STUDENTS SKILLS IN MATHEMATICAL COMPUTATION USING GRAPHING CALCULATOR

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1 STUDENTS SKILLS IN MATHEMATICAL COMPUTATION USING GRAPHING CALCULATOR Parick G. Galleo 1, and Craig N. Refugio 2 1 parick.galleo@yahoo.com, and 2 craig.refugio@gmail.com 1 Jose Rizal Memorial Sae Universiy, Dipolog Ciy, Philippines 2 Negros Orienal Sae Universiy, Dumaguee Ciy, Philippines Absrac: This sudy sough o find ou he sudens skills in mahemaical compuaion using graphing calculaor in eaching Mahemaics among freshmen College Algebra sudens of he College of Educaion of Jose Rizal Memorial Sae Universiy, Philippines. The skills ha he sudens possessed in boh he conrol and he experimenal groups on he opics included in his experimen is equivalen or comparable before he inervenion. The sudy also concludes ha he experimenal group performs significanly skillful han he conrol group afer he inervenion. I can be deduced furher ha here is a significan variaion in he sudens skills in mahemaical compuaion beween he conrol group wih he radiional mehod of eaching and he experimenal group wih he used of graphing calculaor in eaching and learning Mahemaics. In addiion, he sudy concludes ha boh he inervenions, radiional mehod of eaching and using graphing calculaor in eaching and learning Mahemaics, make improvemen in he sudens skills in mahemaical compuaion. This means ha sudens perform skillfully beer during he poses han during he prees. However, sudens skills in mahemaical compuaion in he experimenal group are grealy influenced by he graphing calculaor used by eachers and sudens in College Algebra class. This concludes ha sudens in he experimenal group perform skillfully beer han heir counerpar. 1. Inroducion Today s Mahemaics classrooms are facing rapid change more han any oher educaional discipline. These changes are cenered no only wha is being augh, bu also on how i is being augh. Educaionally, [5] averred ha he world is in a echnological boom which Mahemaics classrooms have been flooded wih elecronic eaching ools. There have been ransiions in Mahemaics classrooms, such as he evoluion from blackboard o whieboard o smarboard, bu ulimaely hose changes do no drasically aler he way in which informaion is presened. Some classrooms have abandoned he use of exbooks o provide sudens wih he chance o discover more on heir own and use each oher as learning resources. Despie he imporance of hese changes, [4] sressed ha he mos imporan change in he pas few decades has been he arrival of graphing calculaors. The user-friendliness and porabiliy of hese devices have had a major effec on he access ha sudens now have o new ways of hinking. In [2], i is poined ou ha eachers and sudens now have a new sense of power in he classroom because of he visual naure of hese graphing calculaors. In he Philippines, one of he challenges confroning a Mahemaics eacher in inegraing echnology like graphing calculaors in Mahemaics eaching is he unavailabiliy and lack of he gadge for use in he classroom [1]. The graphing calculaor has a powerful algebraic funcion. The use of a variey of is buil in programs can carry ou differen kinds of calculaions and ransformaions of polynomials, marices, deerminans, facorizaions, equaion solving, he seeking of limis and rigonomeric funcions, and many ohers. Such funcions have no only provided srong suppor for he eaching of Mahemaics, especially beginning calculus and oher

