- MATHEMATICS AND COMPUTER EDUCATION- TRADITIONAL VS. ONLINE HOMEWORK IN COLLEGE ALGEBRA Kimberly Jrdan Burch and Yu-Ju Ku Mathematics Department 316 Stright Hall Indiana University f Pennsylvania Indiana, Pennsylvania 15705 kjburch@iup.edu; yjku@iup.edu ABSTRACT A year lng study was cnducted in multiple sectins f Cllege Algebra by the authrs using a system f bth traditinal paper hmewrk and nline hmewrk assignments. The nline hmewrk system was Pearsn/Addisn-Wesley's CurseCmpass which was integrated with the textbk. This system allws the students multiple attempts at prblems with extensive hints and examples while prviding instant feedback fr every prblem. Data was cllected frm bth grups including in-class exam scres, final exam scres, and hmewrk averages. Of particular interest t the investigatrs was whether ne methd wuld help facilitate the understanding and retentin f the material better than the ther. We present the analysis and the cnclusins. 1. INTRODUCTION As class times are shrtened and required material is lengthened, many mathematics prfessrs are increasingly turning t nline hmewrk systems such as CurseCmpass (www.cursecmpass.cm), WebAssign (www.webassign.cm), and WeBWrK (http://webwrk.rchester.edu). Systems such as these ffer the student instant feedback and nline help while freeing the prfessrs frm the ften cumbersme task f grading traditinal paper-and-pencil hmewrk. The questin addressed in this paper is whether an nline hmewrk system facilitates the understanding and retentin f the material better than traditinal paper-and-pencil hmewrk. The study was cnducted in Cllege Algebra classes during the 2007-2008 academic year at Indiana University f Pennsylvania (IUP), a state university with apprximately 14,000 students. Cllege Algebra at IUP is a prerequisite fr the calculus and business calculus sequences. Key tpics in this curse include: linear functins, quadratic functins, plynmial functins, graphing and slving equatins, varius 53
- MATHEMATICS AND COMPUTER EDUCATIONapplicatins, expnential, and lgarithmic functins. Certain classes f Cllege Algebra used traditinal paper hmewrk assignments and ther sectins used the nline hmewrk system CurseCmpass by Pearsn/Addisn-Wesley which was bundled with the textbk. The textbk used in all the classes was Beecher, Perma, and Bittinger's Cllege Algebra [2]. 2. LITERATURE REVIEW Althugh research n the effectiveness f nline hmewrk systems has had mixed results, mst studies cnclude that nline hmewrk is as effective as traditinal paper-and-pencil hmewrk r is in fact an imprvement ver the traditinal techniques. Safer and Segalla [7] fund that students using WeBWrK in Cllege Algebra perfrmed as well as thse wh used the traditinal methd. Similarly, Bnham, Beichner, and Deardrff [2] fund that students using WebAssign fr hmewrk submissin in bth Calculus and Algebra had higher test grades than thse wh used traditinal paper-and-pencil hmewrk. They reprted test scres f 78% versus 75% in calculus and 82% versus 77% in algebra but they explained that the difference between the test scres fr the tw methds was nt statistically significant. Hirsch and Weibel [6] fund that students using WeBWrK in calculus classes at Rutgers University shwed a 4% statistically significant imprvement n the final exam grade ver their peers wh were assigned traditinal paper-and-pencil hmewrk. Zerr [8] reprted that an nline hmewrk system created fr University f Nrth Dakta calculus students imprved student learning. This study als fund psitive student attitudes fr the nline hmewrk system and that this resulted in students cmpleting mre hmewrk utside f class. Finally, a recent study cmpleted by Heffeman, Mendicin, and Razzaq [5] fund that fifth grade mathematics students learned significantly mre when using web-based hmewrk than thse given traditinal hmewrk. They reprted an effect size f 0.61 and used this t suggest that schl systems shuld implement such web-based hmewrk systems when feasible. Our study attempts t shw whether there is a statistically significant imprvement in student perfrmance using nline hmewrk versus traditinal paper-and-pencil hmewrk. In the fllwing sectin we give the details f the nline hmewrk system. In Sectin 4, we explain the methd f ur study, including student participatin and an explanatin f the tw types f hmewrk used by the students. In Sectin 5, we prvide statistics and explain ur hypthesis test. 54
