INTERNATIONAL JOURNAL OF RESEARCH IN TECHNOLOGY AND MANAGEMENT (IJRTM) ISSN 2454-6240 www.ijrtm.com SCIENTIFIC CALCULATOR APPS AS ALTERNATIVE TOOL IN SOLVING TRIGONOMETRY PROBLEMS Maria Isabel Lucas, EdD, Pamantasan ng Lungsod ng Maynila, Manila, Philippines [email protected]
ABSTRACT Mark Prensky (2001), the originator of the term digital The present 21st century students belong to the post- natives (Generation Y and Z) and digital immigrants, the millennial generation or Gen Z. They are considered predecessors of the millennials, cited that mathematics have to digital natives who have high penchant on ICT gadgets be reengineered to match the characteristics of the 21st century learners: particularly on smartphones which have already formed In math, for example, the debate must no longer be about part of their daily necessities. The teachers who are digital whether to use calculators and computers – they are a part of immigrants may capitalize this by integrating technology the Digital Natives‟ world – but rather how to use them to as a tool for teaching and learning to cater their learning instill the things that are useful to have internalized, from key needs and interests. Free applications are available both skills and concepts to the multiplication tables. We should be for android and iOS operating systems such as scientific focusing on “future math” – approximation, statistics, binary calculator apps. This study verifies whether the use of the thinking. (p.5) mobile application in computing Trigonometry problems is Practically, not all students in the local university where a good alternative to the commonly used handheld this study was conducted can afford to buy the commercial calculators using a quasi-experiment among 50 students of handheld calculator due to its relatively high cost. The school a local university in the Philippines. Results of the paired- caters to poor but deserving students who are mostly residents samples t-test showed that the mean rating of the students of the local government unit that subsidizes only their school in their summative tests is significantly higher with their tuition and matriculation fees. School materials and other ratings using the handheld calculators. The researcher expenses are still shouldered by their parents, relatives, recommends that teachers may allow their students to use benefactors or by the students themselves through acquiring the mobile calculator apps in solving math exercises and part-time and even full-time jobs. Given this scenario, students tests. Aside from being cost efficient, it will also bring more with very limited funds for schooling are less capable of convenience to students since they do not need to bring two purchasing the best scientific calculator and would result to gadgets in their bags or pockets. Its ergonomics is also students’ failure in the examinations and graded exercises. Hence, these students have likelihood of suffering more favorable as the smartphones size matches the hand ’ psychological inflexibities (PI) during class hours. These are dexterities of the users. With their daily usage of the “rigid attempts to control psychological reactions to discomfort gadgets, the digital natives have already developed in them at the expense of values-guided actions” (Tavakoli, Broyles, attachment and familiarity. The automaticity that they Reid, Sandoval, Correa-Fernández, 2019. p.1). Having no acquired over time facilitates easier navigations on the calculator to be used in solving math problems would result to touch screens which allow faster calculations as compared student’s discomfort brought by worries of failing the subject. to its handheld counterpart. As such, they may attempt to control this by copying answers of their seatmates and hence, they compromise the values of a Keywords- Mobile apps; ICT; smartphone; Generation Z; true scholar. So as to be relieved from this problem, some digital natives; digital immigrants; trigonometry teachers even purchase many units of calculators and lend them to their students. I. INTRODUCTION Another practical benefit on the use of Scientific Calculator Apps is its convenience. Students, as well as teachers, need not While most test problems in Mathematics can be solved bring two gadgets in their classes. Since smartphones have manually, many teachers prefer to employ the most appropriate become a necessity among the present generation of students, tools to help make student s life easier. Considering that ’ their potentials as an aid for learning could be maximized by mathematics, specifically Trigonometry, is not an easy subject teachers. Smartphones, as compared to its analogue for many students, teachers need to be innovative so that their predecessors, have gone extra miles by giving every user students will develop liking instead of aversion to the