ArticlePDF Available

Young children's non‐numerical ordering ability at the start of formal education longitudinally predicts their symbolic number skills and academic achievement in maths


Abstract and Figures

Ordinality is a fundamental feature of numbers and recent studies have highlighted the role that number ordering abilities play in mathematical development (e.g., Lyons et al., 2014), as well as mature mathematical performance (e.g., Lyons & Beilock, 2011). The current study tested the novel hypothesis that non-numerical ordering ability, as measured by the ordering of familiar sequences of events, also plays an important role in maths development. Ninety children were tested in their first school year and 87 were followed up at the end of their second school year, to test the hypothesis that ordinal processing, including the ordering of non-numerical materials, would be related to their maths skills both cross-sectionally and longitudinally. The results confirmed this hypothesis. Ordinal processing measures were significantly related to maths both cross-sectionally and longitudinally, and children's non-numerical ordering ability in their first year of school (as measured by order judgements for everyday events and the parents’ report of their child's everyday ordering ability) was the strongest longitudinal predictor of maths one year later, when compared to several measures that are traditionally considered to be important predictors of early maths development. Children's everyday ordering ability, as reported by parents, also significantly predicted growth in formal maths ability between Year 1 and Year 2, although this was not the case for the event ordering task. The present study provides strong evidence that domain-general ordering abilities play an important role in the development of children's maths skills at the beginning of formal education.
Content may be subject to copyright.
Developmental Science. 2018;e12645.  
 1 of 16
© 2018 John Wiley & Sons Ltd
Young children’s non- numerical ordering ability at the start of
formal education longitudinally predicts their symbolic number
skills and academic achievement in maths
Patrick A. O’Connor | Kinga Morsanyi | Teresa McCormack
School of Psychology, Queen’s University
Belfast, Belfast, UK
Belfast, School of Psychology, David Keir
the role that number ordering abilities play in mathematical development (e.g., Lyons
et al., 2014), as well as mature mathematical performance (e.g., Lyons & Beilock,
2011). The current study tested the novel hypothesis that non- numerical ordering
ability, as measured by the ordering of familiar sequences of events, also plays an
important role in maths development. Ninety children were tested in their first
school year and 87 were followed up at the end of their second school year, to test
the hypothesis that ordinal processing, including the ordering of non- numerical ma-
terials, would be related to their maths skills both cross- sectionally and longitudi-
nally. The results confirmed this hypothesis. Ordinal processing measures were
significantly related to maths both cross- sectionally and longitudinally, and children’s
non- numerical ordering ability in their first year of school (as measured by order
judgements for everyday events and the parents’ report of their child’s everyday
ordering ability) was the strongest longitudinal predictor of maths one year later,
when compared to several measures that are traditionally considered to be impor-
reported by parents, also significantly predicted growth in formal maths ability be-
tween Year 1 and Year 2, although this was not the case for the event ordering task.
The present study provides strong evidence that domain- general ordering abilities
play an important role in the development of children’s maths skills at the beginning
of formal education.
• Numerical and non-numerical ordering ability related to formal
maths skills concurrently and longitudinally.
• Non-numerical ordering abilities in the first year of school were the
strongest predictors of maths one year later.
The study highlights the importance of domain-general ordering
abilities to the early development of formal maths skills.
The relations between order processing abilities and the development
of maths skills have recently attracted the interest of researchers.
Lyons and Beilock (2011) proposed that representing and process-
ing the relative order of numbers is a stepping stone in moving from
approximate representations of number to exact representations.
Separately, other researchers (e.g., Attout, Noël, & Majerus, 2014;
2 of 16 
   O’CONNOR et al.
Attout & Majerus, 2015) have proposed that working memory for
order information is important for early mathematics development.
Ordinalityis a fundamental aspect of the symbolic number sys-
tem, referring to the position in which a numeral is found within the
number sequence. One proposal is that performance in tasks that
tap children’s ability to process symbolic order reflects the extent
to which they have a refined spatialized representation of the num-
ber sequence along a mental number line (Kaufman, Vogel, Starke,
why performance on non- numerical working memory tasks, which
involve temporarily holding short non- numerical sequences in short-
& Majerus, 2015). Existing findings suggest that the representation of
the ordered number sequence in long- term memory and the ability to
hold and process unfamiliar order information in short- term memory
are both important for maths.
We believe that ordering skills and mathematics might be related
for multiple reasons. Most relevant to young children is the fact that
learningto count involveslearning an orderedsequenceof items.In
addition, even the simplest counting principles (Gelman & Gallistel,
1978),such as the stable order principle (i.e., numerals always have
the same order in a count), and the cardinal principle (i.e., the numeral
applied to the last item in a set represents the number of items in the
that it is difficult to envisage how children could acquire knowledge
of the symbolic number system, beyond rote learning or other com-
pensatory strategies, if they do not understand the correct order in
which the numbers are arranged. Successful arithmetic performance
is dependent upon both knowledge of the correct order of the num-
bers, and an understanding of the correct order in which mathematical
operations should be carried out. For example, if children are asked
must understand that they should take 2 away from 5, rather than
vice versa. Thus, calculation itself depends upon temporarily holding
order information in working memory. Processing order information is
alsoessentialforworkingwithmulti-digit numbers.Itcanbe argued,
therefore, that mental representations of order may play a role in the
development of both basic symbolic number knowledge and subse-
quent maths ability, and recent evidence suggests that there is indeed
a relationship between the processing of numerical order relations and
maths achievement in both children and adults.
The most widely used task to assess symbolic ordering ability is the
ordinaljudgementtask(e.g., Goffin&Ansari,2016;Lyons&Beilock,
2011). Participants are shown three numbers on the screen (half of
the pairs or triads are in the correct order, the other half are in the
incorrect order) and they must judge whether the numbers are in the
non- numerical order processing skills is the order working memory
lists of familiar animal names. The lists range from two to seven ani-
mals in length, and participants must re- create the correct sequence
of animals using cards that represent the animals in the list that they
have just heard. Importantly, the cards given to participants inform
them about both the identity and the number of animals within the list.
Thus, the task makes minimal demands on item memory; participants
eral studies have indicated that performance on both these types of
order processing tasks is linked to maths ability, suggesting that both
numerical and non- numerical ordering ability may be important for
formal maths skills.
Vaessen, Blomert, andAnsari (2014) investigated the role of basic
number skills in the development of maths ability. The authors used a
wide range of numerical and non- numerical tasks to investigate what
skills were important for maths at different developmental stages.
They found that the predictive power of numerical ordering ability
(i.e.,the ordinaljudgementtask)increasedacross grades.Attheear-
liest grades, numerical ordering was not a strong predictor of maths,
but by grade 6 (around the age of 12), it was the strongest of all the
relationship between distance effects in number ordering and first-
et al.’s ordering task only contained dyads of numbers, rather than the
triads that are more commonly used in this literature, and it is possible
that the dyad task is less sensitive at detecting the appropriate order
studies suggest that symbolic ordering ability is important to children’s
maths skills, although the strength of this relationship might change
with development.
Attout etal. (2014) investigatedthe links between verbal WM
abilities (non- numerical item and order WM), numerical magnitude
and order processing abilities and calculation performance at three
different time points: 6 months into the final year of kindergarten
(T1), one year later (T2) and during the second grade of school (T3).
merical ordinal judgement and maths was observed cross- sectionally
atT2. Ontheotherhand, children’sperformancein the orderWM
task was cross- sectionally related to maths at each time point, whilst
performance on this task at T1 was longitudinally related to maths at
T2 and T3, suggesting the importance of early non- numerical order
memory to later maths performance. These relationships remained
significant, even after controlling for age, verbal and non- verbal
not only in studies involving typically developing children, but also in
studies involving children with developmental dyscalculia (DD)—a
developmental disorder characterized by difficulties in the retrieval
and storage of arithmetic facts, when no other sensory or intellectual
disabilitiesarepresent (e.g., Butterworth, 2005;vonAster & Shalev,
2007). Attout and Majerus (2015) investigated symbolic and non-
symbolic magnitude and order processing in 8- to 12- year- old children
with DD and a group of typically developing children matched on age,
IQ and reading abilities.The children were given the orderworking
memory task, as well as a calculation task, symbolic and non- symbolic
ordinal judgement tasks (judging whether two sets of lines or numer-
als were in the correct ascending order numerically) and symbolic and
 3 of 16
O’CONNOR et al.
non- symbolic magnitude judgement tasks (judging which of two sets
of lines or numerals was the most numerous). Attout and Majerus
found that the DD group tended to be slower on symbolic magni-
tude and ordering tasks and committed more recall errors in the order
working memory task, suggesting that children with DD may have dif-
ficulties in processing and remembering order information.
Together, the evidence suggests that both numerical and non-
numerical ordering abilities are important to the development of
typical maths skills, and that children with DD have order process-
ing deficits. Whilst the evidence is promising, there are still several
important unresolved issues concerning the link between order pro-
cessingskillsandmaths.Inparticular,we do not know the precise
nature of the order processing skills that are important for maths
development. Two quite distinct types of order processing tasks—
the numerical ordinal judgement task and the order working mem-
ory task—have each shown a link with children’s mathematical skills.
Notably,Attout etal. (2014) found that children’sperformance on
these two types of ordering tasks was not correlated (although see
different patterns of cross- sectional and longitudinal relations with
maths skills. This suggests that they draw on different order process-
these tasks differ in two salient respects: (i) in terms of whether they
involve processing of numerical or non- numerical order information
and (ii) in terms of whether they involve retrieving and processing
information from order representations held in long- term memory
versus unfamiliar sequences temporarily held in short- term memory.
calculation abilities not via access to a common set of (long- term)
ordinal representations but via mechanisms intrinsically associated
clear is whether such short- term memory mechanisms are the only
domain- general order processing ones that are important for maths
development, because previous studies with children have not used
tasks involving long- term ordinal representations of non- numerical
Lyons, Vogel, andAnsari (2016), in their review of the literature
examining the links between ordinality and mathematical skills, argue
that there is a paucity of research investigating the relation between
non- numerical ordering abilities and maths. Recent studies with adults
(Morsanyi,O’Mahony,&McCormack,2017; Sasanguie, De Smedt &
Reynvoet,2017;Vos,Sasanguie, Gevers,& Reynvoet,2017) showed
that non- numerical order processing, as measured by month and letter
ordering tasks that required participants to make judgements about
the order of month/letter triads, was very strongly related to adults’
numerical skills, and the distance effects found in these tasks were
also similar to the distance effects found in number ordering tasks.
Thus, the ordering of familiar non- numerical sequences is also related
to maths ability, atleast in adults. In order to investigate this issue
developmentally, in the current study we included tasks that measured
ordering ability involving familiar, non- numerical sequences.
We investigated the ability to process order information regard-
ing familiar non- numerical sequences held in long- term memory by
introducing two measures that have not been used previously. First,
a temporal ordering task, inspired by previous research with young
children (Friedman, 1977, 1990)was employed. The version of the
task that we developed is similar to the number ordering tasks used in
other studies (e.g., Lyons & Beilock, 2011; Lyons et al., 2014), except
that children were shown a pictorial representation of a triad of daily
events rather than numbers. Each test trial was drawn from a set of six
events (waking up, getting dressed, going to school, eating lunch, eat-
ing dinner and going to bed) and children judged whether the order of
the events was correct or not. Second, to assess the role of everyday
non- numerical ordering skills, we developed a new eight- item ques-
tionnaire to assess the extent to which parents agreed or disagreed
that their child could carry out familiar tasks that all included the re-
quirement to follow a set order (such as getting dressed for school).
Our motivationfor using this measure was the existence of clinical
reports of individuals with DD that describe how they often struggle
with everyday tasks that have a strong ordering component (National
us with a novel way of assessing the relation between domain- general
order processing abilities and emerging maths skills.
In addition to the question of what types of order processing
skills are related to maths at the start of formal education, it is also
of concern that there is a lack of longitudinal research investigating
whether there may be a causal relationship between ordering ability
and the early development of maths skills. This is echoed by Lyons
et al. (2016), who point out that most of the findings concerning the
link between ordering abilities and maths have been based on correla-
tional evidence at a single time point. The only longitudinal study so
farwasconducted byAttoutetal. (2014)who foundseparatecross-
sectional links between both numerical ordering and non- numerical
order working memory and maths, but only a longitudinal link between
order working memory and maths. We employed a longitudinal design
that involved children completing a range of tasks at the very start of
their formal education, and then measuring their formal maths skills
towards the end of their first and second year of school.
