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Pre-school numeracy play as a predictor of children’s attitudes towards mathematics at
age 10
Aidan Clerkin1 and Katie Gilligan2
1Educational Research Centre, Dublin, Ireland.
2University College London, London, UK.
Abstract
Numeracy activities in early childhood have been linked to children’s mathematical
performance in subsequent years. However, few studies have examined associations
between early numeracy play and children’s subsequent attitudes towards
mathematics. This study draws on the TIMSS 2011 assessment to provide a
retrospective snapshot of pre-school numeracy play reported by the parents of 10-
year-old children (N=4560). Most children were found to have engaged frequently
in some form of early numeracy activity. However, children from lower
socioeconomic backgrounds had less regular engagement with numeracy play, while
spatial play (e.g., building blocks) was less common among girls. The extent to which
children engaged in pre-school numeracy play was significantly associated with
greater confidence and (for children from higher-socioeconomic backgrounds) liking
of mathematics at age 10, controlling for other factors. The results highlight
socioeconomic and gendered differences in children’s early activities about which
policymakers, educators and parents should be aware. They also suggest the potential
role of numeracy play in fostering positive attitudes towards mathematics, which
should be considered amidst efforts to increase participation in Science, Technology,
Engineering and Maths (STEM) domains.
Keywords: Confidence, Attitudes, TIMSS, Mathematics, Numeracy Play
Funding
KG was supported by the Bloomsbury Colleges Ph.D. Scholarship Programme, U.K and the
National Centre for Curriculum and Assessment (NCCA) Ireland.
Acknowledgements
An earlier version of this paper was presented at ECER 2016 (European Conference
on Educational Research) in Dublin, Ireland. We thank the attendees of that
presentation, particularly Heike Wendt, for their feedback and stimulating discussion.
Supplementary materials
The TIMSS 2011 data are available for download from
https://timssandpirls.bc.edu/timss2011/international-database.html.
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Pre-school numeracy play as a predictor of children’s attitudes towards mathematics at
age 10
Introduction
Early childhood experiences can have substantial, long-lasting effects on children’s
development, the influence of which can be apparent for many years (Hoff, 2003; World
Bank, 2015). These childhood experiences can confer both positive effects on development
(e.g., learning supported by parental scaffolding of a challenging activity) and negative
effects (e.g., disadvantages arising from childhood stress or non-stimulating environments).
Play has been noted as a particularly important pathway through which young children’s
cognitive development, self-regulation, and social interaction can be enhanced (French, 2013;
Kernan, 2007; Milteer et al., 2012). For example, more frequent fantasy play has been
associated with improved executive functioning (Thibodeau, Gilpin, Brown, & Meyer, 2016),
while child-caregiver engagement during play facilitates the development of memory skills
and problem-solving (Tamis-LeMonda, Shannon, Cabrera & Lamb, 2004). It also appears
that early childhood experiences may be influential in later academic achievement. For
example, parental reports of early learning activities, including both literacy and numeracy
activities, have been positively associated with estimates of children’s ability on starting
primary school (Segers, Kleemans & Verhoeven, 2015).
Early numeracy activities
This paper explores the importance of home-based, early numeracy activities in the pre-
school years (in Ireland, this includes children up to approximately five years old). In this
study numeracy play (or numeracy activity) is defined as play with number toys, shapes,
construction toys, building blocks, or board/card games, in addition to counting things and
singing counting rhymes/songs. Early learning activities, including numeracy activities, can
be differentiated into formal activities (those where there is an element of explicit instruction
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from the caregiver to the child) and informal activities (those that arise in daily life or in play
scenarios). There is evidence to suggest that formal and informal pre-school home numeracy
activities can have substantial, yet differing, effects on later mathematics achievement
(Skwarchuk, Sowinski & LeFevre, 2014; Torbeyns, Gilmore & Verschaffel, 2015). Formal
numeracy activities, such as explicit teaching of numeracy concepts in the early years, are
associated with improvements in symbolic number knowledge, digit naming and counting
abilities (LeFevre, Clarke & Stringer, 2002; Skwarchuk et al., 2014). An example of a formal
numeracy activity might be playing with number toys or singing counting songs together. By
comparison, informal numeracy activities are experienced incidentally as part of daily life or
during play – for example, during a (real or imaginary) shopping trip, while cooking, or while
playing with blocks, shapes, or construction toys (which require spatial skills). Informal
numeracy activities can positively influence both non-symbolic arithmetic skills and
mathematics achievement more generally (LeFevre et al., 2009; Skwarchuk et al., 2014).
Both formal and informal numeracy activities appear to play significant roles in the
development of later numeracy skills.
