# Creating a taxonomy of mathematical errors for undergraduate mathematics

Abstract: In this paper we develop a taxonomy of errors which undergraduate mathematics students may make when tackling mathematical problems. We believe that a taxonomy would be useful for staff in giving feedback to students, and would facilitate students’ higher-level understanding of the types of errors that they could make.

## Summary (2 min read)

### 1. Introduction

- And analysed for patterns so that teacher can then plan what potential remedial action will be necessary to correct any underlying misconceptions.
- On the other hand mathematics undergraduate students possess a strong mathematical ability and have chosen to study the subject further.
- This work was undertaken as part of an undergraduate summer project by the first author.

### 2. Human Error

- Errors can be made in one of two ways – either the plan itself may be inadequate, or else the execution of that plan may include actions that are unintentional and which do not lead to the desired outcome, as illustrated in figure 1.
- Rule-based mistakes occur when an individual wrongly modifies an established process.
- Whilst mistakes and skill based errors are defined as errors made in the individual’s cognitive stages, their behaviour may also be altered by the situation’s social context.
- Suppose a student was answering the question: Differentiate the function .
- A ‘routine violation’ could occur if a student had made the same error often enough so that they no longer realised it was an error, for example, writing for the derivative of .

### 3. Creating a Taxonomy of Mathematical Errors

- A taxonomy is the “theoretical study of classification, including its bases, principles, procedures and rules” (Simpson, 1961, p.11).
- There are a number of major styles of taxonomies used in research, but largely there is a strong relation between how research is conducted and the chosen taxonomy style (Senders and Moray, 1991).
- In other words, the errors of mathematics could be listed under the previously discussed error types.
- Using this method, one would start by first identifying the errors before compiling the headings for each section.
- The types of errors made in mathematical assignments can be very different from one another, giving a wide variety of possible mistakes.

### 4. Conclusion

- In this paper the authors have given a taxonomy of mathematical errors that has been informed by the literature on the different types of human error.
- This resource has the potential to decrease marking time by enabling tutors to quickly flag up general errors using the short codes for each error (e.g. S1), although it is likely that any feedback provided using the taxonomy would still need to be supplemented with some written comments to provide richer feedback.
- If this taxonomy was embedded at programme level and the feedback provided was recorded, then students could be provided with an overall picture summarising the frequency of the types of errors they make, with advice on how to move towards eliminating these errors where possible.
- It might also be possible to design a resource to help students engage with higher-level reflection upon the types of errors they make, and how they may reduce the probability of these errors occurring.

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465 citations

##### References

465 citations

### "Creating a taxonomy of mathematical..." refers methods in this paper

...A taxonomy is the “theoretical study of classification, including its bases, principles, procedures and rules” (Simpson, 1961, p.11)....

[...]

344 citations

### "Creating a taxonomy of mathematical..." refers background in this paper

...The first style is referred to as a taxonomy of cognitive mechanisms (Senders and Moray, 1991)....

[...]

...MSOR Connections 18(1) – journals.gre.ac.uk 41 There are a number of major styles of taxonomies used in research, but largely there is a strong relation between how research is conducted and the chosen taxonomy style (Senders and Moray, 1991)....

[...]

...uk 41 There are a number of major styles of taxonomies used in research, but largely there is a strong relation between how research is conducted and the chosen taxonomy style (Senders and Moray, 1991)....

[...]

...The second style of taxonomy is a phenomenological taxonomy (Senders and Moray, 1991)....

[...]

342 citations

### "Creating a taxonomy of mathematical..." refers background in this paper

...It is a way of classifying entities verifiable by observation (Bailey, 1994, p.6)....

[...]

...A successful taxonomy will provide classes that are both exhaustive (an appropriate class for each entity) and mutually exclusive (only one suitable class for each entity) (Bailey, 1994, p.3)....

[...]

148 citations

87 citations