We studied children in their earliest years of education to address
a further issue arising from the previous literature concerning the
stage of development at which ordering ability becomes an important
predictorofmathsskills.Studies(e.g.,Attout&Majerus,2015; Lyons
etal., 2014; Morsanyi, Devine, Nobes,& Szűcs, 2013) have consis-
tently shown that order processing is strongly related to maths skills
amongstolderchildren(betweentheagesof8and13). However,as
mentioned above, there are mixed findings regarding whether there
is a strong link between ordering abilities and maths at the start of
formaleducation (Attoutetal.,2014; Lyonsetal.,2014;Vogeletal.,
2015), with Lyons et al.’s (2014) finding that this relation only becomes
pronounced with development. The children in the current study were
between the ages of 4 and 5 when they first participated in the study,
which makes them the youngest sample so far in which the link be-
tween order processing skills and maths ability has been investigated.
It was conductedwith a sample of children from Northern Ireland;
all the 37 countries participating in Eurydice, the information network
4 of 16 
   O’CONNOR et al.
on education in Europe (Eurydice at NFER, 2012), and one of the
youngest school starting ages in the world.
Finally, it is also important to compare the predictive value of or-
dering tasks with other tasks that are related to mathematical skills
(see e.g., Attoutetal., 2014; Lyons etal., 2014;Vogel etal., 2015).
Giventhe amount ofresearchinterest inwhetherthe ability topro-
cessmagnitudes is related to maths (e.g.,Chen&Li,2014;Gilmore,
McCarthy,& Spelke,2010; Halberda,Mazzocco& Feigenson, 2008;
Holloway&Ansari,2009; Piazzaetal.,2010; Schneideretal., 2017),
the current study included both symbolic and non- symbolic magni-
tude measures.
Insum, theaimofthe currentstudywasto assess therelative
contributions of numerical and non- numerical order processing to
the development of maths skills in children who have just begun for-
malmathsinstruction. Inalongitudinalstudy,childrenweretested
during their first year of primary school and completed a maths as-
sessment at the end of the school year. The same children com-
pleted another maths assessment at the end of their second year
of primary school. The main research question concerned whether
numerical and non- numerical ordering abilities predicted variance in
mathematical skills both cross- sectionally and longitudinally, after
other powerful predictors of early mathematical skills, as well as
children’s verbal and non- verbal intelligence, were taken into ac-
link between non- numerical ordering tasks including familiar and
everyday sequences and maths performance at the start of formal
2.1 | Participants
Ninety children at the start of their first year of primary school educa-
tion were recruited from four schools in the Belfast area (43 females,
Mean age = 4 years 11 months; SD = 3.73 months). Eighty-seven
years 2 months, SD=3.44months)attheendoftheirsecondschool
their SES is reported below.
2.2 | Materials
2.2.1 | Deprivation measure
Children’s level of socioeconomic deprivation was determined
rivation for the area. The scores can be interpreted as percentiles
(e.g.,a score of 10 means that thearea is less deprived than 90%
ofallpostcode-basedareaswithin NorthernIreland). Inthe current
sample, deprivation scores ranged from 1.85 to 68.57 (Median =
couldnot be calculated. Along with age and both verbal and non-
verbal intelligence, children’s deprivation scores were used as co-
variates in the data analysis.
2.2.2 | IQ
Children’s intelligence was measured using the Vocabulary and
Block Design subtests of the Wechsler Preschool & Primary Scale
of Intelligence – Third UK Edition (WPPSI-III UK; Wechsler, 2003).
method outlined in Sattler and Dumont (2004) and were found to be
2.2.3 | Order processing measures
Parental Order Processing Questionnaire (OPQ)
Parents were asked to complete an eight- item questionnaire (included
extent to which they agreed or disagreed with certain statements re-
garding their child’s ability to perform everyday tasks that involved
an order processing element (e.g., “my son/daughter can easily recall
the order in which past events happened”). The items were devel-
oped based on clinical observations regarding the everyday difficul-
ties that individuals with dyscalculia commonly encounter (National
CenterforLearning Disabilities,2007),buttheyweremodifiedto be
appropriate for young children. Five items were scored positively (i.e.,
higher scores indicated better ordering ability), and three items were
tion showed that the scale had a two- factor structure, with the posi-
tiveitemsloadingonfactor1(whichexplained 41%ofthevariance),
and the negative items loading on factor 2 (which explained 21%
of the variance). The scale demonstrated good internal consistency
(Cronbach’salpha=.75).Thetotal scorefrom thisscalewasusedas
a measure of children’s ability to carry out everyday tasks requiring a
long- term memory representation of the correct order of sequences.
Five parents did not complete the questionnaire, so no score could be
computed on this measure for their children.
Order working memory (WM) task
This task measured children’s ability to retain serial order infor-
mation. The English version was modelled on a task developed by
Majerus,Poncelet, Greffe,&Van der Linden,2006).This taskmeas-
ures children’s ability to retain and manipulate serial order informa-
tion by measuring their ability to re- create the correct sequence of
a list of animal names that were presented to them through a set of
earphones, using cards depicting the animals. The stimuli used were
seven monosyllabic English animal words (bear, bird, cat, dog, fish,
horse, and sheep). The mean lexical frequencies of these words were
established using SUBTLEX- UK word frequencies (SUBTLEX- UK:
Van Heuven, Mandera, Keuleers, & Brysbaert, 2014). SUBTLEX-UK
 5 of 16
O’CONNOR et al.
presents word frequencies as Zipf values, with values between 1 and
3 representing low frequency words and values between 4 and 7 rep-
resenting high frequency words. The stimuli demonstrated high lexical
frequencyaccording to thesevalues(mean lexicalfrequency=4.94,
range = 4.67–5.19). The stimuli were used to create 24 word lists,
which ranged in length from two to seven words, with four trials per
list length. Each word only appeared once per list and the same 24
lists were presented to all participants. The stimuli were recorded by
a female voice, and an inter- stimulus interval of 650 ms was used.
rectly recalled sequence, children were given a score of 1. Split- half
reliability estimates, using the Spearman- Brown formula, indicated
good reliability (r=.93).
Daily events task
used to measure children’s ability to judge the correctness of the
order of familiar daily events. Children were first trained on how
to order events using two training sequences (four cards show-
ing a boy playing on a slide, and six cards depicting a sequence in
rectly order both sequences four times before they could proceed
to the next phase of the training, which involved the items of the
experimental sequence. The experimental sequence consisted of six
cards that represented six familiar events that happen during the
day (waking up, getting dressed, going to school, eating lunch, eat-
ing dinner and going to bed). For the training phase, children were
first told what each picture represented and were shown the cor-
rect order by the experimenter. Then the cards were shuffled and
children were asked to recreate the correct order. For the experi-
mental sequence, children learned the names for each of the daily
events and saw the correct order in which these events should go.
were told that they would see any three of the daily events and that
their task was to judge whether the order was correct or not, from
right to left, by pressing a tick or a cross on the touchscreen moni-
twice) showed a triad of events in the correct order, the other half
a score of 1 for each correct answer and a measure of children’s re-
action times, for correct trials only, was also taken. Since each trial
was presented twice, a split- half reliability was calculated using the
Spearman- Brown coefficient, which was found to be adequate (.57).
Due to the relatively high error rate, reliability for RTs for correct
trials was not computed, and the RT measure was not considered
Symbolic number ordering1
This task assessed children’s early knowledge of the order of symbolic
1–9usingcards. These cards were then shuffled andchildrenwere
asked to re- create the correct forward order (involving two trials). This
procedure was then repeated for the backward sequence of numbers
wards (four trials) and backwards (four trials) from different starting
positions, with a score of 1 given for each correct trial. The proportion
of correct responses was calculated based on performance on all four
This task was based on the number sequence elaboration task, as out-
linedinHannulaand Lehtinen(2005).Inthefirst part,childrenwere
asked to count from 1 until the highest number they could think of
(theywerestopped if they reached 50) in two trials.Intwo further
subtasks, children also counted forwards and backwards from differ-
trial. The reliability estimate for both forward and backward subtasks
Giventhestrong correlationbetweencounting until the highest
number and both forward (r(88)=.76,p < .001) and backward count-
ing (r(88) = .65, p < .001), a total counting score was calculated by
adding z- scores for all three counting measures.
2.2.4 | Magnitude processing measures
Non- symbolic addition2
This task measured the ability to represent and manipulate non-
symbolic quantities and was based on the procedure used by
Gilmoreetal. (2010), in whichchildrenviewtwo sets of bluedots
on the left- hand side of the screen, and have to estimate the sum
of the two arrays (sum array) and compare that sum to the quantity
of a third array (comparison array, composed of red dots) that a dif-
ferent character had, which appeared on the right- hand side of the
screen. The numerical ratio of the sum and comparison arrays was
manipulated across the 24 trials (1:2, 3:5, and 2:3), with eight trials
per ratio. The number of dots for both arrays varied from 6 to 45; 6
being the lowest number of dots as this reduced the possibility that
children could subitize the number of dots presented. Perceptual
variables (dot size, density and array size) were also varied, so that
they correlated with numerosity on half the trials (congruent trials)
and were uncorrelated on the other half of the trials (incongruent
trials), reducing the possibility that children may have used percep-
tual information as a cue when judging which array was the most
numerous. Furthermore, the trials were designed in such a way that
it was not possible for the children to perform above chance if they
simply responded on the basis of a comparison between the num-
berofbluedots in the second set and the number of red dots. In
each trial the number of red dots was at least 1.5 times greater than
the number of blue dots in the second set. Nevertheless, the overall
number of blue dots was larger in half of the trials than the overall
number of red dots, whereas in the other half of trials the opposite
touchscreen to indicate which character they thought had the most
marbles. They completed four practice trials, with feedback given
6 of 16 
   O’CONNOR et al.
ontheir performance, followed by24experimentaltrials. Children
were given a score of 1 if they correctly judged which character
had the most marbles. Reliability for this task for accuracy was quite
low, but acceptable (Cronbach’s alpha = .50). One-sample t tests
confirmed that children performed above chance at each ratio [1:2;
t(89)=4.45,p < .001. 3:5; t(89)=3.76,p < .001. 2:3 t(89)=2.93,p
< .001].
Number comparison
tons to indicate whether they thought that the number on the screen
was bigger or smaller than 5. Each number was presented five times,
in a random order, giving a total of 40 experimental trials. These were
in which they correctly judged whether the target number was bigger
or smaller than 5, with reaction time data also obtained. Reliability
estimates for accuracy (Cronbach’s alpha = .88) and reaction times
2.2.5 | Estimation measure
Number line task
Thenumberline task(Cohen&Blanc-Goldhammer,2011;Laski &
2003) was used to assess children’s ability to spatially represent
numbers along a mental number line. This task used the number-
to- position version, in which children used their finger to indicate
the position on the number line where a target number should go.
Thisversion used 1–10 and 1–20 scales, and itwas framed as a
game in which the children had to help Postman Pat to deliver pre-
sentstohouses ondifferentstreets(Aagten-Murphyetal.,2015).
There were six experimental trials, in which the child was asked
to indicate the position of numbers 3, 4, 6, 7, 8 and 9. For the
1–10 number line, the numbers 5 and 10 wereused as the two
practicetrials; forthe1–20numberline, the numbers 10 and20
were used as the two practice trials, whilst the child was asked to
indicate the position of the numbers 4, 6, 8, 13, 15 and 18 in the six
experimental trials, which were presented in a random order. The
numberline was1000pixels long forbothscales Children’serror
for each individual trial was calculated as the distance in pixels be-
tween children’s estimated position and the actual position of the
targetnumber.The averageofchildren’serrorsacross both 1–10
and 1–20 scales was used as the overall measure of estimation
2.2.6 | Maths achievement
At the end of their first year of school, children’s maths abil-
ity was assessed by administering a 28- item maths achievement
test, consisting of questions from the calculation subtest of the
Woodcock-JohnsonIIItestsof achievement(Woodcock,McGrew,
Ability(TEMA-3;Ginsburg& Baroody, 2003). The questions from
the calculation subtest contained six addition and four subtrac-
tionproblems,whilst thequestionsfromtheTEMA-3includedthe
counting of objects and animals, selecting the next number after a
given number in the counting list, as well as selecting which number
islarger from a choice of two. At the endoftheirsecondyearof
school, children were assessed using the age- appropriate version of
2005) which consisted of 30 questions, assessing counting and un-
derstanding number (nine questions), knowing and using number
facts (seven questions), calculating (eight questions) and measuring
used in the analyses. The reliability estimates for the maths measure
2.3 | Procedure
The study received ethical approval from the university department’s
ethics committee. In Session 1, all children completed the Number
Orderingtask, followed by the NumberComparisontask,theAnimal
drencompletedtheDailyEvents Ordertask, followedby theWPPSI-
IIIsubtests, then the Baseline Reaction Time task,Countingtaskand
then finally, the Number Line task. The computer- based tasks were
designed using E- Prime Version 2.0. These tasks were presented on
(Time1 =endof year1;Time 2= endofyear 2),childrencompleted
themathsachievement test in small groups of 3–6, in which the ex-
perimenter read out the questions and instructed the children to write
Descriptive statistics for both accuracy and reaction times are in-
cluded in Table 1. The median number that children were able to
countupto(outof50)was39.Most childrenperformedwellonthe
two numerical ordering tasks (forward and backward counting mean
accuracy = 76%) and on number ordering (82%). Two children per-
accuracywas65%,whichwasabovechance(t(89)=11.10,p < .001).
