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Further development of the Children’s Mathematics Anxiety
Scale UK (CMAS-UK) for ages 4–7years
Dominic Petronzi, et al. [full author details at the end of the article]
Published online: 31 October 2018
Abstract
There are currently many mathematics anxiety rating scales designed typically for adult and
older children populations, yet there remains a lack of assessment tools for younger children
(< 7 years of age) despite a recent focus on this age range. Following previous testing and
validation, the 26-item iteration of the Children’s Mathematics Anxiety Scale UK (CMAS-
UK) for ages 4–7 years was further validated with 163 children (4–7 years) across two schools
in the UK to test the validity and reliability of the items through subsequent exploratory and
confirmatory factor analysis. The predictive validity of the scale was also tested by comparing
scale scores against mathematics performance on a mathematics task to determine the rela-
tionship between scale and mathematics task scores. Exploratory factor analysis and associated
parallel analysis indicated a 19-item scale solution with appropriate item loadings (> 0.45) and
high internal consistency (α= 0.88). A single factor model of Online Mathematics Anxiety
was related to the experience of an entire mathematics lesson, from first entering the classroom
to completing a task. A significant negative correlation was observed between the CMAS-UK
and mathematics performance scores, suggesting that children who score high for mathematics
anxiety tend to score to perform less well on a mathematics task. Subsequent confirmatory
factor analysis was conducted to test a range of module structures; the shortened 19-item
CMAS-UK was found to have similar model indices as the 26-item model, resulting in the
maintenance of the revised scale. To conclude, the 19-item CMAS-UK provides a reliable
assessment of children’s mathematics anxiety and has been shown to predict mathematics
performance. This research points towards the origins of mathematics anxiety occurring when
number is first encountered and supports the utility of the CMAS-UK. Subsequent research in
the area should consider and appropriately define an affective component that may underlie
mathematics anxiety at older ages. Mathematics anxiety relates to more complex procedures
that elude the experiences of younger children and may instead be the result of number-based
experiences in the early years of education.
Keywords Mathematics anxiety .Factor analysis .Mathematics performance
1 A foundation phase of mathematics anxiety
Although well researched in adult populations, a definitive foundation for mathematics
anxiety has yet to be identified (Harari, Vukovic, & Bailey, 2013). However, there is now
Educational Studies in Mathematics (2019) 100:231–249
https://doi.org/10.1007/s10649-018-9860-1
#The Author(s) 2018
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emerging research that focuses on primary school education (Mizala, Martinez, &
Martinez, 2015; Petronzi, Staples, Sheffield, Hunt, & Fitton-Wilde, 2017; Ramirez,
Gunderson, Levine, & Beilock, 2013) and the influence of early negative experiences
in the classroom is becoming accepted as a key factor in mathematics anxiety
development.
Nicolaidou and Philippou (2003) considered that children are intrinsically motivated to
learn mathematics with positive attitudes but begin to form attitudes that may be negative.
Once mathematics anxiety develops, it can be viewed as cyclic (Ashcraft, 2002;Preis&
Biggs, 2001) as negative attitudes relate to avoidance and poor performance which
escalates negative feelings. This adverse consequence emphasises the importance of
understanding and identifying the issue early in education. Indeed, psychologists (e.g.,
Rossnan, 2006) have posited that mathematics anxiety can develop at any age and is
rooted within a child’s first experience of school mathematics. Mazzocco, Hanich, and
Noeder (2012) also suggest that efforts should begin in early childhood to steer children
away from paths that lead towards negative outcomes. This is made more important by
research findings showing that despite demonstrating normal performance in most think-
ing and reasoning tasks, mathematics anxious individuals demonstrate poor performance
when solving mathematics problems (Maloney & Beilock, 2012). Anxiety is not exclusive
to mathematics and exists in other subjects, particularly when performing in front of
others, including foreign language learning, music performance, and literacy learning,
particularly for those with dyslexia (Dowker, Sarkar, & Looi, 2016). Punaro and Reeve
(2012) reported that whilst children aged 9 years had literacy and mathematics anxiety in
relation to difficult problems in both subjects, mathematics caused more-intense worry
related to performance. This suggests that whilst mathematics is not unique in causing
anxiety, it may be the subject that produces the most intense responses.
Qualitative research conducted by Petronzi et al. (2017) explored and identified factors
contributing to the development of mathematics anxiety in the early years of UK
education. Mathematics anxiety in children aged 4–7 years refers to worrisome thoughts
surrounding the manipulation of numbers in tasks that require basic mathematical skills.
Within this educational context, children encounter number and place value, addition and
subtraction, multiplication and division in accordance with the National Curriculum;
multiplication and division skills are worked on and developed throughout year 1 and
year 2 (UK Key Stage 1; ages 5–7 years) and at the end of this educational phase (UK
year 2; age 7 years), children are expected to count in multiples of 2s, 5s and 10s, should
know number bonds to 20 and be precise in using and understanding place value.
Petronzi et al. identified themes that may have previously been underestimated or not
considered as influencing mathematics-based attitudes in early education, for example,
fear and stigma of failure, peer comparison/competition and awareness of a classroom
hierarchy regarding mathematics ability. These findings highlight the importance of
addressing the very early years of formal schooling to understand the development of
mathematics anxiety. However, the construct of mathematics anxiety and the current,
long-standing definition is grounded within adult research and is associated with more
complex mathematical procedures; it does not address its origins in the early years of
education. Indeed, mathematics anxiety in the early years has been considered as devel-
oping to the point of a rigid educational obstruction (Baptist, Minnie, Buksner, Kaye, &
Morgan, 2007) and could be regarded as a pre-requisite phase of mathematics anxiety in
later childhood and adulthood.