- MATHEMATICS AND COMPUTER EDUCATION- 3. THE ONLINE HOMEWORK SYSTEM The nline hmewrk system used in this sfdy is MyMathLab which is a cmpnent f CurseCmpass, a curse management system created by Pearsn/Addisn-Wesley. Access t this nline system is bundled with the textbk which was used in the class [1]. A Screensht f a typical prblem assigned in Cllege Algebra can be seen in Figure 1. ^ 81M txaxt r ASatace (jit Wt&IOSalw nh j I v. cr p/ciciiien mtf>ä «ítíftí'cw, thn cüi^ C-*5Ï<I. Figure 1 : Hmewrk Prblem in MyMathLab MyMathLab allws the students three attempts at the exact same prblem. If the student needs mre than three attempts t d a prblem, the cmputer algrithmically generates a similar prblem with different numbers. The nline hmewrk system asks the student which scre they want t save t the gradebk fr each prblem they reattempt. It als prvides extensive tutrials with step-by-step instructins wrking ut a prblem similar t the ne assigned. Often, the nly difference between the tw prblems was the numerical values. The tutrial assciated with the prblem in Figure 1 can be seen in Figure 2. In this example, ne can see that the values frm the riginal prblem have been changed. The tutrial then interactively asks the students t cmplete each step, prmpting them with explanatins f rules and definitins. If the student gets any f the intermediate steps incrrect, the prgram prvides feedback and hints n what they need t d t crrectly cmplete that part f the prblem. 55
- MATHEMATICS AND COMPUTER EDUCATION- Step 1. T separate the expressin int several lgartdims, yuil need t use O^- The Qutient Rule. d^b. The Práict Rule. C C Bth die Pràict Rule and the Qutient Rule. Use Ae Prduct Rule. Step 2. Use tiie Pwer Rule t write the lgarithms f pwers as prducts. Similariy, lg ^ (y ) = 8 lg ^. The given es^essin can then be written Step 3. Nne f the lgariúuns in the ejqpressin can be fisüter simplified. Therefre, lg jcx'y^z) = 9 lg ^+8 lg ^+ lg^z. Questin is cmplete. Figure 2: Hmewrk Tutrial in MyMalhLab 4. METHOD The data fr the study spans tw semesters. The paper hmewrk was used during ne semester and the nline hmewrk system was used the fllwing semester. The three sectins f Cllege Algebra using paper hmewrk had a ttal f 65 students wh cmpleted the class. The tw sectins f Cllege Algebra using the nline hmewrk system had a ttal f 61 students wh cmpleted the class. There were slight variatins in cntent between the exams given fr the different semesters because f scheduling and hlidays. After carefully reviewing the exams, the instructrs chse t limit the sample size t nly 21 f the paper hmewrk students because they tk an identical final exam t thse in ne f the nline hmewrk sectins. The instructrs felt the level f difficulty f the ther versin f the fmal exam was t different t include thse students in the sample. There were 31 students in the nline hmewrk sectin. Traditinal paper hmewrk assignments were graded fr crrectness and cmpletin and were returned t the students with 56
- MATHEMATICS AND COMPUTER EDUCATIONcmments. The students had nly ne chance t cmplete these assignments. The nline hmewrk system allwed the students three attempts at the exact same prblem. If the student needed mre than three attempts t d a prblem, the cmputer algrithmically generated a similar prblem with different numbers. The nline hmewrk system asked the students which scre they wanted recrded in the gradebk. This allwed the students t save nly their best scre fr each prblem they attempted. With several attempts and extensive nline help, many students were able t earn perfect scres n nearly all if nt all f their nline hmewrk assignments. Several students expressed their preference fr using the nline hmewrk system ver paper hmewrk. Many explained that they liked being able t d their hmewrk whenever they wanted and still have help via the nline tutrials. They als appreciated the multiple attempts at prblems t get them crrect, ften asking fr help in class if they culd nt get the prblems s that they culd return that night t try the prblems again. 5. RESULTS 5.1 Hmewrk Type and Exams We fund the students wh used the nline hmewrk system perfrmed better n the exams. T statistically examine these results, we set up the fllwing hypthesis test: HQ -.MO =Mp, where //Q = mean exam scre fr all nline hmewrk students and //^ = mean exam scre fr all paper hmewrk students. The /7-values assciated with each f the exams are given in Table 1. Since the /?-value fr Exam 2 is 0.006 < 0.05, there is sufficient evidence at the 5% significance level t cnclude that the mean scre f Exam 2 frm all the nline hmewrk students is higher than the mean scre f Exam 2 frm all paper hmewrk students. Similar statements can be made regarding the/7-values fr Exam 1 and Exam 3 since they are bth less than 0.05. In cntrast, the Final Exam had a /?-value f 0.0685 > 0.05. This means there is insufficient evidence at the 5% significance level t cnclude that the mean scre f the Final Exam frm all nline hmewrk students is higher than thé mean scre f the Final Exam frm all paper hmewrk students. Hwever, the sample mean difference is abut 8% between the nline and paper hmewrk grups. 57
