“Failure is the highway to success,” as John Keats famously didn’t say, seems a popular aphorism in motivational courses today.

But can exposing students to potential failure, or common errors, actually be helpful in learning? Or are we better off preventing them from getting things wrong altogether?

Behaviourist theories suggest that exposure to errors may lead students to make those errors again, and make learning the correct approaches more difficult.

However, a review by Janet Metcalfe (2017) argues that concerns regarding exposure to errors might be overstated. Her review indicates that so-called “errorful learning”, followed by corrective feedback, is actually beneficial to learning.

She stresses that corrective feedback, including analysis of the reasoning leading up to the mistake, is crucial. The beneficial effects are particularly strong, she found, when individuals strongly believe that their error is correct.

In other words, errors committed with high confidence are corrected more easily than errors committed with low confidence.

Metcalfe concludes: “Errors enhance later memory for, and generation of, the correct responses, facilitate active learning, stimulate the learner to direct attention appropriately, and inform the teacher of where to focus teaching.”

There are several mechanisms that try to explain why this might be the case.

First, there is a natural human motivation to seek consistency in contradictory ideas.

A second factor is negativity bias, which demonstrates that humans are naturally more inclined towards attending to negative information over positive information, and that the clash of conflicting information (eg, through corrective feedback) can lead to heightened attention and improvements in memory for the new information.

So, if encountering errors - or having them corrected - is positive for learning, when is it best to expose students to them?

Some researchers will say that you should only do this after the correct knowledge is secure. Others, like Metcalfe, argue that instructional materials that target errors commonly made in the early stages of skill acquisition are likely to be more appropriate and useful to students in that stage, as they help with recognition of errors.

Christina Barbieri and Julie Booth (2020) tried out a slightly different approach to learning from errors. They conducted a study that looked at quadratic equations, distinguishing between the features of such equations and the skill of actually solving them.

In the study, more than 200 students in a secondary school were randomly assigned to four conditions. One “business as usual” problem-solving group served as a control group. Then there was one with a “correct worked example”. Two further conditions were “errorful”, either displaying errors and asking students to explain, or displaying correct solutions and priming students to reflect on potential errors.

The conclusion over which was best was nuanced, but certainly the latter approach could solve the timing dilemma mentioned above: the correct solution is front and centre, but thinking about potential errors helps to strengthen learning.

What is clear from both Metcalfe’s work and the study above is that common (mathematical) errors are a useful learning tool, and discussion of them should not be avoided. Rather, errors should be incorporated into regular classroom practice.

So, it may actually be worthwhile to allow - and even encourage - students to commit and correct errors while they are in low-stakes learning situations, rather than to avoid errors at all costs.

Christian Bokhove is associate professor in maths education at the University of Southampton

This article originally appeared in the 27 November 2020 issue under the headline “Why trying to avoid errors is a mistake”