In the order working memory task, children on average got 9 trials
correct, meaning that they were able to correctly remember ordered
sequencestoasequence length of 3. Children’s mean score on the
highly in terms of being able to carry out everyday tasks with a strong
ordering component.
 7 of 16
O’CONNOR et al.
As previously mentioned, children’s accuracy on the non-
symbolic addition task was relatively low, but their performance
on the task was above chance (t(89) = 5.09, p < .001). Children
about 1.8 numbers away from the target number, whilst their esti-
from the target.
3.1 | Zero- order and partial correlations (after
controlling for age, IQ and socioeconomic status)
between the order and magnitude processing
measures, counting ability and maths achievement
at the end of children’s first year of school
Table 2 shows that vocabulary scores were significantly positively cor-
related with order- processing (order WM, daily events, counting) and
non- symbolic addition and maths scores. Block design scores were
significantly positively correlated with the order- processing measures
(order WM, daily events, number ordering), as well as performance on
the number line task. Finally, higher deprivation scores were signifi-
as well as lower performance on the order WM, daily events, number
ordering and number comparison tasks.
Asshown inTable2,thereweresignificant correlationsbetween
general order- processing measures and maths at the end of chil-
dren’s first year of school; children’s maths ability was related to their
scoreson the OPQ,number ordering ability, daily eventstask accu-
racy, countingability and their order working memoryaccuracy. Of
the magnitude measures, only number comparison was found to be
bal and nonverbal intelligence, number comparison performance was
TABLE1 Descriptive statistics for all measures
Measure Minimum Maximum Mean (SD)
Vocabulary (scaled score) 4 17 8.52 (2.10)
Block Design (scaled
4 16 10.12 (3.15)
21 56 44.02 (7.69)
OrderWM 1 16 9.52(4.54)
Daily events accuracy .38 1 .65 (.13)
Symbolic number
0 1 .82 (.30)
Countingto50 6 50 39(13.15)
0 1 .76 (.22)
Non- symbolic addition .30 .88 .56 (.11)
Number comparison
.40 1 .71 (.19)
Number comparison RT
778 6059 2404.04
Number line task (Mean
scaled error)
64 453 191.52
Baseline RT (ms) 860 2284 1435 (283.71)
Maths (Year 1) 1 28 23.24 (4.88)
Maths (Year 2) 7 29 21.74 (4.71)
TABLE2 Zero- order correlations between all measures
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
(2) Vocabulary .04
(3) Block Design .09 .09
(4) Deprivation .11 −.41*** −.22*
.08 .15 .03 −.09
(6)OrderWM .17 .22* .30** −.22* .18 —
(7) Daily events −.09 .38*** .29** −.27** −.08 .44***
(8) Number ordering .14 .19 .24* −.23* .26* .41*** .24*
(9)Counting .09 .27** .13 −.10 .15 .54*** .34** .36**
(10) Non- symbolic
−.23* .24* .12 −.19 −.14 .11 .22* .19 .02 —
(11) Number
.06 .18 .09 −.22* .20 .28** .34** .29** .29** .15 —
(12) Number line
.21* −.02 −.26* .10 .11 −.05 −.15 −.05 −.20 −.14 −.04
(13) Maths (Year 1) −.004 .32** .16 −.26* .30** .32** .46*** .40*** .54*** .14 .21* .02 —
(14) Maths (Year 2) .10 .37*** .29** −.29** .28* .23* .41*** .38*** .43** .30** .24* −.17 .69***
*p<.05;**p<.01;***p < .001.
8 of 16 
   O’CONNOR et al.
no longer significantly related to maths performance (p= .29).OPQ
scores, r(78)=.26,p < .05; number ordering performance, r(78)=.25,
p < .05; daily events accuracy, r(78) = .36, p < .01; counting ability,
r(78)=.43,p < .001; and order WM accuracy, r(78)=.30,p < .01, re-
mained significantly related to maths after controlling for the covariate
3.2 | Zero- order and partial correlations
between the order and magnitude processing
measures, counting and maths achievement at the
end of children’s second year of school
Table 2 shows that vocabulary, block design and deprivation scores
at T1 weresignificantly related to maths at T2. Children’sT1 OPQ
scores, daily events task accuracy, number ordering ability, order
working memory accuracy, daily events accuracy and counting ability
were related to maths ability at the end of children’s second year of
school. For the magnitude measures, both non- symbolic addition ac-
controlling for age, deprivation scores and verbal and non- verbal intel-
ligence, the only significant relationships with maths were observed
forOPQscores,r(75)=.24,p < .05; counting ability, r(75)= .24, p <
.05; and number ordering performance, r(75)=.24,p < .05.
3.3 | Bootstrap correlations
sess the reliability of the relationship between the measures which
had previously been observed as having a significant zero- order and/
or partial correlation with maths, and maths achievement at each time
point. This procedure allowed for a 95% confidence interval to be
computed for the correlations between each measure and children’s
maths ability and if any measure was found to have a significant boot-
strap correlation with maths, then it was considered to be robustly
related to maths achievement. Figure1 shows 95% bootstrap con-
fidence intervals between the measures and maths achievement at
theend ofchildren’sfirst year ofschool,whilst Figure2shows95%
bootstrap confidence intervals between measures and maths achieve-
ment at the end of children’s second year of school.
Figure 1 shows that the measures which had previously shown sig-
nificant zero- order and/or partial correlations with maths at the end
of children’s first year of school also showed significant zero- order
bootstrap correlations with maths. Figure 2 shows that order working
memory accuracy [r=.17,95% CI (−.11, .41)]wasthe onlymeasure
that was not robustly related to maths at the longitudinal level, of all
the measures that had previously been related to maths at the end of
children’s second year of school.3
3.4 | Regression modelling
The regression analyses regarding the relationship between the pre-
dictor variables and maths performance at each time point followed a
(2013). For each regression model, the variables that had a significant
bootstrap correlation with maths were entered first. Non- significant
predictors of maths in each model were then removed and each pre-
dictor which had a significant partial correlation with maths but not a
significant bootstrap correlation was entered into the model one by
FIGURE1 95%bootstrapconfidenceintervalsforzero-ordercorrelationsbetweenmeasuresandmathsachievementattheendofchildren’s
 9 of 16
O’CONNOR et al.
one to examine whether they became significant. Then, the four co-
variates (age, deprivation scores, vocabulary and block design) were
entered into the model to examine whether they changed significant
predictorsand improved fit. At each time-point,the model that ex-
plained the greatest proportion of variance with only significant pre-
dictors in the model was selected.
Table 3 shows the initial and final models for measures that pre-
dicted maths at the end of children’s first year of school. The initial
model consisted of OPQ scores, order WM, daily events, number
ordering, counting and number comparison accuracy. This model ex-
tained a number of non- significant predictors of maths (order WM; β
=−.07,ns; number ordering; β=.12,ns; number comparison; β=−.03,
ns). These measures were removed and only the significant predictors
next model. When adding them to the model one by one, none of the
remaining predictors explained significant additional variance in maths
performance. Thus, this was accepted as the final model (see Table 3).
Table 4 shows the initial and final models for the measures that
significantly predicted maths at the end of children’s second year of
ber ordering, counting, non- symbolic addition and number comparison
maths scores at the end of their second year of school. The non-
significant predictors (number ordering, counting and number com-
parison) wereremoved and the next model contained OPQ scores,
daily events and non- symbolic addition accuracy, which explained
sures and deprivation scores did not explain significant additional
variance in maths performance, although age was a significant factor
whenincludedin themodelcontainingOPQscores,dailyeventsand
variance in children’s maths performance at the end of their second
year of school.4
FIGURE2 95%bootstrapconfidenceintervalsforzero-ordercorrelationsbetweenmeasuresandmathsachievementattheendofchildren’s
TABLE3 Initialandfinalmodelspredictingmathsachievementat
the end of children’s first year of school
βt p
Initialmodel Daily events .39 3.90 < .001
Counting .33 3.09 .003
.27 2.89 .005
Symbolic number ordering .12 1.25 .214
OrderWM −.07 −.65 .520
Number comparison −.03 −.31 .759
Final model Daily events .38 4.17 < .001
Counting .32 3.49 .001
.28 3.23 .002
Initialmodel:R²=.37,F(6,84)=9.33,p < .001.
Final model: R²=.39,F(3,84)=18.39,p < .001.
10 of 16 
   O’CONNOR et al.
As a final step, we checkedwhether the longitudinal predictors
of formal maths skills at the end of the second year of school also
remained significant if the effect of formal maths skills at the end of
the first school year were taken into account. We did this by adding
formal maths skills at T1 as a predictor to the final regression model
presented in Table 4. This analysis addressed the question of whether
these longitudinal predictors of maths also predicted growth in maths
skills during the second year of school. The model is presented in
skills with formal maths skills at T1, the order processing questionnaire
and non- symbolic addition as significant predictors. The effect of the
daily event ordering task was no longer significant, and the effect of
age was also reduced to a non- significant trend.
Children’s ability to process both numerical order (counting, num-
berordering) andnon-numericalorder (OPQ, dailyeventsand order
working memory) at the start of their first school year were robustly
related to their maths achievement at the end of their first year. These
relationships were significant, even after controlling for age, depriva-
tion scores and verbal and nonverbal intelligence. Multiple regression
analyses revealed that, after controlling for the effect of counting
ability (forwards and backwards), the order processing questionnaire
and the daily events task still remained significant predictors of maths
ability. The longitudinal analysis (i.e., predicting maths performance
at the end of the second school year) showed that children’s numeri-
cal ordering ability (counting forwards and backwards and symbolic
number ordering) at the start of formal education was robustly related
to their maths achievement at the end of their second year of school.
related to maths at the longitudinal level. The regression analyses re-
vealed that early non-numerical ordering abilities (OPQ scores and
daily events task accuracy) were significant predictors of children’s
maths achievement more than 1 year later even when the significant
effects of counting ability, and non- symbolic addition were controlled.
When the effect of T1 formal maths skills was controlled, only the
OPQ and the non-symbolic addition task explained additional vari-
ance in T2 formal maths skills, whereas the effect of the daily events
task was no longer significant. This suggests that the effect of the
daily events task was the strongest during the first school year, and it
related to maths abilities in the second year of school via its links with
early formal maths skills. By contrast, everyday order processing abili-
ties remained significantly related to formal maths skills throughout
the first two years of school.
These results strongly support the notion that ordinality is import-
antto the development ofearlymaths skills (e.g.,Attout & Majerus,
the components of the formal maths tests also showed that ordinality
was important to all aspects of maths, including counting, calculation,
extend previous findings by showing that, even at the very earliest
stages of formal schooling, children’s domain- general ability to pro-
cess order, as demonstrated in familiar everyday tasks and to a lesser
extent, their ability to order daily events, plays an important role in
the successful development of more mature maths skills. This extends
work with adults (Morsanyi et al., 2017; Sasanguie et al., 2017; Vos
et al., 2017) that showed strong relationships between non- numerical
ordering tasks and mathematics abilities. The domain- general ability
to use order information measured by the daily events task must be
based on long- term memory representations of familiar sequences,
and our findings indicate that it is distinct from the ability to process
non- numerical order WM and children’s maths skills, performance on
theOPQandthedailyeventstask were in fact betterpredictorsof
maths skills both concurrently and longitudinally.
Our results are novel in suggesting that there are two distinct
domain- general ordering abilities that support maths development.
quences in working memory is important, and make a strong case for
TABLE4 Initialandfinalregressionmodelspredictingmaths
achievement at the end of children’s second year of school
βt p
Initialmodel OrderProcessing
.28 2.77 .007
Non- symbolic addition .26 2.60 .011
Daily events .25 2.38 .020
Counting .19 1.80 .075
Symbolic number ordering .11 1.07 .289
Number comparison .04 .35 .728
Final model Daily events .35 3.67 < .001
.32 3.36 .001
Non- symbolic addition .30 3.04 .003
Age .20 2.06 .042
Initialmodel:R²=.30,F(6,81)=6.71,p < .001.