2 higher Mahemaics conen a he secondary school level, bu also graphing calculaors have become good ools for independen exploraion and experimens [8]. Imbued wih he ques of providing research based decisions involving graphing calculaors and sudens performance in Mahemaics among Educaion sudens of Jose Rizal Memorial Sae Universiy, Dipolog Campus, Dipolog Ciy, he researchers are encouraged o conduc his sudy o find ou he sudens skills in mahemaical compuaion using calculaors and deermine heir relaionship o sudens performance in Mahemaics. The resul of his sudy is expeced o consruc possible correcive measures in enhancing sudens skills in mahemaical compuaion using calculaors and performance among he eachers and sudens. 2. Theoreical and Concepual Framework of he Sudy This sudy is anchored on Dreyfus Theory of Skill Acquisiion as cied in [7]. The heory saes ha as human beings acquire a skill hrough insrucion and experiences, hey do no appear o leap suddenly from rule-guided knowing ha o experience-based knowing-how. This emphasizes ha many skills could no simply be reduced o knowing ha. The reason ha many are no conscious of heir knowing how is possibly because hey ake heir knowing-how for graned. I is believed ha here is a gradual process involved for a learner o go hrough in order for him o reach he sage of experise or knowing-how. The heory illusraes he five clear sages ha a learner goes hrough in order o evolve from knowing-ha, novice, o knowing-how, exper. The firs sage is called novice. A novice has some general ideas and is in he process of learning he rules, such as knowing he funcions and he uses of he keys of he calculaor. The second sage is advanced beginner sage. In his sage, he learner s performance improves o a relaively accepable level only afer he novice has had enough experience in copying he real siuaion. During he hird sage, compeence, he learner sars becoming personally involved wih he ask. He sars o see more han one opion from which he has o choose he bes one. In he fourh sage or proficiency sage, he learner, while inuiively undersanding his ask, sill hinks analyically abou his acions. The las sage is called experise. Expers in general know wha o do based on maure undersanding of he ask. An exper has had so much experience wih he ask ha he skill of doing he ask is a par of him. He acs upon correc inuiions wihou analyically hinking abou his every mehod. These sages emphasize on he fac ha pracice is required for he learner o mainain he knowing-how. Wihou pracice, he learner will gradually lose his experise and is mos likely o regress as far back as he compeence sage. This sudy is also grounded on he Theory of Performance [3] which saes ha performance develops and relaes conceps o form a framework ha can be used o explain resuls as well as improvemens. According o him, o perform is o produce valued resuls. He said furher ha developing performance is a journey, and level of performance describes locaion in he journey. This heory exacly connecs he presen invesigaion since he presen sudy embraces he deerminaion of sudens Mahemaics performance. Likewise, finding he level of Mahemaics performance among sudens in College Algebra purpors o performance improvemens in he subjec. I is for his reason ha his sudy was conduced o esablish suppor and srenghen research oupus involving he use of graphing calculaors in Mahemaics classroom. The research

3 aimed o invesigae he sudens skills in mahemaical compuaion using graphing calculaor in relaion o sudens Mahemaics performance in College Algebra among sudens in he College of Educaion of Jose Rizal Memorial Sae Universiy, Dipolog Campus in he Ciy of Dipolog. In his invesigaion, he researcher focused and considered wo eaching approaches such as graphing calculaor uilizaion and he radiional model in eaching Mahemaics as independen variables. I is assered in [6] ha graphing calculaor echnology is a hand-held mahemaics compuer ha draws and analyses graphs, compues he values of mahemaical expression, solves equaions, performs symbolic manipulaion, performs saisical analyses, makes program and communicaes informaion beween devices. Simply saed, i is considerably more versaile as a eaching or learning ool in which a graphics screen replaces ha of a numerical display screen. This feaure, coupled wih buil-in sofware, is capable of underaking all kinds of mahemaical work. Some of he asks made possible are graphing funcions, abulaing funcions, analyzing saisical daa, manipulaing marices, equaion-solving, calculus, probabiliy and complex analysis. In his invesigaion, he researchers aemped o find ou he sudens skills in mahemaical compuaion using graphing calculaor which included skill in solving zeros of funcion, skill in wriing equaions of funcions, skill in solving problems involving funcions, skill in solving inequaliies, and skill in graphing funcions. The graphing calculaor can easily be used o solve and/or check algebraic equaions. For example, one solves for x given 4x + 1 = 9. To process he correc value of x, he following seps are o be used, namely: ener he lef side of he equaion ino Y 1, ener he righ side of he equaion ino Y 2, graph (one may need o adjus he window o see where he wo graphs inersec), and find he poin of inersecion o reveal he answer by pressing 2nd CALC above TRACE, #5 Inersec. Figure 2.1 The Screen Windows of he Plo and he Graph of he Equaion Anoher example is finding he soluion of he sysem of inequaliies y < 3x-5 and y 2x 2-8. Using he TI 84 plus, he commands are as follows:

