Abstract
The present paper documents the design and development of a mobile mathematics application targeted to improve magnitude representation skills. Educational experts worked together with an app developer with the goal of creating an educational app as a math learning tool for children 5–8 years old. The description of the app design processes includes five core elements that we believe are central to the creation of a theory driven educational app. Creating a theory driven educational app is a difficult task; it involves a set of complex decisions as illustrated in this article.
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References
Albert, D. (2015). Pushing push—Have notifications come of age? Retrieved from https://www.sitepoint.com/pushing-push-notifications-come-age/
Ally, M., & Tsinakos, A. (2014). Increasing access through mobile learning. Commonwealth of Learning (COL).
Arnab, S., Lim, T., Carvalho, M. B., Bellotti, F., De Freitas, S., Louchart, S., ... De Gloria, A. (2015). Mapping learning and game mechanics for serious games analysis. British Journal of Educational Technology, 46(2), 391–411. https://doi.org/10.1111/bjet.12113
Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–339.
Berkowitz, T., Schaeffer, M. W., Maloney, E. A., Peterson, L., Gregor, C., Levine, S. C., & Beilock, S. L. (2015). Math at home adds up to achievement in school. Science, 350(6257), 196–198. https://doi.org/10.1126/science.aac7427
Blair, K. P. (2013). Learning in critter corral: Evaluating three kinds of feedback in a preschool math app. Proceedings of the 12th international conference on interaction design and children (pp. 372–375). ACM. https://doi.org/10.1145/2485760.2485814
Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016–1031. https://doi.org/10.1111/j.1467-8624.2008.01173.x
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
Bugden, S., & Ansari, D. (2011). Individual differences in children’s mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition, 118(1), 32–44. https://doi.org/10.1016/j.cognition.2010.09.005
Burgstahler, S. (2012). Universal design in education: Process, principles and applications. DO-IT.
Callaghan, M. N., & Reich, S. M. (2018). Are educational preschool apps designed to teach? An analysis of the app market. Learning, Media and Technology, 43(3), 280–293. https://doi.org/10.1080/17439884.2018.1498355
Case, R., Okamoto, Y., Griffin, S., McKeough, A., Bleiker, C., Henderson, B., ... Keating, D. P. (1996). The role of central conceptual structures in the development of children’s thought. Monographs of the Society for Research in Child Development, i-295. https://doi.org/10.2307/1166077
Cayton-Hodges, G. A., Feng, G., & Pan, X. (2015). Tablet-based math assessment: What can we learn from math apps? Journal of Educational Technology & Society, 18(2), 3–20.
Cezarotto, M. A., & Battaiola, A. L. (2016). Game design recommendations focusing on children with developmental dyscalculia. International conference on learning and collaboration technologies (pp. 463–473). Springer. https://doi.org/10.1007/978-3-319-39483-1_42
Cheung, A. C., & Slavin, R. E. (2013). The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Educational Research Review, 9, 88–113. https://doi.org/10.1016/j.edurev.2013.01.001
Cohen, M., Hadley, M., & Frank, M. (2011). Young children, apps & iPad. US Department of Education Ready to Learn Program, 200, 5–10.
Conole, G., Dyke, M., Oliver, M., & Seale, J. (2004). Mapping pedagogy and tools for effective learning design. Computers & Education, 43(1–2), 17–33. https://doi.org/10.1016/j.compedu.2003.12.018
Denham, A. R. (2016). Improving the design of a learning game through intrinsic integration and playtesting. Technology, Knowledge and Learning, 21(2), 175–194. https://doi.org/10.1007/s10758-016-9280-1
Dubé, A. K., Alam, S. S., Xu, C., Wen, R., & Kacmaz, G. (2019). Tablets as elementary mathematics education tools: Are they effective and why. Mathematical learning and cognition in early childhood (pp. 223–248). Springer. https://doi.org/10.1007/978-3-030-12895-1_13
Dubé, A. K., Kacmaz, G., Wen, R., Alam, S. S., & Xu, C. (2020). Identifying quality educational apps: Lessons from ‘top’ mathematics apps in the Apple App Store. Education and Information Technologies, 25, 5389–540. https://doi.org/10.1007/s10639-020-10234-z
Dubé, A. K., & Keenan, A. (2016). Are games a viable home numeracy practice? In B. Blevins-Knabe & A. M. B. Austin (Eds.), Early childhood mathematics skill development in the home environment (pp. 165–184). Springer. https://doi.org/10.1007/978-3-319-43974-7_10
Dubé, A. K., & McEwen, R. N. (2015). Do gestures matter? The implications of using touchscreen devices in mathematics instruction. Learning and Instruction, 40(C), 89–98. https://doi.org/10.1016/j.learninstruc.2015.09.002
Fabian, K., Topping, K. J., & Barron, I. G. (2016). Mobile technology and mathematics: Effects on students’ attitudes, engagement, and achievement. Journal of Computers in Education, 3(1), 77–104. https://doi.org/10.1007/s40692-015-0048-8
Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539. https://doi.org/10.1037/a0025510
Gebuis, T., & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43(4), 981–986. https://doi.org/10.3758/s13428-011-0097-5
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 293–304. https://doi.org/10.1177/00222194050380040301
Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115(3), 394–406. https://doi.org/10.1016/j.cognition.2010.02.002
Gray, P. (2013). Free to learn: Why unleashing the instinct to play will make our children happier, more self-reliant, and better students for life. Basic Books.
