Mathematical skills > Assessment of proof

Question 51
What types/forms of proof-comprehension-related questions can be meaningfully assessed using currently available e-assessment platforms?

• Ben Davies

What motivates this question?

This question is motivated by the need to aid practitioners in developing pedagogically-robust assessment tools for their own classroom.

The framework of Mejía-Ramos et al. (2017) provides a model of the types of questions that can be asked, from the perspective of paper-based tests. Bickerton and Sangwin (2021) made some further suggestions of practical approaches that can be taken with current e-assessment tools.

What might an answer look like?

One answer to this question might focus on design principles for writing automated assessment questions in this area. Researchers might draw on the Design-based Research methodology to iteratively develop theoretical principles and practical artefacts in a cyclic process. Ruth Reynolds and Ben Davies (University College London) have proposed a workshop to this end at the 4th International STACK Conference hosted by TTK University of Applied Sciences in April 2021.

Another answer to this question might focus on convergent validity, comparing student performance on various question formss/types to other existing measures of students’ understanding (see Q49).

Related questions

• This is a specific case of the more general question of automating assessment of proof-based mathematics, Q49: How can the assessment of proof be automated?

• The issue of task design principles is also highlighted in:

  • Q22: What principles should inform the design of e-assessment tasks?
  • Q23: E-assessment task designers often convert questions that could be asked on a traditional pen and paper exam: what are the implications, technicalities, affordances and drawbacks of this approach?

• The question of convergent validity is related to Q36: To what extent do existing e-assessments provide reliable measures of mathematical understanding, as might otherwise be measured by traditional exams?

References

Bickerton, R. and Sangwin, C (2021). Practical online assessment of mathematical proof. International Journal of Mathematical Education in Science and Technology, 1-24. https://doi.org/10.1080/0020739X.2021.1896813

Mejía-Ramos, P., Lew, K., de la Torre, J. & Weber, K. (2017). Developing and validating proof comprehension tests in undergraduate mathematics, Research in Mathematics Education, 19:2, 130-146, https://doi.org/10.1080/14794802.2017.1325776