232 Petronzi D. et al.
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2 Quantifying mathematics anxiety: a new assessment scale for children
Traditionally, measurement scales using Likert-scale response formats have been developed
and adapted to determine the underlying factors of mathematics anxiety in adult populations,
such as the Revised Mathematics Anxiety Rating Scale (RMARS) with emerging factors of (a)
mathematics course anxiety, (b) evaluation anxiety, and (c) arithmetic computation anxiety
(Plake & Parker, 1982); the Short Mathematics Anxiety Rating Scale (sMARS) (a) mathe-
matics test anxiety and (b) numerical test anxiety (Suinn & Winston, 2003); and the Mathe-
matics Anxiety Scale UK, (MAS-UK) (a) mathematics evaluation anxiety, (b) everyday/social
mathematics anxiety, and (c) mathematics observation anxiety (Hunt, Clark-Carter, & Shef-
field, 2011). One notable exception is Dowker, Bennett, and Smith’s(2012) measure of
attitudes to mathematics for primary school children. This scale was developed with children
aged 7–10 years and strayed from a typical Likert-scale response and instead adopted a face
rating scale to ensure appropriateness for primary school-aged children. Children responding
to images on questionnaires has previously been assessed by the Koala Fear Questionnaire
(Muris et al., 2003), which was found to be a valuable instrument for clinicians and researchers
when assessing fears and fearfulness in pre and primary school-aged children. More recently,
the Modified Abbreviated Mathematics Anxiety Scale (Carey, Hill, Devine, & Szucs, 2017)
has been developed for children aged 8–13 years with a sample of 1746 children and
adolescents. This consists of 9-items and participants respond to a 5-point Likert scale, ranging
from low anxiety (1) to high anxiety (5). Typically, mathematics anxiety scales have favoured
a Likert-scale response, although it seems more appropriate for response formats to be adapted
to support children’s understanding. This was a core consideration during the development
process of the Children’s Mathematics Anxiety Rating Scale UK in the current and previous
research (Petronzi, Staples, Sheffield, Hunt, & Fitton-Wilde, 2018).
Many existing mathematics anxiety scales are limited in their use with younger children in
terms of content and format. For example, the sMARS (Suinn & Winston, 2003) comprises
questions focussing on advanced concepts that might be difficult for younger children to
comprehend. Other scales, including those for older children, e.g., the Mathematics Anxiety
Rating Scale for Elementary children (MARS-E) (Suinn, Taylor, & Edwards, 1988), the
Mathematics Anxiety Scale for Children (MASC) (Chiu & Henry, 1990), and the Child
Mathematics Anxiety Questionnaire (CMAQ) (Ramirez et al., 2013) use a response format
that include written labels pertaining to anxiety levels. Such a response format may not be
appropriate for younger children in which comprehension of the labels may be compromised.
Whilst the 26-item MARS-E was developed with 1119 fourth (U.K. age 9–10, year 5), fifth
(U.K. age 10–11, year 6), and sixth graders (U.K. age 11–12, year 7) and the 22-item MASC is
intended for use with children aged 9–14. A focus on older age ranges represents another
limitation with existing scales. To address these points, the current study built on previous
exploratory factor analysis of the CMAS-UK (N= 307) (Petronzi et al., 2018) and focused on
the further development of 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, & Menon, 2012).
In previous research (Petronzi et al., 2018), the CMAS-UK was implemented with children
aged 4–7 years (N= 307). Factor analysis of 44 items resulted in the omission of 18 items and
led to a 26-item iteration of the CMAS-UK. This produced a high internal consistency value
(α= 0.89). Two factors were identified: the first related to prospective mathematics task
Further development of the Children’s Mathematics Anxiety Scale UK... 233
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apprehension, e.g., seeing lots of numbers and walking into a mathematics lesson (and was
thus termed Prospective Mathematics Task Apprehension), and the second was associated with
apprehension when completing mathematics tasks, e.g., making mistakes and explaining a
mathematics problem to the teacher (termed Online Mathematics Anxiety). A preliminary
analysis was conducted to determine the extreme score discriminative power of the 26-items
based on a median split (47). All ttest results were significant, suggesting that each item could
discriminate between extreme scores. Thus, our previous work suggested that the CMAS-UK
is a valid tool for assessing mathematics anxiety in younger children, but further work was
needed to validate the measure, particularly regarding the predictive validity of the scale in the
context of mathematics performance.
3 Further validation of the Children’s Mathematics Anxiety Scale UK
(CMAS-UK)
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 completed a mathematics task with a difficulty
level that was relative to their year group. This was used as a measure of predictive validity to
test whether the scale scores could predict mathematics performance. Predictive validity is
typically established by presenting correlations between a measure of a predictive and other
measures that should be associated with it. Suinn and Edwards (1982) determined the
predictive validity of the MARS-A by comparing scale scores with grade averages. The results
indicated an association between higher anxiety scores and lower mathematics grade averages.