4 Figure 2.2 The Screen Window of he Graph & Soluion of he Sysem of Inequaliies The poins on he shaded area saisfy boh y < 3x-5 and y 2x 2-8 and is considered he soluion. OR you can use he following commands: Figure 2.3 The Screen Window of he Graph & Soluion of he Sysem of Inequaliies The poins on he double shaded area or he inersecion of he wo graphs saisfy boh y < 3x-5 and y 2x 2-8 and is considered he soluion. Anoher imporan variable in he sudy is he radiional mehod of eaching Mahemaics. In his model, purely he alk, chalk, board and eraser mehod of eaching Mahemaics are employed. This convenional sraegy does no employ echnological gadges since i is using chalk and alk scheme. Moreover, his echnique does no allow sudens o see a clear and pedagogically sound connecion beween inpu parameers and oupu resuls of mahemaical conceps. There were wo groups of respondens in he experimen, namely: he conrol and experimenal groups. The wo groups were exposed o he same lessons/subjec maers in College Algebra, o wi: Linear Funcions, Quadraic Funcions, and Polynomial Funcions. The

5 experimenal group was exposed o each of he opics menioned and developed in he sudens he five skills, namely: solving zeros of a funcion, wriing equaions of funcions, solving problems involving funcions, solving inequaliies, and graphing funcions. Funcions in his sudy were limied o linear, quadraic and polynomial funcions. Likewise, he sudy measured he sudens Mahemaics performance in wo ways, he prees and he poses. The prees was adminisered using he validaed eacher made es o he respondens in boh he conrol and he experimenal groups before he experimen commenced, afer which he experimen followed. The poses, on he oher hand, was given using he same eacher made es as adminisered in he prees o he respondens in boh he conrol and experimenal groups afer he experimen ended. 3. Resuls and Discussions Problem No. 1. Wha is he prees skill performance in mahemaical compuaion of he sudens in he conrol and experimenal groups? The daa which are presened in Tables 3.1 and 3.2 are resuls of he prees adminisered o he conrol and experimenal groups. The prees skill performance was obained before he groups were exposed o he assigned inervenions. Table 3.1 Prees Skill Performance in Mahemaical Compuaion of he Sudens in he Conrol Group Sudens Skills No. of Descripion Iems X z Solving Zeros of a Less Skillful Funcion Wriing Equaions No Skillful of Funcions Solving Problems Less Skillful Involving Funcions Solving No Skillful Inequaliies Graphing of No Skillful Funcions Toal No Skillful = hypoheical mean, = sandard deviaion, X = acual mean, z = compued z value Table 3.1 presens he prees skill performance in mahemaical compuaion of he sudens in he conrol group. Five skills were measured in he experimen, namely: skill in solving zeros of funcion, skill in wriing equaions of funcions, skill in solving problems involving funcions, skill in solving inequaliies, and skill in graphing of funcions. Sixy (60) iems were used o deermine he five skills broken ino 12 iems per skill. The expeced performance of he sudens was se a

6 75 percen of he iems ha deermined each skill. In his case, score of 9 was se as he expeced performance per skill and score of 45 for he whole insrumen. As refleced in Table 3.1, he sudens of he conrol group are less skillful in solving zeros of a funcion and solving problems involving funcions. Moreover, he respondens in he conrol group are no skillfull in wriing equaions of funcions, solving inequaliies and graphing funcions. Overall and on average, he conrol group is no skillful o he differen skills presened in he able. Table 3.2 Prees Skill Performance in Mahemaical Compuaion of he Sudens in he Experimenal Group Sudens Skills No. of Descripion Iems X z Solving Zeros of a No Skillful Funcion Wriing Equaions No Skillful of Funcions Solving Problems No Skillful Involving Funcions Solving No Skillful Inequaliies Graphing of No Skillful Funcions Toal No Skillful = hypoheical mean, = sandard deviaion, X = acual mean, z = compued z value As shown in Table 3.2, he sudens in he experimenal group are no skillful in all of he five skills, from solving zeros of funcions o graphing of funcions. Problem No. 2. Is here a significan difference on he prees skill performance in mahemaical compuaion beween he conrol and experimenal groups? Table 3.3 Tes of Difference on he Prees Skill Performance in Mahemaical Compuaion Beween he Conrol and Experimenal Groups Group N Mean Mean Difference Sandard Deviaion Conrol Experim Compued Criical Decision No Significan Refleced in able 4 is he -es analysis of he prees resuls of he skill performance in mahemaical compuaion beween he conrol and experimenal groups. Base on he compued value and he criical value a α=0.05, i is found ou ha here is no significan difference beween he prees skill performance of he conrol and experimenal groups.