Early numeracy play in childhood has been shown to be related to children’s later
academic achievement in mathematics. For example, variation in the home numeracy
environment appears to explain a unique proportion of the variation in children’s early
numeracy skills, even after controlling for the role of the home literacy environment, and
children’s working memory and non-verbal intelligence (Segers et al., 2015). In other words,
the development of numeracy skill is not simply a function of more generic developmental
activities (such as parent-child interaction while reading stories). The home numeracy
environment is created both by access to numeracy related materials and by the involvement
of parents (Payne, Whitehurst & Angell, 1994; Segers et al., 2015). As such, parents have a
vital role in the creation of the home numeracy environment through the provision of
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numeracy-related toys and learning tools, and through parent-child interaction in numeracy-
related scenarios. Findings from older children suggest that one important factor contributing
to the home environment is parental expectations of their children’s later achievement
(Jeynes, 2005). Beyond the home numeracy environment, more specific early numeracy
activities have also been associated with positive numeracy outcomes. Grissmer et al. (2013)
reported improvements in mathematics skills following an intervention promoting play with
visuospatial toys (e.g., Lego, Wikki Stix), while Verdine et al. (2014) found that block
assembly skills predict maths performance in children as young as three years old. Block
play appears to be particularly important in the development of spatial skills and
mathematical language (Jirout & Newcombe, 2015; Ramani, Zippert, Schweitzer & Pan,
2014).
Although recent studies have underlined the importance of pre-school home
numeracy activities to young children’s mathematical development (Anders et al., 2012;
Huntsinger, Jose & Luo, 2016; Segers et al., 2015), the generalisability of many of these
studies is somewhat limited by the small-scale or unrepresentative nature of the samples
(Tudge, Brown & Freitas, 2011). Furthermore, they have tended to consider such experiences
with reference to the acquisition of numerical skills among very young children, rather than
mathematical achievement among older age groups. The relationship between early
numeracy activities (during the pre-school years) and children’s subsequent attitudes and
engagement in formal education – mathematics in particular – has received comparatively
little attention (Mahatmya, Lohman, Matjasko & Farb, 2012).
Attitudes towards mathematics
Students’ attitudes towards mathematics encompass their liking or disliking of mathematics,
their level of engagement in mathematical activities, beliefs about being good or bad at
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mathematics, and beliefs about the usefulness of mathematics (Ma & Kishor, 1997, p.27).
There is convincing evidence that positive attitudes towards maths are related to higher
mathematical achievement and lower levels of maths anxiety among 10- and 11-year-olds
(Dowker, Bennett, & Smith, 2012). Similar findings have been reported for student cohorts at
both primary and post-primary levels and across a range of educational systems (Punaro &
Reeve, 2012; Ramirez, Gunderson, Levine, & Beilock, 2013; Mullis, Martin, Foy & Arora,
2012). Unusually, Irish teenagers report high levels of maths anxiety alongside high
performance in mathematics, relative to their international peers (Radišić, Videnović &
Baucal, 2016), while Irish primary students tend to report much more positive attitudes
towards reading and science than towards mathematics (Clerkin & Creaven, 2013).
Factors underlying negative attitudes towards mathematics and mathematics-related
anxiety include social influences such as parental or teacher attitudes, pressure for success in
mathematics classes, or embarrassment over difficulties in conceptual understanding of
mathematics (Maloney & Beilock, 2012; Turner et al., 2002). However, the relation between
attitudes and achievement is not straightforward and may be further complicated by gender
differences. Female students tend to report greater maths anxiety (Devine, Fawcett, Szűcs, &
Dowker, 2012), while international studies show that boys are more confident in their maths
ability than girls, even while differences in actual mathematical performance are minor (Else-
Quest, Hyde & Linn, 2010). However, few studies have examined the potential role of early
childhood experiences, particularly engagement in early numeracy activities, in the
development of children’s attitudes towards mathematics.
Current study
Despite the proposed cognitive and academic benefits of early numeracy play, findings from
the United States suggest that the amount of time children spend playing – especially in free
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or child-driven play – is in decline (Ginsburg, 2007). Furthermore, it has been reported that
parents in Ireland tend to engage in early literacy activities with their children to a greater
degree than numeracy activities (Gustafsson, Hansen & Rosén, 2013). However, to our
knowledge, relatively little descriptive information is available in Ireland on the nature and
extent of play practices in early childhood, particularly early numeracy play that takes place
in everyday, generalisable contexts (Anders et al., 2012; Tudge & Doucet, 2004). Hence, the
first aim of this study is to provide a snapshot of early numeracy activities among Irish
children using a large-scale, nationally-representative dataset. Patterns of differences in
numeracy play by children’s gender and socioeconomic background will also be described.