subject. tremendous benefits through applications from android or iOS Positive correlations between enjoyment of subjects and directory. These applications (native, web, or hybrid) are increased academic performance have already been established capable of performing tasks that made life easier ranging from in many researches. gaming, business, lifestyle, entertainment, utility, and One learning innovation that could be adopted by any math educational apps. Most importantly, many of these applications teacher is the use of Scientific Calculator Mobile Application often go for free only with some annoying advertisements or Apps in solving math problems as an alternative to the usual which are tolerable anyway. A variety of scientific calculators handheld commercial calculator. Some advantages of the are available for free both in android and iOS operating adoption of this innovation on the part of students are reduction systems. In fact, the leading brand of handheld calculator has a of expenses, convenience, and utility. On the other hand, free application in the android having equal capability and teachers will no longer experience the nuisances of performance. admonishing students who do not have calculators during class Current norms dictate the necessity of smart phones in times and reason out that they forgot to bring their handheld everyday life and this includes the students. While primary and calculators or they really do not own one. secondary schools have restrictions for the usage of phones, 1 Volume 5 Issue 6, DECEMBER 2019
INTERNATIONAL JOURNAL OF RESEARCH IN TECHNOLOGY AND MANAGEMENT (IJRTM) ISSN 2454-6240 www.ijrtm.com tertiary levels are more lax with it, allowing students to bring While the modern learners’ characteristics may seem them to classrooms for various purposes. It is unlikely to harmful for the instructor, such as advance knowledge on the encounter a student without a smartphone and this has been a topic being discussed, this could also be advantageous like stepping point for the researcher’s study. minimization of time on explaining the concepts. Instead, Many educational applications which are available on the actual class hours could be used for inquiry, activities, and two operating systems (OS) are of great help for both teachers assessments. Teaching strategies, such as flipped classroom, and students when they are maximized for academic purposes. can be employed to maximize learning hours on the three In teaching the 21st century learners who belong to Generation aforementioned activities. Z (born 1995-2009), there is a need to integrate specialized In the Philippines, there have been numerous programs that learning tools in consonance to their learning needs and attempt to improve the delivery of teaching through the use of interests as digital natives. Although most educators now are instructional materials in the classroom setting. The digital immigrants, it is still necessary for them to integrate Department of Education (DepEd) has been consistently trying Information Communication Technology (ICT) and upgrade to ride on the technological wave by integrating ICT which is their teaching strategies by using technologies that provide defined as “basic information handling tools, a varied set of exchange of information through gadgets capable for academic goods, applications, and services that are used to produce, purposes. store, process, distribute, and exchange information” From a teacher’s standpoint, this also holds a way to (Nwokeafor, 2015, p. xix). Even with the attempts to integrate improve the delivery of information to their students through ICT to improve upon current learning paraphernalia, there is the advancement of instructional materials (IMs). It is an still a distinct lack of knowledge about the realm of umbrella term for two things: teaching aids, or anything that possibilities held by ICT. Technology is a broad spectrum and assists the information and message delivery to learners, and there are advancements that are found every day, which makes learning materials, or the things that learners directly learn the common instructor unable to keep up with the rising trends from (Forsyth, Jolliffe, Stevens, 2002). “With Generation Z as in practical knowledge. Agostinho, Oliver, Harper, Hedberg the present student population in colleges and universities, it is and Wills (2002, p.36) agreed that ICT foster high quality imperative that instructors meet their educational needs and learning “but there is also a pressing need to provide them with expectations with regard to learning with technology”, advise tools to assist them to assess whether their learning designs can Schnackenberg and Johnson (2019, p.xv). On the contrary, not be, or are indeed, effective”. There is also an issue of cost, many teachers integrate ICT in their teaching. In