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The impact of collaborative problem posing and solving with ubiquitous-decimal app in authentic contexts on math learning

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Abstract

The research focuses on integrating collaborative problem posing and solving (CPPS) activity into mathematics learning practice with authentic contextual support. We designed a ubiquitous learning application called “U-Decimal” to facilitate CPPS activity supporting decimal learning. The application facilitated the CPPS activity in three ways: designing questions in an authentic context, answering questions designed by students and teachers, and peer assessment. The study aimed to investigate the effect of student’s learning behaviors in CPPS activity supported by U-Decimal on their decimal learning achievement. In total, 54 fourth graders from two different classes were engaged in the experiment. The experimental group completed CPPS activity using U-Decimal installed on tablet PCs, whereas the control group followed traditional CPPS activity with a paper-based approach. The results highlighted three main findings. First, the experimental students scored significantly higher on the post-test than the control students. Second, this study found the contributing functional aspects (i.e., picture-taking function, multimedia-text and voice explanation, and peer assessment) and behavioral factors that predict learning achievement (i.e., quality of multiple-choice question design, quality of comment, and explaining answer using multimedia-text and voice explanation). Most importantly, our findings showed that U-Decimal is useful in supporting decimal learning achievement.

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References

  • Aharony, N. (2014). Mobile libraries: Librarians’ and students’ perspectives. College & Research Libraries, 75(2), 202–217. https://doi.org/10.5860/crl12-415

    Article  Google Scholar 

  • Bray, A., & Tangney, B. (2017). Technology usage in mathematics education research: A systematic review of recent trends. Computers & Education, 114, 255–273. https://doi.org/10.1016/j.compedu.2017.07.004

    Article  Google Scholar 

  • Cai, J., & Hwang, S. (2002). Generalized and generative thinking in the U.S. And Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21, 401–421. https://doi.org/10.1016/S0732-3123(02)00142-6

    Article  Google Scholar 

  • Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. In E. A. Silver (Ed.), Mathematical problem posing (pp. 3–34). Springer.

    Chapter  Google Scholar 

  • Cai, J., & Jiang, C. (2017). An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks. International Journal of Science and Mathematics Education, 15, 1521–1540. https://doi.org/10.1007/s10763-016-9758-2

    Article  Google Scholar 

  • Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83, 57–69. https://doi.org/10.1007/s10649-012-9429-3

    Article  Google Scholar 

  • Căprioară, D. (2015). Problem solving-purpose and means of learning mathematics in school. Procedia-Social and Behavioral Sciences, 191, 1859–1864. https://doi.org/10.1016/j.sbspro.2015.04.332

    Article  Google Scholar 

  • Carbonneau, K. J., Wong, R. M., & Borysenko, N. (2020). The influence of perceptually rich manipulatives and collaboration on mathematic problem-solving and perseverance. Contemporary Educational Psychology, 61, 101846. https://doi.org/10.1016/j.cedpsych.2020.101846

    Article  Google Scholar 

  • Chang, K. E., Wu, L. J., Weng, S. E., & Sung, Y. T. (2012). Embedding game-based problem-solving phase into problem-posing system for mathematics learning. Computers & Education, 58(2), 775–786. https://doi.org/10.1016/j.compedu.2011.10.002

    Article  Google Scholar 

  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM – the International Journal on Mathematics Education, 37(3), 149–158.

    Article  Google Scholar 

  • Conway, P. F., & Sloane, F. C. (2005). International trends in post-primary mathematics education. Dublin: National Council for Curriculum and Assessment.

    Google Scholar 

  • Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270. https://doi.org/10.1023/A:1024364304664

    Article  Google Scholar 

  • Crespo, S., & Harper, F. K. (2019). Learning to pose collaborative mathematics problems with secondary prospective teachers. International Journal of Education Research. https://doi.org/10.1016/j.ijer.2019.05.003

    Article  Google Scholar 

  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415.

    Article  Google Scholar 

  • Davis, F. D. (1898). Perceived usefulness, perceived ease of use and user acceptance of information technology. MIS Quarterly. https://doi.org/10.2307/249008

    Article  Google Scholar 

  • DeBellis, V. A., & Goldin, G. A. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63(2), 131–147. https://doi.org/10.1007/s10649-006-9026-4

    Article  Google Scholar 

  • Denny, P., Hamer, J., Luxton-Reilly, A., & Purchase, H. (2008). PeerWise: Students sharing their multiple choice questions. In Proceeding of the fourth international workshop on computing education research (pp. 51–58), Sydney, Australia. https://doi.org/10.1145/1404520.1404526.

  • Dickerson, V. M. (1999). The impact of problem-posing instruction on the mathematical problem-solving achievement of seventh graders (Doctoral dissertation, Emory University).