Similarly, Suinn et al. (1988) correlated children’s Standardized Assessment Test scores
(SATs) with their scores on the MARS-E. A relationship was found, supporting the predictive
validity of the MARS-E. Chiu and Henry (1990) determined predictive validity of the MASC
by comparing participants’scores against, for example, the shortened version of the MARS,
their most recent mathematics results, and scores from completing the Test Anxiety Scale for
Children (Wren & Benson, 2004). Participants who scored higher on the MASC had lower
achievement in mathematics, higher test anxiety, and lower achievement motivation. Thus, the
current study hypothesised that a higher score on the CMAS-UK would predict lower
mathematics performance. Table 1demonstrates the factor loadings and belonging of each
of the items for the 26-item version of CMAS-UK following Exploratory Factor Analysis
(Petronzi et al., 2018).
4 Method
4.1 Design and participants
The study employed a cross-sectional design to further determine the reliability and validity of
a mathematics anxiety rating scale (CMAS-UK), in its 26-item iteration following factor
analysis in previous research (Petronzi et al., 2018). Measurements of mathematics perfor-
mance were also taken.
Participants for the research were recruited through opportunity sampling from two state
primary schools across the East Midlands region in the UK. Active informed consent from
234 Petronzi D. et al.
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parents was obtained via a question and answer information letter that was sent through the
school administration system. Following conformation of parental consent, children verbally
consented in response to an age-appropriate script. The demographics of the two schools were
similar, with a catchment of predominantly white, middle class families. In total, 163 children
between the ages of four and seven participated in the research. A total of 39 males (23.9%)
and 36 females (22.1%) participated from school one, accounting for 46% of the overall
sample size. In school two, 51 males (31.3%) and 37 females (22.7%) participated and
accounted for a total of 54% of the sample size. The children in the research were pupils in
either reception (age 4–5), year 1 (age 5–6), or year 2 (age 6–7). Seventy-five children
participated from the first school (19 reception (25.3%); 36 year one (48%); 20 year two
(26.7%)) and 88 participated from the second school (40 reception (45.4%); 21 year one
(23.9%), and 27 year two (30.7%)). Across all schools, a total number of 59 children were in
reception (36.2%), 57 children were in year one (35%) and 47 children were in year two
(28.8%). Reflecting on the guidelines of Tinsley and Tinsley (1987) who suggest a ratio of 5 to
10 participants per item, the sample size of the research (n= 163) can be regarded as sufficient
and acceptable for exploratory factor analysis, as this equates to 6.27 participants per item (26
items). Despite this, Comrey and Lee (1992) have previously stated 200 to be an adequate
sample size for confirmatory factor analysis, and so a low variance could be explained by the
relatively small sample size.
Table 1 Factor loadings of items for the CMAS-UK, 2-factor 26-item model (N= 307) (Petronzi et al., 2018)
Item Prospective
mathematics
task anxiety
Online
Mathematics
Anxiety
[15] Listening to the teacher in a numeracy class makes me feel…0.780 –
[26] Walking into the numeracy class makes me feel…0.742 –
[6] When I read questions in numeracy, I feel…0.673 –
[7] Starting a new topic in numeracy makes me feel…0.592 –
[16] When I practise numeracy, I feel…0.567 –
[5] If I have to do numeracy work in my head, I feel…0.547 –
[21] When I watch or listen to my teacher explain a
numeracy problem, I feel…
0.533 –
[25] When my teacher wants me to do numeracy at home, I feel…0.533 –
[14] If I have to finish all my numeracy work in lesson, I feel…0.487 –
[20] Thinking about numeracy outside of class makes me feel…0.477 –
[24] When I explain how I got my answer to my teacher, I feel…0.410 –
[2] When I am asked to do lots of numeracy in class, I feel…0.393 –
[12] When I see lots of numbers, I feel…0.381
[13] When I have to explain a numeracy problem to my friends, I feel…0.368 –
[3] If I am the last to finish numeracy work on my table, I feel…–0.711
[17] If I answer questions and get them wrong, I feel…–0.643
[11] If I think I cannot do my numeracy work, I feel…–0.640
[23] If other children finish their numeracy work very quickly, I feel…– 0.618
[4] If I make a mistake in numeracy, I feel…–0.594
[22] If I do not finish my number work in class, I feel…–0.586
[8] When I cannot do my numeracy work, I feel…–0.577
[1] When my friends finish their numeracy before me, I feel…–0.551
[19] If other children know that I find numeracy hard, I feel…–0.501
[9] When I have someone watching me while I do my numeracy, I feel…– 0.416
[18] If I have to tell the teacher that I do not understand
my numeracy work, I feel…
0.397
[10] When I have to explain a numeracy problem to my teacher, I feel…0.390 –
Further development of the Children’s Mathematics Anxiety Scale UK... 235
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4.2 The Children’s Mathematics Anxiety Scale UK
The 26 items from the CMAS-UK were randomly numbered and related to general thoughts
and feelings about mathematics and typical day-to-day mathematics experiences, for example,
teachers; peers and friends; difficulties with work; and receiving help or not. These items had
been created in collaboration with teachers who advised on the term “numeracy”instead of
“maths”,“mathematics”,or“sums”. It was advised that children are more familiar with
“numeracy”at this key stage and the National Curriculum in England predominantly refers
to “mathematics”for Key Stage 2 (above the age range of the current research) and refers to
“number”for Key Stage 1 (ages 4–7 years). Indeed, within the UK education system, children
are familiar with the scheme “numeracy hour”(as well as “literacy hour”) and so are
accustomed to this consistently used terminology. Furthermore, our qualitative research
reinforced UK children’s understanding of “numeracy”(Petronzi et al., 2017)—the term is
commonplace in the context of UK Key Stage 1 education. Following factor analysis (Petronzi
et al., 2018), all items fell into either factor 1 (14-items; prospective mathematics task
apprehension) or factor 2 (12-items; Online Mathematics Anxiety) (α=0.89). Children could
respond to each item using an emoticon three-point Likert-scale, with one face representing
“happy”, another signified uncertainty and the final face representing “sad”,forexample“If I
have to finish all my mathematics work in lesson, I feel…”.
