the statistical hypotheses, relevant column graphs are also to be constructed to have a basic understanding of the factors from both the tests. Two-sample t-Test assuming unequal variances will be conducted to test the respective hypotheses. Two-similar tests will be selected from the Texas Essential Knowledge and Skills website for the 7^th and 8^th grade respectively.

The chosen school for this research is a middle school in Temple, Texas. According to the report published in the ‘Public School Review Website’, sixth to eighth grade consists of 521 students in total. Among the selected population of students, 48% were Hispanic, 32% were White, 17% were Black, 2% were Mixed Races and the rest 1% were Asians (Public School Review, 2003-2016).

As the sample, the performance data of 50 students is chosen. Among these, 25 students will be from each “Regular math class” and “AP math class”. The students appeared in two tests for consecutive weeks. Both the tests will have the same level of hardness and would be presented unabashedly to the students. Students can use the calculator only in the second test. The study is designed to include everyone and Individualized Educational Plan (IEP) has been implemented for those who need it. Among the selected students, there are four students with English as native language and two students who need Special Education. Both the tests are taken on Friday, at the end of the week.

Data has been collected based on the tests taken. With relevance to the mentioned hypotheses, data for respective factors has been recorded for analysis. The time taken by the students to finish the test has been recorded. The total word count in each solution papers is also counted. Number of calculation errors made by the students while having and not having access to a calculator is tabulated. Finally, after evaluation of the tests, scores are also tabulated. Further, depending on the level of toughness in which each student has decided to use the calculator has also been recorded as data. The tests will be of 20 minutes each and full marks will be 20.

The data is gathered manually from recent activity. Therefore, the data is experimental data. It is collected in a specific time point. Hence, the sampled data is cross sectional data.

Before conducting the test, students became aware of the test and its procedures. The tests were taken according to the school syllabus of the students. A brief introduction will be provided to the students about the use the graphical calculators along with its relevant use. Students are further encouraged to use the calculators to be acquainted, in case the student is not fully aware of the functions of a calculator (Ruthven, 1990).

The instrumental techniques used before data collection is the personal investigation taking prior permission from the beholder of the educational data. The confidentiality and professionalism were maintained before data collection. 

Procedure is the most crucial aspect in research methodology. Without proper planning and procedure, researcher is unable to reach any conclusion. After choosing and finalizing the tools for data collection, the researcher can begin the data collection procedure. After gathering data from the sample, collected data was scored in the second cases.  

The sample size is 50. The source of the data is also limited and authentic. Hence, the data is collected by complete enumeration method. Complete enumeration process usually is applied for intensive in-depth investigation, when the number of population is not large. The method is expected to yield correct information. However, the huge non-sampling errors influence outputs whose magnitudes cannot be determined. Complete enumeration refers a complete count.

The researcher is supposed to arrange the tests from the students to take and then evaluate them. Help from teachers to evaluate the tests is permissible. From further analysis of the data, it can be understood whether taking calculators help, hinder or just simply have no effect on the various aspects of education of the students. If the scores of the test in which students are permitted to access calculators, are higher than the other test, one could conclude that using the help of calculator, the students score better. On the other hand, if the test scores differ significantly, then it would imply that the basic concepts of the relevant subjects are not being clearly retained by the students.

Statistical technique is applied to comprehend the data analysis methods. This technique has classified and arranged the data and tried to explain the inherent patterns of the dataset. Statistical technique is the utmost crucial method to solve a research problem. From data collection to inference drawing, statistical procedures are systematically adopted. 

It is essential to state that students have utilised to a calculator only in the second test. The data table refers the data for a variety of factors that have been tabulated to perform the essential statistical hypothesis testing. To comprehend the impact of using calculators in assessment tests, the following charts have been represented. The use of calculator in class is beneficial for students that could dramatically change the scores of the tests. The researcher is trying to find that fact.