the study given that every new advancement requires purchasing the conducted by Umar, Sazali and Hassan (2015) among latest goods to stay updated in technological trends. Malaysian Teachers, the results revealed that “(i) the teachers’ This study adopts the SAMR Model of Ruben Puentedura ICT integration is at the low level, while their pre-integration of (2006, p.1) who attested that “mobile devices become more ICT is at the moderate level, (ii) ICT is perceived to bring prominent in the lives of students, the use of mobile devices positive impact on their teaching although time constraint has the potential to transform learning”. SMAR stands for might hinder its use, and (iii) ICT is also perceived to influence Substitution, Augmentation, Modification, and Redefinition. their students’ learning” (p.2015). Substitution and augmentation entail enhancement of the At the turn of the 21st century, the world has seen the technology while redefinition and substitution require biggest technological advancements in all aspects of life. transformation. This model is a good guide to determine what Mannerisms and schematics are also being contested due to the level of integration a teacher can do for their class, depending on-going and abrupt changes in the world’s norms; what may on the subject being discussed. Mathematics is no exception to be widely accepted on the previous generation would be the model. uncalled for today, and scholars are in a buzz to quickly resolve Further, Mobile Computing Devices (MCD) refers to the widening gap between age groups. As far as learning is portable devices capable of operating, executing and providing concerned, there is an underlying shift in the learning habits of services and applications, such as cellphones, smartphones, and the current generation. While old folks were used in browsing tablet computers. With the turn of the 21st century, ownership encyclopedias and libraries to seek information for their school of a smartphone has been ubiquitous in the current living work, students nowadays are just browsing in the Internet and landscape, to which Statista predicts 41.09% of the population have an unlimited access of information from all over the would carry one in the year 2020. Smartphones are not the globe. typical “call and text” devices people have used years ago. These brought distracting characteristics of the modern Lenheart, Ling, Campbell and Purell (2010) described these learner such as impatience and short attention span. The former new devices as “multimedia recording devices and pocket- could have been influenced by immediate access to information sized Internet connected computers”, highlighting on its and how they demand for it outright. The existence of search expanding functionality. Gikas (2011) expounds on the engines gives instant access on unlimited number of potential of MCD in learning by organizing the existing information on demand. Second, their short attention span may research around it into three categories: (a) engaging learners have caused by multiple distractions in the same avenue as with constant connectivity, or giving learners access to where information is held. “The teacher must understand and information and communication between co-learners on acknowledge that the new learner has a very short attention demand; (b) fostering collaborative learning, or using MCD as span, has an arsenal of electronic devices at her fingertips (and an avenue to collaborate and discuss given learning materials; in the classroom)” suggests Bradshaw and Lowenstein (2007, and (c) enabling authentic learning on the move, or taking p.113). The existence of information channels are common in advantage of MCD’s portability to ensure remote learning. the current landscape, but with distractions like display ads and However, even with this, MCD has its own share of barriers in widgets leading to games and social media, which are integration, to which Ertmer (2012) narrows down to completely unrelated to the information being searched for, infrastructure, training and support. In 2012, Ertmer and their attention is contested, and causes an internal rift. Leftwich has reviewed 48 studies about the barriers in pedagogical technology integration, and found out that 40% of 2 Volume 5 Issue 6, DECEMBER 2019