4.3 The mathematics task
Three primary school teachers in a single school (not teachers of the participating children)
were asked to create a set of intermediate mathematics problems that were age appropriate for
reception, year one and year two children and utilised teacher expertise and understanding of
children’s abilities in each year group. These mathematics problems were deemed acceptable
by teachers in the participating schools. The mathematics task for reception children was more
pictorial based and called upon knowledge of shapes (searching for these in a house structure),
addition, subtraction, missing numbers and visual identification of more and less (in water
beakers); these were ratified by other teachers (appendix Fig. 5). Examples include:
Fill in the missing numbers:
1, 2, _ 4, 5, _ 7
Add the two numbers together to find the answer:
2+3=
5+4=
For years one and two children, the mathematics task included longer addition (adding more
than two numbers together), money, division, multiplication, and using numbers to make a
specified value. In order for the tasks to be age appropriate, the year 2 task was of greater
difficulty then the year 1 task (although tasks for each year group were set at medium ability).
A time limit was not enforced when children were completing the mathematics task, as the
intention was to measure their ability without pressure acting as a confounding variable.
However, teachers typically allowed up to 15 min for task completion, although this was
not stipulated to the children. The children were asked to work independently and to complete
236 Petronzi D. et al.
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as much of the task as possible. To avoid children becoming too anxious when asked to do
their own work, they were informed that the task was not a test and that the teacher would not
see their answers. Reception children could achieve a maximum score of 18 (1 point for each
correct answer), whilst years 1 and 2 children could achieve a maximum score of 20 (1 point
per answer); all scores were converted to percentages to reflect accuracy, which was the
outcome variable for mathematics performance.
4.4 Research procedure
For each research group, children in reception, year one and year two were taken to a
separate and quiet area of the school to avoid distractions and to encourage concentration.
For children in reception, the researcher again limited the group size to a maximum of
three, as previous research experience had taught that, although emotionally aware,
younger children can struggle to understand the response procedure for scales and may
require assistance. A small group size enabled the researcher to ensure that all children
responded to the appropriate statement after it had been read aloud to them twice. For
children in years one and two, the maximum group size was eight, as children in these
years were able to understand and follow the response procedure with minimal assistance.
Once children had sat down in the research area of the school, introductions were made,
and children were given time to talk generally. This time was used to record names, age,
and year group. Following this, the researcher redirected the children’sattentiontothe
research. A standard introduction to the research that had been written at an age appro-
priate level was read to each group. Children also had the opportunity to ask any questions
and raise any concerns and were informed that they could stop whenever they liked.
Children in all groups were also kindly asked to not discuss their statement responses with
each other, as the researcher’s previous research experience had shown that some children
can alter their responses if others are expressing more confidence. Measures were taken in
terms of seating to avoid response copying, and avoid creating an anxiety evoking
situation, similar to a test. All children were provided with the 26-item CMAS-UK and
given a pencil for circling the appropriate emoticon that reflected their feelings. Each
group was informed that the researcher would read each statement to the group and then
time would be given for their response. For each scale statement, the researcher read the
statement twice to ensure understanding. Once all children had responded, the researcher
read the next statement. When the CMAS-UK had been completed, the children were
thanked for their time and then returned to their class. The CMAS-UK was completed
prior to the mathematics task to ensure that children were more inclined to respond
generally rather than to the task. However, it is possible that children’s mathematics task
performance may have been influenced by a priming effect of the CMAS-UK and is an
area of research interest.
Participating children completed the mathematics task in their classroom as a group the
following day, to avoid fatigue. It was explained to the children that this was not a test and that
they should complete as much of the task as possible. They were also informed that there was
no time limit, and that they did not need to rush their work. The class teacher 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 were not made aware of their mathematics anxiety scale or
mathematics tasks scores and these were calculated off site.
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5Results
5.1 Internal consistency and exploratory factor analysis
An exploratory factor analysis on the 26-items was conducted using principal component
analysis (PCA) and varimax rotation. Bartlett’s test of sphericity was significant (p<0.01),
indicating that factor analysis was possible. The Kaiser-Meyer-Olkin (KMO) value was
also sufficiently high (0.870) (Pallant, 2001). Considering the discrepancy between eigen-
values suggesting 5-factors and the scree plot suggesting 1-factor (Fig. 1) a parallel
analysis (PA) was conducted simulating 1000 data files. According to Franklin, Gibson,
Robertson, Pohlmann, and Fralish (1995), when comparing PA with the use of PCA in
previous research, PCA alone was shown to have potentially resulted in over-extraction of
components, and therefore potentially misleading results. Accordingly, Franklin et al.
