Abstract
This essay highlights a rationale for pen and touch in K16 mathematics classrooms, arguing that digitizing mathematical cognition can promote learner flow. The personal computing and mobile technologies that have transformed society since the 1980s left a large element of mathematics learning, which relies on non-keyboard symbol systems and drawing, untouched in comparison to learning in disciplines that involve construction and manipulation of written text that can be expressed with a keyboard. Yet over the past decade pen and touch has gradually brought into the digital era that large fraction of K16 mathematics that relies on symbol and visual systems that exceed the representational capacity of the standard keyboard. It has become a portal for research in new forms of research and new forms of mathematical learning. The paper argues that learner flow can be promoted through pen and touch and identifies a three-tier initial taxonomy for classifying such applications.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Anderson, M.L.: Embodied cognition: a field guide. Artif. Intel. 149(1), 91–130 (2003)
Collins, A., Brown, J.S., Holum, A.: Cognitive apprenticeship: making thinking visible. Am. Educ. 15(3), 6–11 (1991)
Csikszentmihalyi, M.: Flow and the Psychology of Discovery and Invention. Harper Collins, New York (1996)
Hamilton, E.R.: Computer assisted instructional delivery system and method. US Patent 5,176,520 (1993)
Hamilton, E.: Remote sharing of electronic paper (slatemate®;). In: International Conference on Technology in Education (ICTE), London (1994)
Hamilton, E.R.: Computer assisted instructional delivery system and method. United Kingdom Patent 479408 (1999)
Hamilton, E.: Advancing a complex systems approach to personalized learning communities: bandwidth, sightlines, and teacher generativity. J. Interact. Learn. Res. 26(1), 89–104 (2015)
Hamilton, E., Kapenda, L., Mbasu, Z., Miranda, H., Ngololo, E., Ogwel, J.C., Stern, D.: A model and research agenda for teacher and student collaboration using pen-based tablets in digital media making in sub-Saharan Africa. In: Revolutionizing Education with Digital Ink, pp. 223–230. Springer International Publishing (2016)
Hamilton, E., Harding, N., Berque, D., Reed, R.: Tablet computing, creativity and teachers as applied microgenetic analysts: a paradigm shift in math teacher professional development. In: Impact of Pen-Based Technology on Education, pp. 47–56 (2010)
Hamilton, E., Hurford, A.: Combining collaborative workspaces with tablet computing: research in learner engagement and conditions of flow. In: 2007 37th Annual Frontiers In Education Conference-Global Engineering: Knowledge Without Borders, Opportunities Without Passports, pp. T3C–3. IEEE (2007)
Hamilton, E., Jago, M.: Toward a theory of personalized learning communities. In: Jacobson, M.J., Reimann, P. (eds.) Designs for Learning Environments of the Future, pp. 263–281. Springer, Boston (2010)
Hamilton, E., Kapenda, L., Mbasu, Z., Miranda, H., Ngololo, E., Ogwel, J.C., Stern, D.: A model and research agenda for teacher and student collaboration using pen-based tablets in digital media making in sub-Saharan Africa. In: Revolutionizing Education with Digital Ink, pp. 223–230. Springer International Publishing (2016)
Hiebert, J.: A theory of developing competence with written mathematical symbols. Educ. Stud. Math. 19(3), 333–355 (1988)
LeFevre, J.: Flow and the quality of experience during work and leisure. In: Csikszentmihalyi, M., Csikszentmihalyi, I.S. (eds.) Optimal Experience: Psychological Studies of Flow in Consciousness, pp. 307–318. Cambridge University Press, New York (1988)
Lesh, R., Hoover, M., Hole, B., Kelly, A., Post, T.: Principles for developing thought-revealing activities for students and teachers. In: Kelly, A.E., Lesh, R.A. (eds.) Handbook of Research Design in Mathematics and Science Education. Routledge, Abingdon (2000). Accessed 10 Nov 2017, Routledge Handbooks Online
Ma, J., Cole, R., Pellom, B., Ward, W., Wise, B.: Accurate visible speech synthesis based on concatenating variable length motion capture data. IEEE Trans. Vis. Comput. Graph. 12(2), 266–276 (2006)
Mangen, A., Velay, J.L.: The haptics of writing: cross-disciplinary explorations of the impact of writing technologies on the cognitive-sensorimotor processes involved in writing. In: Learning to Write Effectively: Current Trends in European Research, pp. 405–407. Brill, Bradford (2012)
Nakamura, J., Csikszentmihalyi, M.: The concept of flow. In: Csikszentmihalyi, M. (ed.) Flow and the Foundations of Positive Psychology, pp. 239–263. Springer, Dordrecht (2014)
O’Halloran, K.L.: Interdependence, interaction and metaphor in multisemiotic texts. Soc. Semiot. 9(3), 317–354 (1999)
O’Malley, C.: Design considerations for tangible and embodied learning. In: Proceedings of the 31st European Conference on Cognitive Ergonomics, p. 2. ACM (2013)
Radford, L.: The ethics of being and knowing: towards a cultural theory of learning. In: Semiotics in Mathematics Education: Epistemology, History, Classroom, and Culture, pp. 215–234. Sense, Rotterdam/Taipei (2008)
Shapiro, L.: Embodied Cognition. Routledge, New York (2010)
Acknowledgements
The author acknowledges the generous support of the US National Science Foundation, the US State Department, the US Department of Education, Microsoft Research, and Pepperdine University in the research reported here, which reflects the views only of the author.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Hamilton, E. (2017). Digitizing Mathematical Symbolism Through Pen and Touch Technology: A Beginning Taxonomy of Affordances for Learner Flow in Mathematics. In: Hammond, T., Adler, A., Prasad, M. (eds) Frontiers in Pen and Touch. Human–Computer Interaction Series. Springer, Cham. https://doi.org/10.1007/978-3-319-64239-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-64239-0_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64238-3
Online ISBN: 978-3-319-64239-0
eBook Packages: Computer ScienceComputer Science (R0)