Design and Implementation of Ubiquitous Fraction App for Fraction Learning in Authentic Contexts


  • uun hariyanti Graduate Institute of Network Learning Technology, National Central University, Taiwan
  • wu-yuin hwang Graduate Institute of Network Learning Technology, National Central University, Taiwan



authentic contexts; ubiquitous fraction; authentic learning; peer sharing; peer assessment


An amount of research had identified some difficulties that were faced by students when they learned fractions, which known as one of the essential parts of mathematics. On the other hand, designing mathematics learning in authentic contexts could beneficial to students, such as increase their motivation and collaboration. Thus, we develop a Ubiquitous App, namely Ubiquitous Fraction (U-Fraction), to facilitate fraction learning in authentic contexts by providing useful features. This study was designed to investigate the relationship among three categories of learning variables, including quantity of learning, quality of learning, and learning achievement, and to identify sequences of interactions when students use U-Fraction in authentic contexts. There were 27 five-grade students participated in this study. The data were analyzed using parametric and nonparametric tests, including pair t-test, correlation, lag sequential, and descriptive analysis. In summary, four important findings are highlighted in this study. First, the pair t-test result showed that there was a significant difference in students’ acquisition of fraction knowledge before and after the learning process. Second, the importance of correlation analysis results indicated that students’ learning achievement would more depend on their quality of learning rather than their quantity of tasks that had been solved by them. Third, results from sequential analysis indicated that students intended to do the next steps after they finished the previous step in fraction learning with authentic contexts. Fourth, a questionnaire, which is Sustainable and Scalable Authentic Learning (SSAL), results indicated that most students agree that learning with U-Fraction in authentic contexts could have a positive impact on the ability to collaborate with others. Finally, the limitations of this study also discussed.


Bakeman, R., and Gottman, J.M. (1997). Observing Interaction: An Introduction to Sequential Analysis (2nd ed.). Cambridge: Cambridge University Press.

Belk, M., Fidas, C., Germanakos, P., and Samaras, G. (2017, November). The interplay between humans, technology and user authentication: A cognitive processing perspective. Computers in Human Behavior, 76, 184-200. doi: 10.1016/j.chb.2017.06.042

Boticki, I., Wong, L.H., and Looi, C. (2013). Designing Technology for Content-Independent Collaborative Mobile Learning. IEEE Transaction on Learning Technology, 6(1), pp. 14-24. doi: 10.1109/TLT.2012.8

Brizuela, B. M. (2006). Young children's notations for fractions. Educational Studies in Mathematics, 2006, 62, 281-305. doi: 10.1007/s10649-005-9003-3

Chung, G. K., and Baker, E. L. (2003). An Exploratory Study to Examine the Feasibility of Measuring Problem-Solving Processes Using a Click-Through Interface. The Journal of Technology, Learning and Assessment, 2(2). Retrieved from

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. doi: 10.1007/s10649-006-9026-4

Fornell, C., and Larcker, D.F. (1981). Structural Equation Models with Unobservable Variables and Measurement Error: Algebra and Statistics. Journal of Marketing Research, 18(3), 382-388. doi: 10.2307/3150980

Hair, J. F., Sarstedt, M., and Ringle, C. M. (2019). Rethinking some of the rethinking of partial least squares. European Journal of Marketing, 53(4), 566-584. doi: 10.1108/EJM-10-2018-0665

Herrington, J., and Oliver, R. (2000). An instructional design framework for authentic learning environments. Educational Technology Research and Development, 48(3), 23-48. doi: 10.1007/BF02319856

Herrington, J., Reeves, T.C., and Oliver, R. (2014). Authentic learning environments. In Spector J., Merrill M., Elen J., Bishop M. (Eds), Handbook of research on educational communications and technology (pp. 401-412). New York: Springer. doi: 10.1007/978-1-4614-3185-5_32

Hwang, W. -Y., Purba, S.W.D., Liu, Y., Zhang, Y., and Chen, N. (2019a). An Investigation of the Effects of Measuring Authentic Contexts on Geometry Learning Achievement. IEEE Transaction on Learning Technology, 12(3), 291-302. doi: 10.1109/TLT.2018.2853750

Hwang, W. -Y., Shadiev, R., Tseng, C. -W., and 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. Journal of Educational Technology & Society, 18(4), 459-473

Hwang, W. -Y., Utami, I. Q., Purba, S. W. D., and Chen, H. S. L. (2019b). Effect of Ubiquitous Fraction App on Mathematics Learning Achievements and Learning Behaviors of Taiwanese Students in Authentic Contexts’, IEEE Transaction on Learning Technology, 1-1. doi: 10.1109/TLT.2019.2930045

