Impact of worked-out examples via a Web 2.0 tool on fifth graders' achievement, attitudes, and motivation in mathematics
Neşe Gökdeniz Tahiroğlu 1, Zeynep Çiğdem Özcan 2 *
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1 Cemile Copuroglu Middle School, Istanbul, Türkiye
2 Mathematics and Science Education Department, Istanbul Medeniyet University, Istanbul, Türkiye
* Corresponding Author

Abstract

This research examines the effects of worked-out examples, grounded in Cognitive Load Theory, which incorporate different solution methods through the Nearpod application—a Web 2.0 tool—on fifth-grade students' achievement in fractions, as well as their attitudes and motivation towards mathematics. The study group consisted of 77 fifth-grade students from two separate classes at a public secondary school in Istanbul. These two classes were randomly assigned, with one serving as the control group and the other as the experimental group. The intervention lasted for six weeks. The research was conducted using an explanatory sequential mixed design, which included both quantitative and qualitative methods. Quantitative data were collected through fraction achievement tests, a mathematics motivation scale, and a mathematics attitude scale. Qualitative data were obtained from students' responses to interview questions to evaluate the effectiveness of the intervention. The findings revealed a statistically significant improvement in the post-test scores for fractions achievement, mathematics motivation, and attitudes towards mathematics in favor of the experimental group, even after controlling for pre-test scores. The results of the interviews also supported these findings, with all interviewed students stating that they found the intervention helpful and engaging. This study contributes to the growing body of literature on the integration of technology in mathematics education, highlighting the need for further research on the application of different solution strategies in digital learning environments.

Keywords

References

  • Abdrafikova, A. R., & Ulianova, A. N. (2015). The Use of Nearpod web 2.0-platform for organization of independent work of students at English language lessons. Kazan Pedagogical Journal, 6, 2-5.
  • Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183-198. https://doi.org/10.1016/j.learninstruc.2006.03.001
  • Aktan, S., & Tezci, E. (2013). Validity and reliability study of the Mathematics Motivation Scale (MMS). The Journal of Academic Social Science Studies, 6(4), 57–77. https://doi.org/10.9761/JASSS1173
  • Aloufi, F., Tashtoush, M., Shirawia, N., Tashtoush, R., & Az-Zo’bi, E. (2024). Internet of Things (IoT) in education: Teachers’ perspectives, practices and challenges. WSEAS Transactions on Computer Research, 12, 429–442. https://doi.org/10.37394/232018.2024.12.42
  • Anglin, J. P. (2004). Creating “well-functioning” residential care and defining its place in a system of care. Child and Youth Care Forum, 33(3), 175–192. https://doi.org/10.1023/B:CCAR.0000029689.70611.0f
  • Arabacı, A. (2021). The effects of activities carried out with Web 2.0 tools on some field competencies of mathematics teacher candidates (Publication no. 694272) [Master’s thesis, Amasya University]. Council of Higher Education Thesis Center.
  • Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181–214. https://doi.org/10.3102/00346543070002181
  • Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2021). Curriculum review guidelines paper. https://www.australiancurriculum.edu.au/media/7118/curriculum-review-guidelinespaper_feb-2021.pdf
  • Barbieri, C.A., Booth, J.L., & Chawla, K. (2023). Let’s be rational: Worked examples supplemented textbooks improve conceptual and fraction knowledge. Educational Psychology, 43, 1–21. https://doi.org/10.1080/01443410.2022.2144142
  • Barnes, M. (2018). Encouraging language development through an online community: Lessons learnt from an action research project. In M. Barnes, M. Gindidis, & S. Phillipson (Eds.), Evidence based learning and teaching: A look into Australian classrooms (pp. 35-47). Routledge.
  • Baron, N. S. (2004). See you online: Gender issues in college student use of instant messaging. Journal of Language and Social Psychology, 23(4), 397–423. https://doi.org/10.1177/0261927X04269585
  • Bart, W. M. (1970). Mathematics education: The views of Zoltan Dienes. The School Review, 78(3), 355–372. https://doi.org/10.1086/442914
  • Baykul, Y. (2021). Ortaokul matematik öğretimi: 5-8. sınıflar [Mathematics teaching in middle school: Grades 5–8]. Pegem Akademi.
  • Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–333). Macmillan.