Gröger, C., Silcher, S., Westkämper, E., & Mitschang, B. (2013). Leveraging apps in manufacturing. A framework for app technology in the enterprise. Procedia CIRP, 7, 664–669. https://doi.org/10.1016/j.procir.2013.06.050
Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “number sense”: The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5), 1457. https://doi.org/10.1037/a0012682
Harari, G. M., Müller, S. R., Stachl, C., Wang, R., Wang, W., Bühner, M., Rentfrow, P. J., Campbell, A. T., & Gosling, S. D. (2019). Sensing sociability: Individual differences in young adults’ conversation, calling, texting, and app use behaviors in daily life. Journal of Personality and Social Psychology. https://doi.org/10.1037/pspp0000245
Hawes, Z., Nosworthy, N., Archibald, L., & Ansari, D. (2019). Kindergarten children’s symbolic number comparison skills predict 1st grade mathematics achievement: Evidence from a two-minute paper-and-pencil test. Learning and Instruction, 59, 21–33.
Highfield, K., & Goodwin, K. (2013). Apps for mathematics learning: A review of ‘educational’ apps from the iTunes App Store. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow. Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 378–385). MERGA.
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511. https://doi.org/10.1080/07370000802177235
Hirsh-Pasek, K., Zosh, J. M., Golinkoff, R. M., Gray, J. H., Robb, M. B., & Kaufman, J. (2015). Putting education in “educational” apps: Lessons from the science of learning. Psychological Science in the Public Interest, 16(1), 3–34. https://doi.org/10.1177/1529100615569721
Hourcade, J. P. (2008). Interaction design and children. Foundations and Trends® in Human—Computer Interaction, 1(4), 277–392. https://doi.org/10.1177/00222194050380040901
Joyce, B., Weil, M., & Showers, B. (1992). Models of teaching (4th ed.). Boston: Allyn & Bacon.
Kafai, Y. B. (2016). From computational thinking to computational participation in K–12 education. Communications of the ACM, 59(8), 26–27. https://doi.org/10.1145/2955114
Kalchman, M., Moss, J., & Case, R. (2001). Psychological models for the development of mathematical understanding: Rational numbers and functions. In S. M. Carver & D. Klahr (Eds.), Cognition and instruction: Twenty-five years of progress (pp. 1–38). Erlbaum.
Kato, P. M., Cole, S. W., Bradlyn, A. S., & Pollock, B. H. (2008). A video game improves behavioral outcomes in adolescents and young adults with cancer: A randomized trial. Pediatrics, 122(2), e305–e317. https://doi.org/10.1542/peds.2007-3134
Kaufmann, L., Koppelstaetter, F., Siedentopf, C., Haala, I., Haberlandt, E., Zimmerhackl, L. B., ... Ischebeck, A. (2006). Neural correlates of the number–size interference task in children. Neuroreport, 17(6), 587
Ke, F. (2016). Designing and integrating purposeful learning in game play: A systematic review. Educational Technology Research and Development, 64(2), 219–244. https://doi.org/10.1007/s11423-015-9418-1
Kebritchi, M., & Hirumi, A. (2008). Examining the pedagogical foundations of modern educational computer games. Computers & Education, 51(4), 1729–1743. https://doi.org/10.1016/j.compedu.2008.05.004
Kloos, H., & Van Orden, G. C. (2005). Can a preschooler’s mistaken belief benefit learning? Swiss Journal of Psychology, 64(3), 195–205. https://doi.org/10.1024/1421-0185.64.3.195
Ku, O., Chen, S. Y., Wu, D. H., Lao, A. C., & Chan, T. W. (2014). The effects of game-based learning on mathematical confidence and performance: High ability vs. low ability. Journal of Educational Technology & Society, 17(3), 65–78.
