Abstract
Effective communication and collaboration of symbolic and quantitative knowledge requires the digitization of mathematical expressions. The multi-dimensionality of mathematical notation creates a challenge for mathematical software editors. There are two different approaches for handling the multi-dimensionality of mathematical notation: either using a two-dimensional writing environment in which symbols can be placed freely (unit-based) or using an environment in which single-dimensional structural elements can be nested (structure-based). The structure-based approach constrains how users write expressions. These constraints may conflict with how mathematics is normally written. A study is reported that examines how users write mathematical expressions using two graphic based editors: one that is structure-based and one that allows the free-form manipulation of selected symbols in a diagrammatic fashion (unit-based). The results are contrasted with how users handwrite mathematics in a physical medium and implications are drawn for future software design.
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References
Carlisle, D., Ion, P., Miner, R., Poppelier, N., et al.: Mathematical Markup Language (MathML) Version 2.0. W3C Recommendation (February 21, 2001) http://www.w3.org/TR/2001/REC-MathML2-20010221/
Edwards, L.D.: Embodying mathematics and science: Microworlds as representations. Journal of mathematical Behavior 17, 53–78 (1998)
Gibson, J.: The Ecological Approach to Visual Perception. Lawrence Erblbaum Associates, Inc., Hillsdale (1986)
Kadar, E.E., Effken, J.: From discrete actors to goal-directed actions: Toward a process-based methodology for psychology. Philosophical Psychology 18, 353–382 (2005)
Knuth, D.E.: The TeX book. Addison-Wesley, Reading (1984)
Lakoff, G., Núñez, R.: Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. Basic Books, New York (2000)
Landy, D., Goldstone, R.L.: How abstract is symbolic thought? Journal of Experimental Psychology 33, 720–733 (2007)
Landy, D., Goldstone, R.L.: Formal notations are diagrams: Evidence from a production task. Memory and Cognition 35(8), 2033–2040 (2007)
Nakano, Y., Murao, H.: BrEdiMa: Yet Another Web-browser Tool for Editing Mathematical Expressions. In: Proceedings of MathUI 2006 (2006) (online)
O’Malley, S., Reynolds, M.G., Stolz, J.A., Besner, D.: Reading aloud is not automatic: Lexical and sub-lexical spelling to sound translation use central attention. Journal of Experimental Psychology Learning Memory and Cognition 34, 422–429 (2008)
Padovani, L., Solmi, R.: An Investigation on the Dynamics of Direct-Manipulation Editors for Mathematics. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 302–316. Springer, Heidelberg (2004)
Pollanen, M., Wisniewski, T., Yu, X.: Xpress: A Novice Interface for the Real-Time Communication of Mathematical Expressions. In: Proceedings of MathUI 2007 (2007) (online)
Reynolds, M., Besner, D.: Reading aloud is not automatic: Phonological recoding and lexical activation use central processing capacity. Journal of Experimental Psychology: Human Perception and Performance 32, 799–810 (2006)
Roberts, T.L., Moran, T.P.: The evaluation of text editors: methodology and empirical results. Communications of the ACM 26, 265–283 (1983)
Smithies, S., Novins, K., Arvo, J.: Handwriting-Based Equation Editor. In: Proceedings of Graphics Interface 1999, pp. 84–91 (1999)
Vicente, K.: The Human Factor: Revolutionizing the Way People Live with Technology. Knopf, Toronto (2003)
Zanibbi, R., Blostein, D., Cordy, J.R.: Directions in Recognizing Tabular Structures of Handwritten Mathematics Notation. In: Proc. Fourth Int’l IAPR Workshop on Graphics Recognition, pp. 493–499 (2001)
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Gozli, D.G., Pollanen, M., Reynolds, M. (2009). The Characteristics of Writing Environments for Mathematics: Behavioral Consequences and Implications for Software Design and Usability. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds) Intelligent Computer Mathematics. CICM 2009. Lecture Notes in Computer Science(), vol 5625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02614-0_26
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DOI: https://doi.org/10.1007/978-3-642-02614-0_26
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