  • Beirat, M. A., Tashtoush, D. M., Khasawneh, M. A., Az-Zo’bi, E. A., & Tashtoush, M. A. (2025). The effect of artificial intelligence on enhancing education quality and reducing the levels of future anxiety among Jordanian teachers. Applied Mathematics & Information Sciences, 19(2), 279–290. https://doi.org/10.18576/amis/190205
  • Beranek, M., Bory, P., & Vacek, V. (2016). Platform for supporting student learning at Unicorn College. International Journal of Education and Learning Systems, 1, 61–67.
  • Biber, A. C., Tuna, A., & Aktaş, O. (2013). Students’ misconceptions of fractions and its effect on solving fractions problems. Trakya University Journal of Education, 3(2), 152–162.
  • Bokosmaty, S., Sweller, J., & Kalyuga, S. (2015). Learning geometry problem solving by studying worked examples: Effects of learner guidance and expertise. American Educational Research Journal, 52(2), 307–333. https://doi.org/10.3102/0002831214549450
  • Booth, J. L., Lange, K. E., Koedinger, K. R., & Newton, K. J. (2013). Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, 24–34. https://doi.org/10.1016/j.learninstruc.2012.11.002
  • Braun, V., & Clarke, V. (2019). Reflecting on reflexive thematic analysis. Qualitative Research in Sport, Exercise and Health, 11(4), 589–597. https://doi.org/10.1080/2159676X.2019.1628806
  • Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2003). Learning mathematics in elementary and middle schools. Merrill Prentice Hall.
  • Christensen, L., Johnson, R. B. & Turner, L. (2014). Research methods: Design and analysis. Pearson.
  • Clark, R. C., Nguyen, F., & Sweller, J. (2005). Efficiency in learning: Evidence-based guidelines to manage cognitive load. Pfeiffer.
  • Cohen, E. (1988). Traditions in the qualitative sociology of tourism. Annals of Tourism Research, 15(1), 29–46. https://doi.org/10.1016/0160-7383(88)90069-2
  • Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347–362. https://doi.org/10.1037/0022-0663.79.4.347
  • Cramer, K. A., Post, T. R., & del Mas, R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number Project curriculum. Journal for Research in Mathematics Education, 33(2), 111–144. https://doi.org/10.2307/749646
  • Cramer, K., & Wyberg, T. (2009). Efficacy of different concrete models for teaching the part-whole construct for fractions. Mathematical Thinking and Learning, 11(4), 226–257. https://doi.org/10.1080/10986060903246479
  • Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. Pearson Education.
  • Dienes, Z. P. (1967). Some basic processes involved in mathematics learning. In J. M. Scandura (Ed.), Research in mathematics education (pp. 21–34). National Council of Teachers of Mathematics.
  • Durkin, K., & Rittle-Johnson, B. (2012). The effectiveness of using incorrect examples to support learning about decimal magnitude. Learning and Instruction, 22(3), 206–214. https://doi.org/10.1016/j.learninstruc.2011.11.001
  • Erduran, A., Muslu, B. İ., & Özcan, Ö. (2019, July). Pre-service mathematics teachers' views on formative evaluation with Web 2.0 tools: Kahoot! Example [Paper presentation]. International Symposium of Turkish Computer and Mathematics Education, İzmir, Türkiye.
  • Eroi, E. (1989). Prevalence and correlates of math anxiety in Turkish high school students skills (Publication no. 7949) [Master’s thesis, Boğaziçi University]. Council of Higher Education Thesis Center.
  • Fossa, J. A. (2003). On the ancestry of Z. P. Dienes' theory of mathematics education. Revista Brasileira de História da Matemática, 3(6), 79–81.
  • George, D., & Mallery, M. (2010). SPSS for Windows step by step: A simple guide and reference, 17.0 update. Pearson.
  • Gningue, S. (2006). Students working within and between representations: An application of Dienes's variability principles. For the Learning of Mathematics, 26(2), 41–47.