(1995) recommend the routine use of PAwhich creates a random dataset based on original
data (comparing eigenvalues from a pre-rotated data set from a matrix of random values of
the same dimensionality). Regarding interpretation of this test, when parallel analysis
eigenvalues (based on the random data) exceed the eigenvalues from PCA, these can be
ignored and the number of suggested components prior to intersect (if both PCA and PA
eigenvalues and components were plotted on a graph) can be judged as the number of
components to extract.
Our results suggested extraction of 1-factor explaining 31.26% of the variance as the
second simulated eigenvalue (1.68) was higher than the empirical eigenvalue (1.37). A 1-
factor solution with a loading threshold of more than .45 was forced, as the scale could be
made more statistically robust by implementing a higher cut-off. Stevens (1992) suggests that
factors should load above 0.5 for a sample of 100 and 0.3 for a sample of 200, the current
study (n= 163) can be judged as between these values and thus > 0.45 was judged to be
Fig. 1 Factor analysis scree plot suggesting 1-factor
238 Petronzi D. et al.
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acceptable. This resulted in the removal of seven items (2, 5, 6, 7, 9, 16, and 20), leaving a 19-
item iteration of the CMAS-UK with high internal consistency (α= 0.88). A subsequent
analysis was conducted to determine the extreme score discriminative power of the 19-items
based on a median split (33). All ttest results were significant, suggesting that each item could
discriminate between extreme scores.
1
The current 19-item measure of mathematics anxiety corresponds to the 22-item MASC
(Chiu & Henry, 1990) and 26-item MARS-E (Suinn et al., 1988) in terms of number of
items and time to complete and should be more manageable for younger children. Future
comparison against these validated scales is justified as, like the CMAS-UK, they were
developed for use with children, albeit somewhat older. In terms of a practical application
to classrooms, it is beneficial for the CMAS-UK to have fewer items due to its intended
lower age range, with issues surrounding attention and fatigue in younger children,
particularly those in reception. Table 2shows the factor loadings of each item and the
response frequencies, whilst Fig. 2shows the range of CMAS-UK scores indicating a wide
spread and normal distribution.
5.2 Factor labelling
Items that loaded onto the single observed factor appeared to have a strong association with
feelings and situations during the moment-to-moment experience of performing a mathematics
task, i.e., explaining an answer to the teacher, being the last to finish mathematics work,
making mistakes and getting work wrong. This factor was thus named, “Online Mathematics
Anxiety”, maintaining the factor 2 name from the previous research (Petronzi et al., 2018).
This factor consists of merged items from the initial factor 1 and factor 2. The entire
mathematics lesson could be viewed as being an online task, as it requires the learner to not
only complete work, but to observe and listen closely to instruction—something that high
anxious children may find difficult.
5.3 Confirmatory factor analysis—2-factor 26-items
A series of confirmatory factor analyses was used to test the previous 26-item version of the
CMAS-UK against the revised 19-item scale that emerged in this research. Testing the 2-factor
model of the CMAS-UK identified in previous research (Petronzi et al., 2018), the fit indices
showed that the data were not a perfect match to the model. The analysis of the 2-factor
solution (Fig. 3) resulted in a large and highly significant chi square, χ2(298) = 409.358,
p< 0.001 although this can be sensitive to sample size (Goffin & Jackson 1988, as cited in
Kline (1994)). The comparative fit index (CFI)= 0.88 and the Tucker-Lewis Index (TLI) =
0.87 did not indicate a good model fit (<0.95), although the root mean for approximation was
acceptable (RMSEA = .05). Based on the CFI and TLI criteria (Table 3), the model did not
indicate a good fit.
1
When a 2-factor solution was forced on the data collected with 26-items (N= 163) with a loading threshold to
replicate our previous study (0.35) (Petronzi et al. 2018), almost all of the same items were found to load on the
same factors according to the Rotated Component Matrix. First factor items (2, 5, 6, 7, 12, 13, 14, 15, 16, 24, 26)
and second factor items (1, 4, 8, 11, 17, 18, 19, 21, 22, 25). The only disparity was observed with items 3 (reverse
direction loading), 10, and 23 (loaded onto both factors) although the same items were removed (9 & 20) due to
insufficient loading (< 0.35) (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.
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5.4 Confirmatory factor analysis—1-factor 26-items
A confirmatory factor analysis was used to further test a 1-factor model (Online Mathe-
matics Anxiety) of the previous 26-item CMAS-UK to replicate the single factor identified
in the current research. The fit indices showed that the data were not a perfect match to the
model. The analysis of the 1-factor solution resulted in a large and highly significant chi
square, χ2(299) = 454.01, p< 0.001 although this can be sensitive to sample size. The
comparative fit index (CFI) = 0.84 and the Tucker-Lewis Index (TLI) = 0.82 did not
indicate a good model fit (< 0.95), although the root mean for approximation was accept-
able (RMSEA = 0.05). Based on the CFI and TLI criteria (Table 4), the model did not
indicate a good fit.