  • English, L. D. (2020). Teaching and learning through mathematical problem posing: Commentary. International Journal of Educational Research, 102, 101451. https://doi.org/10.1016/j.ijer.2019.06.014

    Article  Google Scholar 

  • Ernest, P. (1997). Popularization: Myths, massmedia and modernism. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education. Springer.

    Google Scholar 

  • Fellenz, M. R. (2004). Using assessment to support higher level learning: The multiple-choice item development assignment. Assessment & Education in Higher Education, 29(6), 703–719. https://doi.org/10.1080/0260293042000227245

    Article  Google Scholar 

  • Foster, C. (2013). Mathematical études: Embedding opportunities for developing procedural fluency within rich mathematical contexts. International Journal of Mathematical Education in Science and Technology, 44(5), 765–774. https://doi.org/10.1080/0020739X.2013.770089

    Article  Google Scholar 

  • Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410–8415. https://doi.org/10.1073/pnas.1319030111

    Article  Google Scholar 

  • Gielen, S., Peeters, E., Dochy, F., Onghena, P., & Struyven, K. (2010). Improving the effectiveness of peer feedback for learning. Learning and Instruction, 20, 304–315. https://doi.org/10.1016/j.learninstruc.2009.08.007

    Article  Google Scholar 

  • Goodell, J. (2006). Using critical incident reflections: A self-study as a mathematics teacher educator. Journal of Mathematics Teacher Education, 9(3), 221–248. https://doi.org/10.1007/s10857-006-9001-0

    Article  Google Scholar 

  • Hadamard, J. W. (1945). Essay on the psychology of invention in the mathematical field. Princeton University Press.

    Google Scholar 

  • Hitt, F. (2002). Representations and mathematical visualization: PME-NA Working Group (1998–2002). Cinvestav-IPN.

    Google Scholar 

  • Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C. A. (2007). Scaffolding and achievement in problem-based and inquiry learning: A response to Kirschner, Sweller, and Clark (2006). Educational Psychologist, 42, 99–107. https://doi.org/10.1080/00461520701263368

    Article  Google Scholar 

  • Hoogland, K., Pepin, B., Bakker, A., de Koning, J., & Gravemeijer, K. (2016). Representing contextual mathematical problems in descriptive or depictive form: Design of an instrument and validation of its uses. Studies in Educational Evaluation, 50, 22–32. https://doi.org/10.1016/j.stueduc.2016.06.005

    Article  Google Scholar 

  • Hoyles, C. (2016). Engaging with mathematics in the digital age. Cuadernos de Investigacion y Formacion en Educacion Matematica 15: Trabajos de la XIV CIAEM (pp. 225–236). Universidad di Costa Rica.

    Google Scholar 

  • Hughes, C., & Acedo, C. (2014). Guiding principles for learning in the twenty-first Century. International Bureau of Education UNESCO.

    Google Scholar 

  • Hwang, G. J., Chu, H. C., Lin, Y. S., & Tsai, C. C. (2011). A knowledge acquisition approach to developing Mindtools for organizing and sharing differentiating knowledge in a ubiquitous learning environment. Computers & Education. https://doi.org/10.1016/j.compedu.2010.12.013

    Article  Google Scholar 

  • Hwang, G. J., Hung, C. M., & Chen, N. S. (2014). Improving learning achievements, motivations and problem-solving skills through a peer assessment-based game development approach. Educational Technology Research and Development, 62(2), 129–145. https://doi.org/10.1007/s11423-013-9320-7

    Article  Google Scholar 

  • Hwang, W. Y., Shadiev, R., Tseng, C. W., & Huang, Y. M. (2015). Exploring effects of multi-touch tabletop on collaborative fraction learning and the relationship of learning behavior and interaction with learning achievement. Educational Technology & Society, 18(4), 459–473.

    Google Scholar 

  • Hwang, W. Y., Su, J. H., Huang, Y. M., & Dong, J. J. (2009). A study of multi-representation of geometry problem solving with virtual manipulatives and whiteboard system. Journal of Educational Technology & Society, 12(3), 229–247.

    Google Scholar 

  • Hwang, W. Y., Utami, I. Q., & Chen, H. (2018, July). An Evaluation Study of Learning Behaviors and Achievements with Ubiquitous Fraction (u-Fraction) for Elementary School Student. In 2018 IEEE 18th International Conference on Advanced Learning Technologies (ICALT) (pp. 350–354). IEEE. https://doi.org/10.1109/ICALT.2018.00087.