These data will provide a baseline for comparison in future studies.
As outlined above, the promotion of positive attitudes towards maths is key to
improving students’ experience in maths lessons and their maths achievement (Dowker et al.,
2012). It is also pertinent to wider industry concerns about low uptake of mathematics and
science courses, student proficiency in mathematics and science, preparing an adequately
qualified STEM (science, technology, engineering and mathematics) workforce, and
presenting STEM options as viable opportunities for female students (Engineers Ireland,
2010; Frome, Alfeld, Eccles, & Barber, 2006; Science, Technology. Engineering and
Mathematics Education Research Group [STEMERG], 2016). However, few studies have
examined how early numeracy activities relate to subsequent attitudes towards maths. The
second aim, therefore, is to extend previous findings by exploring the associations between
children’s engagement in early numeracy play (before beginning primary school) and their
self-reported attitudes towards mathematics in Fourth grade (at approximately age 10). More
specifically, this study examines the relationship between early numeracy activities and three
separate indicators of children’s attitudes towards mathematics after accounting for other
known covariates such as gender, socioeconomic status and actual mathematical
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achievement. The results are presented in light of the strengths and limitations of using
retrospective self-report measures with large representative samples.
Finally, we wish to highlight a recent appeal for wider utilisation of data from large-
scale studies, particularly with regard to “articles exploring important aspects of the teaching
and learning environment, such as… students’ affective characteristics” (Lenkeit, Chan,
Hopfenbeck, & Baird, 2015). In this paper, we hope to draw the attention of a broader
community to the breadth of information collected in large-scale assessments such as TIMSS
(Trends in International Mathematics and Science Study), which are nominally focused on
educational achievement but also offer a wealth of cross-national psychological and
sociological data. In addition to their power in informing more in-depth studies, large-scale
assessments provide valuable snapshots of educational, social and psychological differences
in well-defined populations of children, and provide a reliable platform from which these
features can be monitored over time.
Material and methods
This paper draws on the TIMSS 2011 dataset. TIMSS, organised by the International
Association for the Evaluation of Educational Achievement (IEA), is among the world’s
largest studies of mathematics and science achievement at both primary (Grade 4) and post-
primary (Grade 8) levels. TIMSS was administered in Ireland by the Educational Research
Centre on behalf of the Department of Education and Skills. The data were made available to
the public and researchers in early 2013 (see https://timss.bc.edu). Full details on the
outcomes for Irish Fourth grade students are available in the Irish national reports (Eivers &
Clerkin, 2012, 2013). International results are presented in Mullis et al. (2012).
Participants and measures
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Participants were Irish students (N = 4560; mean age: 10.3 years; 51% boys) and their
parents (N = 4568), sampled and weighted to be representative of the national population of
Fourth grade students. Students completed a test of mathematics performance and a
questionnaire with questions on their attitudes to mathematics (confidence in, liking of, and
engagement in lessons). An accompanying parent questionnaire asked about the type of early
numeracy activities that children experienced before beginning primary school and
information on the home environment. Responses to the student and parent questionnaires
can be directly linked for each student-parent dyad.
Table 1 shows a summary of the measures used in this paper. Children’s
engagement in early numeracy activities was ascertained by parents’ responses to six items
listing different forms of numeracy activity (for example: counting things, playing with
number toys, playing with building blocks). These items were preceded by the prompt,
“Before your child began primary school, how often did you or someone else in your home
do the following activities with him or her?”. Parents also completed nine items focusing on
children’s engagement in early literacy activities. The same prompt was used, followed by a
list of literacy activities (for example: write letters or words). All items were answered on a
three-point ordinal scale (‘often’, ‘sometimes’, or ‘never or almost never'). The Home
Resources for Learning scale was derived from parents’ answers to six questions relating to
their highest level of educational attainment, parental occupation (selected from twelve
categories), the number of books in the home, the number of children’s books in the home,
the availability of an internet connection at home, and whether the child has their own room
to study in at home.
The remaining measures were provided directly by participating students. Students’
liking of mathematics was based on their responses to five items included in the student
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questionnaire (for example: I enjoy learning maths); their confidence with mathematics was
based on six items (for example: I learn things quickly in maths); and their level of
engagement in mathematics lessons was based on five items (for example: I am interested in
what my teacher says [during mathematics lessons]). For each of these three scales, students
indicated their level of agreement on a four-point Likert scale ranging from ‘agree a lot’ to
‘disagree a lot’. Finally, students’ mathematics achievement was based on student’
performance on the TIMSS mathematics assessment, which is developed to be broadly
representative of the expected mathematics curriculum experienced by Fourth grade students
in all participating countries. Full technical details on the development and construction of
each of these measures are available in Martin and Mullis (2012).
