Affordances offered by e-assessment tools > Free-form student input

Question 39
What methods are available for student input of mathematics?

Common approaches include typing mathematics, often using the syntax of an underlying CAS, or a menu-driven system. These can be difficult for students to learn and are not well-aligned to the process of producing mathematics offline. It may be worthwhile investigating alternative methods for input of mathematics. Such methods might include the following.

  • Typed expressions.
  • Drag and drop equation editors, including special mathematical symbols.
  • Optical character recognition of handwriting.
  • Mechanisms for encoding the meaning of a complete mathematical agrument, including the logic of deduction.

What motivates this question?

An informal linear syntax for mathematics is impossible to precisely define (Sangwin, 2015), so systems typically use some non-standard syntax (Lawson, 2002), the mathematical typesetting language LaTeX (Foster, Perfect & Youd, 2012) or the syntax of an underlying CAS.

An answer which is mathematically correct may be marked incorrect due to syntax issues. Jones (2008) points out that the student may not know whether the problem is mathematical or typographical. Approaches to avoid such errors impacting marks include the e-assessment system rejecting inproper input, use of practice questions or a process called “double submission”, in which input is interpreted and displayed in two-dimensional format for checking by the student before submission (Sangwin, 2015). Some systems build up as the user types it (Foster et al., 2012). These methods are somewhat adequate, but clearly present a barrier to engagement for students and risk adding extra learning requirements unrelated to the assessment objectives (Lawson, 2002).

There is interesting work in touch interfaces for mathematics following approaches used for non-Latin alphabets (Nakamura & Nakahara, 2017; Shirai & Fukui, 2017) and in converting hand-written mathemaatics into computer input (Pacheco-Venegas et al., 2015). These topics should be investigated for more recent references. Recent developments in handwriting recognition apps such as Mathpix and photomath show promise. Speech should also be investigated.

What might an answer look like?

A desk research project could usefully investigate the current state of the literature and test available software for mathematics input and the capabilities of current e-assessment systems to take input from such software.

References

Foster, B., Perfect, C. & Youd, A. (2012). A completely client-side approach to e-assessment and e-learning of mathematics and statistics. International Journal of e-Assessment, 2(2). Retrieved from http://journals.sfu.ca/ijea/index.php/journal/article/viewFile/35/37

Jones, I.S. (2008). Computer-aided assessment questions in engineering mathematics using MapleTA. International Journal of Mathematical Education in Science and Technology, 39(3), 341-356. https://doi.org/10.1080/00207390701734523

Lawson, D. (2002). Computer-aided assessment in mathematics: Panacea or propaganda? International Journal of Innovation in Science and Mathematics Education, 9(1). Retrieved from https://openjournals.library.sydney.edu.au/index.php/CAL/article/view/6095

Nakamura, Y. & Nakahara, T. (2017). A New Mathematics Input Interface with Flick Operation for Mobile Devices. MSOR Connections, 15(2), 76-82. https://doi.org/10.21100/msor.v15i2.413

Pacheco-Venegas, N.B., López, G. & Andrade-Aréchiga, M. (2015). Conceptualization, development and implementation of a web-based system for automatic evaluation of mathematical expressions. Computers & Education, 88, 15-28. https://doi.org/10.1016/j.compedu.2015.03.021

Sangwin, C. (2015). Computer Aided Assessment of Mathematics Using STACK. In S.J. Cho (Ed.), Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 698-713). Cham: Springer. https://doi.org/10.1007/978-3-319-17187-6_39

Shirai, S. & Fukui, T. (2017). MathTOUCH: Mathematical Input Interface for E-Assessment Systems. MSOR Connections, 15(2), 70-75. https://doi.org/10.21100/msor.v15i2.415