  • Hwang, W. Y., Utami, I. Q., Purba, S. W. D., & Chen, H. S. (2019). Effect of ubiquitous fraction app on mathematics learning achievements and learning behaviors of Taiwanese students in authentic contexts. IEEE Transactions on Learning Technologies, 13(3), 530–539. https://doi.org/10.1109/TLT.2019.2930045

    Article  Google Scholar 

  • Jeong, H. (2011). An investigation of user perceptions and behavioral intentions towards the e-library. Library Collections, Acquisitions, and Technical Services, 35(2–3), 45–60. https://doi.org/10.1016/j.lcats.2011.03.018

    Article  Google Scholar 

  • Kartoglu, U., Vesper, J., Teräs, H., & Reeves, T. (2017). Experiential and authentic learning approaches in vaccine management. Vaccine, 35(17), 2243–2251. https://doi.org/10.1016/j.vaccine.2016.11.104

    Article  Google Scholar 

  • Keller, J. M. (1987). Development and use of the ARCS model of instructional design. Journal of Instructional Development, 10(3), 2–10. https://doi.org/10.1007/BF02905780

    Article  Google Scholar 

  • Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Lawrence Erlbaum.

    Google Scholar 

  • Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during in-struction does not work: An analysis of the failure of constructivist, discovery, pro- blem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41, 75–86. https://doi.org/10.1207/s15326985ep4102_1

    Article  Google Scholar 

  • Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: A case of the Billiard Task. Educational Studies in Mathematics, 83, 71–86. https://doi.org/10.1007/s10649-012-9431-9

    Article  Google Scholar 

  • Kotsopoulos, D., & Cordy, M. (2009). Investigating imagination as a cognitive space for learning mathematics. Educational Studies in Mathematics, 70, 259–274. https://doi.org/10.1007/s10649-008-9154-0

    Article  Google Scholar 

  • Kroll, L. R. (2005). Constructivism in teacher education: Rethinking how we teach teacher. In L. Kroll, R. Cossey, D. M. Donahue, T. Galguera, V. LaBoskey, A. Richert, & P. Tucher (Eds.), Teaching as principled practice: Managing complexity for social justice (pp. 57–80). Sage Publications.

    Chapter  Google Scholar 

  • Leikin, R. (2005). Qualities of professional dialog: Connecting graduate research on teaching and the undergraduate teachers’ program. International Journal of Mathematical Education in Science and Technology, 36(2–3), 237–256. https://doi.org/10.1080/00207390412331316960

    Article  Google Scholar 

  • Limin, C. H. E. N., Van Dooren, W., & Verschaffel, L. (2013). The relationship between students’ problem posing and problem-solving abilities and beliefs: A small-scale study with Chinese elementary school children. Frontiers of Education in China, 8(1), 147–161. https://doi.org/10.3868/110-002-013-0010-5

    Article  Google Scholar 

  • Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why are learning fraction and decimal arithmetic so difficult? Developmental Review, 38, 201–221. https://doi.org/10.1016/j.dr.2015.07.008

    Article  Google Scholar 

  • Maaß, K., & Artigue, M. (2013). Implementation of inquiry-based learning in day-to-day teaching: A synthesis. ZDM Mathematics Education, 45(6), 779–795.

    Article  Google Scholar 

  • Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. Journal of Applied Developmental Psychology, 23(1), 9–50.

    Article  Google Scholar 

  • Olive, J., Makar, K., Hoyos, V., Kor, L. K., Kosheleva, O., & Sträßer, R. (2009). Mathematical knowledge and practices resulting from access to digital technologies. In C. Hoyles & J. B. Lagrange (Eds.), Mathematics education and technology-rethinking the Terrain. New ICMI study series. (Vol. 13). Springer.

    Google Scholar 

  • Osborne, J. (2010). Arguing to learn in science: The role of collaborative, critical discourse. Science, 328, 463–466. https://doi.org/10.1126/science.1183944

    Article  Google Scholar 

  • Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67, 37–58. https://doi.org/10.1007/s10649-007-9083-3

    Article  Google Scholar 

  • Palm, T. (2009). Theory of authentic task situations. In L. Verschaffel, B. Greer, W. V. Dooren, & S. Mukhopadhyay (Eds.), Words and worlds—Modelling verbal descriptions of situations (pp. 3–20). Sense.

    Google Scholar 

  • Pande, M., & Bharathi, S. V. (2020). Theoretical foundations of design thinking—A constructivism learning approach to design thinking. Thinking Skills and Creativity, 36, 100637. https://doi.org/10.1016/j.tsc.2020.100637

    Article  Google Scholar 

  • Rafique, H., Anwer, F., Shamim, A., & Minaei-bidgoli, B. (2018). Factors affecting acceptance of mobile library Applications: Structural equation model. Libri - International Journal of Libraries and Information Services, 68(2), 99–112. https://doi.org/10.1515/libri-2017-0041

    Article  Google Scholar 

  • Savery, J. R., & Duffy, T. M. (1995). Problem based learning: An instructional model and its constructivist framework. Educational Technology, 35(5), 31–38. http://www.jstor.org/stable/44428296

    Google Scholar 

  • Schoenfeld, A. (2004). The math wars. Educational Policy: an Interdisciplinary Journal of Policy and Practice, 18(1), 253–286.

