Paper
My objective in carrying out this research was to identify the situations and tasks that created high anxiety in maths lessons. Self-reporting anxiety levels is very subjective, so I focused on relative levels of anxiety foreach of these tasks within each individual. So, for example, ‘An end-of-term maths exam’ ranked as top for anxiety in the largest number of students.
Ultimately, we should try to create a classroom ethos which encourages risk-taking as opposed to a place that is overly concerned with being right every time. We need to remove the fear of negative evaluation. My research shows that withdrawal from maths is a major problem, starting at a very young age.
The extract below has been edited for the purposes of this website.
Steve Chinn
Independent Maths LD/Dyscalculia Consultant
Over 2000 students in independent and mainstream schools in England were given a twenty-item questionnaire ‘How I feel about maths’ in order to investigate anxiety levels. The same questionnaire was given to over 440 dyslexic males in the same age range in specialist schools. The results are analysed and discussed.
Many people confess to being anxious about mathematics. It is socially acceptable to admit to having low abilities with numbers, a strategy that lowers maths anxiety in adults. If expectations can be pre-empted, then poor performance and anxiety have less impact on self-esteem.
Several researchers have tried to describe mathematics anxiety, for example, it has been defined as a ‘feeling of tension, apprehension or fear that interferes with maths performance’ (Richardson and Shuinn, 1972) or as ‘a state of discomfort which occurs in response to situations involving mathematics tasks which are perceived as threatening to self-esteem.’ (Cemen, 1987 quoted in Trujillo and Hadfield, 1999). Richardson and Shuinn focus on the impact of anxiety on cognitive performance whilst Cemen considers the impact on self-esteem, an affective issue. These two focuses illustrate the influence of anxiety on the ability to learn maths and on the confidence to learn maths.
The dual influences of anxiety were also noted by Data and Scarfpin (1983) who identified two types of maths anxiety which they describe by the factors that cause them. One is caused by mental blocks in the process of learning maths and the other is a result of socio-cultural factors (for example, ‘Maths is hard, but it doesn’t matter in life if you can’t do it.’).
Mental block anxiety may be triggered by a symbol or a concept that creates a barrier for the person learning maths. This could be the introduction of letters for numbers in algebra or the seemingly irrational procedure for long division or failing to memorise the seven times multiplication facts. This type of maths anxiety may be addressed by appropriate teaching, if the maths curriculum allows for this.
Ashcraft, Kirk and Hopko (1998) have shown that, under certain circumstances, anxiety can adversely affect the working memory that is used for mathematical tasks. Working memory has been shown to be a significant predictor of mathematical achievement (Keeler and Swanson, 2001). Thus anxiety does not just block the willingness to learn, it can also reduce the capacity of one of the key sub skills needed to succeed.
Socio-cultural maths anxiety is a consequence of the common beliefs about maths such as; only very clever (and slightly strange) people can do maths or that there is only ever one right answer to a problem or if you cannot learn the basic facts you will never be any good at maths. This type of maths anxiety may well lead to maths phobia, but also sanctions people to admit in social situations that they are unable to do maths.
Hadfield and McNeil (1994) suggest that there are three causes of mathematics anxiety, environmental, intellectual and personality. Environmental anxiety includes classroom issues, parental pressure and the perception of maths as a rigid set of rules. Intellectual anxiety includes a mismatch of learning styles and self-doubt and personality factors include a reluctance to ask questions in class and low self-esteem. From my experience as a teacher I consider this ‘triple causes’ construct as realistic in that it considers many, often inter-related factors. The anxiety questionnaire used in this study was structured to reflect these factors.
Maths anxiety can impact on many aspects of learning, for example, in a classroom study (Chinn, 1995) comparing the errors made in basic computation by dyslexic and non-dyslexic students, the error patterns and frequency of particular errors were not different in the two groups with one notable exception, the error of ‘no response’. There was a marked tendency within the dyslexic group to not attempt questions. This strategy avoids failure. Fear of failure exacerbates feelings of anxiety. Learning involves taking risks, but the extremely judgmental nature of maths exacerbates the sense of risk and thus can soon discourage children from being involved in maths tasks.
Lundberg and Sterner (2006) commented on the importance of affective factors on learning mathematics, ‘however, over and above the common cognitive demands and neurological representations and functions, performance in reading and arithmetic is influenced by a number of motivational and emotional factors such as need of achievement, task orientation, helplessness, depression, anxiety, self-esteem, self-concept, locus of control ….’
Two consequences of the impact of maths anxiety on the processes of learning maths were noted by Skemp. He observed (1986) that the reflective activity of intelligence is most easily inhibited by anxiety. Skemp (1971) also explained how an over-reliance on rote learning as a dominant culture in maths may lead to anxiety and loss of self-esteem for many pupils. Unfortunately, thirty five years later a 2006 report shows that little has changed in the culture of mathematics education. ‘Evaluation of maths provision for 14-19 year olds’ by Ofsted, the English Government school inspection body noted that, ‘Maths became an apparently endless series of algorithms (formulas) for them (students), rather than a coherent and inter-connected body of knowledge.’