Table 2 Factor loadings and response frequencies of the 19-item CMAS-UK (> 0.45 threshold)
Item Online number
apprehension
Frequency—
happy
Frequency—
uncertain
Frequency—
sad
Q1: When my friends finish their work before
me, I feel…
0.540 73 47 43
44.8% 28.8% 26.4%
Q3: If I am the last to finish numeracy work
on my table, I feel…
0.572 47 52 64
28.8% 31.9 39.3
Q4: If I make a mistake in numeracy, I feel…0.565 48 77 38
29.4% 47.2% 23.3%
Q8: When I cannot do my numeracy work,
I feel…
0.552 40 50 73
24.5% 30.7% 44.8%
Q10: When I have to explain a numeracy
problem to my teacher, I feel…
0.540 74 60 29
45.4% 36.8% 17.8%
Q11: If I think I cannot do my numeracy
work, I feel…
0.617 46 56 61
28.2% 34.4% 37.4%
Q12: When I see a lot of numbers, I feel…0.520 105 45 13
64.4% 27.6% 8%
Q13: When I have to explain a numeracy
problem to my friends, I feel…
0.520 89 53 21
54.6% 32.5% 12.9%
Q14: IfIhavetofinishallmynumeracy
work in lesson, I feel…
0.583 78 37 48
47.9% 22.7% 29.4%
Q15: Listening to the teacher in my numeracy
class makes me feel…
0.496 115 35 13
70.6% 21.5% 8%
Q17: If I answer questions and get them
wrong, I feel…
0.624 41 53 69
25.2% 32.5% 42.3%
Q18: If I have to tell the teacher that I do not
understand my numeracy work, I feel…
0.542 50 70 43
30.7% 42.9% 26.4%
Q19: If other children know that I find
numeracy hard, I feel…
0.639 53 46 64
32.5% 28.2% 39.3%
Q21: When I watch or listen to my teacher
explain a numeracy problem, I feel…
0.465 87 55 21
53.4% 33.7% 12.9%
Q22: If I do not finish my number work in
class, I feel…
0.615 40 62 61
24.5% 38% 37.4%
Q23: If other children finish their numeracy
work very quickly, I feel…
0.606 64 49 50
39.3% 30.1% 30.7%
Q24: When I explain how I got my answer
to my teacher, I feel…
0.479 91 45 27
55.8% 27.6% 16.6%
Q25: When my teacher wants me to do
numeracy at home, I feel…
0.515 92 37 34
56.4% 22.7% 20.9%
Q26: Walking into the numeracy class
makes me feel…
0.567 98 45 20
60.1% 27.6% 12.3%
240 Petronzi D. et al.
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5.5 Confirmatory factor analysis of the current CMAS-UK: a 1-factor, 19-item model
A final confirmatory factor analysis was used to test the 1-factor model of the CMAS-UK. The
analysis of the 1-factor solution (Fig. 4) resulted in a large and highly significant chi square,
χ2(152) = 244.860, p< 0.001, although this can be sensitive to sample size. The comparative
fit index (CFI) = 0.87 and the Tucker-Lewis Index (TLI) = 0.86 did not indicate a good model
fit (< 0.95), although the root mean for approximation was acceptable (RMSEA = 0.06). In
sum, the model fit indices (Table 5) matches the acceptable and non-acceptable parameters of
the 2-factor 26-item CMAS-UK and the 1-factor 26-item model, indicating that a refined 19-
item version of the scale—which will be more manageable for younger children—can be
retained and subsequently tested using a larger sample size in future work.
The results show that CFA standardised regression weights are only marginally smaller than
the EFA factor loadings. The standardised regression weights in the CFA are favourable as
they closely link to the EFA, supporting the 19-item model and this is shown to be consistent
across statistical tests. The small observed difference between regression weights and factor
loadings exert no effects on the model that would lead to differential theoretical interpretations.
5.6 CMAS-UK scores and the mathematics task
As expected due to the age-appropriateness of the mathematics tasks for each year group, there
was no significant effect of year group on mathematics task scores, F(2,160) = 1.88, p=0.16;
the means and standard deviations for each year group are shown in Table 6. There was no
significant effect of primary school on mathematics performance F(1,161) = 1.71, p= 0.19, or
mathematics anxiety F(1,161) = 1.00, p= 0.32. However, correlational analysis demonstrated a
large, negative correlation between scores on the 19-item CMAS-UK and performance on the
mathematics task (overall score accuracy), r(163) = −0.620, p< 0.001. This correlation can be
seen by year group: (1) reception, r(59) = −0.597, p< 0.01, (2) year 1, r(57) = −0.557,
p< 0.01, and (3) year 2, r(47) = −0.807, p< 0.01.
Fig. 2 The distribution of children’s CMAS-UK Scores (19-items)
Further development of the Children’s Mathematics Anxiety Scale UK... 241
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6Discussion
The extant literature on mathematics anxiety has given limited attention to the early years
of mathematics education. Knowledge has therefore been limited with regard to the onset
of mathematics anxiety and whether factors in the early educational years have an
Fig. 3 CMAS-UK confirmatory factor analysis structure (2-factor 26-item model). *Measurement error. **Ob-
served variables. ***Percent of variance explained. ****Standardised regression weights. *****Common factors
Table 3 Fit indices for the CMAS-UK (2-factor 26-items)
X2 df pCFI TLI NFI RMSEA Pclose
M1 409.358 298 < 0.001 0.88 0.87 0.67 0.05 0.603
Cut off values
(Hu & Bentler, 1999)
N/A N/A > 0.05 > 0.95 > 0.95 > 0.095 < 0.06 > 0.05
242 Petronzi D. et al.
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association with this. Consequently, the CMAS-UK was developed to measure mathe-
matics anxiety in young children (4–7 years), younger than those targeted by other
measures (Chiu & Henry, 1990; Dowker et al., 2012). The current study further validated
the scale using exploratory and confirmatory factor analysis and demonstrated a negative
relationship between mathematics anxiety and mathematics performance. The 19-item
CMAS-UKwasshowntohavehigh internal consistency (α= 0.88) (Lacobucci &
Duhachek, 2003; Rattray & Jones, 2005) and is similar to that obtained in (Petronzi
et al., 2018) (α=0.89).