  • Gningue, S. M. (2016). Remembering Zoltan Dienes, a maverick of mathematics teaching and learning: Applying the variability principles to teach algebra. International Journal for Mathematics Teaching and Learning, 17(2), 122–146. https://doi.org/10.4256/ijmtl.v17i2.17
  • Große, C. S. (2015). Fostering modeling competencies: Benefits of worked examples, problems to be solved, and fading procedures. European Journal of Science and Mathematics Education, 3(4), 364–375. https://doi.org/10.30935/scimath/9444
  • Große, C. S., & Renkl, A. (2007). Finding and fixing errors in worked examples: Can this foster learning outcomes? Learning and Instruction, 17(6), 612–634. https://doi.org/10.1016/j.learninstruc.2007.09.008
  • Hansen, N., Jordan, N. C., & Rodrigues, J. (2017). Identifying learning difficulties with fractions: A longitudinal study of student growth from third through sixth grade. Contemporary Educational Psychology, 50, 45–59. https://doi.org/10.1016/j.cedpsych.2015.11.002
  • Hesser, T. L., & Gregory, J. L. (2015). Exploring the use of faded worked examples as a problem-solving approach for underprepared students. Higher Education Studies, 5(6), 36–46. http://dx.doi.org/10.5539/hes.v5n6p36
  • Hossain, M. M., & Quinn, R. J. (2012, March). Prospective use of Web 2.0 technologies in promoting mathematics education in the United States. In P. Resta (Ed.), Society for Information Technology & Teacher Education International Conference (SITE 2012) (pp. 3637–3642). Association for the Advancement of Computing in Education (AACE).
  • Hung, H. T., & Yuen, S. C. Y. (2010). Educational use of social networking technology in higher education. Teaching in Higher Education, 15(6), 703–714. https://doi.org/10.1080/13562517.2010.507307
  • Hurlburt, S. (2008). Defining tools for a new learning space: Writing and reading class blogs. MERLOT Journal of Online Learning and Teaching, 4(2), 182–189.
  • Hussein, L. A., Alqarni, K., Hilmi, M. F., Agina, M. F., Shirawia, N., Abdelreheem, K. I., Hassan, T., & Tashtoush, M. A. (2024). The mediating role of learning management system use in enhancing system effectiveness. WSEAS Transactions on Business and Economics, 21, 2067–2078. https://doi.org/10.37394/23207.2024.21.169
  • İltüzer, Y. (2016). The impact of an online learning process supported with self-explained worked examples on applying decision rules skills (Publication no. 446890) [Master’s thesis, Hacettepe University]. Council of Higher Education Thesis Center.
  • Kartika, H. (2018). Teaching and learning mathematics through web-based resource: An interactive approach. Mapan: Jurnal Matematika dan Pembelajaran, 6(1), 1–10. https://doi.org/10.24252/mapan.2018v6n1a1
  • Kuckartz, U., & Rädiker, S. (2023). Qualitative content analysis: Methods, practice and software. Sage.
  • Kurt, A. A., Sarsar, F., Filiz, O., Telli, E., Orhan-Göksün, D., & Bardakçı, S. (2019). Teachers' use of Web 2.0: Education bag project experiences. Malaysian Online Journal of Educational Technology, 7(4), 110–125. https://doi.org/10.17220/mojet.2019.04.008
  • Lee, N. (2013). The effects of self-explanation and reading questions and answers on learning computer programming language [Unpublished doctoral dissertation]. University of Nevada.
  • Lesh, R. (1979). Mathematical learning disabilities: Considerations for identification, diagnosis, and remediation. In R. Lesh, D. Mierkiewicz, & M. G. Kantowski (Eds.), Applied mathematical problem solving (pp. 235–264). ERIC/SMEAC.
  • Lesh, R. A., & Doerr, H. M. (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Lawrence Erlbaum Associates.
  • Lesh, R., Post, T. R., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representations in the teaching and learning of mathematics (pp. 33–40). Lawrence Erlbaum.
  • Lewis, C., & Perry, R. (2017). Lesson study to scale up research-based knowledge: A randomized controlled trial of fractions learning. Journal for Research in Mathematics Education, 48(3), 261–299. https://doi.org/10.5951/jresematheduc.48.3.0261
  • Marmur, O., Yan, X., & Zazkis, R. (2020). Fraction images: The case of six and a half. Research in Mathematics Education, 22(1), 22–47. https://doi.org/10.1080/14794802.2019.1627239
  • McLoughlin, C., & Lee, M. J. W. (2007). Social software and participatory learning: Pedagogical choices with technology affordances in the Web 2.0 era. In R. Atkinson, C. McBeath, S. Soong, & C. Cheers (Eds.), ICT: Providing choices for learners and learning (pp. 664–675). ASCILITE.
