Mathematical skills > Problem solving

Question 46
How can we assess problem solving using e-assessment?

How to assess mathematical problem solving using e-assessment is intimately tied into how to assess mathematical problem solving more generally. Really this is a question of task-design and how we can create tasks fine-tuned to the capabilities of e-assessment tools.

What motivates this question?

This question is somewhat complicated by the common use of ‘problem’ as a synonym for ‘question’ in mathematics assessment literature. Presumably the question here means ‘problem solving’ as the more open-ended, creative approach to solving unfamiliar problems. So we might refer to a student repeating techniques and methods as they have been shown as completing ‘exercises’ and reserve ‘problem’ for this.

Beevers and Paterson (2003) say e-assessment may be too structured to test problem-solving abilities because students do not have “freedom to work…in a variety of ways, all equally correct”. Marking extended work where students do not feel restrictions on their work is very difficult (Sangwin, 2015; Harjula, 2017).

Combined tests may be an option, where e-assessment is used for some routine calculations within a larger piece of work.

What might an answer look like?

Some thoughts on how to assess mathematical proof were discussed recently in Sangwin and Bickerton (2021). This rather practical paper contains many ideas, but these individual ideas currently lack research investigating the efficacy of these ideas. An answer to this research question might look like the counterpart to this paper in the context of problem solving, but with some specific research studies looking at individual recommendations. An anwer might also have some specific examples of task sequences.

References

Beevers, C.E. & Paterson, J.S. (2003). Automatic assessment of problem-solving skills in mathematics. Active Learning in Higher Education, 4(2), 127-144. https://doi.org/10.1177/1469787403004002002

Harjula, M. (2017). STACK with state. MSOR Connections, 15(2), 60-69. https://doi.org/10.21100/msor.v15i2.408

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

Sangwin, C. J. and Bickerton, R. (2021). Practical Online Assessment of Mathematical Proof. International Journal of Mathematical Education in Science and Technology. http://arxiv.org/abs/2006.01581