INTERNATIONAL JOURNAL OF RESEARCH IN TECHNOLOGY AND MANAGEMENT (IJRTM) ISSN 2454-6240 www.ijrtm.com the studies highlighted lack of resources (such as limited test. The data were encoded and treated using IBM SPSS hardware, access, time, and technological support) as the most Statistics. commonly-reported barrier. This makes it harder for instructors to integrate MCD to be addressed through in-service training III. RESULTS and on-going curriculum support to be able to incorporate it in Based from the statistical computations, the following meaningful ways (Ertmer, 2012). tables are presented to provide a snapshot of the findings of the With this in mind, the researcher wants to test whether the study. The first table corresponds to descriptive problem and use of Scientific Calculator Apps still yield the same academic the second table provides the result of the inferential statistics performance as compared to the use of handheld scientific calculations. calculator in solving trigonometry test problems. Specifically, this study answered the following questions: TABLE I. MEAN RATINGS OF THE TRIGONOMETRY STUDENTS IN THEIR 1. What are the mean ratings of the Trigonometry students SUMMATIVE TESTS USING HANDHELD CALCULATOR AND USING THE in their summative tests using handheld calculator and SCIENTIFIC CALCULATOR APPS using the Scientific Calculator Apps? HANDHELD CALCULATOR 2. Is there a significant difference in the performance of the ACADEMIC CALCULATOR APPS PERFORMANCE students using the handheld calculator and using the f % f % Scientific Calculator Apps? Excellent (1.00 to 1.25) 5 10% 22 44% Very Good (1.50 to 1.75) 9 18% 18 36% II. METHODS Good (2.00 to 2.25) 21 42% 6 12% Satisfactory (2.50 to 2.75) 14 28% 4 8% Participants. There were 50 participants of the study who Poor (3.00) 1 2% 0 0% were enrolled in Trigonometry, a minor subject that introduces Failed (5.00) 0 0% 0 0% circular and trigonometric functions, trigonometric identities, TOTAL 50 100% 50 100% and to the polar coordinate system. For the sex distribution, 24 are males and 26 are females. Their mean age is 18. Most of Comparisons of student mean ratings in the students’ them are residents of the local government unit under a first summative tests in Trigonometry are detailed in Table 1. Under class highly urbanized city category. The remainders are either the distribution, the frequencies and their corresponding from the neighboring cities or from other provinces. The percentages are tabulated on the six academic performance students were informed that their class was under pilot study on indicators- excellent, very good, good, satisfactory, poor, and the use of the scientific calculator apps and their ratings in the failed. Comparing the students’ ratings of handheld calculator summative test shall be used as data of the research. and calculator apps, the students scored relatively higher in the Data Gathering Method. This study employed a quasi- latter. The graph is also eschewed to right which means that all experimental design particularly the Single-Group Interrupted of the students exceeded the passing mark (3.00). Though the Time-Series Design. Using this design, the “researcher records ratings in the handheld calculator are also eschewed to the measures for a single group both before and after a treatment” right, it is only marginal at 2%. (Creswell, 2014, p.221). The single group comprises 50 Under the Excellent range (1.00 to 1.25), a great disparity students of Trigonometry subject during the second semester of on the mean ratings could be observed. Only 10% of the school year 2018-2019 in a local university of Metro Manila, students were excellent as a result from using handheld Philippines. The researcher has measured before and after the calculators and 44% landed on the highest range using the treatment using scientific calculator apps. The basis of mobile calculator apps. As to the second range, 18% are very comparison is the mean ratings of the students using the good for the traditional tool and 36% for the modern tool, traditional tool (handheld calculator) against their mean ratings which is twice higher. On the third range (Good), 42% for using the mobile calculator apps. handheld calculator and 6% for the calculator apps. For the Data are presented in a quantitative method. Tables are used Satisfactory range, 28% of the students fell under it and only to summarize the results for easy understanding of the 8% obtained such ratings when they used the mobile apps in condensed data in the form test scores collected during the calculating the tests problems. No student failed which is a administration of summative tests. Two of which were normal tendency for universities which students are scholars administered using the handheld calculator during the 2-month and admitted only after passing rigid entrance examinations. mid-term grading period and another two using the mobile application calculator during the 2-month final grading period, TABLE II. DIFFERENCE IN THE PERFORMANCE OF THE STUDENTS USING both calculators have scientific applications. THE HANDHELD CALCULATOR AND USING THE SCIENTIFIC CALCULATOR APPS There were four researcher-made instruments used in the GROUPS N Mean SD t-value p-value study in the form of summative tests. The first summative has Handheld Calculator 50 77.01 8.81 46 items and 30 for the second one which were