Further development of the Children’s Mathematics Anxiety Scale UK (CMAS-

Sensitivity: Internal 1 Further development of the Children’s Mathematics Anxiety Scale UK (CMAS2 UK) for ages 4-7 years 3 4 Dominic Petronzi * 5 University of Derby (UK) 6 7 Paul Staples 8 University of Derby 9 10 David Sheffield 11 University of Derby 12 13 Thomas E Hunt 14 University of Derby 15 16 Sandra Fitton-Wilde 17 University of Derby 18 19 * Correspondence concerning this article should be addressed to Dr. Dominic Petronzi, University of Derby, 20 Enterprise Centre, Bridge Street, Derby, DE1 3LD, UK. Tel: (01332) 597990. E-mail: 21 d.petronzi@derby.ac.uk 22 23 Declaration of Competing Interests 24 The author(s) declare no potential competing interests with respect to the research, authorship, and/or 25 publication of this article. 26

learning, music performance and literacy learning, particularly for those with dyslexia (Dowker, Sarkar and Looi 2016).

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Punaro and Reeve (2012) reported that while children aged nine years had literacy and mathematics anxiety in relation 4 to difficult problems in both subjects, mathematics caused more-intense worry related to performance. This suggests 5 that, while mathematics is not unique in causing anxiety, it may be the subject that produces the most intense responses.   consists of 9-items and participants respond to a 5-point Likert scale, ranging from low anxiety (1) to high anxiety (5).

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Typically, mathematics anxiety scales have favoured a Likert-scale response, although it seems more appropriate for 42 this scale using simple emoticons with three response choices. Notably, both the MARS-E and MASC have the advantage of being applicable to a wider age-range, unlike other scales, for example, the Scale for Early Mathematics Anxiety (ages 8-9 years) (Wu, Barth, Amin, Malcarne and Menon 2012).

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Factor analysis of 44 items resulted in the omission of 18 items and led to a 26-item iteration of the CMAS-UK. This 21 produced a high internal consistency value (α = .89). Two factors were identified: the first related to prospective mathematics task apprehension e.g. seeing lots of numbers and walking into a mathematics lesson (and was thus termed

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Prospective Mathematics Task Apprehension), and the second was associated with apprehension when completing 24 mathematics tasks, e.g. making mistakes and explaining a mathematics problem to the teacher (termed Online 25 Mathematics Anxiety). A preliminary analysis was conducted to determine the extreme score discriminative power of 26 the 26-items based on a median split (47). All t test results were significant, suggesting that each item could 27 discriminate between extreme scores. Thus, our previous work suggested that the CMAS-UK is a valid tool for 28 assessing mathematics anxiety in younger children, but further work was needed to validate the measure, particularly 29 regarding the predictive validity of the scale in the context of mathematics performance.

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In the current study, the 26-item CMAS-UK was completed by a new sample of children (N=163) to further refine the scale items and to achieve a simple-to-administer scale for younger children. In conjunction with this, children also 35 completed a mathematics task with a difficulty level that was relative to their year group. This was used as a measure of 36 predictive validity to test whether the scale scores could predict mathematics performance. Predictive validity is  Scale for Children (Wren and Benson 2004). Participants who scored higher on the MASC had lower achievement in 3 mathematics, higher test anxiety and lower achievement motivation. Thus, the current study hypothesised that a higher 4 score on the CMAS-UK would predict lower mathematics performance. Table 1    Measurements of mathematics performance were also taken.

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Participants for the research were recruited through opportunity sampling from two state primary schools across the 5 East Midlands region in the UK. Active informed consent from parents was obtained via a question and answer 6 information letter that was sent through the school administration system. Following conformation of parental consent, 7 children verbally consented in response to an age-appropriate script. The demographics of the two schools were similar, The 26 items from the CMAS-UK were randomly numbered and related to general thoughts and feelings about 24 mathematics and typical day-to-day mathematics experiences, for example, teachers; peers and friends; difficulties with 25 work and receiving help or not etc. These items had been created in collaboration with teachers who advised on the term 26 'numeracy' instead of 'maths', 'mathematics' or 'sums'. It was advised that children are more familiar with 'numeracy' 27 at this key stage and the National Curriculum in England predominantly refers to 'mathematics' for Key Stage 2 (above 28 the age range of the current research) and refers to 'number' for Key Stage 1 (ages 4-7 years). Indeed, within the UK For years one and two children, the mathematics task included longer addition (adding more than 2 numbers together), 12 money, division, multiplication and using numbers to make a specified value. In order for the tasks to be age 13 appropriate, the year 2 task was of greater difficulty then the year 1 task (although tasks for each year group were set at 14 medium ability). A time limit was not enforced when children were completing the mathematics task, as the intention 15 was to measure their ability without pressure acting as a confounding variable. However, teachers typically allowed up 16 to 15 minutes for task completion, although this was not stipulated to the children. The children were asked to work 17 independently and to complete as much of the task as possible. To avoid children becoming too anxious when asked to 18 do their own work, they were informed that the task was not a test and that the teacher would not see their answers.