Whilst the association between mathematics anxiety scores and mathematics perfor-
mance scores was significant and large (r=−0.620), this should be viewed with a degree
of caution. In some cases, children who obtained a high score on the mathematics task also
obtained a high score on the CMAS-UK. Ashcraft (2002)alsopreviouslyfoundthat
despite some children claiming a degree of mathematics anxiety, their competence scores
Table 4 Fit indices for the CMAS-UK (1-factor 26-items)
X2 df pCFI TLI NFI RMSEA Pclose
M1 454.014 299 < 0.001 0.84 0.82 0.64 0.05 0.151
Cut off values
(Hu & Bentler, 1999)
N/A N/A > 0.05 > 0.95 > 0.95 > 0.095 < 0.06 > 0.05
Fig. 4 CMAS-UK confirmatory factor analysis structure (1-factor 19-item model). *Measurement error. **Ob-
served variables. ***Percent of variance explained. ****Standardised regression weights. *****Common factor
Further development of the Children’s Mathematics Anxiety Scale UK... 243
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
remained unaffected. Previously, Ashcraft, Kirk, and Hopko (1998) found that the effects
of anxiety were only apparent on certain mathematical concepts. Thus, it may be that the
children were highly anxious, but were comfortable with the concepts on the mathematics
task, and thus performance was unaffected. Ashcraft (2002) stated that researchers should
always consider the competence-anxiety relationship, as those with higher anxiety may
demonstrate increased competence in varying circumstances. However, for the most part
our data demonstrates that children with low CMAS-UK scores performed better on the
mathematics task whilst children with higher scores on the CMAS-UK generally had
lower mathematics performance scores. This large correlation supports the use of items
created following qualitative research with the target population (Petronzi et al., 2017)and
suggests that the items are an accurate reflection of children’s experiences. Indeed, it was
also found that the items could discriminate extreme scores. In the current research, a
range of anxiety scores was evident and there was a strong negative association between
CMAS-UK scores and mathematics task scores; this addressed the aim of testing the
predictive validity of the CMAS-UK and has shown that it can be an appropriate measure
for early childhood difficulties in mathematics. Nevertheless, further research is required
to assess the direction of causation. Previously, research by Ma and Xu (2004)useda
longitudinal study with 3116 students from grade seven to twelve (UK age 12–17) to
determine causal ordering. Throughout the 6 years, students completed achievement tests
in mathematics and science and a questionnaire which covered a variety of measures,
including mathematics anxiety, basic numeracy skills, algebra, geometry, and quantitative
literacy. Results from the study indicated that lower mathematics achievement scores in
earlier grades were associated with higher mathematics anxiety scores in the later grades,
suggesting that mathematics achievement had a causal priority over mathematics anxiety.
The current analyses suggested a 19-item single factor solution was appropriate and
contrasts to the previous 2-factor scale (Petronzi et al., 2018). Comparing the participation
numbers from our previous work (reception = 82; year 1 = 108; year 2 = 117) to the current
research’s (reception = 59; year 1 = 57; year 2 = 47) suggests a possible explanation for the
difference in model structure. In the previous research, the reception year group was
considerably less represented than year one and two—whilst in the current research were
similar across the year groups. Adding to this, the numbers of participating schools in the
Table 5 Fit indices for the CMAS-UK (19-items)
X2 df pCFI TLI NFI RMSEA Pclose
M1 244.860 152 < 0.001 0.87 0.86 0.72 0.06 0.095
Cut off values
(Hu & Bentler, 1999)
N/A N/A > 0.05 > 0.95 > 0.95 > 0.095 < 0.06 > 0.05
Table 6 Means and standard devi-
ations for year groups and mathe-
matics performance scores
N Mean (SD)
Reception 59 72.46 (20.54)
Year 1 57 68.77 (25.60)
Year 2 47 77.23 (19.50)
Total 163 72.55 (22.29)
