Student interactions with e-assessment > Student behaviour

Question 14
To what extent does repeated practice on randomized e-assessment tasks encourage mathematics students to discover deep links between ideas?

• Tim Lowe
• Peter Rowlett
• John Meyer
• George Kinnear

E-assessment systems allow the possiility of randomising question parameters and offering different students different variants of questions, or indeed different question variants to the same student for repeated practice. Does such practice promote deep learning of the concepts, or does is simply promote “pattern spotting”?

What motivates this question?

Martin and Greenhow (2004) say repeated practice on similar questions with study of resulting feedback allows students to develop deep understanding, by learning what underlies a question type. However, Rønning (2017) says students experiment by trying out different variations on their input when it is marked incorrect, suggesting this does not encourage deep learning. Can experimenting with input in an e-assessment system develop conceptual understanding, and, if so, how? It is claimed by some that immediate feedback decreases students’ independence, need to check their own answers and control of their learning. How do we avoid immediate feedback producing dependency among students when we are trying to develop independent learners?

Lowe and Mestel (2020) note that a student taking repeated parameterised version of a question stated that “I think that answering them repeatably allows to get a view on a broader picture behind a problem, instead of focusing on the calculation techniques, which become more obvious then.” This is related to ideas from variation theory, and the observation that “learners will notice and generalize from patterns and relationships between what aspects vary and what aspects are invariant” (Watson, 2017, p. 85). However, it should be noted that in discussions of variation theory, the way that tasks are changed “is not random but relates closely to the concepts or conventions being introduced” (Watson, 2017, p. 86). Thus, if the goal is to prompt learners to recognise particular ideas, then relying on randomisation to provide repeated practice could be less effective than a carefully-designed sequence of tasks.

What might an answer look like?

This may involve interviews with students who have used system permitted mulitple attempts at variants of questions to establish the insight they gained from the experience, and the reasons for attempting the question multiple times.

This question should also be considered in light of the literature on interleaving (e.g. Rohrer, Dedrick & Stershic, 2015), and, literature regarding repeated practice for developing a deep understanding of mathematical concepts (independent of the e-assessment format, e.g. Anderson, Reder & Simon, 1999).

An experimental approach could be possible; for instance, comparing the learning outcomes of students who work on randomised versions of a problem, with students who work through a similar number of problems that have been carefully designed with ideas from variation theory in mind.

Related questions

• The issue of randomisation/parameterisation is related to:
  • Q25: What effect does the use of random versions of a question (e.g. using parameterised values) have on the outcomes of e-assessment?
  • Q24: To what extent does the randomisation of question parameters, which makes sharing answers between students difficult, adequately address plagiarism?
  • Q16: What should students be encouraged to do following success in e-assessment?
  • Q15: How do students engage with automated feedback? What differences (if any) can be identified with how they would respond to feedback from a teacher?
• The way students make use of repeated practice with random variants is relevant to Q13: How do students interact with an e-assessment system?

References

Anderson, J. R., Reder, L. M., & Simon, H. A. (1999). Applications and misapplications of cognitive psychology to mathematics education. ERIC. https://files.eric.ed.gov/fulltext/ED439007.pdf

Lowe, T. W., & Mestel, B. D. (2020). Using STACK to support student learning at masters level: a case study. Teaching Mathematics and its Applications: An International Journal of the IMA, 39(2), 61-70. https://doi.org/10.1093/teamat/hrz001

Martin, E. & Greenhow, M. (2004). Setting objective tests in linear algebra using QM Perception. MSOR Connections, 4(3), 49-53.

Rønning, F. (2017). Influence of computer-aided assessment on ways of working with mathematics. Teaching Mathematics and its Applications, 36(2), 94-107. https://doi.org/10.1093/teamat/hrx001

Rohrer, D., Dedrick, R. F., & Stershic, S. (2015). Interleaved practice improves mathematics learning. Journal of Educational Psychology, 107(3), 900. https://doi.org/10.1037/edu0000001

Watson, A. (2017). Pedagogy of Variations. In R. Huang & Y. Li (Eds.), Teaching and Learning Mathematics through Variation: Confucian Heritage Meets Western Theories (pp. 85–103). SensePublishers. https://doi.org/10.1007/978-94-6300-782-5_5