Antje and David Leigh-Lancaster, Leigh-Lancaster Consulting 

Introduction

Many students worry about getting an ‘incorrect answer' when working through mathematics problems. This fear of failure can lead to a reluctance to take risks, increased maths anxiety and disengagement. Creating a classroom environment where errors are seen as a natural part of learning – and handled positively with constructive feedback – can help address some of these issues. 

Emerging research suggests that we may need to reconsider how we think about errors altogether, as it’s been found they can be more beneficial for learning than previously thought. It seems intentionally having students make and correct errors in low-stakes learning contexts can significantly enhance learning. This article explores these findings. 

In 2021, Sarah Shi Hui Wong and Stephen Wee Hun Lim first published their research findings in their paper, ‘The derring effect: Deliberate errors enhance learning’.  

The research involved conducting three separate experiments, with learners engaging in a variety of educationally relevant tasks within each experiment. 

Rank the following learning scenarios

Below are three learning scenarios (A, B and C), listed in no particular order. How would you rank them from 1: greatest impact on recall and retention to 3: least impact on recall and retention? 

Note that while the 2021 research related to learning scientific terms and their definitions, the example for this article has been changed to a mathematics-related statement: ‘The sum of the interior angles of a triangle is 180 degrees’. 

Learning scenario A

Students: 

• copy the statement 
• underline key words and main ideas 
• create an alternative conceptually correct statement. 

Example statement: The sum of the interior angles of a triangle is 180 degrees. 

Alternative statement: The three different angles inside a triangle always sum to 180 degrees. 

Learning scenario B 

Students: 

• rewrite the statement and deliberately make a conceptually believable error 
• correct the deliberate error. 

Example statement with deliberate error: The sum of the interior angles of any polygon is 180 degrees. 

Correcting the deliberate error: The sum of the interior angles of any polygon (triangle) is 180 degrees. 

Learning scenario C  

This is the same as Learning scenario A, with the additional task that students also generate a one-sentence example that highlights or applies the concept in a real-world setting. 

Example statement: The sum of the interior angles of a triangle is 180 degrees. 

Alternative statement: The three different angles inside a triangle always sum to 180 degrees. 

Real-world example: A rope supports a tent pole forming a right-angled triangle with angles 90, 50 and 40 degrees. 

Research findings 

The research findings placed the three learning scenario rankings from 1 to 3 as follows: Scenario B, C and then A. It is interesting that even when participants were actively engaged in generating their own real-world examples, the deliberate act of making and then correcting errors resulted in a better learning outcome. The researchers termed this phenomenon the derring (deliberately erring) effect – that is, deliberately committing errors even when one already knows the correct answer. 

They hypothesised that this is likely because deliberately making errors can help students focus better on the correction, making it more memorable. When students intentionally make an error, the correct answer stands out more, helping them to remember it better than if they hadn't made an error first. Further research is needed to fully understand how this process works. 

In 2023, Sarah Shi Hui Wong published additional findings which highlighted that the derring effect not only improved recall and retention but also improved the ability to apply the learned content to different subjects.  

Applying these findings in the classroom 

A natural place to have students deliberately make and then correct errors is during the practice, review and consolidation stages of a learning sequence.

A good starting point is to focus on common errors and areas where you know students often have misconceptions.

Example 1: adding fractions

Start with 15 + 25 = 35.

 Likely deliberate student errors (LDSE):

•  310 (adding denominators) 
•  225 (treating it as multiplication of fractions) 

Example 2: multiplying decimals by 10 

Start with 9.5 x 10 = 95

LDSE: 

• 9.50 (simply ‘adding a zero’)
• 90.5 (separating integer and decimal parts) 
• 950 (ignoring the decimal point) 

Example 3: solving equations 

Start with 2x - 3 = 13

LDSE:

• 2x = 13 - 3 (not adding 3 to both sides)
• x = 2 x 16 (not dividing by 2)
• x – 3 = 13 2 (not applying the division to all terms) 

Example 4: expanding algebraic expressions 

Start with (x - 5)² = x² - 10x + 25

LDSE: 

• x² + 25 (forgetting to fully expand, leaving out middle terms) 
• (x - 5)² = x² - 10x - 25 (incorrectly multiplying negative integers) 

Along with the benefit for students, this process can provide teachers with insights on the depth and robustness of students’ understanding in relation to the deliberate error they selected. 

Implementation considerations 

Self-made errors: It is more effective when a student creates their own deliberate errors and corrections rather than being shown someone else's errors. 

Conceptually believable errors: Deliberate errors should be conceptually believable, meaning they are errors in understanding, not simple mistakes in calculations or procedures. 

Low-stakes contexts: Use this approach in low-stakes learning contexts. 

Explain the strategy: Be explicit with students about the strategy and its benefits, as it may initially seem counterintuitive. 

Reduce emotional impact of errors: Deliberately creating errors can minimise negative emotional responses to making errors in general. 

Consider learner needs: Research suggests an errorless learning approach may be more suitable for learners on the autism spectrum, who may struggle with deliberate error strategies due to their preference for rule adherence, and the potential for negative behaviours in response to perceived failures. 

Key references

Mera, Y., Rodríguez, G. & Marin-Garcia, E. (2022). Unraveling the benefits of experiencing errors during learning: Definition, modulating factors, and explanatory theories. Psychonomic Bulletin & Review, 29, 753–765. 

Wong, S. S. H. & Lim, S. W. H. (2022). The derring effect: Deliberate errors enhance learning. Journal of Experimental Psychology: General, 151(1), 25–40. 

Wong, S. S. H. (2023). Deliberate erring improves far transfer of learning more than errorless elaboration and spotting and correcting others’ errors. Educational Psychology Review, 35, 16. 

 

The following reference provides an overview of key research and findings on the role of errors in learning. 

Metcalfe, J. (2017). Learning from errors. Annual Review of Psychology, 68, 465–489. 

Rushton, S.J (2018). Teaching and learning mathematics through error analysis. Fields Math Educ J 3, 4.