- MATHEMATICS AND COMPUTER EDUCATION- Exam 1 Exam 2 Exam 3 Final Exam /?-value 0.000 0.006 0.014 0.0685 Table 1 : p-values fr the Hypthesis Tests Estimated Marginal Means rmeasure_1 -n-ihe.ppef fact Ii Figure 3: Results by Hmewrk Type Figure 3 shws the means fr Exam 1, Exam 2, Exam 3, and the Final Exam (4) fr the students wh used nline hmewrk and thse wh cmpleted traditinal paper hmewrk assignments. The line segments in Figure 3 are nt parallel, which indicates sme level f interactin between hmewrk types and the fur exams. In cmparing the same exams fr different hmewrk types, the line segments preserve the same slpe regardless f the hmewrk type. This shws that hmewrk types have the same impact (bth either increasing r decreasing) n exam grades. Furthermre, bserving the gap between the plts f the nline hmewrk and paper hmewrk, we see that the gap is decreasing frm Exam 3 t the Final Exam (4). In general, the nline hmewrk exam averages drp mre significantly than the paper hmewrk exam averages, causing the gap between the tw means t decrease. The means fr the nline hmewrk students' exams were higher than thse wh cmpleted paper hmewrk assignments. We believe these higher scres are a result f the extensive repetitin and assistance the nline hmewrk prgram prvides. Students are able t review hmewrk befre exams and can reattempt the hmewrk prblems withut penalty. Students als had every prblem graded and therefre knew if their answers were crrect. This is in cntrast t the paper 58
-MATHEMATICS AND COMPUTER EDUCATIONhmewrk assignments which had nly selected prblems graded. Students culd nt be sure their techniques were crrect fr slving prblems that were ungraded. These advantages ver traditinal paper hmewrk cntribute t the successñil mastery f the material by the nline hmewrk students. 5.2 Crrelatin between Hmewrk Grades and Exam Perfrmance Additinally, we examined the individual scres f the students n the varius exams based n their hmewrk types. The scatter plts f the hmewrk z-scres versus the exam scres fr bth nline and paper hmewrk are prvided in Figure 4, Figure 5, Figure 6, and Figure 7. The crrelatin cefficients fr bth the paper hmewrk students and the nline hmewrk students' Exam 1, 2, 3, and Final Exam can be seen in Table 2. The paper hmewrk students' exam scres had a strnger a psitive linear pattern than the nline hmewrk students' exams. This means the paper hmewrk scres prvide a better predictin f their exam scres. The paper hmewrk students d nt actually perfrm better n the exams than the nline hmewrk students (in fact the ppsite is true), but the hmewrk scres are a better measure f their exam success. 10O- O O qp O O^ 8 O 100-0 0 0 0 0-2.00000-1.00000 O.OÓOOO 1.00000 2.00000 O 1 Zscre(Scre5) HW Figure 4: Exam 1 Scres by Hmewrk Type Althugh the scatter plts fr the nline hmewrk students did nt fit a psitive linear pattern, many had a nearly vertical line f exam scres with a z-scre f almst 1. Within this pattern, the exam scres ranged frm 20 t 100. We believe this can be attributed t the multiple attempts 59
- MATHEMATICS AND COMPUTER EDUCATIONallwed n every hmewrk prblem and the extensive nline tutrials and help. The students may simply be mimicking the steps f the wrked-ut examples withut having any true understanding f the cncepts. 100^ OO 0- O O O S Qsn 0 O % 0 S % 0 0-0 OQÛ 0 ^ -2.00000 0.00000 1.00000 Zscre(ScFe5) HW OQ ç, Figure 5: Exam 2 Scres by Hmewrk Type O 100-100- OO O 9 8$ 0 8 " 0 " 0-100- O 0 0 0- -2.00000-1.00000 2.00000 Zscre(Scre5) HW Figure 6: Exam 3 Scres by Hmewrk Type 60
O - MATHEMATICS AND COMPUTER EDUCATION- 1 100- ñ 0- O O 0 Qe ** H- 1 100- ^ O 0 0- -2.00000-1.00000 0.00000 1.00000 2.00000 Zscre(Scre5) HW Figure 7: Final Exam Scres by Hmewrk Type PAPER HOMEWORK ONLINE HOMEWORK Exam 1 0.342 0.154 Exam 2 0.373 0.193 Exam 3 0.421 0.092 Table 2: Crrelatin Cefficients fr Exam Grades vs Hmewrk Type Final Exam 0.476 0.180 Yet, withut the repetitin that is allwed in the nline hmewrk system, we feel the students verall wuld nt have learned the material as well. We feel being able t red hmewrk prblems and review them interactively was a key factr in the nline hmewrk students btaining higher exam scres than the traditinal paper hmewrk students. What we nticed with the paper hmewrk students was that if they had pr hmewrk averages, they had little t n chance f perfrming well n exams. They did nt have the same pprtunity t interactively review their hmewrk and get instant feedback as the nline hmewrk students did. 6. CONCLUSIONS Sme factrs that we wuld like t address are the fact that the breakdwn f material frm the exams in the Fall semester differs slightly frm the exams in the Spring semester due t hlidays and the general difference in semesters. Ideally, we wuld like t run the study by 61