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Reception children could achieve a maximum score of 18 (1 point for each correct answer), whilst year 1 and 2 children 20 could achieve a maximum score of 20 (1 point per answer); all scores were converted to percentages to reflect accuracy,

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which was the outcome variable for mathematics performance. their class. The CMAS-UK was completed prior to the mathematics task to ensure that children were more inclined to 3 respond generally rather than to the task. However, it is possible that children's mathematics task performance may 4 have been influenced by a priming effect of the CMAS-UK and is an area of research interest.

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Participating children completed the mathematics task in their classroom as a group the following day, to avoid fatigue.

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It was explained to the children that this was not a test and that they should complete as much of the task as possible. 8 They were also informed that there was no time limit, and that they did not need to rush their work. The class teacher 9 assisted in overseeing the completion of the mathematics task and to ensure that children completed their work independently, although they were given assistance in reading the questions, particularly children in reception. Children

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were not made aware of their mathematics anxiety scale or mathematics tasks scores and these were calculated off site. items were removed (9 & 20) due to insufficient loading (<.35) (see Table 1). This suggests reliability of the scale across our development studies, despite a 1 factor solution ultimately being indicated by more robust parallel analysis in the current research.  Items that loaded onto the single observed factor appeared to have a strong association with feelings and situations 5 during the moment-to-moment experience of performing a mathematics task i.e. explaining an answer to the teacher, 6 being the last to finish mathematics work, making mistakes and getting work wrong. This factor was thus named, 7 'Online Mathematics Anxiety', maintaining the factor 2 name from the previous research (Petronzi et al. 2018). This 8 factor consists of merged items from the initial factor 1 and factor 2. The entire mathematics lesson could be viewed as 9 being an online task, as it requires the learner to not only complete work, but to observe and listen closely to instruction 10 something that high anxious children may find difficult.

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The results show that CFA standardised regression weights are only marginally smaller than the EFA factor loadings.

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The standardised regression weights in the CFA are favourable as they closely link to the EFA, supporting the 19-item 26 model and this is shown to be consistent across statistical tests. The small observed difference between regression 27 weights and factor loadings exert no effects on the model that would lead to differential theoretical interpretations.  The extant literature on mathematics anxiety has given limited attention to the early years of mathematics education.

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Knowledge has therefore been limited with regards to the onset of mathematics anxiety and whether factors in the early

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Whilst the association between mathematics anxiety scores and mathematics performance scores was significant and 18 large (r = -.620) this should be viewed with a degree of caution. In some cases, children who obtained a high score on 19 the mathematics task also obtained a high score on the CMAS-UK. Ashcraft (2002) also previously found that despite 20 some children claiming a degree of mathematics anxiety, their competence scores remained unaffected. Previously,

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Ashcraft, Kirk and Hopko (1998) found that the effects of anxiety were only apparent on certain mathematical concepts.

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Thus, it may be that the children were highly anxious, but were comfortable with the concepts on the mathematics task,

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and thus performance was unaffected. Ashcraft (2002) stated that researchers should always consider the competence-24 anxiety relationship, as those with higher anxiety may demonstrate increased competence in varying circumstances.

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However, for the most part our data demonstrates that children with low CMAS-UK scores performed better on the

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Other examples pertain to other children finishing their work quickly and having an awareness of someone struggling (failure and peer comparison); providing incorrect answers; making mistakes (failure and low self-efficacy); and holding the belief of being unable to complete work (low sense of ability and self-esteem). These items also identified 36 in quantitative mathematics anxiety research with older populations, suggesting that the early years of education may 37 somewhat contribute to later difficulties and negative attitudes, although this requires further investigation.
As a point of reflection, it can be argued that younger children may not have the capacity to accurately recall and rate therefore restricted in how much information and experiences they can store in their short-term memory (Croker 2012).
cases children rate their learning-based feelings on a scale of 1-10 using emojis for visual support. Indeed, educational 3 psychology services in the UK also implement and refer teachers and childcare workers to a test bank of scales for the 4 measurement of children's emotional and mental well-being using quantitative measurement. In light of this, the 5 CMAS-UK (with visual emoji support) aligns with current UK practise. CMAS-UK can support projects evaluating intervention techniques that are known to be efficacious with older children.

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For example, Park, Ramirez and Beilock (2014) that expressive writing following and prior to a mathematics task 27 increases the mathematics performance of those with university students with higher mathematics anxiety.

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In sum, previous research has neglected the assessment of affect towards numbers among younger children. Our work 30 has gone some way to address this shortfall by providing an easily administrable scale with a parsimonious factor 31 structure. Previous attempts to measure mathematics anxiety among older children and adults have emphasised the 32 multidimensionality of the construct whereas the current findings highlight the limited context in which young children 33 are exposed to numbers. We demonstrate the importance of mathematics anxiety at a young age and the relation this has