Jordan, N. C., Resnick, I., Rodrigues, J., Hansen, N., and Dyson, N. (2017). Delaware longitudinal study of fraction learning: Implications for helping children with mathematics difficulties. Journal of Learning Disabilities, 50(6), 621-630. doi: 10.1177/0022219416662033

Kara, F., & Incikabi, L. (2018). Sixth Grade Students’ Skills of Using Multiple Representations in Addition and Subtraction Operations in Fractions. International Electronic Journal of Elementary Education, 10(4), 463-474. Retrieved from

Kong, S. C., and Kwok, L. F. (2003). A graphical partitioning model for learning common fraction: designing affordances on a web-supported learning environment. Computers & Education, 40(2), 137-155. doi: 10.1016/S0360-1315(02)00118-5

Kukulska‐Hulme, A., and Viberg, O. (2018). Mobile collaborative language learning: State of the art. British Journal of Education Technology, 49(2), 207-218. doi: 10.1111/bjet.12580

Nakahara, T. (2008). Cultivating Mathematical Thinking through Representation: Utilizing the Representational System. Retrieved from

Newmann, F.M., and Wehlage, G.G. (1993). Five standards of authentic instruction. Educational Leadership, 50(7), 8-12.

Pohl, M., Smuc, M., and Mayr, E. (2012). The user puzzle-explaining the interaction with visual analytics systems. IEEE Transactions on Visualization and Computer Graphics, 18(12), 2908-2916. doi: 10.1109/TVCG.2012.273

Pohl, M., Wallner, G., and Kriglstein, S. (2016, December). Using lag-sequential analysis for understanding interaction sequences in visualizations. International Journal of Human-Computer Studies, 96, 54-66. doi: 10.1016/j.ijhcs.2016.07.006

Radinsky, K., Svore, K. M., Dumais, S. T., Shokouhi, M., Teevan, J., Bocharov, A., and Horvitz, E. (2013). Behavioral dynamics on the web: Learning, modeling, and prediction. ACM Transactions on Information Systems, 31(3), 1-37. doi: 10.1145/2493175.2493181

Reychav, I., and Wu, D. (2016, September). The interplay between cognitive task complexity and user interaction in mobile collaborative training. Computers in Human Behavior, 62, 333-345. doi: 10.1016/j.chb.2016.04.007

Spiro, R. J., Feltovich, P. J., Jacobson, M. J., & Coulson, R. L. (1992). Cognitive flexibility, constructivism, and hypertext: Random access instruction for advanced knowledge acquisition in ill-structured domains. In T. M. Duffy, & D. H. Jonassen, (Eds.), Constructivism and the technology of instruction: A conversation, (pp. 57-75). Lawrence Erlbaum Associates, Inc.

Shadiev, R., Hwang, W.Y., Huang, Y.M., and Liu, T.Y. (2018). Facilitating application of language skills in authentic environments with a mobile learning system. Journal of Computer Assisted Learning, 34(1), 42-52. doi: 10.1111/jcal.12212

Wadsworth, B. J. (1996). Piaget's theory of cognitive and affective development: Foundations of constructivism. New York: Longman Publishing.

Wang, C., Fang, T., and Gu, Y. (2020, January). Learning performance and behavioral patterns of online collaborative learning: Impact of cognitive load and affordances of different multimedia. Computers & Education, 143, 103683. doi: 10.1016/j.compedu.2019.103683

Wu, S. -Y., Chen, S. Y., and Hou, H. -T. (2016). Exploring the interactive patterns of concept map-based online discussion: a sequential analysis of users’ operations, cognitive processing, and knowledge construction. Interactive Learning Environments, 24(8), 1778-1794. doi: 10.1080/10494820.2015.1057740

Van Gog, T., Kester, L., and Paas, F. (2011). Effects of concurrent monitoring on cognitive load and performance as a function of task complexity. Applied Cognitive Psychology, 25(4), 584-587. doi: 10.1002/acp.1726

Volk, M., Cotič, M., Zajc, M., and Starcic, A.I. (2017, November). Tablet-based cross-curricular maths vs. traditional maths classroom practice for higher-order learning outcomes. Computers & Education, 114, 1-23. doi: 10.1016/j.compedu.2017.06.004




How to Cite

hariyanti, uun, & hwang, wu- yuin. (2020). Design and Implementation of Ubiquitous Fraction App for Fraction Learning in Authentic Contexts. Proceedings of the International Conference on Education, 6(2), 01–16.