computed using the handheld calculator. The third test has 25 items while the Calculator Apps 50 87.83 8.52 -8.76 <.001 fourth has 40 items which were administered to the students Average 50 82.84 8.67 using the calculator mobile apps. All these summative tests were peer evaluated prior their administration. The paired samples t-test statics yielded significant Data Analysis Plan. The type of data that was treated is difference between the mean ratings of the 50 Trigonometry interval. The 11 point system adopted by the university was students in their summative tests using handheld calculator and obtained after the ordinal raw scores were transmuted into in using the Scientific Calculator Apps. As can be gleaned in percentage and eventually transmuted into the 11 point system, Table 2, the computed t-value is -8.76 and p-value is <.001. an interval data. Problem 1 was calculated using descriptive This suggests that the mean rating of the students in their statistics. On the other hand, problem 2 was computed using summative tests in Trigonometry is significantly higher (Σ xi = parametric inferential statistics test known as paired-samples t- 87.73; SD=8.52) than their mean ratings using the handheld 3 Volume 5 Issue 6, DECEMBER 2019
INTERNATIONAL JOURNAL OF RESEARCH IN TECHNOLOGY AND MANAGEMENT (IJRTM) ISSN 2454-6240 www.ijrtm.com calculator (Σ xi = 77.01; SD=8.81). The p-value is less than the computations with just one hand using the thumb in pressing designated level of significance (α=.05 or 5%), hence, the result the numeric and operation keys while the other hand writes the is statistically significant. As pointed out by Utts and Heckard results on the paper. With this, both hands are working (2011, p.457), “[i]n any statistical hypothesis test, the smaller simultaneously which results to faster and more efficient the p-value is, the stronger is the evidence against the null computing. hypothesis. It is common research practice to call a result Moreover, the post-millennial students or Gen Z’s have statistically significant when the p-value is less than or equal to developed psychological attachment with their smartphones. .05”. Thus, the researcher is highly confident to conclude that “For many Gen Zs, social media forms such an integral part of there is a strong evidence to reject the null hypothesis (Ho), their lives that without it, a Gen Z feels everything from that is, there is significant difference between the mean ratings disconnected or bored to a degree of separation anxiety” of the students. confirmed Madden (2017, n.p.). In fact, other authors averred that many of the youth have addictions to their gadgets in the IV. DISCUSSION form of “compulsive checking for updates, mindlessly Scientific calculator apps is a reliable alternate tool to the browsing news feeds and posts, and thinking about social handheld counterpart in solving Trigonometry problems. This media activity when not actively engaged with social media” is attested by the statistics presented in Table 2. In fact, as the (Schnackenberg & Johnson 2019, p.141, citing data suggest, the performance of the students is significantly Zaremohzzabieh, Samah, Omar, Bolong & Karudin, 2014). higher when they used the scientific calculator apps than in This attachment of the students with their smartphones makes it using the traditional handheld calculator at Σ xi = 87.73 and Σ easier for them to calculate math problems since the cellphone xi =77.01 respectively. The use of the mobile phone could have gadgets are already assimilated in their systems while the mediated the increased performance of the students owing to handheld calculators are considered burden not only of its their automaticity, dexterity, and psychological attachment with commercial price but also the inconvenience of carrying them their mobile phones. However, this is still subject to validation in their bags or pockets. through experimentation. The Generation Z students consider smartphones as V. CONCLUSION “integral part of their lives” (Dingli & Seychell, 2015, p.2). In order to achieve effective learning outcomes, teachers They carry with them their mobile phone gadgets everywhere must be able to match instructional strategies with the learners’ they go. Their smartphones are the first things that they see needs and interests. Post-millennial students or Gen Z’s are upon waking up and also the last object they stare at until they digital natives whose world revolves on their smartphones. This fall asleep. Elsewhere in the Philippines, it is common to see can be capitalized by teachers by exploring the potentials of the the youth actively texting, navigating or scrolling on their mobile phones for academic purposes. There are also free cellphones especially in the public transportations. There were applications available in the two leading operating