Mathematics is a unique subject in the school curriculum in that pupils have to answer questions to which there is almost always only one correct answer. The subject is inherently judgmental. This situation, combined with many other factors such as unsuitable curricula, the culture of doing maths quickly, can lead pupils towards a negative attributional style (Chinn, 2004 and Chinn and Ashcroft, 2007) and ultimately learned helplessness (Seligman, 1998).
This helplessness can persist into adulthood. Zaslavsky (1999) looked at over 200 maths ‘autobiographies’ from maths anxious adults in the USA. She observed a common thread. The respondents felt powerless, out of control and lacking in self-esteem.
There is a concern that mathematics abilities (CBI, 2006) in the adult population of the UK are unacceptably low. Anxiety will be one of the contributing factors to this situation where approximately 50% of the adult population cannot do maths at a level beyond that they were taught at age 11 years.
This study looks at the anxiety levels of students in secondary education, which is a stage in education where students approach adulthood. The answers and results of this study could also be perceived of as a consumer survey of maths education and students’ experiences of maths in schools.
There may well be a connection between significantly low achievement in mathematics and anxiety. Recently there has been an interest in dyscalculia (DfES 2001). Dyscalculia is a specific learning difficulty that is, compared to dyslexia, in its infancy in terms of research. Of the few researchers in the field the work of Butterworth stands out. His Dyscalculia Screener (Butterworth, 2003) is based on a model of dyscalculia which is, essentially, a deficit in numerosity.
However, if maths anxiety reached a level where the student removed himself from any future learning and this occurred early in his schooling, then he may well present with seriously low maths achievement levels. A contributing factor to this scenario could be a mismatch between the learner and the instruction he receives.
In a small study Chinn (1996) looked at the relationship between WISC scores and the grades achieved in GCSE maths by dyslexic pupils at the specialist school where I was Principal. Although the correlations between the various sub-scores and maths grades were interesting, a key informal outcome were the results for the average band of students where affective factors played the dominant role. Although I had no standardised measure of these contributing factors I was well aware of individual attitudes, motivation, anxiety as I taught each student for at least one lesson per week. I would suggest that some measure of anxiety should be a part of any diagnostic protocol for dyscalculia.
METHOD
Responses to a questionnaire on math anxiety from 442 dyslexic male students were provided by 9 schools from the Specialist Provision and Special Unit categories of CReSTeD (Council for the Registration of Schools Teaching Dyslexic Students). There were not enough responses from female dyslexics to make a viable sample.
Responses for the 2084 mainstream students were provided by 19 schools from around England. Five of these schools were independent. The sample was taken from Year groups 7 to 11. Students enter secondary education in Year 7 at age 11 years and will be 17 years at the end of Year 11.
Schools were selected to provide a geographical spread across England.
The Questionnaire is the one used in my book, ‘More Trouble with maths. A complete manual to identifying and diagnosing mathematical difficulties.’ (2nd edition, 2017)
The questionnaire is a mixture of items focusing on different activities which might cause anxiety. For example, some items refer directly to specific tasks in maths, such as long division. Others relate to classroom activities, such as mental arithmetic, others to maths culture such as having to do maths questions quickly and others to social aspects such as showing a maths report to Mum or Dad. As English education is currently in the grip of almost obsessive levels of testing, the questionnaire includes items related to this all too frequent experience.
The students’ gradings of their feelings of anxiety for each item are, obviously, entirely subjective.
The questionnaires were presented to the students by teachers in each of the participating schools.
The results were analysed as 15 groups: males and females for each of the five Year groups and male dyslexic students for each Year group.
The average ‘score’ was calculated for each item for each group. The twenty items from the questionnaire were then ranked for each group. It is this ranking of the items that identifies the activities create the most anxiety.
The maximum possible score on the questionnaire is 80. The minimum possible score is 20. On the basis that a rating of the ‘often’ anxiety level was 3 and that there are 20 items, for each group the percentages of students scoring at 60 and above were calculated to provide an indication of high levels of anxiety.
The group showing the greatest anxiety as measured by the ‘high anxiety scores’ (>59) were Year 7 dyslexic males. The percentage of high anxiety scores then decreased, with a slight increase in Year 11. There was an increase in high anxiety scores (>59) for females in Years 11 with values higher than those for the males. Year 11 is the GCSE examination year.
An individual score on the questionnaire may not reflect the true levels of anxiety in every student, for example, a Year 8 female scored a total of 45, but wrote on her questionnaire, ‘I hate maths. I can never do it. If I’m with the right teacher then I can do it easily, but I cannot.‘ The scores are, inevitably, subjective.