Larkin, K. (2015). “An app! an app! my kingdom for an app”: An 18-month quest to determine whether apps support mathematical knowledge building. Digital games and mathematics learning (pp. 251–276). Springer. https://doi.org/10.1007/978-94-017-9517-3_13
Laurillard, D. (2016). Learning number sense through digital games with intrinsic feedback. Australasian Journal of Educational Technology. https://doi.org/10.14742/ajet.3116
Libertus, M. E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14(6), 1292–1300. https://doi.org/10.1111/j.1467-7687.2011.01080.x
Martens, M., Rinnert, G. C., & Andersen, C. (2018). Child-centered design: Developing an inclusive letter writing app. Frontiers in Psychology, 6(9), 2277. https://doi.org/10.3389/fpsyg.2018.02277
Matejko, A. A., & Ansari, D. (2016). Trajectories of symbolic and non-symbolic magnitude processing in the first year of formal schooling. PLoS ONE, 11(3), e0149863. https://doi.org/10.1371/journal.pone.0149863
Mayer, R. E. (2014). Computer games for learning: An evidence-based approach. The MIT Press.
McEwen, R. N., & Dubé, A. K. (2015). Engaging or distracting: Children’s tablet computer use in education. Journal of Educational Technology & Society, 18(4), 9–23.
McEwen, R., & Dubé, A. K. (2016). Intuitive or Idiomatic? An information studies and cognitive psychology study of child-tablet computer interaction. Journal of the Association for Information Science and Technology, 67, 1169–1181.
McEwen, R., & Dubé, A. K. (2017). Understanding tablets from early childhood to adulthood: Encounters with touch technology. Routledge. https://doi.org/10.4324/9781315389486
Melhuish, K., & Falloon, G. (2010). Looking to the future: M-learning with the iPad. Computers in New Zealand Schools: Learning, Leading, Technology, 22, 1–16.
Mera, C., Ruiz, G., Aguilar, M., Aragón, E., Delgado, C., Menacho, I., ... Navarro, J. I. (2019). Coming together: R&D and children’s entertainment company in designing apps for learning early Math. Frontiers in Psychology, 9, 2751. https://doi.org/10.3389/fpsyg.2018.02751
Merkley, R., & Ansari, D. (2010). Using eye tracking to study numerical cognition: The case of the ratio effect. Experimental Brain Research, 206(4), 455–460. https://doi.org/10.1007/s00221-010-2419-8
Moss, J., Bruce, C. D., & Bobis, J. (2016). Young children’s access to powerful mathematical ideas: A review of current challenges and new developments in the early years. In L. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 153–190). Routledge.
Moyer-Packenham, S., Salkind, G., & Bolyard, J. J. (2008). Virtual manipulatives used by K-8 teachers for mathematics instruction: The influence of mathematical, cognitive, and pedagogical fidelity. Contemporary Issues in Technology and Teacher Education, 8(3), 202–218.
Mozelius, P., Fagerström, A., & Söderquist, M. (2017). Motivating factors and tangential learning for knowledge acquisition in educational games. Electronic Journal of e-Learning, 15(4), 343–354.
Mussolin, C., Noël, M. P., Pesenti, M., Grandin, C., & De Volder, A. (2013). Neural correlates of the numerical distance effect in children. Frontiers in Psychology, 4, 663. https://doi.org/10.3389/fpsyg.2013.00663
Naismith, L., Lonsdale, P., Vavoula, G., & Sharples, M. (2004). ‘Mobile technologies and learning’ in futurelab literature review series. Report No. 11, Futurelab. NESTA (National Endowment for Science Technology and the Arts), Bristol, UK.
Odic, D., Hock, H., & Halberda, J. (2014). Hysteresis affects approximate number discrimination in young children. Journal of Experimental Psychology, 143(1), 255. https://doi.org/10.1037/a0030825
Paas, F., Renkl, A., & Sweller, J. (2004). Cognitive load theory: Instructional implications of the interaction between information structures and cognitive architecture. Instructional Science, 32(1), 1–8.