Final model: R²=.30,F(4,81)=9.53,p < .001.
TABLE5 Regression model predicting formal maths achievement
at the end of children’s second year of school taking into account the
effect of formal maths achievement at the end of the first school
βt p
T1 maths .41 3.92 <.001
Daily events .16 1.62 .109
.19 2.03 .045
Non- symbolic addition .26 2.93 .004
Age .17 1.95 .054
R²=.41,F(5,81)=12.13,p < .001.
 11 of 16
O’CONNOR et al.
our results indicate that representing and processing familiar ordered
sequences in long- term memory may be fundamental for the emer-
gence of very early maths skills, when children are learning to repre-
sent and use numbers as an intrinsically ordinal sequence. The idea
that such domain- general abilities underpin early maths skills is con-
sistent with Rubinsten and Sury’s (2011) claim that processing order
information forms part of the cognitive foundations of mathematics.
Such a domain- general ability is likely to be in operation well be-
fore children learn mathematics, and indeed a considerable body of
research indicates that children rapidly acquire representations of re-
peated event sequences over multiple time scales during the preschool
using ordered representations of repeated events forms a crucial part
of children’s learning about the world, and indeed has been argued to
provide the first evidence that suggests that the same processes also
support emerging maths abilities.
domain- general representational format for representing ordered in-
formation in long- term memory, and specifically whether such repre-
to 5- year- olds have spatialized representations of familiar events (and,
indeed, our daily event ordering task and our number ordering task
required children to understand the mapping of temporal order to spa-
tial order; although see Tillman, Tulagan, & Barner, 2015, for evidence
that 4- year- olds do not do this mapping spontaneously). Friedman and
Brudos (1988) claimed that 4-year-olds use a common representa-
tional system for coding both spatial and temporal order information,
raising the possibility that the ability to represent items in this way is
then utilized in the context of mathematics as well. Such an idea is
broadly consistent with other claims regarding the way temporal order
and numbers are represented (e.g., see Bonato, Zorzi, & Umiltà, 2012,
forreviewofresearchon the“mentaltimeline”and“mentalnumber
what could be interpreted as a contrasting claim, namely that children’s
conception of numerical order develops first and is then generalized to
othernon-numerical sequences.Itis important topointout that the
non- numerical sequences that they studied are those acquired later
than the number sequence during formal education (the alphabet and
months of the year), rather than familiar event sequences which are
acquired very early in development. Moreover, the issue that Berteletti
et al. are concerned with is whether the items in sequences in ques-
tion are spaced linearly (by contrast to log spacing), rather than the
more basic issue of whether they share a spatialized representational
format. We note that children’s performance on our number line task
did not relate to performance either on the daily event task or on the
cision of children’s placing of numbers on a line measures something
different from the ability to represent and process either numerical or
non- numerical ordinal information.
Despite focused research on this issue, there is much that is not
yet known about the commonalities between temporal, numerical,
and spatial representation; we would suggest that our findings provide
new impetus for considering such commonalities, particularly those
between time (understood here as event order) and number, and how
such commonalities may play a role in the acquisition of maths skills.
Another important contribution of the current work is that it
provided the first evidence for a link between parentally reported
everyday ordering abilities and formal maths skills. Whereas clinical
observations of individuals with developmental dyscalculia have de-
scribed everyday order processing difficulties, this study was the first
to show that this link is also present in the case of a sample of young,
typically developing children. Indeed, the OPQ longitudinally pre-
dicted growth in formal maths skills during the second year of school.
This finding could have great practical importance, as it offers the
possibility to screen children for vulnerability to develop mathemat-
icsdifficulties even beforethey start theirformaleducation. Indeed,
our questionnaire was designed for 4- year- old children; in many coun-
tries,this would be 2–3 years before the children start theirformal
education in maths. The questionnaire that we developed to measure
children’s everyday order processing abilities had good psychometric
properties, and it only took a few minutes to complete, which makes
it very convenient to use. Nevertheless, future work could further
improve the psychometric properties and the predictive value of this
used in previous studies. As we have pointed out, we replicated
Attout etal.’s (2014) finding that order WM was related to maths
skills in the first year of school, but in our sample, order working
memory at the start of formal schooling did not longitudinally pre-
dict maths performance at the end of the second year of schooling.
Regarding other predictors of maths performance, Lyons et al. (2014)
found that number comparison and number line performance were
the best predictors of maths performance in the first school year. We
also found a robust relationship between number comparison perfor-
mance and maths skills both at the cross- sectional and longitudinal
levels, which is also in line with several other studies that showed
a strong relationship between number comparison and maths skills
atthe start of formal education (e.g., Attout etal., 2014; Holloway
&Ansari, 2009;Mundy&Gilmore,2009; Rousselle& Noël, 2007).
Giventhewell-establishedlinkbetween this taskandmathsability,
and the fact that it involves symbolic number processing, it is striking,
though, that number comparison did not explain additional variance
in maths skills, once the effect of counting skills and everyday order-
ing abilities were controlled.
Regarding number line performance, several studies found a re-
liable relationship between this task and maths achievement in chil-
dren from as young as 3 years old (e.g., Berteletti, Lucangeli, Piazza,
Dehaene, & Zorzi, 2010; Booth & Siegler; 2006, 2008; Link et al.,
2014; Siegler & Booth, 2004). Studies typically use a paper- and- pencil
version of this task, and it is possible that the link between maths skills
and performance on the number line task would have been stronger
had we used the typical presentation format. Nevertheless, the task
showed good reliability, and children’s estimations were not very far
from the correct positions of target numbers. Performance on this task
12 of 16 
   O’CONNOR et al.
was also related to children’s block design scores, which supports the
validity of the tasks. There was also a non- significant trend (p=.118)
toward a relationship between number line performance and formal
maths skills at T2.
Number ordering performance was significantly related to math
abilities both in Year 1 and Year 2. Nevertheless, surprisingly, non-
numerical ordering tasks were more strongly related to maths abilities
than number ordering. This raises the question of whether our version
ofthe task was ideally suited to measure number ordering skills. As
we noted earlier, other researchers used computer- based verification
tasks to measure number ordering skills in young children (e.g., Lyons
et al., 2014) that were analogous to our daily events task, albeit involv-
sion of the task too challenging, possibly because they were younger
than the participants in all the other studies. Some researchers (e.g.,
Attout& Majerus, 2015; Attoutetal.,2014;Vogeletal.,2015)pre-
sented children with dyads of numbers rather than triads in their num-
ber ordering task. The dyad version was successfully performed by
childrenasyoungas5–6years old(Attoutetal.,2014).However,an
issue with this version of the task is that Vogel et al. (2015) reported
no reverse distance effects on the task, which have been consistently
found by researchers who used number triads in their ordering task.
Thus, it is possible that the two versions of the number ordering task
(i.e., using dyads vs. triads) do not rely on exactly the same cognitive
processes. In particular,it is less certain that participants must rely
on order information per se in the dyad task than in the triad task.
For these reasons, we employed a production version of the number
ordering task.
We believe that this task was appropriate for our sample, given
that we found stronger correlations between number ordering and
maths skills than other researchers who looked at this relationship in
Vogeletal., 2015). Indeed, the typical finding in the case of young
children is a weak/non- significant relationship.5 By contrast, we found
that number ordering was significantly related to all aspects of maths
at both T1 and T2. Furthermore, we found a moderate relationship be-
tween the daily events task and the number ordering task, suggesting
that both tasks were assessing some of the same skills. Regarding the
predictive value of production vs. verification tasks, whilst we did not
use the verification version of the number ordering task, our number
better on that task than on the daily events task (i.e., a verification task
that measured ordering ability), performance on the number compar-
ison task was less strongly related to maths than the daily events task
at both T1 and T2.
There is evidence that, as children get older, number ordering skills
become increasingly strongly related to maths abilities (see Lyons et al.,
2014). Regarding non- numerical ordering skills, the developmental
pattern of their links with maths abilities has not been investigated so
far. Some recent studies (e.g., Morsanyi et al., 2017, Sasanguie et al.,
2017; Vos et al., 2017) have demonstrated that non- numerical order-
ing skills remain strongly related to arithmetic skills even in the case
of adults, although these links are not quite as strong as the relations
between numerical ordering skills and maths. Thus, it is plausible to
assume that at some point in development (most likely during the first
years of school) number ordering skills become more strongly related
to maths skills than non- numerical ordering. Nevertheless, this ques-
tion requires further investigation.
Non- symbolic addition performance was a significant predictor of
children’s later maths achievement, and growth in formal maths skills
during the second year of school, although it was not related to maths
performance at the end of the first school year. The task was designed
in such a way that children could not perform above chance if they
onlyrelied on simple perceptualstrategies(see Gilmoreetal.,2010;
young children found this task difficult. Whereas the finding that per-
formance on this task predicted maths performance is in line with
studies that found a link between non- symbolic estimation skills and
mathematicsperformance(seeChen &Li, 2014,fora meta-analysis),
it is important to note that the non- symbolic addition task has further
cognitive requirements, including memory, spatial attention and inhi-
bition, which are also important for maths development.
Indeed,one limitationofthe currentstudyis thatitdid not con-
sider some domain- general factors that are likely to play a role in nu-
mericaldevelopment.Although IQ and orderworking memorywere
measured in the current study, other general cognitive skills were not
considered. There is much evidence to suggest that other aspects of
Passolunghi,Vercelloni,& Shadee, 2007; Szűcsetal., 2013;Vander
Ven, Van der Maas, Straatemeier, & Jansen, 2013) and executive func-
tions(Gilmoreetal., 2013;Passolunghi&Siegel,2001;Soltészetal.,
interesting to investigate verbal and spatial working memory and inhi-
bition skills together with the ordering tasks, as these skills might play
Fias, 2013; van Dijck & Fias, 2011; Morsanyi et al., 2017).
Anotherlimitationthatcould benotedisthatformal mathsskills
we used a broad range of tasks to measure basic maths abilities (in-
cluding non- symbolic measures, counting skills, and measures that
required the knowledge of symbolic numbers, such as the number
line task, and the number ordering task), it is possible that children
had already possessed some of the formal maths skills (e.g., addition
and subtraction) that were assessed at the end of the first school year.
Thus, although our findings demonstrated that early, non- numerical
ordering skills were strongly related to formal maths skills at the end
of the first school year, it is unclear whether early ordering abilities
predicted growth in formal math abilities during the first school year.
This question might be explored in future studies.
Finally, we have already discussed the possibility of using every-
day ordering abilities as early indicators of potential vulnerability to
is to develop non- numerical training exercises that could be used to
helpyoungchildrento improvetheirorderingabilities. Oneinterest-
ing question is whether the effects of training in non- numerical or-
dering might generalize to number ordering skills, and numerical skills
 13 of 16
O’CONNOR et al.
ingeneral.In fact,there isa possibilitythatorderingskillsmightplay
an important role in the development of other academic skills as well,
as Perez, Majerus, and Poncelet (2012) found that order WM capac-
ity longitudinally predicted reading development in the case of young
children. The same authors (Perez, Majerus, & Poncelet, 2013) also
reportedthatadultswithdyslexia displayedadeficitin orderWM.It
is possible that the link between domain- general order processing and
other academic skills is specific to short- term memory mechanisms,
but our findings suggest that it might be useful to examine whether
such a link also extends to the sort of ordering processing skills mea-
sured in our study.
In conclusion, the currentstudy has shown that children’s abil-
ity to process order, at the earliest stage of formal schooling, is an
important predictor of maths achievement concurrently and 1 year
later.In particular, it seems that non-numericalorderingability(for
familiar tasks and daily events) is a stronger predictor of children’s
maths ability than numerical order at the early stages of education.
tablish whether early non- numerical ordering abilities predict growth
in formal maths skills during the first school year, such evidence was
found in the second year of school, at least in the case of the parental
report of children’s ordering skills. General orderingability may be
a suitable target for intervention for young children, and measuring
ordering ability could potentially be used to identify children who are
at risk of developing maths difficulties, even before they start formal
1 The typical task in the literature that is used to measure number ordering
ability is a computer- based task in which children are shown dyads or triads
of numbers and have to judge whether the order is correct or incorrect/
ascending or descending. We piloted a computer- based number ordering
task with children from this age group using triads (i.e., comparable to our
daily events ordering task) and found that they struggled to perform the
task, even after a short training that was provided using cards representing
the numbers. By contrast, they were able to complete the computer- based
version of the daily events task after a training session with cards represent-
ing the events.