- MATHEMATICS AND COMPUTER EDUCATIONswitching back and frth between nline and paper hmewrk in the same class in the same semester. Unfrtunately, this is bth impractical frm a teaching standpint and the fact that the students incur a cst t use the nline hmewrk systems. T annunce that we wuld nt be using the nline system exclusively wuld mst likely be met with much disdain. Als, the students in the nline hmewrk sectins were given the paper hmewrk sectins' exams as a sample. Students were nt given the slutins and had t wrk the sample exams t btain slutins. Fr this reasn, different prblems were chsen fr the nline hmewrk semester exams while the same level f difficulty was maintained. The nline hmewrk students earned higher exam scres than the traditinal paper hmewrk students. We believe this is due t the repetitin and prblem hints available t the nline hmewrk students. Additinally, the nline hmewrk students culd review and reattempt their hmewrk assignments withut penalty. They als had scres fr every hmewrk prblem and were assured their answers were crrect. In cntrast, the paper hmewrk students nly had crrect slutins t the prblems that were graded and were therefre unsure if sme f their prblem slving techniques were crrect. Als, students' scres n the paper hmewrk assignments were a better predictr f exam perfrmance. Additinally, we nte that the retentin rate in the nline hmewrk sectins was much higher than that f her traditinal paper hmewrk sectins. The retentin rate fr the nline hmewrk sectins was 86% while the retentin rate fr the paper hmewrk sectins was just 58%. Bth hmewrk types ended with nearly the same number f students but it is imprtant t nte that there were three sectins using paper hmewrk and nly tw sectins using nline hmewrk. The instructrs recgnize that there is n way t verify wh is actually cmpleting the nline hmewrk. Als, if the nline questins are multiple-chice, the students may successfully cmplete the prblem by repeatedly guessing withut understanding the cncepts. Hwever, the instructrs fund that nline hmewrk helped t streamline the class, eliminating the need t wait fr papers t be graded and returned. Students were als able t check their averages in the class at all times by lgging in t the nline hmewrk system. Mst imprtantly, the student exam scres were higher fr the nline sectins than thse f the traditinal paper hmewrk sectins. This cmbined with the better retentin rate achieved by the nline classes makes using the nline hmewrk systems, althugh nt withut flaws, extremely appealing. 62
- MA THEMA TICS AND COMPUTER EDUCA TION - REFERENCES 1. J. A. Beecher, J. A. Penna, and M. L. Bittinger, Cllege Algebra, Custm Editin fr Indiana University f Pennsylvania, Pearsn/Addisn Wesley, ISBN: 0321466071 (2008). 2. S. Bnham, R. Beichner, and D. Deardrff, " Online hmewrk: Des It Make a Difference?", The Physics Teacher, Vl. 39, pp. 293-296, ISSN: 0031-921x (2001). 3. N. Demirci, "University Students' Perceptins f Web-based vs. Paper-based Hmewrk in a General Physics Curses", Eurasia Jurnal f Mathematics, Science and Technlgy Educatin, Vl. 3, N. 1, pp. 29-34, ISSN: (electrnic): 1305-8223 (2007). 4. J. Dillard-Eggers, T. Wten, B. Childs, and J. Cker, "Evidence On The Effectiveness Of On-Line Hmewrk", Cllege Teaching Methds & Styles Jurnal, Vl. 4, N. 5, pp. 9-16, ISSN: 1548-9566 (2008). 5. N. Heffeman, M. Mendicin and L. Razzaq, "A cmparisn f Traditinal Hmewrk t Cmputer-Suuprted Hmewrk", Jurnal f Research n Technlgy in Educatin, Vl. 41, N. 3, pp. 331-359, ISSN.- 1539-1523 (2009). 6. L. Hirsch and C. Weibel, "Statistical Evidence that Web-Based Hmewrk Helps", FOCUS, Vl. 23, N. 2, p. 14, ISSN.- 0731-040 (2003). 7. A. Safer and A.Segalla, " Web-based Mathematics Hmewrk: A case Study Using WeBWrK in Cllege Algebra Classes", Exchanges: The Online Jurnal f Teaching and Learning in the CSV, http://wvsw.exchangesjumal.rg (2006). 8. R. Zerr, "A Quantitative and Qualitive Analysis f theeffectiveness f Online Hmewrk in First-Semester Calculus", Jurnal f Cmputers in Mathematics and Science Teaching, Vl. 26, N. 1, pp. 55-73, ISSN: 0731-9258 (2007). 63
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