7 Problem No. 3. Wha is he poses skill performance in mahemaical compuaion of he sudens in he conrol and experimenal groups? Table 3.4 Poses Skill Performance in Mahemaical Compuaion of he Sudens in he Conrol Group Sudens Skills No. of Descripion Iems X z Solving Zeros of a Skillful Funcion Wriing Equaions Skillful of Funcions Solving Problems Skillful Involving Funcions Solving Skillful Inequaliies Graphing of Skillful Funcions Toal Skillful = hypoheical mean, = sandard deviaion, X = acual mean, z = compued z value Manifesed in Table 3.4 is he performance of he conrol group in he pos es skill in mahemaical compuaions. As seen in he able, sudens in he conrol group are skillful in all of he five skills from solving zeros of a funcion o graphing of funcions. Table 3.5 Poses Skill Performance in Mahemaical Compuaion of he Sudens in he Experimenal Group Sudens Skills No. of Descripion Iems X z Solving Zeros of a Very Much Skillful Funcion Wriing Equaions Very Much Skillful of Funcions Solving Problems Very Much Skillful Involving Funcions Solving Very Much Skillful Inequaliies Graphing of Very Much Skillful Funcions Toal Very Much Skillful = hypoheical mean, = sandard deviaion, X = acual mean, z = compued z value

8 Revealed in Table 3.5 is he pos es skill performance in mahemaical compuaion in he experimenal group. As refleced, he experimenal group is very much skilful in all of he five skills from solving zeros of a funcion o graphing funcions. Problem No. 4. Is here a significan difference on he poses skill performance in mahemaical compuaion beween he conrol and experimenal groups? Table 3.6 Tes of Difference on he Poses Skill Performance in Mahemaical Compuaion Beween he Conrol and Experimenal Groups Group N Mean Mean Difference Sandard Deviaion Conrol Experim Compued Criical Inerpreaion Significan Table 3.6 shows he -es analysis on he pos es skill performance in mahemaical compuaion beween he conrol and experimenal groups. Based on he compued -value and he criical -value a α=0.05, here is a significan difference on he pos skill performance beween he experimenal and conrol groups. Problem No. 5. Is here a significan difference beween he prees and poses skill performance in mahemaical compuaion of he conrol group? Table 3.7 Tes of Difference Beween he Prees and Poses Skill Performance in Mahemaical Compuaion of he Conrol Group Conrol Group N Mean Mean Difference Sandard Deviaion Prees Poses Compued Criical Inerpreaion Significan Viewed in Table 3.7 is he -es analysis beween prees and pos es skill performance of he conrol group. Based on he compued -value and criical -value a α=0.05, here is a significan difference beween prees and pos es skill performance of he conrol group. Problem No. 6. Is here a significan difference beween he prees and poses skill performance in mahemaical compuaion of he experimenal group? Table 3.8 Tes of Difference Beween he Prees and Poses Skill Performance in Mahemaical Compuaion of he Experimenal Group Experi Group N Mean Mean Difference Sandard Deviaion Prees Poses Compued Criical Inerpreaion Significan

