Errors and feedback > Optimising feedback efforts

Question 11
What are the relative merits of addressing student errors up-front in the teaching compared with using e-assessment to detect and give feedback on errors after they are made?

What motivates this question?

Might it be more efficient overall to avoid attempting to diagnose and instead treat everyone? In medicine we diagnose rare things but we give everyone a vaccination.

The “treat all” approach is being taken up by Foster et al. (2021) in their school mathematics curriculum design work:

“Rather than focusing on attempting to identify which particular students might show evidence of which particular misconceptions, in a ‘diagnose and treat’ model, we will instead largely adopt a ‘treat all’ approach, in which we will address the most common difficulties head-on with all students”

Foster et al. (2021) also argue that there may be benefits to discussing misconceptions up-front:

“an error that a student does not seem inclined to make today might be one that they make on a future occasion. Indeed, even where a student might never make a certain error, there may still be considerable value in including discussion of it within the mathematical narrative”

There is some support for this view in recent experimental psychology work, where the results suggested that “studying and explaining errors in the form of incorrect worked examples significantly improve students’ ability to solve quadratic equations in comparison to traditional practice problems alone” (Barbieri & Booth, 2020). However, in an experiment on number-line estimation that compared study of correct and incorrect worked examples alongside a third group who received feedback on their answers, it was found that study of correct worked examples and receiving feedback were both effective in improving performance, but study of incorrect worked examples was not (Fitzsimmons et al., 2021).

It should be noted that the “up-front” approach still leaves room for students to make errors and learn from them, unlike an “error avoidance” approach (Metcalfe, 2017).

What might an answer look like?

Experiments could be used to compare the two approaches in various topics and with different groups of students. One possible answer could be a selection of topics where the up-front approach has been found to be particularly efficient. The findings may also show where misconceptions are particularly persistent (e.g., Cangelosi et al., 2013), even after explicit up-front discussion, where diagnostic feedback may be most effective.

References

Barbieri, C. A., & Booth, J. L. (2020). Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge. Applied Cognitive Psychology, 34(4), 862-878. https://doi.org/10.1002/acp.3663

Cangelosi, R., Madrid, S., Cooper, S., Olson, J., & Hartter, B. (2013). The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions. The Journal of Mathematical Behavior, 32(1), 69–82. https://doi.org/10.1016/j.jmathb.2012.10.002

Fitzsimmons, C. J., Morehead, K., Thompson, C. A., Buerke, M., & Dunlosky, J. (2021). Can feedback, correct, and incorrect worked examples improve numerical magnitude estimation precision?. The Journal of Experimental Education, 1-26. https://doi.org/10.1080/00220973.2021.1891009

Foster, C., Francome, T., Hewitt, D., & Shore, C. (2021). Principles for the design of a fully-resourced, coherent, research-informed school mathematics curriculum. Journal of Curriculum Studies, 1–21. https://doi.org/10.1080/00220272.2021.1902569

Metcalfe, J. (2017). Learning from errors. Annual review of psychology, 68, 465-489. https://doi.org/10.1146/annurev-psych-010416-044022