These scores for high anxiety in maths show that between 2% and 6% of mainstream students experience high levels of anxiety about maths, at a level which suggests they are ‘often’ anxious. Dyslexic males do not consistently show greater percentages of high anxiety across the Year groups, but the comparatively high percentage in Year 7 is notable. A possible hypothesis is that Year 7 could be their first year in specialist education and the benefits of provision have yet to take affect.
The responses to the questionnaire could almost be considered as consumer feedback on maths, the maths curriculum and the maths culture that exist in England.
There are more similarities between the groups than there are differences. However, females tended to score with slightly higher levels of anxiety than males and dyslexic males tended to score with higher levels than mainstream females or males. The average total scores across Year groups were close. There was no consistent trend, up or down, from Year 7 to Year 11, although there is an indication of increased anxiety in Year 11, the year in which students take the national GCSE examination.
The same observation regarding similarities applies to the separate items in the test. For example, ‘long division without a calculator’ (Item 5) was ranked from 2nd to 4th for all but one of the ten mainstream groups and the dyslexic groups. This could well be a reflection on the way division is taught. The traditional algorithm does make many demands on several sub-skills, not least of which is memory for basic facts and sequential memory. There is also a significant contribution from the organisation and layout of work on paper.
One of the demands of mathematics is that answers are computed quickly. Item 13 concerning this issue was ranked highly by all groups, with the dyslexic males ranked it higher than mainstream males in all Year groups.
Not surprisingly the ‘End of term exam’ (Item 20) ranked 1st for all fifteen groups. ‘Taking a written maths test’ (Item 3) and ‘Waiting to hear your score on a maths test’ (Item 15) were also consistently ranked as high anxiety. It could be that our current test culture contributes too much to maths anxiety. (Whitaker et al, 2007).
‘Following your teacher’s explanation of a new maths topic’ (Item 19) did not rank highly, though for dyslexic males in Years 7 to 9 it was ranked two or three places higher than for males in mainstream.
More surprisingly, but then perhaps an indirect comment on our consumer society as well as the way purchases are processed in shops, the item on ‘money when shopping’ was ranked as 18th, 19th or 20th for the mainstream groups and for three of the dyslexic year groups. For Years 8 and 9 dyslexic males it ranked at 16th. In these days of touch cards for payment this may fall even lower in the rankings.
Items concerning anticipation, ‘opening a maths book’ (Item 12) and ‘knowing that the next lesson will be maths’ (Item 1) ranked towards the bottom of the list for all groups.
When the ranks were averaged for mainstream and for the dyslexic group, then the differences that stood out were for items 7 (long multiplication without a calculator) and Item 14 (learning the hard times table facts) both of which the dyslexic students rated much higher in anxiety levels. The items on answering questions quickly and long division without a calculator were also rated higher than in the mainstream sample, but since these two items were ranked high in the twenty items by the mainstream sample, the difference was less marked.
Item 15 (hearing your score on a maths test) was ranked much lower by the dyslexic group, which may be due to the specialist schools managing this issue more sensitively. Public feedback of low scores can be humiliating.
Perhaps the relatively low ranking of word problems (Item 4) is unexpected, but the higher ranking of long division and fraction questions is not a surprise. It could be that the seemingly irrational procedures taught for these two topics inevitably lead to anxiety. It is interesting to note the much lower ranking of anxiety levels for division when a calculator is available, but experience tells me that this is not necessarily an educational, in the sense of the understanding of mathematics, benefit.
There were relatively few sex differences in ranking. The items that were ranked with a difference of 5 or more were:
Item 2 (mental arithmetic). Females ranked this with higher anxiety scores for Years 7, 8 and 10.
Item 8 (fraction questions) was given higher anxiety ranking by females in Year 8.
Item 14 (learning the hard times table facts) was ranked at higher anxiety for females in Year 9.
Item 17 (answering questions in class) was given a higher anxiety level by females in Year 10.
Item 9 (revising for a maths test) was given a higher anxiety ranking by Year 8 males than by females.
Item 10 (maths homework) was ranked as higher anxiety by Year 8 and 9 males.
Item 11 (looking at marks for homework) was ranked higher in anxiety by Year 9 males.
This survey highlights some of the cognitive and affective areas of mathematics that create anxiety for students in secondary schools in England. The levels of anxiety are relatively consistent across ages and gender and dyslexic males, with the same items creating similar rankings in each of the groups.
Examinations and tests created high anxiety levels in all groups. The lower anxiety levels in dyslexic students for tests show that this anxiety can be managed, but the universal top ranking of the end of term maths exam (Item 20) for all groups shows how students view this activity negatively.
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(2019) The on-going work of David Sheffield and Thomas Hunt at the University of Derby is fascinating and revealing.