    Article  Google Scholar 

  • Shadiev, R., Hwang, W.-Y., Huang, Y.-M., & Liu, T.-Y. (2015). The impact of supported and annotated mobile learning on achievement and cognitive load. Journal of Educational Technology & Society, 18(4), 53–69.

    Google Scholar 

  • Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83, 1–7. https://doi.org/10.1007/s10649-013-9478-2

    Article  Google Scholar 

  • Singer, F. M., Ellerton, N., & Cai, J. (Eds.). (2015). Mathematical problem posing: From research to effective practice. Springer.

    Google Scholar 

  • Singer, M., Ellerton, N., Silver, E. A., Cai, J., Pelczer, I., Imaoka, M., et al. (2009). Problem posing in mathematics learning: Establishing a theoretical base for research. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33th conference of the international group for the psychology of mathematics education (p. 229). Thessaloniki, Greece: PME.

  • ter Vrugte, J., de Jong, T., Vandercruysse, S., Wouters, P., van Oostendorp, H., & Elen, J. (2015). How competition and heterogeneous collaboration interact in prevocational game-based mathematics education. Computers & Education, 89, 42–52. https://doi.org/10.1016/j.compedu.2015.08.010

    Article  Google Scholar 

  • Thompson, A. G., Philipp, R. A., Thompson, P. W., & Boyd, B. A. (1994). Calculational and conceptual orientations in teaching mathematics. In A. Coxford (Ed.), 1994 yearbook of the NCTM (pp. 79–92). NCTM.

    Google Scholar 

  • Tobias, S., & Duffy, T. M. (2009). The success or failure of constructivist instruction: An introduction. In S. Tobias & T. M. Duffy (Eds.), Constructivist instruction: Success or failure? (pp. 3–10). Routledge/Taylor & Francis Group.

    Chapter  Google Scholar 

  • Van Leeuwen, A., & Janssen, J. (2019). A systematic review of teacher guidance during collaborative learning in primary and secondary education. Educational Research Review, 27, 71–89. https://doi.org/10.1016/j.edurev.2019.02.001

    Article  Google Scholar 

  • Verschaffel, L., Greer, B., Vandooren, W., & Mukhopadhyay, S. (2009). Words and worlds—Modelling verbal descriptions of situations. Sense.

    Book  Google Scholar 

  • Yoon, H. (2016). User acceptance of mobile library applications in academic libraries: An application of the technology acceptance model. The Journal of Academic Librarianship, 42(6), 687–693. https://doi.org/10.1016/j.acalib.2016.08.003

    Article  Google Scholar 

  • Yu, F. Y. (2011). Multiple peer-assessment modes to augment online student question-generation processes. Computers & Education, 56(6), 484–494. https://doi.org/10.1016/j.compedu.2010.08.025

    Article  Google Scholar 

  • Yu, F. Y., & Liu, Y. H. (2009). Creating a psychologically safe online space for a student-generated questions learning activity via different identity revelation modes. British Journal of Educational Technology, 40(6), 1109–1123. https://doi.org/10.1111/j.1467-8535.2008.00905.x

    Article  Google Scholar 

  • Yu, F. Y., Liu, Y. H., & Chan, T. W. (2005). AWeb-based learning system for question-posing and peer assessment: Pedagogical design and preliminary evaluation. Innovations in Education and Teaching International, 42, 337–348. https://doi.org/10.1080/14703290500062557

    Article  Google Scholar 

  • Zha, X., Zhang, J., & Yan, Y. (2015). Comparing digital libraries in the web and mobile contexts from the perspective of the digital divide. Journal of Librarianship and Information Science, 47(4), 330–340. https://doi.org/10.1177/0961000614532677

    Article  Google Scholar 

  • Zhao, Y., Deng, S., & Zhou, R. (2015). Understanding mobile library apps continuance usage in China: A theoretical framework and empirical study. Libri - International Journal of Libraries and Information Services, 65(3), 161–173. https://doi.org/10.1515/libri-2014-0148

    Article  Google Scholar 

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  1. Faculty of Advanced Technology and Multidiscipline, Universitas Airlangga, Mulyorejo, Surabaya City, East Java, 60115, Indonesia

    Ika Qutsiati Utami

  2. Graduate Institute of Network Learning Technology, National Central University, No.300, Zhongda Rd., Zhongli District, Taoyuan City, 320, Taiwan

    Wu-Yuin Hwang

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Example of pre-test and post-test questions.

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Utami, I.Q., Hwang, WY. The impact of collaborative problem posing and solving with ubiquitous-decimal app in authentic contexts on math learning. J. Comput. Educ. 9, 427–454 (2022). https://doi.org/10.1007/s40692-021-00209-5

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