Analytic strategy
As a baseline study of early childhood numeracy activities, descriptive statistics were used to
create a snapshot of the activities of Irish children prior to commencing school. The
prevalence of particular types of numeracy play are reported, followed by variation in each
type of play by student gender and home background (focusing on educationally-relevant
characteristics of the home environment rather than purely economic indicators). An overall
measure of early numeracy activities (a composite of the different play types) was used to
compare pre-school numeracy activities in Ireland to those internationally and to describe
how attitudes towards mathematics in later childhood are associated with early numeracy
play.
Analyses were performed using the International Database Analyzer (IDB-A), an
add-on for SPSS, which is developed by the IEA specifically for use with surveys such as
TIMSS (International Association for the Evaluation of Educational Achievement, 2017). It
facilitates the accurate use of weights, which is an essential (and often neglected) step in
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analysing data of this nature which allows the responses provided by the participating sample
to be accurately generalised to the national population of Fourth grade students (Liou &
Hung, 2015). The IDB-A is designed to facilitate the correct use of plausible values in
estimating mathematics scores. Analyses are repeated five times using five plausible values
for each student’s maths achievement. These scores are subsequently combined into a single
best estimate of an individual’s ‘true’ mathematics achievement (Rutkowski, Gonzalez,
Joncas & von Davier, 2010; von Davier, Gonzalez & Mislevy, 2009). IDB-A also enables
users to account for complex survey design (students within schools within countries) by
using a jackknife repeated replications (JRR) method to estimate accurate standard errors.
Results
Correlations between the continuous scale variables are shown in Table 2. Significant
bivariate associations between each pair of variables were observed, with the exception of a
very small negative correlation between students’ home background and their liking of
mathematics. The three attitudinal indicators exhibited moderately strong correlations (r =
.43 to r = .57). Mathematics achievement (test performance) was most strongly associated
with students’ level of confidence and with their home background. The extent to which
students had been exposed to literacy and numeracy activities before starting school was
quite strongly correlated (r = .70).
Engagement in early numeracy play (pre-school age)
The frequency of various types of early numeracy play among Irish children is shown in
Figure 1. Counting objects was the most common activity, with more than two-thirds of
children (68%) often counting objects with their parents and only 2% (almost) never counting
at home. Playing board games or card games was the least common form of early numeracy
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play. It was the only activity where fewer than half of those surveyed did so often, with
nearly one-in-ten children (almost) never playing with board or card games. Most children
played with building blocks, games involving shapes, and sang counting rhymes or songs on
a regular basis. Playing with number toys was often done in just over half of the surveyed
households but (almost) never by about 8%.
There was little difference in patterns of play between boys and girls, with parental
reports indicating that both genders were exposed to most types of play to a broadly similar
extent (Table 3). The notable exception is the tendency for boys to play with building blocks
or construction toys to a greater extent than girls. Three-quarters of boys (75%) often played
with building blocks, compared to 58% of girls. Girls were more likely to engage in spatial
play of this nature (almost) never or only sometimes.
In general, children in homes with many resources for learning were approximately
twice as likely as those with few resources to have often experienced most of the specified
early numeracy activities (Table 3). A substantial minority of students in homes with few
educational resources (almost) never engaged in any numeracy play. For example, 21% of
children with few educational resources at home (almost) never played with number toys,
20% (almost) never sang counting songs or rhymes, and 10% (almost) never engaged in
counting the objects around them before beginning school. The greatest difference is seen in
play involving shapes, where children with few resources at home were much more likely
than those with many resources to (almost) never play with shape toys or puzzles (16% vs
1%), and were less than half as likely to do so often (33% vs 72%).
As shown in Figure 2, Irish children engaged in early numeracy play to a greater
extent than most of their international peers. About two-thirds of Irish students (66%) often
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engaged in early numeracy activities before beginning school, compared to half (49%) of
students internationally. Conversely, fewer than 2% of Irish students (almost) never
experienced such activities, almost three times lower than the international average (6%).
Among the 32 countries for which comparable data are available, parents in only six
countries reported more frequent early numeracy play than Irish parents – the Czech Republic
(75% often; <1% never or almost never), Hungary (75%; 1%), Slovakia (73%; 2%), Northern
Ireland (70%; 1%), the Russian Federation (69%; 2%) and Poland (68%; 1%). By
comparison, early numeracy play was much less common in a diverse range of countries,
including Morocco (18%; 28%), Hong Kong (29%; 11%), Sweden (33%; 6%), Iran (34%;
12%), Singapore (40%; 8%), and Portugal (45%; 5%).
