The irrationality of quick maths

Why is being quick at maths associated with being good at maths? Dr Tom Hunt, Associate Professor of Psychology, and Steve Chinn, Visiting Professor, both at the University of Derby, explore ‘quick maths’ and its role in the world of mathematics.

It is part of our maths culture that being good at maths is synonymous with being quick with number problems and retrieving number facts from memory. As soon as children enter formal education, they begin to associate being quick at maths with praise from teachers. Yet, when teachers are asked why formal maths learning and assessment is so time-based, they often struggle to give a response. Often, they will resort to emphasising that formal assessments require them to teach in ways that encourage children to get faster and faster at retrieving numerical facts, particularly multiplication facts. 

Quick maths as a stressor

Sadly, there is plenty of empirical and anecdotal evidence that tells us just how stressful and anxiety-provoking quick-maths can be. For example, researchers interested in the human stress response have used timed mental arithmetic tasks to induce a stress reaction, including heightened psychophysiological reactivity. Paradoxically, competitive, timed testing is commonplace in the UK maths education system. A large-sample study of maths anxiety in secondary aged pupils (11 to 13 years old) in England, found that the item ‘having to work out answers to maths questions quickly’ was ranked as fifth out of 20 anxiety-provoking classroom experiences. Why would a known stressor be thought of as the most appropriate learning strategy? This important question is one that has not been suitably addressed. 

Questioning the status-quo

Rote (repeated) learning for speeded response is more a feature of maths than other subjects such as art. Rote learning of multiplication facts leads to a greater likelihood of retention in long-term memory, but for what percentage of children? Of course, speedy retrieval of those facts from memory can aid problem solving, but this demand can be counter-productive. In classrooms with a competitive ethos, children quickly identify perceived hierarchies of ability and will often refer to how quick their classmates are as a rationale for those hierarchies. This is problematic in several ways.

Firstly, time provides a way of grading children’s performance, which is then displayed on leader-boards, but consequences are a) the majority of children in a class cannot be the fastest b) some children will be slowest and c) irrespective of their position within the hierarchy, children will unduly focus on the speed of their response as being the key factor, reinforcing the belief that “being good at maths means being quick at maths” rather than an emphasis on understanding the subject.

Early and long-standing associations between maths and speed

The availability of technology and the internet has provided schools with the means to implement timed testing of facts, mental arithmetic and problem solving. Many people look back at their time in primary school and remember daily rote chanting of multiplication facts. This, however, was rarely accompanied by measuring how quickly these facts could be retrieved, largely because the technology was not available to do this.

We should ask what purpose does it serve to be a few seconds faster at performing a times table test, or faster than one’s classmates? In our opinion, this only provides more instances of perceived negative experiences, often associated with the development of maths anxiety and withdrawal. For instance, a recent study showed how primary school children can associate slower maths performance with consequent punishment, such as having to “see the teacher”, stay behind at breaks or simply being the last pupil to finish their work. Further behaviourist principles are evidenced through the language teachers use, their facial expressions and body language and the way they reinforce quick completion of maths tasks, sometimes before even checking responses. How often is such praise administered following, say, the completion of a drawing in art class? 

It is likely the association between maths and fast processing continues in adulthood. In a study of over 100 adults, around half experienced thoughts about time pressure during a computer-based maths task even when the instructions made no reference to being timed. In fact, those who experienced such thoughts performed significantly worse than those who did not experience such thoughts, suggesting intrusive thoughts about time pressure are counter-productive. 

The impact on performance

Of course, some children enjoy the competitive nature of maths assessments, but these are often children who perform well anyway. For most, timed testing only ups the ante for fear of negative evaluation. So, there are two ways to fail: being wrong and being slow. Compared to other tasks, children (and many adults) find mental arithmetic challenging. It is irrational to emphasise quick responding. For example, being told to swim faster will not be efficacious if one has not mastered the basic techniques. Indeed, it is likely to lead to panic, and a general avoidance of swimming in the future. 

It is also important to consider the type of task. For example, Chinn (1994) compared children’s performance in retrieving basic addition and multiplication facts at 4-second and 12-second intervals. Results showed that extra time has a big influence on addition, probably due to students having time to finger count. There was much less impact on the retrieval of multiplication facts (it is hard to finger count for 7 x 8). A similar pattern was observed in a study of adults, in which highly maths anxious people made significantly more errors on addition problems when they were given a time limit. 

Forcing a person to respond quickly represses metacognitive processes. Metacognition, or “thinking about thinking”, refers to an individual’s mathematical reasoning and problem-solving procedures. As outlined by Morsanyi, maths anxiety may impact on such processes, suppressing strategy choice or appraisal of solutions. Pupils need time to consider options, to decide which strategy and which solution they have more confidence in. This relates to a consistent finding within the academic literature, which is that maths anxiety is frequently correlated with response time, especially on problems that place greater demands on working memory, such as multi-step problems. Doing maths quickly pressurises learners to rush into questions without overviewing and thinking. It discourages appraisals of answers and pre-and post-estimations. It does not encourage metacognition.

Although those who are highly maths anxious may make more errors, it is more likely they will simply take longer. One argument is that people with high maths anxiety focus their attention on the anxiety, rather than the task at hand (reduced attentional control). How often are children focusing on the time they are taking, and the perceived negative consequences of “taking too long”, rather than putting their energies into solving the mathematical problem? Maths anxiety uses up the working memory resources required for successful problem solving. We need to protect those resources, rather than suppressing them through unnecessary time pressure. 

A focus on time, rather than the maths

Maths lessons often begin with a “warm-up” exercise. However, in the same way the body might need an appropriate, gentle warm-up before serious exercise, maths lessons require a similar approach. Warming up in an inappropriate way, especially asking for quick responses, does not set up the child for learning. Indeed, maths anxious children may be apprehensive about even entering a maths class, so the warm-up should be low-pressure. Pupils with high maths anxiety are much more likely to have low maths self-efficacy. Setting them up for failure at the start of a lesson only demotivates children and further reinforces their sense of inadequacy. The answers to 7 x 6 or 506 – 68 are not a matter of opinion. They are 42 and 438 respectively. Anything else is wrong. It’s a double negative, fear of being wrong and fear of being slow. 

Conclusion

Whilst there may be some advantages in retrieving basic number facts and performing mathematical problem solving quickly, achieving this through an over-emphasis on speeded responses and frequent timed testing is irrational and demotivating from many perspectives, especially those of the learners.

Recommendations:

  • Avoid a focus on speeded responses
  • Don’t underestimate the value of simple warm-up activities
  • Avoid unnecessary competition and public displays of performance
  • Allow extra time if needed – if a child takes a particularly long time to perform a maths task, find out why. Don’t let this become an issue for the child
  • Avoid inappropriate and pervasive messages that over-emphasise the importance of quick completion of every task in mathematics.

For further press information please contact the Corporate Communications Team on 01332 593419, pressoffice@derby.ac.uk or @derbyunipress

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