Patino, A., Romero, M., & Proulx, J. N. (2016). Analysis of game and learning mechanics according to the learning theories. 2016 8th International conference on games and virtual worlds for serious applications (VS-GAMES) (pp. 1–4). IEEE. https://doi.org/10.1109/VS-GAMES.2016.7590337
Pham, X. L., & Chen, G. D. (2019). PACARD: A New interface to increase mobile learning app engagement, distributed through App Stores. Journal of Educational Computing Research, 57(3), 618–645. https://doi.org/10.1177/0735633118756298
Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., ... Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33-41. https://doi.org/10.1016/j.cognition.2010.03.012
Pilli, O., & Aksu, M. (2013). The effects of computer-assisted instruction on the achievement, attitudes and retention of fourth grade mathematics students in North Cyprus. Computers & Education, 62, 62–71. https://doi.org/10.1016/j.compedu.2012.10.010
Plass, J. L., Frye, J., Kinzer, C., Homer, B., & Perlin, K. (2011). Learning mechanics and assessment mechanics for games for learning (G4LI White Paper 01–2011). Games for Learning Institute. https://doi.org/10.13140/2.1.3127.1201
Plowman, L., Stevenson, O., Stephen, C., & McPake, J. (2012). Preschool children’s learning with technology at home. Computers & Education, 59(1), 30–37. https://doi.org/10.1016/j.compedu.2011.11.014
Porter, J. (2018). Entering Aladdin’s cave: Developing an app for children with Down syndrome. Journal of Computer Assisted Learning, 34(4), 429–439. https://doi.org/10.1111/jcal.12246
Proulx, J.-N., Romero, M., & Arnab, S. (2016). Learning mechanics and game mechanics under the perspective of self-determination theory to foster motivation in digital game-based learning. Simulation & Gaming, 48(1), 81–97. https://doi.org/10.1177/1046878116674399
Salen, K., Tekinbaş, K. S., & Zimmerman, E. (2004). Rules of play: Game design fundamentals. MIT press.
Sarnecka, B. W., & Carey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition, 108(3), 662–674. https://doi.org/10.1016/j.cognition.2008.05.007
Schaefer, C., & Millman, H. L. (1994). How to help children with common problems. Jason Aronson Inc.
Senge, P. M. (2006). The fifth discipline: The art and practice of the learning organization. Broadway Business.
Shuler, C., Levine, Z., & Ree, J. (2012). iLearn II An analysis of the education category of Apple’s app store. The Joan Ganz Cooney Center.
Sicart, M. (2008). Defining game mechanics. Game Studies, 8(2), 1–14.
Siegler, R. S. (2016). Magnitude knowledge: The common core of numerical development. Developmental Science, 19(3), 341–361. https://doi.org/10.1111/desc.12395
Siegler, R. S., & Lortie-Forgues, H. (2014). An integrative theory of numerical development. Child Development Perspectives, 8(3), 144–150. https://doi.org/10.1111/cdep.12077
Skinner, B. F. (1968). The technology of teaching. Appleton-Century-Crofts.
Slavin, R. E., & Lake, C. (2008). Effective programs in elementary mathematics: A best-evidence synthesis. Review of Educational Research, 78(3), 427–515. https://doi.org/10.3102/0034654308317473
Statista Research Development. (July 14, 2021). Most popular Apple App Store categories in June 2021, by share of available app. Retrieved from https://www.statista.com/statistics/270291/popular-categories-in-the-app-store/
Tsay, C.H.-H., Kofinas, A., & Luo, J. (2018). Enhancing student learning experience with technology-mediated gamification: An empirical study. Computers & Education, 121, 1–17. https://doi.org/10.1016/j.compedu.2018.01.009
Tucker, S. I., Moyer-Packenham, P. S., Shumway, J. F., & Jordan, K. E. (2016). Zooming in on children’s thinking: How a number line app revealed, concealed, and developed children’s number understanding. Australian Primary Mathematics Classroom, 21(1), 23.
Vatavu, R. D., Cramariuc, G., & Schipor, D. M. (2015). Touch interaction for children aged 3 to 6 years: Experimental findings and relationship to motor skills. International Journal of Human—Computer Studies, 74, 54–76. https://doi.org/10.1016/j.ijhcs.2014.10.007
Warwick, J. (2008). Mathematical self-efficacy and student engagement in the mathematics classroom. MSOR Connections, 8(3), 31–37. https://doi.org/10.11120/msor.2008.08030031
Willoughby, D., Evans, M. A., & Nowak, S. (2015). Do ABC eBooks boost engagement and learning in preschoolers? An experimental study comparing eBooks with paper ABC and storybook controls. Computers & Education, 82, 107–117. https://doi.org/10.1016/j.compedu.2014.11.008
Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. Human behavior, learning, and the developing brain: Atypical Development (Vol. 2, pp. 212–237). Guilford Press.
Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006). Principles underlying the design of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioural and Brain Functions, 2, 1–14.
Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24(2), 220–251. https://doi.org/10.1016/0010-0285(92)90008-P
Zichermann, G., & Cunningham, C. (2011). Gamification by design: Implementing game mechanics in web and mobile apps. O’Reilly Media Inc.
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This study was funded by Social Sciences and Humanities Research Council of Canada (Grant No. 430-2017-00230).
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Alam, S.S., Dubé, A.K. Theoretically driven educational app design: the creation of a mathematics app. Education Tech Research Dev 70, 1305–1327 (2022). https://doi.org/10.1007/s11423-022-10109-9
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DOI: https://doi.org/10.1007/s11423-022-10109-9