244 Petronzi D. et al.
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current research were less than in our previous scale development work; however, the
schools were of similar socioeconomic status and ethnicity intake. The omission of an item
relating to mental arithmetic is somewhat surprising as previous research, e.g., Ashcraft
(2002) indicated that this is a particularly difficult aspect of mathematics and may act as a
key differentiator between mathematics attitudes. Nevertheless, at the age of reception,
children are learning and practising calculations, becoming familiar with numbers and
strategies to facilitate their learning. Thus, there is less emphasis on mental arithmetic
within this younger age group, which becomes a more essential skill as children progress
through education. Therefore, the mental arithmetic item (and its low factor loading) has
low saliency in this context for younger children. Again, this finding is a change in model
structure from our previously observed 2-factor solution to the 1-factor solution in the
current research. However, CFA results showed that a 1-factor 19-item scale had similar
acceptable and non-acceptable parameters as a 2-factor 26-item version of the CMAS-UK,
indicating that the change in model structure—whilst warranting further research—should
not be considered concerning. Indeed, this shorter version is preferable and more man-
ageable for younger children. Further to this, the current research also implemented a
slightly increased and more robust loading threshold for items (> 0.45), although this had
no impact on the factor solution of the CMAS-UK. It is also notable that a forced 2-factor
solution on data for the 26-items with a loading threshold to replicate our previous study
(0.35) indicated almost all the same items were found to load on the same factors
according to Rotated Component Matrix. Although a 1-factor solution on the current data
was advised by parallel analysis, the same items loading onto either of the two factors
indicates reliability of the scale across our development studies, again suggesting that
there should be little concern in the change of model structure.
Of the 19-items that remained from the previous 26-item version of the scale, 11 were
maintained from the “Online Mathematics Anxiety”factor and it was thus preserved as the
single dominant factor of the CMAS-UK. The additional 8 items were maintained from the
“Prospective Mathematics Task”factors. The 19-items seemingly encapsulate a typical
mathematics lesson, from feelings when walking into a mathematics lesson, to being
unable or the last in a group to finish the work set and may explain the incorporation of
“Prospective Mathematics Task”into the single factor solution. Other examples pertain to
other children finishing their work quickly and having an awareness of someone strug-
gling (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 in quantitative mathematics anxiety
research with older populations, suggesting that the early years of education may some-
what 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 their mathematics experiences. Young children’s
memories are still developing throughout earlier years and are therefore restricted in how
much information and experiences they can store in their short-term memory (Croker,
2012). However, currently in the UK, children from 4 years are expected to engage in self-
assessment and self-reflection of their learning and emotional state using school specific
self-report measures (there is no standard measure). Yet in most cases children rate their
learning-based feelings on a scale of 1–10 using emojis for visual support. Indeed,
educational psychology services in the UK also implement and refer teachers and
Further development of the Children’s Mathematics Anxiety Scale UK... 245
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childcare workers to a test bank of scales for the measurement of children’s emotional and
mental well-being using quantitative measurement. In light of this, the CMAS-UK (with
visual emoji support) aligns with the current UK practise.
The development of the CMAS-UK is a positive response to Ashcraft and Moore (2009)
and Mazzocco (2007) who stated that the appropriate tools have not been developed to
examine anxiety and those at risk of mathematics difficulties in early education. Rossnan
(2006) argued that mathematics anxiety can develop at any age and the associated fear is
deeply rooted within a child’s first experience of school mathematics. The current study
highlights an adverse relationship between young children’s early mathematics experiences
and performance that could potentially develop and progress into the later educational years.
This relationship may be impacting performance much earlier than previously anticipated by
research. Longitudinal studies may be beneficial to test the long-term consequences of
worrisome thoughts about mathematics from the ages of 4–7 years. The results of this study
support that the early years and experiences of working with numbers are critical. Mazzocco
et al. (2012) further considered that mathematics anxiety in older children may be rooted
within the early years of education and that efforts should be made in early childhood to steer
them away from negative outcomes. This contention is supported by the current research and
reinforces the utility of the CMAS-UK in identifying children at risk of developing mathe-
matics anxiety.
Moreover, it is necessary for future researchers to consider the multitude of potential
influences on the development of mathematics anxiety (Petronzi et al., 2018) including the
use of negative mathematics-based language around children, using mathematics as a punish-
ment and exposing children to evaluation and pressure from peers. These and other influences
should be considered when using an assessment measure such as the CMAS-UK to quantify
feelings and experiences. Further predictive and convergent validation work on the scale is
needed with younger children, whilst the CMAS-UK can support projects evaluating inter-
vention techniques that are known to be efficacious with older children. For example, Park,
Ramirez, and Beilock (2014) that expressive writing following and prior to a mathematics task
increases the mathematics performance of those with university students with higher mathe-
matics anxiety.
In sum, previous research has neglected the assessment of affect towards numbers
among younger children. Our work has gone some way to address this shortfall by
providing an easily administrable scale with a parsimonious factor structure. Previous
attempts to measure mathematics anxiety among older children and adults have
emphasised the multidimensionality of the construct whereas the current findings high-
light the limited context in which young children are exposed to numbers. We demonstrate
the importance of mathematics anxiety at a young age and the relation this has on
mathematics performance. The current work should encourage further investigation into
the developmental relations between mathematics anxiety and mathematics performance;
improved theoretical understanding may inform educational practices and support the
design of effective interventions that stop negative trajectories of mathematics anxiety
and performance from a young age.
Compliance with ethical standards
Competing interests The authors declare that they have no conflict of interest.
246 Petronzi D. et al.
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Appendix 1
Fig. 5 Reception mathematics task
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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International
License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and repro-
duction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a
link to the Creative Commons license, and indicate if changes were made.
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Affiliations
Dominic Petronzi
1
&Paul Staples
1
&David Sheffield
1
&Thomas E. Hunt
1
&
Sandra Fitton-Wilde
1
*Dominic Petronzi
d.petronzi@derby.ac.uk
1
University of Derby, Enterprise Centre, Bridge Street, Derby DE1 3LD, UK
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1.
2.
3.
4.
5.
6.
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