systems even road accidents that were reported in many areas in the which could be used in aid of instruction such as the scientific country due to the unmindfulness of either the pedestrians or calculator apps. The students’ ratings in the summative tests the drivers while using their cellphones. As a consequence, the using the mobile apps are significantly higher than their ratings government has legislated in 2016 the Republic Act 10913 or using the handheld calculators. It can be concluded that the the Anti-Distracted Driving Act that prohibits a driver of mobile application is a good alternative tool for the handheld vehicle from using mobile phones while driving. ones. This minimizes students’ expenses especially for the With over familiarization with their gadget, Gen Z’s have underprivileged groups. Smartphones are also entrenched on developed automaticity of navigating the phone’s touchscreens the students and their detachment in their bodies would cause even without looking at them. Automaticity means that “tasks separation anxiety. Their dexterities also match the size of the can be done smoothly, without the person having to mentally gadget that one hand alone could do navigations on the keypad monitor or pay attention to how he or she is performing” allowing the other hand to scribble the answers in the paper. (Spector, 2003, p.169). The researcher’s association on Without much effort, they can do calculations even without automaticity is based from the concept of schema, “the means looking at the touch screens as their penchant to the technology by which similar experiences are assimilated and aggregated in has developed automaticity in their system. such a way as to be quickly and easily remembered” (Marshall,1995, p.vii). The same author further explained that REFERENCES “procedural skills” is one important feature of schema. As [1] M. Prensky (2001). Digital Natives Digital Immigrants. On the Horizon. compared to the handheld calculators that are only use only MCB University Press. Vol. 9 No. 5, October 2001. during class sessions in mathematics, the students are more [2] N. Tavakoli, A. Broyles, E.K. Reid, J.R. Sandoval, & V. Correa- accustomed to the calculator apps and their computations could Fernández (2019). Psychological inflexibility as it relates to stress, be done faster since the pressing of the numeric keys are done worry, generalized anxiety, and somatization in an ethnically diverse sample of college students. Journal of Contextual Behavioral Science. automatically with lesser efforts. Volume 11. January 2019. Pages 1-5. Another probable factor that may have contributed to the [3] I. Forsyth, A. Jolliffe, D. Stevens (2002). 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INTERNATIONAL JOURNAL OF RESEARCH IN TECHNOLOGY AND MANAGEMENT (IJRTM) ISSN 2454-6240 www.ijrtm.com [6] M.J. Bradshaw & A.J. Lowenstein (2007). Innovative Teaching [12] P.A. Ertmer & A.O. Leftwich (2012). Removing obstacles to the Strategies in Nursing and Related Health Professions. Boston: Jone and pedagogical changes required by Jonassen’s vision of authentic Barlett Publishers. technology-enabled learning. Computers & Education 64, 175-182. [7] C.U. Nwokeafor (2015). Information Communication Technology (ICT) [13] J. Creswell (2014). Qualitative, Quantitative, Mixed Methods Integration to Educational Curricula: A New Direction for Africa. MD: Approaches, 4th ed. CA: SAGE. University Press of America. [14] J.M. Utts & R.F. Heckard (2011). Mind on Statistics, 4th ed. MA: [8] S. Agostinho, R. Oliver, B. Harper, J. Hedberg, & S. Wills (2002). A Cengage Learning. tool to evaluate the potential for an ICT-Based learning design to foster [15] A. Dingli & D. Seychell (2015). The New Digital Natives: Cutting the "high quality learning“. University of Wollongong Research Online. Chord. London: Springer. [9] R. Puentedura (2014). The SAMR Model as a Framework for Evaluating [16] P.E. Spector (2003). Industrial and organizational psychology: Research mLearning. Journal of Asynchronous Learning Network. 18(2). August and practice. NY: J. Wiley & Sons. 2014. [17] S.P. Marshall (1995). Schemas in Problem Solving. Melbourne: [10] A. Lenhart, R. Ling, S. Campbell & K. Purcell (2010). Teens and mobile Cambridge University Press. phones. Washington, DC: Pew Internet & American Life Project. [18] S.M. Tillery & T.N. Tillery (2017). Essentials of Personal Financial Retrieved from http://pewinternet.org/Reports/2010/Teens-and-Mobile- Planning. NY: J. Wiley & Sons. Phones.aspx [19] C. Madden (2017). Hello Gen Z: Engaging the Generation of Post- [11] J. Gikas (2011). Understanding change: Implementing MCDs in higher Millennials. Sidney: McPherson s Printing Group. education. Unpublished doctoral dissertation. University of Memphis, ’ Memphis, TN.
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