2 We selected this task, rather than non- symbolic comparison, due to the in-
consistency of the evidence supporting a link between non- symbolic com-
parisonand maths in developmental studies (DeSmedt,Noël,Gilmore, &
has been found to be a longitudinal predictor of maths achievement, as well
as being related to mastery of both number words and symbols, which un-
derlies much of earlymaths learning (Gilmore etal., 2010). Furthermore,
Hall,& Butterworth,2008)has shown thatperformance on non-symbolic
addition and comparison tasks is correlated, suggesting that both tasks are
measuring the same underlying construct, whereas non- symbolic compar-
ison performance has been found to be unrelated to symbolic comparison
performance (e.g., Sasanguie, Defever, Maertens, & Reynvoet, 2014).
3Although in our main analyses we considereddifferent types of for-
mal maths skills together, the standardized tests that we used included
several different types of problems (see Methods section). We pres-
ent zero- order correlations between the measures that were robustly
related to maths at each time point and the different components of the
formal maths tasks (see Supplementary Tables 1 and 2). Typically, the
best predictors of maths at each time point (in particular, the counting
task and the daily events task) were significantly related to all aspects
all aspects of maths at T1 and T2, although it was not included in the
final regression models (see below), which suggests that its effect on
maths was mediated by other tasks.
the results of the cross- sectional and longitudinal regression models
were the same for predicting only the arithmetic/calculation measures
at T1 and T2. We conducted these analyses to demonstrate that order-
ing abilities were not simply related to a composite measure of maths
achievement (which included various basic components of early maths
ability, including some that were closely related to ordering). The same
dicted maths achievement at T1 also predicted arithmetic scores at T1
scores). Three of the four significant longitudinal predictors of maths
atT2(OPQ,non-symbolic additionand dailyevents)alsosignificantly
predictor of calculation abilities. (Detailed results of these analyses can
be found in Supplementary Tables 3 and 4.)
5 The sample in Vogel et al. (2015) consisted of children in 1st grade in
find a relationship between the size of the numerical distance effect or
meanreaction timesfortheorderjudgementtaskand maths. InAttout
et al. (2014), the children were between 5 and 6 at T1; 6 and 7 at T2
and 7 and 8 at T3. There were significant associations between numerical
ordering and maths at T2 and T3, but not at T1. Lyons et al. (2014) found
that number ordering ability was not a significant predictor of math in
grades 1 and 2 (between 6 and 8 years old) but was a significant predictor
Patrick A. O’Connor
(2015). Numerical estimation in children with autism. Autism Research,
dyscalculia: The importance of serial order. Child Neuropsychology, 21,
study. Developmental Psychology, 50,1667–1679.
Berteletti, I., Lucangeli, D., Piazza, M., Dehaene, S., & Zorzi, M. (2010).
Numerical estimation in preschoolers. Developmental Psychology, 46,
Berteletti, I., Lucangeli, D., & Zorzi, M. (2012). Representation of nu-
merical and non- numerical order in children. Cognition, 124,
Bonato,M., Zorzi,M., & Umiltà,C. (2012). Whentimeis space:Evidence
for a mental time line. Neuroscience and Biobehavioral Reviews, 36,
Booth, J.L., & Siegler, R.S. (2006). Developmental and individual differences
in pure numerical estimation. Developmental Psychology, 42,189–201.
Booth, J.L., & Siegler, R.S. (2008). Numerical magnitude representations in-
fluence arithmetic learning. Child Development, 79,1016–1031.
14 of 16 
   O’CONNOR et al.
Butterworth,B.(2005). Developmentaldyscalculia.InJ.D.Campbell (Ed.),
The handbook of mathematical cognition (pp. 455–469). New York:
Psychology Press.
Psychologica, 148,163–172.
Cohen,D.J., & Blanc-Goldhammer,D. (2011).Numericalbias in bounded
and unbounded number line tasks. Psychonomic Bulletin and Review, 18,
ital?Analogicalandsymboliceffectsin two-digitnumbercomparison.
Journal of Experimental Psychology: Human Perception and Performance,
and non- symbolic numerical magnitude processing skills relate to indi-
from brain and behavior. Trends in Neuroscience and Education, 2,48–55.
Compulsory age ofstarting school in European countries. Retrieved
Fivush,R., & Hammond, N. (1990). Autobiographical memory across the
preschool years: Toward reconceptualising childhood amnesia. In R.
Fivush& J.Hudson(Eds.), Knowing and remembering in young children
aspects of time. Child Development, 48,1593–1599.
Friedman,W.J. (1990). Children’s representationsof the pattern of daily
activities. Child Development, 61,1399–1412.
Friedman,W.J.,& Brudos, S.L. (1988). On routes and routines:Theearly
development of spatial and temporal representations. Cognitive
Development, 3,167–182.
Gelman,R.,&Gallistel,C.(1978).Young children’s understanding of numbers.
Gilmore,C.,Attridge,N., Clayton,S.,Cragg,L.,Johnson,S., Marlow,N.,…
Inglis,M. (2013).Individualdifferencesininhibitory control,not non-
verbal number acuity, correlate with mathematics achievement. PLoS
ONE, 8, e67374.
Gilmore, C., Attridge, N., De Smedt, B., & Inglis, M. (2014). Measuring
the approximate number system in children: Exploring the relation-
ships among different tasks. Learning and Individual Differences, 29,
Gilmore,C.K., McCarthy,S.E., & Spelke, E.S. (2010). Non-symbolic arith-
metic abilities and mathematics achievement in the first year of formal
schooling. Cognition, 115,394–406.
Ginsburg,H.P.,&Baroody,A.J.(2003).Test of early mathematics ability (3rd
Goffin, C., &Ansari, D. (2016). Beyond magnitude: Judging ordinalityof
symbolic number is unrelated to magnitude comparison and inde-
pendently relates to individual differences in arithmetic. Cognition, 150,
in nonverbal number acuity predict maths achievement. Nature, 455,
and mathematical skills of young children. Learning and Instruction, 15,
Holloway,I.D., &Ansari, D. (2009). Mapping numerical magnitudes onto
symbols: The distance effect and children’s mathematical competence.
Journal of Experimental Child Psychology, 103,17–29.
Acta Psychologica, 145,147–155.
processing deficits in developmental dyscalculia and low numeracy.
Developmental Science, 11,669–680.
Kaufmann,L.,Vogel,S.E.,Starke,M., Kremser, C., & Schocke, M. (2009).
Numerical and non- numerical ordinality processing in children with
Development, 24,486–494.
Laski, E.V., & Siegler,R.S. (2007). Is 27 a big number? Correlational and
causal connections among numerical categorization, number line esti-
mation, and numerical magnitude comparison. Child Development, 78,
tal number line: New evidence on children’s spatial representation of
numbers. Frontiers in Psychology, 4, 1021.
relation between number- sense and arithmetic competence. Cognition,
Lyons, I.M., Price, G.R., Vaessen, A., Blomert, L., & Ansari, D. (2014).
Science, 17,714–726.
Areview ofneuraland behavioralstudies. Progress in Brain Research,
between vocabulary development and verbal short- term memory: The
relative importance of short- term memory for serial order and item in-
formation. Journal of Experimental Child Psychology, 93,95–119.
Morsanyi,K.,Devine,A.,Nobes,A.,& Szűcs,D. (2013).Thelinkbetween
logic, mathematics and imagination: Evidence from children with devel-
opmental dyscalculia and mathematically gifted children. Developmental
Science, 16,542–553.
and number ordering as predictors of arithmetic performance in adults:
Exploring the link between the two skills, and investigating the ques-
tion of domain- specificity. Quarterly Journal of Experimental Psychology,
Mundy,E.,&Gilmore, C.K.(2009).Children’smappingbetween symbolic
and nonsymbolic representations of number. Journal of Experimental
Child Psychology, 103,490–502.
NationalCenterforLearningDisabilities(2007).Understanding dyscalculia.
Nelson,K. (1986).Event knowledge: Structure and function in development.
Nelson,K.(1998). Language in cognitive development: The emergence of the
mediated mind.Cambridge:CambridgeUniversityPress.
Nieder,A.,& Dehaene, S. (2009).Representationofnumberin the brain.
Annual Review of Neuroscience, 32,185–208.
NorthernIrelandStatisticsandResearchAgency(2010). NorthernIreland
multiple deprivation measure 2010: Blueprint document. February
2010. Retrieved from:
Passolunghi,M.C., Cargnelutti,E., & Pastore,M. (2014).Thecontribution
of general cognitive abilities and approximate number system to early
mathematics. British Journal of Educational Psychology, 84,631–649.
Passolunghi, M.C., & Siegel, L.S. (2001). Short-term memory, working
memory, and inhibitory control in children with difficulties in arith-
metic problem solving. Journal of Experimental Child Psychology, 80,
Passolunghi,M.C.,Vercelloni,B.,& Schadee,H.(2007).Theprecursorsof
mathematics learning: Working memory, phonological ability and nu-
merical competence. Cognitive Development, 22,165–184.
Perez, T.M., Majerus, S., & Poncelet, M. (2012). The contribution of short-
term memory for serial order to early reading acquisition: Evidence
from a longitudinal study. Journal of Experimental Child Psychology, 111,
Perez, T.M., Majerus, S., & Poncelet, M. (2013). Impaired short-term
memory for order in adults with dyslexia. Research in Developmental
Disabilities, 34,2211–2223.
 15 of 16
O’CONNOR et al.
severe impairment in developmental dyscalculia. Cognition, 116,33–41.
Price,G.R., Palmer,D.,Battista, C., &Ansari, D. (2012). Nonsymbolicnu-
merical magnitude comparison: Reliability and validity of different task
variants and outcome measures, and their relationship to arithmetic
achievement in adults. Acta Psychologica, 140,50–57.
Rousselle,L., & Noël, M.P. (2007). Basic numerical skills in childrenwith
mathematics learning disabilities:A comparison of symbolic vs. non-
symbolic number magnitude processing. Cognition, 102,361–395.
Rubinsten,O., & Sury, D. (2011). Processingordinalityand quantity: The
case of developmental dyscalculia. PLoS ONE, 6,e24079.
Sasanguie, D., Defever, E., Maertens, B., & Reynvoet, B. (2014). The ap-
proximate number system is not predictive for symbolic number pro-
cessing in kindergarteners. Quarterly Journal of Experimental Psychology,
Sasanguie, D., De Smedt, B., & Reynvoet, B. (2017). Evidence for dis-
tinct magnitude systems for symbolic and non- symbolic number.
Psychological Research, 81,231–242.
Sattler, J.M., & Dumont, R. (2004). Assessment of children: WISC-IV and
WPPSI-III supplement.SanDiego,CA:JeromeM.Sattler,Publisher.
Schneider,M., Beeres, K., Coban, L., Merz, S., Schmidt, S., Stricker,J., &
DeSmedt, B. (2017). Associations ofnon-symbolicandsymbolicnu-
analysis. Developmental Science, 20, e12372.
Siegler, R.S., & Booth, J.L. (2004). Development of numerical estimation in
young children. Child Development, 75,428–444.
Siegler,R.S., & Opfer,J.E. (2003). Thedevelopmentof numerical estima-
tion: Evidence for multiple representations of numerical quantity.
Psychological Science, 14,237–250.
representation,counting and memory in 4- to 7-year-old children: A
developmental study. Behavioral and Brain Functions, 6,1–14.
Szűcs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013).
Developmental dyscalculia is related to visuo- spatial memory and inhi-
bition impairment. Cortex, 49,2674–2688.
Tillman, K., Tulagan, N., & Barner, D. (2015). Building the mental timeline:
Spatial representations of time in preschoolers. Proceedings of the
Cognitive Science Society.
VanDer Ven,S.H., VanDer Maas, H.L., Straatemeier,M., & Jansen, B.R.
(2013). Visuospatial working memory and mathematical ability at
different ages throughout primary school. Learning and Individual
Differences, 27,182–192.
tion interacts with serial- order retrieval from verbal working memory.
Psychological Science, 24,1854–1859.
merical associations. Cognition, 119,114–119.
Van Heuven, W.J., Mandera, P., Keuleers, E., & Brysbaert, M. (2014).
English. Quarterly Journal of Experimental Psychology, 67,1176–1190.
bolic numerical magnitude and order in first- grade children. Journal of
Experimental Child Psychology, 129,26–39.
vonAster, M.G., & Shalev,R.S. (2007). Number development and devel-
opmental dyscalculia. Developmental Medicine and Child Neurology, 49,
eral and number- specific order processing in adults’ arithmetic perfor-
mance. Journal of Cognitive Psychology, 29,469–482.