Exploratory Data Analysis:

In the first test taken, students would not have right to use to a calculator. In the next maths test, students are permitted to do so. The following hypotheses are structured in congruence with the foresaid research questions. Exploratory data analysis is used in any investigation to determine the testing. The collected data conducts the research. The analysis of data relies upon the nature of the data. It adopts the systematic procedures to gather necessary data. Relevant data, adequate inequality and quantity are gathered for exploratory data analysis with sufficient validity and reliability.

For understanding the effects of using calculators while taking a test, the following graphs are required to be investigated at the beginning.

From the graphs, it is evident that average time taken by the students in the first test, without using calculators is 18.04 minutes. Whereas, in the second test, where students had the access to calculators show an average time of 14.54 minutes. In addition, the average total word count has increased by (571.62 – 521.42) = 50.20 for the use of calculator. This indicates a better descriptive answer from the students. Similarly, the average number of calculation errors has reduced by 2.2. On the other hand, the overall scores of the students have increased by a factor of 1.88 marks successfully.

The levels of difficulty of the sums at which students have started using the calculators can be inferred from the table below. Majority of the students have opted to start using the calculators at moderate or hard level problems.

The hypothesis testing tables are given below to conduct the relevant hypothesis testing.

Table 1: t-Test table for H_0A

t-Test: Two-Sample Assuming Unequal Variances
	Test 1	Test 2
Mean	18.04	14.54
Variance	2.284082	3.110612
Observations	50	50
Hypothesized Mean Difference	0
df	96
t Stat	10.6554
P(T<=t) one-tail	2.93E-18
t Critical one-tail	1.660881
P(T<=t) two-tail	5.85E-18
t Critical two-tail	1.984984

(Rietveld and Van Hout, 2015)

Table 2: t-Test table for H_0B

t-Test: Two-Sample Assuming Unequal Variances
	Test 1	Test 2
Mean	521.42	571.62
Variance	2313.269	2871.424
Observations	50	50
Hypothesized Mean Difference	0
df	97
t Stat	-4.92978
P(T<=t) one-tail	1.7E-06
t Critical one-tail	1.660715
P(T<=t) two-tail	3.4E-06
t Critical two-tail	1.984723

Table 3: t-Test table for H_0C

t-Test: Two-Sample Assuming Unequal Variances
	Test 1	Test 2
Mean	3.6	1.4
Variance	1.142857	1.061224
Observations	50	50
Hypothesized Mean Difference	0
df	98
t Stat	10.47837
P(T<=t) one-tail	5.56E-18
t Critical one-tail	1.660551
P(T<=t) two-tail	1.11E-17
t Critical two-tail	1.984467

Table 4: t-Test table for H_0D

t-Test: Two-Sample Assuming Unequal Variances
	Test 1	Test 2
Mean	15.4	17.28
Variance	3.469387755	2.777143
Observations	50	50
Hypothesized Mean Difference	0
df	97
t Stat	-5.318919471
P(T<=t) one-tail	3.34914E-07
t Critical one-tail	1.660714611
P(T<=t) two-tail	6.69827E-07
t Critical two-tail	1.984723136

The four two-sample t-tests referred that tier1 and tier2 have unequal averages at 95% confidence interval for all the four variables that are “Time taken to finish the test”, “Word country for theory”, “Number of calculation error” and “Scores”.

The two-sample t-tests of “Easy” difficulty level show that with the use of calculator more word count, less number of calculation errors, less time consumption and more scores are achieved. The two-sample t-tests of “Hard” difficulty level indicates that with the use of calculator less time consumption, less number of calculation errors and more scores are achieved. However, word count did not receive effective change due to use of calculators. The two-sample t-tests of “Moderate” difficulty level refers that less time consumption, more word count and less number of calculation errors are received as the advantage of calculator. However, score of the exam has not changed due to use of calculators in moderate level of difficulty.   