Attitudes towards mathematics and science (Fourth grade)
In Ireland, more than two-fifths of Fourth grade students reported a high degree of liking
mathematics (41%), strong engagement in mathematics lessons (45%), and high levels of
confidence in mathematics (43%) (Clerkin & Creaven, 2013). Three logistic regression
models (one for each of these attitudinal outcomes) were conducted to examine which
characteristics were most strongly associated with students who report positive attitudes
towards mathematics and science (versus those with moderate or negative attitudes) in Fourth
grade.
For comparability and consistency across each attitudinal indicator, the same set of
covariates was specified for each model. These included students’ gender (entered as a
dummy variable); continuous scale measurements of students’ home resource for learning,
the extent to which they engaged in early literacy activities before starting school, and the
extent to which they engaged in early numeracy activities before starting school (all
standardized before analysis); interaction terms between engagement in early numeracy
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activities and students’ gender and home resources for learning; and students’ mathematical
achievement in Fourth grade. The model therefore takes account of the contemporaneous
correlation between academic achievement and student attitudes, as well as controlling for
other early learning activities (e.g., reading books) that would not be classified as numeracy
play but would still be expected to contribute to the child’s development. Associations that
remain significantly associated with early numeracy activities, taking account of these
factors, are therefore unlikely to be spurious.
Table 4 presents the results of the three models. As expected, students’ actual
mathematical achievement was significantly positively associated with their attitudes towards
the subject; it was also the only factor that was consistently associated with each of the
attitudinal outcomes. Boys were significantly less likely to report a high level of engagement
in mathematics lessons, but were significantly more likely to report a high level of confidence
in mathematics than girls. Students with greater resources for learning at home were, all else
being equal, less likely to report a high level of confidence in mathematics.
The frequency of students’ engagement in early numeracy activities before starting
school was the only other factor to show significant associations with the attitudinal
outcomes. Early numeracy play was not related to students’ level of engagement in formal
mathematics lessons in Fourth grade. However, children who engaged in more frequent
numeracy play at a young age were significantly more likely to report a high level of
confidence in mathematics at approximately 10 years of age. In addition, an interaction
between early numeracy activities and home resources for learning was observed to be
significantly associated with students’ liking of mathematics.
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The interaction between children’s liking of mathematics, gender, their engagement in
early numeracy play and their home background is clarified in Figure 3, which shows the
odds ratios associated with each combination of factors (with other variables held constant).
The chart depicts the odds ratios for reporting a high liking of mathematics in Fourth grade,
given four possible combinations of a child’s home background (‘high’ or ‘low’ levels of
learning resources at home) and engagement in pre-school numeracy play (to a ‘high’ or
‘low’ degree). ‘High/low’ are defined for these purposes as any value above/below half a
standard deviation from the population mean on each indicator. About 41% of the total
sample were thus categorised into one of four groups (Figure 3).
In general, girls were more likely than boys to report a strong liking of mathematics, a
tendency that was evident across all four categories. In addition, students were more likely to
report liking mathematics in Fourth grade if they had been exposed to a high frequency of
early numeracy play before starting school. This pattern was observed for both genders
(albeit to a slightly lesser extent for boys in low-HRL homes; OR=.92 vs OR=.97), and was
evident regardless of whether children came from homes with a very low level of educational
resources (OR=.97 for low-ENA vs 1.03 for high-ENA) or from homes with a very high level
of educational resources (OR=.82 for low-ENA vs .96 for high-ENA). The latter difference
is particularly marked – children from homes with many resources being especially unlikely
to express a strong liking for mathematics where they engaged very infrequently in early
numeracy play – as highlighted by the significant interaction term in the logistic regression
equation.
Discussion
This paper is the first to provide a detailed overview of the early numeracy activities
experienced by Irish children, with findings strengthened by the nationally-representative
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nature of the study sample. The results show that most Irish children frequently engage in
some form of early numeracy play, with relatively few children never engaging in these
activities. From an international perspective, pre-school numeracy play is found to be more
common in Ireland than in most other countries. Within-country analysis shows that patterns
of numeracy play were broadly similar among boys and girls – however, a notable exception
was the greater prevalence of spatial play involving building blocks or construction toys
among boys. Greater differences in patterns of play were evident for sociodemographic
factors, such that children in homes where fewer resources for learning are available were
much less likely to engage in numeracy play of any type. Particularly large differences in
spatial play (using shape toys, puzzles, or building blocks) and parent-child counting were
found.