9 Disclosed in Table 3.8 is he -es analysis beween prees and pos es skill performance of he experimenal group. Based on he compued -value and criical -value a α=0.05, here is a significan difference beween prees and pos es skill performance of he experimenal group. Problem No. 7. Is here a significan difference in he prees and poses mean gain on skill performance in mahemaical compuaion beween he conrol and experimenal groups? Table 3.9 Tes of Difference on he Prees and Poses Mean Gain on Skill Performance in Mahemaical Compuaion Beween he Conrol and Experimenal Groups Group N Mean Gain Mean Difference Sandard Deviaion Conrol Experim Compued Criical Inerpreaion * Significan Table 3.9 discloses he -es analysis of he prees and pos es mean gain on skill performance in mahemaical compuaion beween he conrol and experimenal groups. Based on he compued -value and criical -value a α=0.05, here is a significan difference of he prees and pos es mean gain on skill performance beween he conrol and experimenal groups. 4. Findings Base on he analysis and inerpreaion of he daa colleced in his sudy, he following findings were revealed: (1) The prees skill performance in mahemaical compuaion of he conrol and he experimenal groups was described as no skillful. Prees performance of he conrol group was while in he experimenal group was in which boh were far behind he 75 percen of he oal iems esed; (2) There was no significan difference in he prees skill performance in mahemaical compuaion beween he conrol and experimenal groups; (3) The poses skill performance in mahemaical compuaion of he conrol group which was was described as skillful while he poses skill performance in mahemaical compuaion of he experimenal group which was was described as very much skillful ; (4) There was a significan difference in he poses skill performance in mahemaical compuaion beween he conrol and experimenal groups; (5) There was a significan difference beween he prees and poses skill performance in mahemaical compuaion of he conrol group; (6) There was a significan difference beween he prees and poses skill performance in mahemaical compuaion of sudens in he experimenal group; and (7) There was a significan difference in he mean gain obained on sudens skills in mahemaical compuaion beween he conrol and experimenal groups. 5. Conclusions Based on he findings, he skills ha he sudens possessed in boh he conrol and he experimenal groups on he opics included in his experimen is equivalen or comparable before he inervenion. The sudy also concludes ha he experimenal group performs significanly skillful han he conrol group afer he inervenion. I can be deduced furher ha here is a significan variaion in he sudens skills in mahemaical compuaion beween he conrol group

10 wih he radiional mehod of eaching and he experimenal group wih he used of calculaor in eaching and learning Mahemaics. In addiion, he sudy concludes ha boh he inervenions, radiional mehod of eaching and using calculaor in eaching and learning Mahemaics, make improvemen in he sudens skills in mahemaical compuaion. This means ha sudens perform skillfully beer during he poses han during he prees. However, sudens skills in mahemaical compuaion in he experimenal group are grealy influenced by he calculaor used by eachers and sudens in College Algebra class. This concludes ha sudens in he experimenal group perform skillfully beer han heir counerpar. References [1] De Las Peñas, Ma. Louise Anonee and Bauisa, Debbie Marie (2012). On Maximizing Technology Resources and Their Benefis In Teaching and Learning Mahemaics. Aeneo de Manila Universiy, Philippines. [2] Edwards, M. T., Meagher, M., &Ozgun-Koca, S. A. (2008). When is a good fi no a good fi? Dynamic regression wih he TI-nspire graphing calculaor. Mahemaics Teacher, 102(4), [3] Elger, Don (2011). Theory of Performance. Mechanical Engineering, Universiy of Idaho. hp:// [4] Heid, M. K., & Edwards, M. T. (2001). Compuer algebra sysems: Revoluion or rerofi for oday's mahemaics classrooms? Theory ino Pracice, 40(2), [5] Huoppi, David (2009). The Evoluion of Technology in Mahemaics Classrooms. [6] Jones, Keih (2005). Graphing Calculaors in he Teaching and Learning of Mahemaics: A Research Bibliography. Conemporary Issues in Technology and Teacher Educaion (2005) Volume: 21, Issue: 1990, Pages: hp:// [7] Sedaei, Sam (2003). Theory of Skill Acquisiion by Huber and Suar Dreyfus. hp://samsedaei.com/huberandsewardreyfus.pdf [8] Shore, M. A., & Shore, J. B. (2003). An inegraive curriculum approach o developmenal mahemaics and he healh professions using problem-based learning. Mah Compuaion Educaion, 37(1),