Through respective statistical analysis, the constructed hypotheses were tested. Graphs were also produced to provide a visual presentation of the scores for comparing the scores between the two tests. From the detailed table report of the scores, it is evident that usage of calculator helps the student score higher. From average values of the first two columns, the average time taken by the students to finish the test decreased by 3.5 minutes. This emphasizes the increment of word count. Students have more time to aim on writing the descriptive part of the test. It would help student to have a thorough understanding of the inherent mathematical theories and help them express at the time of tests. Calculation errors are major drawbacks in mathematics assignments or tests. A simple miscalculation could render the whole problem wrong. Thus, it is very important to solve the sums or calculate not only faster, also correctly. Calculating with the help of calculator ensures the both time saving and higher accuracy. It is evident from the data under study. There is a significant drop of 2.2 errors for each student when they were permitted to use the calculator. On the other hand, 1.88 marks have enhanced on an average for the students. This refers the utilization of the calculators in a positive way.

Relevant statistical hypotheses testing actions were accomplished. The research questions and respective statistical hypotheses have been declared before. Two-sample t-Tests assuming unequal variances were executed to test the hypotheses. From table 1, the t Statistics has been found out to be 10.665. Since p-value is less than the chosen level of significance (0.05), the null hypothesis, H_0A, has been rejected at 95% confidence interval. Implying that the time needed to finish the test is less while using a calculator. From table 3, same results could be drawn. The t-Stat value -4.9298. The p-value is also lower than the level of significant value of 0.05. Thus, the null hypothesis, H_0B, is rejected at 95% confidence interval. This means students tend to provide better theoretical descriptions while using calculator. Similarly, the null hypotheses, H_0C and H_0D have been rejected at 95% confidence interval as both the p-values were less than 0.05. Thus, it could be concluded that while the scores do improve while using a calculator, it also minimizes the calculation errors.

As mentioned before, if the scores of the two tests differed by a large scale, it would have indicated inconsistency in the teaching methods as the students’ grades improved significantly when they were given the opportunity to use the calculator. However, no such indications could be observed from the data.

Conclusion

The outcomes for attitudes of students and analogous independent variable analysis help to draw inference in the result section. Duration of the test, broader summary analysis and the number of errors in calculation are the influences of using a calculator in the tests. If the scores of the pre-test were significantly greater than post-test, it would have preferred a deficit of efficiency of concepts.  Although, no such trend could be concluded from the graphs and tables, most of the students have used calculators in the moderate and hard sums.

 The necessity and calculator is least in case of easy sums. This refers a requirement dependent tendency to use calculators amongst student. Proper usage of technology is suggested, and its credibility is suggested in the study. If majority of the student utilized the calculator at comparatively easier sums, it might have raised the question of learning capabilities of the students (Shirley et al., 2011). However, since no such symbols could be witnessed, we can infer that students do not exercise.

It was also found that use of calculator is effective for all the three levels of difficulties especially for “Easy” level difficulties of calculation problems.

As the analysis proceeded, it is realized that a mediator variable may be more helpful for testing without calculators. Prior researches showed that use of calculator might increase the score of mathematical tests of the students specifically when the test involves a large proportion of computational sums. It is also understood from the most current studies that legal usage of calculator, utilization of right type of calculator and incorporation of calculator in mathematical function maximizes the optimistic effect of permitting students to use calculator on mathematical tests (Drier et al., 2000).

Suitable and integrated usage of technology influences every aspect of mathematics. The education system should consider what kind of mathematics is to be taught and learned. Misuse of technology should be discouraged while using calculator (Power and Blubaugh, 2005). Users of calculators must avoid learning multiplication skills and usage of computers to practice (Dunham and Dick, 1994). Students would be familiar with the use of graphing calculators and practice too. Simultaneously, teachers would use technology properly and efficiently in their mathematics classroom if they are common and contented with the technology (Dion et al., 2001). This research maintains same consideration with many of previous research topic in this field.

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