Beyond describing the prevalence of numeracy play in Ireland, the second main aim
of this research was to examine the extent to which numeracy play at home during the pre-
school years is associated with children’s subsequent attitudes towards mathematics in
primary school (in Fourth grade, at approximately 10 years old). Controlling for other
relevant factors – including students’ gender, their home background, their performance on a
test of mathematical achievement, and their exposure to other types of (non-numeracy)
educational activities at a young age – the data show that engagement in early numeracy play
was significantly positively associated with children’s confidence with mathematics in Fourth
grade. Early numeracy play was also positively associated with liking mathematics in Fourth
grade, particularly for children from more socioeconomically-advantaged homes, for whom
infrequent numeracy play at a young age appeared to be a risk factor for more negative
attitudes in later years. The third attitudinal indicator – engagement during mathematics
lessons in school – showed no association with students’ early numeracy activities.
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These findings suggest that promoting numeracy activities in the home at a young age
could represent an effective method of supporting positive attitudes towards mathematics –
both cognitive attitudes such as ‘confidence’ and affective attitudes such as ‘liking’ – later in
childhood and potentially into adulthood. The promotion of positive attitudes is particularly
salient in Ireland, considering the relatively high proportion of Irish students who report
disliking mathematics compared to reading or science. As well as feeding into students’
attitudes and happiness at school more generally, negative attitudes are of some concern
given evidence that students with more negative attitudes towards mathematics tend to
achieve at a lower level (Mullis et al., 2012). Beyond the association with academic
achievement, these findings can inform the ongoing efforts to increase the uptake of STEM
subjects in Ireland, particularly among girls (Department of Children and Youth Affairs,
2014, STEMERG, 2016). Although several initiatives exist that seek to promote STEM
subjects to Irish students, they are often aimed at older age groups. The results reported in
this study suggest that interested parties – such as policy-makers, early childhood educators
and parents’ groups – could be advised to look at simple numeracy play activities in early
childhood as a way of facilitating positive experiences at a young age that may support more
positive attitudes, and achievement, in future generations.
The finding that girls and more socioeconomically-disadvantaged children tended to
engage in spatial play less regularly in their early years is concerning, given previous positive
associations found between early spatial thinking, spatial play, and later mathematical skill
(Gilligan, Flouri & Farran, 2017; Jirout & Newcombe, 2015; Verdine et al., 2014).
Concerted efforts should therefore be made to promote spatial play at an early age among
girls, and to promote regular numeracy play more generally among children with fewer
resources for learning at home. One difficulty is that children in more disadvantaged
contexts may have less access to toys or material resources for early numeracy play (e.g.,
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puzzles). As such, the importance of integrating relatively resource-independent activities
(such as counting everyday objects or singing counting songs) into children’s daily routine
should also be highlighted as a priority. Niklas, Cohrrsen and Tayler (2016) provide an
accessible example of a low-cost and relatively non-intrusive intervention that could serve as
a template for encouraging greater involvement in numeracy activities at a young age –
involving an information session for parents and an example of a game that can be played by
rolling dice and counting out a corresponding number of objects.
Limitations
Readers should note that the data reported here are based on students’ self-reported attitudes
(via written questionnaire) and retrospective reports of early play given by parents. Previous
studies indicate that parents’ recall of their children’s activities may not be completely
accurate. For example, parental reports of children’s play are limited to times in which
children are in their line of sight, and may be shaped by the degree to which parents pay
attention to their children’s play habits (Tudge et al., 2011). Furthermore, where parents do
report their children engaging in a particular activity it is difficult to measure, with precision,
the extent of this activity. Measurement is restricted to broad patterns of behaviour, without
clear demarcations. For example, one person’s interpretation of ‘often’ engaging in singing
counting songs may be equivalent to another person’s ‘sometimes’ singing counting songs.
Equally, parents’ reports of activities when their children were younger can also be
influenced by their current perceptions of their child’s engagement in mathematics activities,
or by their child’s current attitudes towards maths.
However, the accuracy of parents’ retrospective recall is unlikely to vary
systematically (i.e., in a biased manner) across participants, and any grey areas in the data are
likely to be somewhat mitigated by the large and randomly-selected sample. Bearing these
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caveats in mind, the survey-based methods used here can be viewed as representing a
practical approach to assessing large cohorts of children. The high participation rates and a
large nationally-representative sample, together with the strict quality control measures that
all participating countries in TIMSS must adhere to (Martin & Mullis, 2012), support the
view that the data reported here can be regarded as providing an unbiased and representative
view of Fourth grade students in Ireland.