  • Meşe, C. (2012). The effect of instructional software of worked examples designed in accordance with principles of multimedia modality and presentation forms on students' academic success and learning experience (Publication no. 430180) [Master’s thesis, Çukurova University]. Council of Higher Education Thesis Center.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
  • Ministry of National Education [MoNE]. (2018). Mathematics curriculum (grades 1–8). Author.
  • Mishra, P., & Koehler, J. (2003). Not “what” but “how”. Becoming desing-wise about educational technology. In Y. Zhao (Ed.), What should teachers know about technology: Perspectives and practices, (pp. 99-122). Information Age Publishing.
  • Mitchelmore, M. C. (1994). Abstraction, generalisation and conceptual change in mathematics. Hiroshima Journal of Mathematics Education, 2, 45–57.
  • Moschkovich, J. (2013). Principles and guidelines for equitable mathematics teaching practices and materials for English language learners. Journal of Urban Mathematics Education, 6(1), 45-57. https://doi.org/10.21423/jume-v6i1a204
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. https://www.nctm.org/uploadedfiles/standards_and_positions/pssm_executivesummary.pdf
  • National Council of Teachers of Mathematics. (2014). Principles to actions: Executive summary. http://www.nctm.org/uploadedFiles/Standards_and_Focal_Points/Principles_to_Action/PtAExecutiveSummary.pdf
  • Nazlıçiçek, N., & Ertekin, E. (2002, September 16–18). A shortened mathematics attitude scale for elementary mathematics teachers. In Proceedings of the 5th National Science and Mathematics Education Congress (pp. 117–121). METU Culture and Convention Center, Ankara, Turkey.
  • Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and Teacher Education, 21(5), 509–523. https://doi.org/10.1016/j.tate.2005.03.006
  • Norton, A., & Wilkins, J. L. M. (2012). The splitting group. Journal for Research in Mathematics Education, 43(5), 557–583. https://doi.org/10.5951/jresematheduc.43.5.0557
  • Olkun, S., & Toluk Uçar, Z. (2012). İlköğretimde etkinlik temelli matematik öğretimi [Activity-based mathematics instruction in elementary education]. Eğiten Kitap.
  • O'Reilly, T. (2007). What is Web 2.0: Design patterns and business models for the next generation of software. Communications & Strategies, 65, 17–37.
  • Orhun, N. (2007). The cognitive gap between formal arithmetic and visualization in fraction operations. İnönü University Journal of the Faculty of Education, 8(13), 99–111. https://dergipark.org.tr/tr/pub/inuefd/issue/8709/108731
  • Özcan, Z. Ç., Kılıç, Ç., & Obalar, S. (2018). Worked examples supported with explanatory prompts to identify and correct students’ errors in mathematics. Mehmet Akif Ersoy University Journal of Education Faculty, 45, 1–22. https://doi.org/10.21764/maeuefd.322223
  • Paas, F., Renkl, A., & Sweller, J. (2003). Cognitive load theory and instructional design: Recent developments. Educational Psychologist, 38(1), 1–4. https://doi.org/10.1207/S15326985EP3801_1
  • Petit, M. M., Laird, R. E., & Marsden, E. L. (2010). A focus on fractions: Bringing research to the classroom. Routledge. https://doi.org/10.4324/9781315746098
  • Pierson, M. (1999). Technology practice as a function of pedagogical expertise [Unpublished doctoral dissertation]. Arizona State University.
  • Post, T. R. (1981). The role of manipulative materials in the learning of mathematical concepts. In E. L. Coxford (Ed.), Selected issues in mathematics education (pp. 109–131). McCutchan Publishing Corporation.