Wechsler, D. (2003). Wechsler Preschool and Primary Scale of Intelligence –
Third UK Edition (WPPSI-III).Oxford:PsychologicalCorp.
Williams, J. (2005). Mathematics assessment for learning and teaching.
Woodcock,R.W.,McGrew, K.S., & Mather,N. (2001). Woodcock-Johnson
tests of achievement.Itasca,IL:RiversidePublishing.
Additional Supporting Information may be found online in the
supporting information tab for this article.
How to cite this article:O’ConnorPA,MorsanyiK,
at the start of formal education longitudinally predicts their
symbolic number skills and academic achievement in maths.
Dev Sci. 2018;e12645.
16 of 16 
   O’CONNOR et al.
Please circle the number which you feel best applies to your child for
each question
My son/daughter:
Iseasilyconfusedbychangesinroutine 1- - - - 2- - - - 3- - - - 4- - - - 5- - - - 6- - - - 7
Understands how the seasons of the year follow each other (e.g., that
autumn always comes after summer)
1- - - - 2- - - - 3- - - - 4- - - - 5- - - - 6- - - - 7
Caneasilyrecalltheorderinwhichpasteventshappened 1- - - - 2- - - - 3- - - - 4- - - - 5- - - - 6- - - - 7
Isabletoplanasequenceofactivitiesindependently 1- - - - 2- - - - 3- - - - 4- - - - 5- - - - 6- - - - 7
Finds it difficult to learn new activities which involve a sequence of
actions which have to be performed in a particular order (e.g.,
putting together the parts of a toy in the right order)
1- - - - 2- - - - 3- - - - 4- - - - 5- - - - 6- - - - 7
Would be able to recall the order of typical daily events 1- - - - 2- - - - 3- - - - 4- - - - 5- - - - 6- - - - 7
Understands that some things always have to be done in a particular
order (e.g., putting on a school shirt before putting on a tie)
1- - - - 2- - - - 3- - - - 4- - - - 5- - - - 6- - - - 7
Finds it difficult to understand how the days of the week follow each
other (e.g., knowing that Wednesday comes after Tuesday)
1- - - - 2- - - - 3- - - - 4- - - - 5- - - - 6- - - - 7
... Symbolic magnitude skills (as measured by number comparison tasks), as well as number line estimation, have also been shown in meta-analytic studies to predict mathematical performance at the age of six and above (Schneider et al. 2017(Schneider et al. , 2018. Symbolic ordering skills are also predictive of mathematical performance in both cross-sectional (e.g., Attout and Majerus 2018;Lyons and Ansari 2015;Lyons et al. 2014;Sasanguie and Vos 2018; but see Vogel et al. 2015) and longitudinal studies (Liang et al. 2023;Malone et al. 2021;O'Connor et al. 2018). Recent research has demonstrated that non-numerical ordering skills (measured by an everyday ordering questionnaire and a temporal ordering task) measured at age 4-5 are longitudinally predictive of children's mathematical performance one year later (O'Connor et al. 2018). ...
... Symbolic ordering skills are also predictive of mathematical performance in both cross-sectional (e.g., Attout and Majerus 2018;Lyons and Ansari 2015;Lyons et al. 2014;Sasanguie and Vos 2018; but see Vogel et al. 2015) and longitudinal studies (Liang et al. 2023;Malone et al. 2021;O'Connor et al. 2018). Recent research has demonstrated that non-numerical ordering skills (measured by an everyday ordering questionnaire and a temporal ordering task) measured at age 4-5 are longitudinally predictive of children's mathematical performance one year later (O'Connor et al. 2018). Performance on temporal ordering and order working memory (WM) tasks have also demonstrated good intra-individual stability as predictors of early formal mathematical skills amongst 4-6-year-olds (O'Connor et al. 2019). ...
... Our longitudinal study involved assessing pupils' performance on a variety of basic cognitive and mathematical tasks at T1 and T2 to examine whether they were predictive of MA at T3. We used a range of numerical and non-numerical skills (including measures of symbolic and non-symbolic magnitude processing, ordering ability, working memory, and verbal and non-verbal intelligence), skills that have been found to be relevant to early mathematical development (O'Connor et al. 2018(O'Connor et al. , 2019. In terms of our outcome measures, we assessed both children's levels of MA and their formal mathematical performance at the end of year 4, in order to better understand to what extent the early predictors of MA and mathematical performance might overlap. ...
Full-text available
Mathematical anxiety (MA) and mathematics performance typically correlate negatively in studies of adolescents and adults, but not always amongst young children, with some theorists questioning the relevance of MA to mathematics performance in this age group. Evidence is also limited in relation to the developmental origins of MA and whether MA in young children can be linked to their earlier mathematics performance. To address these questions, the current study investigated whether basic and formal mathematics skills around 4 and 5 years of age were predictive of MA around the age of 7-8. Additionally, we also examined the cross-sectional relationships between MA and mathematics performance in 7-8-year-old children. Specifically, children in our study were assessed in their first (T1; aged 4-5), second (T2; aged 5-6), and fourth years of school (T3; aged 7-8). At T1 and T2, children completed measures of basic numerical skills, IQ, and working memory, as well as curriculum-based mathematics tests. At T3, children completed two self-reported MA questionnaires, together with a curriculum-based mathematics test. The results showed that MA could be reliably measured in a sample of 7-8-year-olds and demonstrated the typical negative correlation between MA and mathematical performance (although the strength of this relationship was dependent on the specific content domain). Importantly, although early formal mathematical skills were unrelated to later MA, there was evidence of a longitudinal relationship between basic early symbolic number skills and later MA, supporting the idea that poorer basic numerical skills relate to the development of MA.
... Longitudinal studies following children from an age of four years showed that verbal serial order WM abilities (in contrast to item WM abilities requiring to reproduce verbal stimuli without specific serial order recall requirements), predicted later counting and mental calculation abilities O'Connor et al., 2018O'Connor et al., , 2019. Furthermore, children and adults presenting mathematical disabilities have been shown to exhibit order but not item WM impairment Attout et al., 2015;De Visscher et al., 2015;Morsanyi et al., 2018). ...
... For the verbal domain, we used two tasks, one focusing on the maintenance of serial order information and the other one focusing on the maintenance of phonological item information. Both tasks had been validated in previous studies (see for example Ordonez Magro et al., 2018;O'Connor et al., 2018). In the verbal serial order STM task, children had to reconstruct the serial order of animal names presented in auditory lists of increasing length. ...
... On the one hand, these data replicate previous results of a specific link between verbal serial order STM and mathematical abilities O'Connor et al., 2018). ...
Many studies have shown that both verbal and visuospatial working memory (WM) abilities predicted arithmetic abilities but we do not know if they represent a modality-specific contribution or reflect the involvement of an often shared WM aspect: the serial order storage. We administered verbal and visuospatial short-term memory (STM) tasks with variable serial order storage requirements and a mental calculation task in children. We observed that verbal serial order STM abilities predicted early mathematical abilities independently of verbal item STM and visuospatial STM abilities. For visuospatial STM abilities, a more general link with overall arithmetic abilities was observed in 8-year-old children, with the serial order task predicting additions, and the simultaneous task predicting subtractions. In 9-year-old children, no link with mathematical abilities was observed anymore for any STM measure. These data confirm a specific and complementary role of verbal and visuospatial serial order STM abilities in mathematical development.
... Additionally, ordinal skills also played a critical role in accelerating the transformation from non-symbolic numerical representations to symbolic numerical representations (Lyons et al., 2014;Merkley, 2015), and positively predicting mathematical achievement cross-sectionally (Lyons et al., 2014;Lyons et al., 2016) and longitudinally (Geary & van Marle, 2016;O'Connor et al., 2018) for both children and adults. Evidence also showed that deficits in numeral order processing may contribute to mathematical learning difficulties and dyscalculia Rubinsten & Sury, 2011). ...
... Such as mastery of number concepts in kindergarten is a strong predictor for third-grade students in the matter of calculating numbers and solving mathematical problems (McGuire et al., 2012). Other research states that good early childhood ability to sequence numbers is positively correlated to early math skills, influences mature math performance, and continues significantly to the first and second-grade students' math skills to grow and develop well (O'Connor et al., 2018). The abilities possessed by children do not necessarily develop just like that, but there needs to be stimulation from the surrounding environment, namely by applying the approaches, methods, and learning strategies used by the teacher. ...
The ability to recognize the concept of early numbers in early childhood is very important to develop so that children are ready to take part in learning mathematics at a higher level. This study aims to determine the effect of mathematics learning approaches and self-regulation to recognize the concept of early numbers ability in kindergarten. The study used an experimental method with a treatment design by level 2x2. The sample used was 32 children. Score data, ability to recognize number concepts, analyzed and interpreted. The results showed that: (1) The Realistic Mathematics Education approach is better than the Open Ended Approach in improving the ability to recognize children's number concepts; (2) There is an interaction effect between mathematics learning approaches and Self-Regulation to recognize the concept of early numbers ability; (3) The Realistic Mathematics Education approach is more suitable for children with high self-regulation, (4) The Open Ended approach is more suitable for children with low self-regulation. Subsequent experiments are expected to find mathematics learning approaches for children whose self-regulation is low on recognizing the concept of early numbers ability. Keywords: mathematics learning approach, self-regulation, early number concept ability References: Adjie, N., Putri, S. U., & Dewi, F. (2019). Penerapan Pendidikan Matematika Realistik (PMR) dalam Meningkatkan Pemahaman Konsep Bilangan Cacah pada Anak Usia Dini. Jurnal Obsesi : Jurnal Pendidikan Anak Usia Dini, 4(1), 336. Adjie, N., Putri, S. U., & Dewi, F. (2020). Peningkatan Kemampuan Koneksi Matematika melalui Pendidikan Matematika Realistik (PMR) pada Anak Usia Dini. Jurnal Obsesi : Jurnal Pendidikan Anak Usia Dini, 5(2), 1325–1338. Adjie, N., Putri, S. U., & Dewi, F. (2021). Improvement of Basic Math Skills Through Realistic Mathematics Education (RME) in Early Childhood. Jurnal Obsesi : Jurnal Pendidikan Anak Usia Dini, 6(3), 1647–1657. Amalina, A. (2020). Pembelajaran Matematika Anak Usia Dini di Masa Pandemi COVID-19 Tahun 2020. Jurnal Obsesi : Jurnal Pendidikan Anak Usia Dini, 5(1), 538. Amalina, A., Yanti, F., & Warmansyah, J. (2022). Penerapan Pendekatan Matematika Realistik terhadap Kemampuan Pemahaman Konsep Pengukuran pada Anak Usia 5-6 Tahun. Aulad: Journal on Early Childhood, 5(2), 306–312. Amini, F., Munir, S., & Lasari, Y. L. (2022). Student Mathematical Problem Solving Ability in Elementary School: The Effect of Guided Discovery Learning. Journal of Islamic Education Students (JIES), 2(2), 49. Anselmus, Z., & Parikaes, P. (2018). Regulasi Diri Dalam Belajar Sebagai Konsekuen. Jurnal Penelitain Dan Pengembangan Pendidikan, 1(1), 82–95. Apriani, N., & Maryam, K. (2020). Pengaruh Pendekatan Realistic Matematick Edukation (RME) Terhadap Kemampuan Pemecahan Masalah. 