It is also important to recognise that the cross-sectional design of the study means that
these findings cannot provide evidence of a causal association between young children’s
early numeracy play and their later attitudes towards mathematics, and no causal inferences
are claimed. The associations described here do not rule out the possibility of reciprocal
effects. For example, children who show a greater interest in numeracy play at a very young
age may find that their expressions of interest encourage more frequent numeracy activities
with their parents or siblings, thereby facilitating the continuance of their interest. In this
way, positive attitudes towards maths in early childhood may increase engagement with early
numeracy activities.
Future studies could corroborate these findings by assessing early childhood play
through concurrent methods; for example, by collecting more detailed observations of the
extent and precise nature of actual childhood play alongside an assessment of children’s
attitudes at an early age, followed by longitudinal assessments of attitudes and mathematical
skill with those children in subsequent years. Such methodologies are both time-consuming
and costly, and thus are often limited to small-scale research with convenience samples.
Therefore, the findings reported here – with attendant caveats – hold the potential to inform
future research by generating insightful research questions and enabling the design of
effective and efficient studies that are designed more explicitly to address these questions.
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Conclusion
The findings presented here provide an overview of play patterns among Irish children, and a
baseline against which future Irish cohorts and their international counterparts can be
compared. In addition, the study highlights positive associations between frequent
engagement in numeracy play with young children and their confidence in mathematics and
liking of mathematics at age 10, even with other factors such as home background and
mathematical achievement accounted for.
Finally, this paper demonstrates the potential offered by large-scale educational
studies such as TIMSS. We highlight the availability of a wealth of high-quality cross-
national information related to children’s social and cognitive development and home
background factors. The TIMSS 2011 database has provided a novel snapshot of early
numeracy activities in Ireland, and we propose that future iterations of the study can be used
to inform future work in this domain. This paper utilised a limited selection of measures with
a focus on Irish children. Further within- and between-country analyses could be performed
using this and similar datasets.
20
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Tables
Table 1: Summary of variables used
Measure
Type
Description
Data source
Early
numeracy
play
Ordinal
(individual
items)
Six items describing specific numeracy activities that parents engaged
in with their children before the child started primary school
(often/sometimes/never or almost never).
Parents
Continuous
(with ordinal
cutpoints)
Composite scale representing ‘average’ frequency of numeracy play
derived from these six items. Scale set to an international mean of 10
(standard deviation = 2) using Item Response Theory (IRT). Parents
with a score below 6.9 on this scale (almost) never engage in early
numeracy play overall, and a score above 10.3 denotes often engaging
in early numeracy play. Scores between these two cutpoints
correspond to sometimes engaging in early numeracy play.
Early
literacy play
Continuous
Composite scale representing ‘average’ frequency of literacy play
derived from nine items (e.g., “read books”, “tell stories”, “sing
songs”). Scale set to an international mean of 10 (SD = 2) using IRT.
Parents
Home
Resources
for Learning
Continuous
(with ordinal
cutpoints)
Composite scale incorporating several measures related to the home
learning environment: parents’ highest level of educational attainment,
parental occupation, the number of books in the home, the number of
children’s books, the availability of an internet connection, and
whether the student has their own room to study in. Scale set to an
international mean of 10 (SD = 2) using IRT. A score below 7.3 on this
scale corresponds to having few resources for learning at home overall,
while a score above 11.3 shows many resources for learning. Scores
between these cutpoints correspond to having some resources.
Parents (parental
education,
occupation,
children’s books)
and students
(books, study
supports).
Gender
Categorical
Male or female.
Students
Maths
achievement
Continuous
Student performance on a test of mathematics. International scale
centrepoint is set to 500 (SD = 100). Five plausible values are
provided in the TIMSS International Database.
Students
Engagement
in maths
lessons
Continuous
(with ordinal
cutpoints)
Composite scale comprising five items (e.g., “I am interested in what
my teacher says [in maths lessons]”). Scale set to an international mean
of 10 (SD = 2) using IRT. Scores below 7.4 are not engaged in maths
lessons, while scores above 10.2 are highly engaged. Between these
cutpoints, students are somewhat engaged.
Students
Like
learning
maths
Continuous
(with ordinal
cutpoints)
Composite scale comprising five items (e.g., “I enjoy learning maths”).
Scale set to an international mean of 10 (SD = 2) using IRT. Scores
below 8.1 denote that students do not like learning maths, and scores
above 10.1 describe students who have a high liking for learning maths.
Between these cutpoints, students somewhat like maths.
Students
Confidence
in maths
Continuous
(with ordinal
cutpoints)
Composite scale comprising seven items (e.g., “I learn things quickly
in maths”). Scale set to an international mean of 10 (SD = 2) using
IRT. Below 8.5, students are, on average, not confident in maths, and
above 10.6 they are described as highly confident. Between these
cutpoints, students are somewhat confident in maths.