  • Putra, A. P., Arafik, M., & Pratiwi, I. (2021, September). Use of Nearpod to enhance student engagement in online learning. In 2021 7th International Conference on Education and Technology (ICET) (pp. 298–303). IEEE. https://doi.org/10.1109/ICET53279.2021.9575062
  • Renkl, A. (2017). Learning from worked-examples in mathematics: Students relate procedures to principles. ZDM Mathematics Education, 49, 571–584. https://doi.org/10.1007/s11858-017-0859-3
  • Renkl, A., & Atkinson, R. K. (2003). Structuring the transition from example study to problem solving in cognitive skill acquisition: A cognitive load perspective. Educational Psychologist, 38(1), 15–22. https://doi.org/10.1207/S15326985EP3801_3
  • Renkl, A., Atkinson, R. K., Maier, U. H., & Staley, R. (2002). From example study to problem solving: Smooth transitions help learning. The Journal of Experimental Education, 70(4), 293–315. https://doi.org/10.1080/00220970209599510
  • Renkl, A., Berthold, K., Grosse, C. S., & Schwonke, R. (2013). Making better use of multiple representations: How fostering metacognition can help. In R. Azevedo (Ed.), Springer international handbook of metacognition and learning technologies (pp. 397-408). Springer.
  • Retnowati, E., Ayres, P., & Sweller, J. (2010). Worked example effects in individual and group work settings. Educational Psychology, 30(3), 349–367. https://doi.org/10.1080/01443411003659960
  • Reys, B. J., Suydam, M., Lindquist, M. M., & Smith, N. (1998). Helping children learn mathematics. Allyn & Bacon.
  • Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561-574. https://doi.org/10.1037/0022-0663.99.3.561
  • Ryan, R. M., & Deci, E. L. (2017). Self-determination theory: Basic psychological needs in motivation, development, and wellness. Guilford.
  • Sanmugam, M., Selvarajoo, A., Ramayah, B., & Lee, K. W. (2019). Use of Nearpod as interactive learning method. In L. Gómez Chova, A. López Martínez, & I. Candel Torres (Eds.), INTED2019 Proceedings, (Vol. 1, pp. 8908–8915). IATED. https://doi.org/10.21125/inted.2019.2219
  • Sarı, M. H. (2015). The effect of geometry activities structured according to dienes principles in the elementary 4th grade on student achievement, retention and academic self - concept perception (Publication no. 421436) [Doctoral dissertation, Gazi University]. Council of Higher Education Thesis Center.
  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
  • Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–23. https://doi.org/10.17763/haer.57.1.j463w79r56455411
  • Sinicrope, R., Mick, H., & Kolb, J. (2002). Fraction division interpretations. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions: 2002 Year Book (pp. 153–161). National Council of Teachers of Mathematics.
  • Soylu, Y., & Soylu, C. (2005). Fifth-grade students’ learning difficulties in the topic of fractions: Ordering, addition, subtraction, multiplication, and word problems involving fractions. Erzincan University Journal of Education Faculty, 7(2), 101–118.
  • Sriraman, B., & English, L. D. (2005). On the teaching and learning of Dienes' principles. ZDM – Mathematics Education, 37(3), 258–262. https://doi.org/10.1007/BF02655809
  • Steffe, L. P. (2010). Perspectives on children’s fraction knowledge. In L. P. Steffe & J. Olive (Eds.), Children’s fractional knowledge (pp. 13–26). Springer.
  • Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285. https://doi.org/10.1207/s15516709cog1202_4
  • Tatlı, Z., Akbulut, H. İ., & Altınışık, D. (2016). The effect of Web 2.0 tools on pre-service teachers’ self-efficacy in technological pedagogical content knowledge (TPACK). Turkish Journal of Computer and Mathematics Education, 7(3), 659–678. https://doi.org/10.16949/turkbilmat.277878
  • Üner, S., & Biber, A. (2020). The effect of activities structured according to Dienes’ learning theory on student achievement. Asya Journal of Teaching, 8(1), 1–14.
  • Uysal, M. Z. (2020). The effect of using web 2.0 animation tools in the science course for 4th grade students on various variables (Publication no. 629901) [Master’s thesis, Niğde Ömer Halisdemir University]. Council of Higher Education Thesis Center.
  • Van Loon Hillen, N., Van Gog, T., & Brand Gruwel, S. (2012). Effects of worked examples in a primary school mathematics curriculum. Interactive Learning Environments, 20(1), 89–99. https://doi.org/10.1080/10494821003714676
  • Yılmaz, T. Y., & Köse, N. Y. (2015). Students’ challenge with multiple-solution problems: Identifying the strategies used in solutions. Journal of Qualitative Research in Education, 3(3), 78–101.

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