Students
Student weight
Weighting variable used for all analyses, ensuring that the sample data
are representative of the broader national student population.
IEA
29
Table 2: Correlations between variables
1
2
3
4
5
6
7
1. Engagement in maths lessons
1
2. Liking learning maths
.53
1
3. Confident in maths
.43
.57
1
4. Maths achievement
.10
.11
.32
1
5. Home resources for learning
.03
-.00
.09
.42
1
6. Early literacy activities
.07
.04
.08
.17
.28
1
7. Early numeracy activities
.04
.04
.09
.15
.21
.70
1
p ≤ .01 in bold.
30
Table 3: Frequency of early numeracy play among Irish children by gender and family SES
Gender
Home resources for learning
Frequency of play
Girls
Boys
Few
Some
Many
Count different things
(Almost) never
2
2
10
2
2
Often
67
69
39
65
77
Play with building blocks or
construction toys
(Almost) never
7
3
15
5
2
Often
58
75
39
65
75
Play games involving shapes (e.g.,
shape-sorting toys, puzzles)
(Almost) never
3
4
16
4
1
Often
63
64
33
62
72
Say counting rhymes or sing
counting songs
(Almost) never
5
5
20
5
3
Often
65
62
35
61
73
Play with number toys (e.g., blocks
with numbers)
(Almost) never
8
8
21
7
7
Often
55
53
26
54
58
Play board games or card games
(Almost) never
10
8
14
10
7
Often
43
43
35
41
48
31
Table 4: Logistic regressions predicting High Engagement in maths lessons, High Liking of maths, and
High Confidence in maths in Fourth grade
High engagement in lessons
High liking
High confidence
b
(SE)
Odds ratio
b
(SE)
Odds ratio
b
(SE)
Odds ratio
Intercept
-1.69***
.45
-
-1.48**
.47
-
-4.76***
.52
-
Boy
-.39**
.12
.68
-.12
.09
.89
.23*
.11
1.25
Maths achievement
.00***
.00
1.00
.00**
.00
1.00
.01***
.00
1.01
Home resources for learning
-.09
.05
.91
-.12
.06
.89
-.11*
.05
.90
Early literacy activities
.10
.07
1.10
.05
.05
1.05
-.02
.06
.99
Early numeracy activities
.06
.07
1.06
.12
.07
1.13
.19*
.08
1.21
ENA * Boy
-.09
.09
.92
-.02
.08
.98
-.07
.08
.93
ENA * HRL
-.06
.04
.94
.10**
.04
1.11
.06
.05
1.06
R2
.03
.02
.11
* p≤ .05**,p≤ .01, *** p≤ .001
32
Figures
Figure 1: Parental reports of the frequency of their child’s engagement in various types of early
numeracy play before beginning primary school
68
30
2
67
29
5
64
33
3
63
32
5
54
38
8
43
48
9
0
10
20
30
40
50
60
70
Often Sometimes Never or almost never
%
Count different things
Play with building
blocks/construction toys
Play games with shapes
Recite counting
rhymes/counting songs
Play with number toys
Play board games/card games
33
Figure 2: Parental reports of often engaging in early numeracy play with their children before they
started school, Ireland and other TIMSS countries
0
10
20
30
40
50
60
70
80
Hungary
Czech Republic
Slovak Republic
Northern Ireland
Russian Federation
Poland
Ireland
Australia
Austria
Croatia
Germany
Slovenia
Malta
Canada Quebec
Italy
United Arab Emirates (Dubai)
Spain
Average
Lithuania
Romania
Portugal
United Arab Emirates
United Arab Emirates (Abu Dhabi)
Norway
Qatar
Singapore
Georgia
Saudi Arabia
Iran(Islamic Rebublic of)
Finland
Sweden
Chinese Taipei
Hong Kong, SAR
Azerbaijan (republic of)
Oman
Honduras (republic of)
Botswana
Morocco
% of students
34
Figure 3: Odds ratios predicting High Liking of mathematics in Fourth grade, showing interactions
between gender, home resources for learning & frequency of early numeracy play (% of national student
population in each category). ‘High’ and ‘low’ HRL/ENA are defined as .5 standard deviations
above/below the mean.
0.92
0.97
0.77
0.90
0.97
1.03
0.82
0.96
1.03
1.16
0.86
1.02
Low HRL & low ENA (13%) Low HRL & high ENA (9%) High HRL & low ENA (6%) High HRL & high ENA (12%)
Boys Overall Girls