3(1), 12–19. Ardiniawan, D. Y., Subiyantoro, S., & Kurniawan, S. B. (2022). Peningkatan Kemampuan Penalaran Matematis Siswa Sekolah Dasar Melalui Pendekatan Realistic Mathematics Education ( RME ) Siswa SD Se-Kecamatan Pacitan. April, 607–613. Asri Devi, N. M. I. (2020). Pengembangan Media Pembelajaran Puzzle Angka untuk Meningkatkan Kemampuan Mengenal Lambang Bilangan. Jurnal Ilmiah Pendidikan Profesi Guru, 3(3), 416. Aulia, M., & Amra, A. (2021). Parent’s Participation in Improving the Quality of Education in Elementary Schools. Journal of Islamic Education Students (JIES), 1(2), 58. Aziza, A., Pratiwi, H., & Ageng Pramesty Koernarso, D. (2020). Pengaruh Metode Montessori dalam Meningkatkan Pemahaman Konsep Matematika Anak Usia Dini di Banjarmasin. AL-ATHFAL : JURNAL PENDIDIKAN ANAK, 6(1), 15–26. Becker, D. R., Miao, A., Duncan, R., & Mcclelland, M. (2014). Behavioral self-regulation and executive function both predict visuomotor skills and early academic achievement. Early Childhood Research Quarterly, 1–14. Bohlmann, N. L., & Downer, J. T. (2016). Self-Regulation and Task Engagement as Predictors of Emergent Language and Literacy Skills. Early Education and Development, 27(1), 18–37. Brandes-Aitken, A., Braren, S., Swingler, M., Voegtline, K., & Blair, C. (2019). Sustained attention in infancy: A foundation for the development of multiple aspects of self-regulation for children in poverty. Journal of Experimental Child Psychology, 184, 192–209. Charlesworth, R. (2005). Experiences in Math for Young Children Fifth Edition (3rd edition). Delmar Cengage Learning. Charlesworth, R. (2011). Understanding child development. Wadsworth Publishing. Chisara, C., Hakim, D. L., & Kartika, H. (2018). Implementasi Pendekatan Realistic Mathematics Education (RME) Dalam Pembelajaran Matematika. Prosiding Sesiomadika, 65–72. Cobb, P., Zhao, Q., & Visnovska, J. (2008). Learning from and adapting the theory of realistic mathematics education. Éducation et Didactique, 2(1), 105–124. Coelho, V., Cadima, J., Pinto, A. I., & Guimarães, C. (2019). Self-Regulation, Engagement, and Developmental Functioning in Preschool-Aged Children. Journal of Early Intervention, 41(2), 105–124. Cohen−Swerdlik. (2009). Psychology: Psychological Testing and Assessment An Introduction to Test and Measurement 7th Edition. In McGraw-Hill (7th ed.). McGraw-Hill. 9780767421577 Costa, P., Ermini, T., & Sigaud, C. H. de S. (2019). Effects of an educational playful intervention on nasal hygiene behaviors of preschoolers: a quasi-experimental study. Health Promotion Perspectives, 9(1), 50–54. Deflorio, L., Klein, A., Starkey, P., Swank, P. R., Taylor, H. B., Halliday, S. E., Beliakoff, A., & Mulcahy, C. (2018). A study of the developing relations between self-regulation and mathematical knowledge in the context of early math intervention. Early Childhood Research Quarterly. Delyana, H. (2015). Peningkatan Kemampuan Pemecahan Masalah Matematika Siswa Kelas VII Melalui Penerapan Pendekatan Open Ended. Lemma, 2(1), 26–34. Dennick, R. (2016). Constructivism: reflections on twenty-five years teaching the constructivist approach in medical education. International Journal of Medical Education, 7(July), 200–205. Deny, S. (2019). Survei PISA 2018: Skor Pendidikan Indonesia Masih di Bawah Rata-Rata. 04 Desember. Dwipayana, I. K. A. A., & Diputra, K. S. (2019). Pengaruh Pendekatan Pendidikan Matematika Realistik Berbasis Open Ended Terhadap Kemampuan Berpikir Kreatif Siswa. Journal of Education Technology, 2(3), 87. Egbert, J., Herman, D., & Lee, H. (2015). Flipped Instruction in English Language Teacher Education : A Design- ­ ‐ based Study in a Complex, Open- ­ ‐ ended Learning Environment. 19(2), 1–23. Eisenberg, N., Pidada, S., & Liew, J. (2001). The Relations of Regulation and negative emotionality to Indonesian Children’s social functioning. Child Development, 72(6), 1747–1763. Eisenberg, N., Valiente, C., & Eggum, N. D. (2010). Self-Regulation and School Readiness. Early Education & Development, 21(5), 681–698. Eka, F. (2016). Penerapan Model Pembelajaran Open Ended Pada Pembelajaran Matematika Kelas V Untuk Meningkatkan Keterampilan Berpikir Kritis Siswa di Madrasah Ibtidaiyah Al-Munawwarah Kota Jambi. Skripsi, 4(1), 1–23. Elina, R. (2021). Journal of Islamic Education Students The Effect of Administrative Services on Students’ Satisfaction. JIES: Journal of Islamic Education Students, 1(1), 39–47. Elliott, W., Jung, H., & Friedline, T. (2016). Math Achievement and Children’s Savings: Implications for Child Development Accounts. Journal of Family and Economic Issues, 31(2), 171–184. Evi, S. (2011). Pendekatan Matematika Realistik (PMR) untuk Meningkatkan Kemampuan Berfikir Siswa di Tingkat Sekolah Dasar. Jurnal Penelitian Pendidikan, Edisi Khus(2), 154–163. Fajriah, N., & Asiskawati, E. (2015). Kemampuan Berfikir Kreatif Siswa dalam Pembelajaran Matematika Menggunakan Pendidikan Matematika Realistik di SMP. Pendidikan Matematika, 3(2), 157–165. Faridah, N., Isrok’atun, I., & Aeni, A. N. (2016). Pendekatan Open-Ended Untuk Meningkatkan Kemampuan Berpikir Kreatif Matematis Dan Kepercayaan Diri Siswa. Jurnal Pena Ilmiah, 1(1). Fathonah, R. N. (2021). Video Kegiatan Rote Counting dan Rational Counting untuk Menstimulasi Berhitung Permulaan pada Anak Usia ( 4-5 ) Tahun. Febriyani, E., & Warmansyah, J. (2021). Akreditasi Satuan PAUD Berbasis Sistem Penilaian Akreditasi (SISPENA). Journal of Science and Technology, 1(2), 3. Friskilia, O., & Winata, H. (2018). Regulasi Diri (Pengaturan Diri) Sebagai Determinan Hasil Belajar Siswa Sekolah Menengah Kejuruan. Jurnal Pendidikan Manajemen Perkantoran, 3(1), 184. Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., & McDowell, J. (2014). Teaching math to young children: A practice guide (NCEE 2014-4005). Department of Education. García-Sánchez, P., Tonda, A., Mora, A. M., Squillero, G., & Merelo, J. J. (2018). Automated playtesting in collectible card games using evolutionary algorithms: A case study in Hearthstone. Knowledge-Based Systems, 153, 133–146. Greenberg, J. (2012). M ore, A ll G one , E mpty , Every Day in Every Way Coming soon ! May, 62–64. Hamidah, N. H., Lidinillah, D. A. M., & Muslihin, H. Y. (2021). Desain Lembar Kerja Anak Berbasis Realistic Mathematika Education ( RME ) untuk Mengenalkan Konsep Bilangan Anak Usia Sciencs Study ) siswa Negara Indonesia. 5(1), 1–9. Handayani, S. D., & Irawan, A. (2020). Pembelajaran matematika di masa pandemic covid-19 berdasarkan pendekatan matematika realistik. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah Di Bidang Pendidikan Matematika, 6(2), 179–189. Haryuni, S. (2013). Peningkatan Kemampuan Mengenal Bilangan Melalui Media Domino Segitiga di PAUD Kenanga I Kabupaten Pesisir Selatan. Spektrum PLS, 1(1), 103–118. Hayati, N., & Fitri, R. (2016). Bombik Modifikasi Pada Anak Kelompok Bermain. Jurnal Paud Teratai, 5(3), 1–5. Hendrik, J., & Susanti. (2019). Perancangan Aplikasi Tes Psikologi Kecerdasan Majemuk Menggunakan Howard Gardner ’ S Theory of Multiple Intelligences Dengan Microsoft Visual Basic . Net. Jurnal TIMES, VIII(1), 54–62. Hidayat, E. I. F., Vivi Yandhari, I. A., & Alamsyah, T. P. (2020). Efektivitas Pendekatan Realistic Mathematics Education (RME) Untuk Meningkatkan Kemampuan Pemahaman Konsep Matematika Siswa Kelas V. Jurnal Ilmiah Sekolah Dasar, 4(1), 106. Hurtado, C. M. (2017). The Role Of And Quality Of Head Start Experiences In the Development Of Self-Regulatation. Ivrendi, A. (2011). Influence of Self-Regulation on the Development of Children’s Number Sense. Early Childhood Education Journal. Jampel, I. N., & Puspita, K. R. (2017). Peningkatan Hasil Belajar Siswa Sekolah Dasar Melalui Aktivitas Pembelajaran Mengamati Berbantuan Audiovisual. International Journal of Elementary Education, 1(3), 197. Jaramillo, J. M., Rendón, M. I., Muñoz, L., Weis, M., Trommsdorff, G., & Medina, A. M. (2017). Children s Self-Regulation in Cultural Contexts : The Role of Parental Socialization Theories, Goals, and Practices. 8(June), 1–9. Jennifer, J. C., Margaret, M., & Leow, C. (2014). A Survey Study of Early Childhood Teachers ’ Beliefs and Confidence about Teaching Early Math. 367–377. Kurnia. (2015). Penerapan Model Problem Based Learning Untuk Meningkatkan Kemampuan Menulis Teks Eksposisi Pada Siswa Kelas X II-4 SMA Negeri 8 Makassar. Jurnal Pepatudzu, 9(1), 72–84. Laela, M. N., Ashari, F. A., & Nurcahyani, L. D. (2023). Development of APE Jemari Keahlian to Develop Cognitive Abilities in Children 4-5 Years Old. Indonesian Journal of Early Childhood Educational Research, 1(2), 97–106. Lau, Y. S., & Rahardjo, M. M. (2020). Meningkatkan Budaya Antri Anak Usia 4-5 Tahun melalui Metode Berbaris Sesuai Warna. Jurnal Obsesi : Jurnal Pendidikan Anak Usia Dini, 5(1), 755. Liwis, N. W. N., & Antara, P. A. (2017). Pengaruh Model Pembelajaran Matematika Realistik Terhadap Kemampuan Mengenal Konsep Bilangan Pada Anak Kelompok A Taman Kanak-Kanak Gugus V Kecamatan Buleleng Gugus V Kecamatan Buleleng Tahun Ajaran 2016/2017. Jurnal Pendidikan Anak Usia Dini Undiksha, 5(1). Manab, A. (2016). Memahami regulasi diri: Sebuah tinjauan konseptual. Psychology & Humanity, 7–11. McGuire, P., Kinzie, M. B., & Berch, D. B. (2012). Developing Number Sense in Pre-K with Five-Frames. Early Childhood Education Journal. Mclaughlin, T., Gordon, C., & Ayivor, J. (2013). An Evaluation of the Direct Instruction Model-Lead-Test Procedure and Rewards on Rote Counting, Number Recognition... Indonesian Journal of Basic and Applied Science, 2(1), 98–109. Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2015). TIMSS 2015 International Results in Mathematics. Mulyana, F. A. P., Nandiyanto, A. B. D., & Kurniawan, T. (2022). E-learning Media for the Ability to Recognize and Count Numbers in Kindergarten Students. International Journal of Research and Applied Technology, 2(1), 151–157. Mulyati, C., Muiz, D. A., & Rahman, T. (2019). Pengembangan Media Papan Flanel Untuk Memfasilitasi Kemampuan Konsep Bilangan Anak Pada Kelompok B. Jurnal Pendidikan Dan Konseling (JPDK), 1(1), 59–68. Mulyati, S., & Sisrazeni, S. (2022). The Relationship Between Stressful Study And Students’ Sleep Pattern During Covid-19 Pandemic. Journal of Islamic Education Students (JIES), 2(1), 21. Mustikasari, M., Zulkardi, Z., & Aisyah, N. (2013). Pengembangan Soal-Soal Open-Ended Pokok Bahasan Bilangan Pecahan Di Sekolah Menengah Pertama. Jurnal Pendidikan Matematika, 4(2). . Muzakki, M., & Fauziah, P. Y. (2015). Implementasi pembelajaran anak usia dini berbasis budaya lokal di PAUD full day school. Jurnal Pendidikan Dan Pemberdayaan Masyarakat, 2(1), 39. Nabighoh, W. N., Mustaji, M., & Hendratno, H. (2022). Meningkatkan Kecerdasan Logika Matematika Anak Usia Dini melalui Media Interaktif Puzzle Angka. Jurnal Obsesi : Jurnal Pendidikan Anak Usia Dini, 6(4), 3410–3417. Narayani, N. P. U. D. (2019). Pengaruh Pendekatan Matematika Realistik Berbasis Pemecahan Masalah Berbantuan Media Konkret Terhadap Hasil Belajar Matematika. Jurnal Ilmiah Sekolah Dasar, 3(2), 220. Ningsih, S. (2014). Realistic Mathematics Education: Model Alternatif Pembelajaran Matematika Sekolah. Jurnal Pendidikan Matematika, 1(2), 73. Nisva, L., & Okfrima, R. (2019). Hubungan Antara Regulasi Diri Dengan Palang Merah Indonesia. Jurnal PSYCHE, 12(2), 155–164. Nurina, D. L., & Retnawati, H. (2015). Keefektifan Pembelajaran Menggunakan Pendekatan Problem Posing dan Pendekatan Open-Ended Ditinjau Dari HOTS. PYTHAGORAS: Jurnal Pendidikan Matematika, 10(2), 129. Nurlatifah, D., Sudin, A., Maulana, M., & Kontekstual, P. (2017). Perbedaan Pengaruh Antara Pendekatan Realistik Dan Pendekatan Kontekstual Terhadap Pemahaman Matematis Siswa Pada Materi Kesebangunan. Jurnal Pena Ilmiah, 2(1), 961–970. Nurlita, M. (2015). Pengembangan Soal Terbuka (Open-Ended Problem) pada Mata Pelajaran Matematika SMP Kelas VIII. Pythagoras: Jurnal Pendidikan Matematika, 10(1), 38–49. O’Connor, P. A., Morsanyi, K., & McCormack, T. (2018). Young children’s non-numerical ordering ability at the start of formal education longitudinally predicts their symbolic number skills and academic achievement in maths. Developmental Science, 21(5), e12645. Oktaviana, W., Warmansyah, J., & Trimelia Utami, W. (2021). The Effectiveness of Using Big Book Media on Early Reading Skills in 5-6 Years Old. Al-Athfal: Jurnal Pendidikan Anak, 7(2), 157–166. Östergren, R., & Träff, U. (2013). Early number knowledge and cognitive ability affect early arithmetic ability. Journal of Experimental Child Psychology, 115(3), 405–421. Pendidikan, M., Kebudayaan, D. A. N., & Indonesia, R. (2014). No Title. Ponitz, C. C., McClelland, M. M., Matthews, J. S., & Morrison, F. J. (2009). A Structured Observation of Behavioral Self-Regulation and Its Contribution to Kindergarten Outcomes. Developmental Psychology, 45(3), 605–619. Portilla, X. A., Ballard, P. J., Adler, N. E., Boyce, W. T., & Obradović, J. (2014). An integrative view of school functioning: Transactions between self-regulation, school engagement, and teacher-child relationship quality. Child Development,85(5), 1915–1931. Prasetya, I., Ulima, E. T., Jayanti, I. D., Pangestu, S. G., Anggraeni, R., & Arfiah, S. (2019). Kegiatan Bimbingan Belajar dalam Meningkatkan Minat Belajar Siswa di Kelurahan Bolong Karanganyar. Buletin KKN Pendidikan, 1(1). Purnomo, Y. W., Kowiyah, K., Alyani, F., & Assiti, S. S. (2014). Assessing Number Sense Performance of Indonesian Elementary School Students. International Education Studies, 7(8). Putra, A. P. (2014). Aji Permana Putra, Eksperimen Pendekatan Pembelajaran... I, 1–10. Qistia, N., Kurnia, R., & Novianti, R. (2019). Hubungan Regulasi Diri dengan Kemandirian Anak Usia Dini. Aulad : Journal on Early Childhood, 2(3), 61–72. Rahma, A., & Haviz, M. (2022). Implementation of Cooperative Learning Model with Make A Match Type on Students Learning Outcomes in Elementary School. Journal of Islamic Education Students (JIES), 2(2), 58. Rahmawati, F. (2013). Pengaruh Pendekatan Pendidikan Realistik Matematika dalam Meningkatkan Kemampuan Komunikasi Matematis Siswa Sekolah Dasar. Prosiding SEMIRATA 2013, 1(1), 225–238. Rakhman, A., & Alam, S. K. (2022). Metode Bermain Kooperatif Dalam Meningkatkan Antusias Belajar Anak Usia Dini Pada Masa Covid-19. Abdimas Siliwangi, 5(1). Riley, D., Juan, robert R. S., Klinkner, J., & Ramminger, A. (2008). Social and Emotional Development. redleaf press. Rismaratri, D., & Nuryadi. (2017). Pengaruh Model Pembelajaran Quantum Dengan Pendekatan Realistic Mathematic Education ( RME ) Terhadap Kemampuan Berfikir Kreatif Dan Motivasi Belajar Matematika. Jurnal Edukasi Matematika Dan Sains, 5(2). Rohmalina, R., Aprianti, E., & Lestari, R. H. (2020). Pendekatan Open-Ended dalam Mempengaruhi Kemampuan Mengenal Konsep Bilangan Anak Usia Dini. Jurnal Obsesi : Jurnal Pendidikan Anak Usia Dini, 5(2), 1409–1418. Roliana, E. (2018). Urgensi Pengenalan Konsep Bilangan Pada Anak Usia Dini. Nasional Pendidikan Dasar, 417–420. Rosdiani, A., & Warmansyah, J. (2021). Perancangan Game Edukasi Berhitung Berbasis Mobile Aplikasi Inventor. Journal of Science and Technology, 1(2), 198–206. Rudyanto, H. E. (2016). Pengembangan Kreativitas Siswa Sekolah Dasar Melalui Pembelajaran Matematika Open-Ended. Premiere Educandum : Jurnal Pendidikan Dasar Dan Pembelajaran, 3(02), 184–192. Sa’diah, H., Zulhendri, Z., & Fadriati, F. (2022). Development of Learning Videos with Kinemaster-Based Stop Motion Animations on Thematic Learning in Elementary Schools. Journal of Islamic Educational Students (JIES), 2(2), 91. Safitri, N. D., Hasanah, U., & Masruroh, F. (2023). The Development of Thematic Board Educational Game Tools to Train The Literacy Skills of Children 5-6 Years Old. Indonesian Journal of Early Childhood Educational Research, 1(2), 75–86. Salminen, J., Guedes, C., Lerkksnen, M. K., Pakarinen, E., & Cadima. (2021). Teacher – child interaction quality and children s self-regulation in toddler classrooms in Finland and Portugal. December 2020, 1–23. Sarnecka, B. W., & Lee, M. D. (2019). Levels of number knowledge during early childhood. Journal of Experimental Child Psychology, 103(3), 325–337. Sawyer, A. C. P., Chittleborough, C. R., Mittinty, M. N., Miller-Lewis, L. R., Sawyer, M. G., Sullivan, T., & Lynch, J. W. (2015). Are trajectories of self-regulation abilities from ages 2-3 to 6-7 associated with academic achievement in the early school years? Child: Care, Health and Development, 41(5), 744–754. Setiyawati, Y. (2019). Regulasi Diri Mahasiswa Ditinjau Dari Keikutsertaan Dalam Suatu Organisasi. EMPATI-Jurnal Bimbingan Dan Konseling, 6(1), 245–259. Shah, P. E., Weeks, H. M., Richards, B., & Kaciroti, N. (2018). Early childhood curiosity and kindergarten reading and math academic achievement. Pediatric Research, 84(3), 380–386. Sriwahyuni, E., Asvio, N., & Nofialdi, N. (2017). Metode Pembelajaran Yang Digunakan Paud (Pendidikan Anak Usia Dini) Permata Bunda. ThufuLA: Jurnal Inovasi Pendidikan Guru Raudhatul Athfal, 4(1), 44. Sudono, A. (2000). Sumber belajar dan alat permainan untuk pendidikan anak usia dini. Grasindo. Sumardi, S., Rahman, T., & Gustini, I. S. (2017). Peningkatan Kemampuan Anak Usia Dini Mengenal Lambang Bilangan Melalui Media Playdough. Jurnal Paud Agapedia, 1(2), 190–202. Supriaji, U., & Soliyah, S. (2021). Upaya Meningkatkan Kemampuan Mengenal Angka Melalui Pendekatan Realistik Matematik Education ( Rme ) Pada Anak Usia 5-6. Jurnal Kridatama Sains Dan Teknologi, 03(01), 1–12. Suseno, P. U., Ismail, Y., & Ismail, S. (2020). Pengembangan Media Pembelajaran Matematika Video Interaktif berbasis Multimedia. Jambura Journal of Mathematics Education, 1(2), 59–74. Sutama, I. W., Astuti, W., Pramono, P., Ghofur, M. A., N., D. E., & Sangadah, L. (2021). Pengembangan E-Modul “Bagaimana Merancang dan Melaksanakan Pembelajaran untuk Memicu HOTS Anak Usia Dini melalui Open Ended Play” Berbasis Ncesoft Flip Book Maker. SELING: Jurnal Program Studi PGRA, 7(1), 91–101. Syah, M. (2003). Pendekatan pembelajaran Pendidikan Matematika. Remaja Rosdakarya. Taman, D. I., Cimahi, K. K., Masa, P., & Covid, P. (2020). Jurnal tunas siliwangi. 6(2), 51–62. Utami, N. R., & Warmansyah, J. (2019). Cerita gambar berseri untuk meningkatkan hasil belajar sains di lembaga paud Yogyakarta. Jurnal Tunas Cendekia, 2(2), 89–100. Utami, R. W., Endaryono, B. T., & Djuhartono, T. (2020). Meningkatkan Kemampuan Berpikir Kreatif Matematis Siswa Melalui Pendekatan Open-Ended. Faktor : Jurnal Ilmiah Kependidikan, 7(1). Utami, S. Y., Muawwanah, U., & Moha, L. (2023). Implementation of Loose Part Media to Increase Creativity in Early Childhood. Indonesian Journal of Early Childhood Educational Research, 1(2), 87–96. Utoyo, S., & Arifin, I. N. (2017). Model Permainan Kinestetik Untuk Meningkatkan Kemampuan Matematika Awal Pada Anak Usia Dini. JPUD - Jurnal Pendidikan Usia Dini, 11(2), 323–332. Van Herwegen, J., Costa, H. M., Nicholson, B., & Donlan, C. (2018). Improving number abilities in low achieving preschoolers: Symbolic versus non-symbolic training programs. Research in Developmental Disabilities, 77, 1–11. Warmansyah, J., Sari, R. N., Febriyani, E., & Mardiah, A. (2022). The Effect of Geoquarium Magic Educational Game Tool on The Ability to Recognize Geometry Shapes in Children 4-5 Years Old. The 6th Annual Conference on Islamic Early Childhood Education, 2017, 93–100. Warmansyah, J., Zulhendri, Z., & Amalina, A. (2021). The Effectiveness of Lore Traditional Games Towards The Ability to Recognize The Concept of Numbers on Early Childhood. Ta’dib, 24(2), 79. Weller, S. C., Vickers, B., Bernard, H. R., Blackburn, A. M., Borgatti, S., Gravlee, C. C., & Johnson, J. C. (2018). Open-ended interview questions and saturation. 1–18. Widyastuti, N. S., & Pujiastuti, P. (2014). Pengaruh Pendidikan Matematika Realistik Indonesia (PMRI) Terhadap Pemahaman Konsep Dan Berpikir Logis Siswa. Jurnal Prima Edukasia, 2(2), 183. Wijaya, A. (2011). Pendidikan Matematika Realistik Suatu Alternatif Pendekatan Pembelajaran Matematika. Graha Ilmu. Wulandani, C., Afina Putri, M., Indah Pratiwi, R., & Sulong, K. (2022). Implementing Project-Based Steam Instructional Approach in Early Childhood Education in 5.0 Industrial Revolution Era. Indonesian Journal of Early Childhood Educational Research (IJECER), 1(1), 29–37. Wulandari, N. P. R., Dantes, N., & Antara, P. A. (2020). Pendekatan Pendidikan Matematika Realistik Berbasis Open Ended Terhadap Kemampuan Pemecahan Masalah Matematika Siswa. Jurnal Ilmiah Sekolah Dasar, 4(2), 131. Yanti, D., Widada, W., & Zamzaili. (2018). Kemampuan Pemecahan Masalah Open Ended Peserta Didik Sekolah Negeri Dan Swasta Dalam Pembelajaran Matematika Realistik Berorientasi Etnomatematika Bengkulu. Jurnal Pendidikan Matematika Raflesia, 3(1), 203–209. Yilmaz, Z. (2017). Young Children s Number Sense Development : Age-Related Complexity across Cases of Three Children. 9(June), 891–902. Zhou, N., & Yadav, A. (2017). Effects of multimedia story reading and questioning on preschoolers’ vocabulary learning, story comprehension, and reading engagement. Educational Technology Research and Development. Zulkarnain, I., & Amalia Sari, N. (2016). Model Penemuan Terbimbing dengan Teknik Mind Mapping untuk Meningkatkan Kemampuan Pemahaman Konsep Matematis Siswa SMP. EDU-MAT: Jurnal Pendidikan Matematika, 2(2), 240–249.
... This might have implications for theories about the mechanisms that contribute to the normal course of numerical development. In view of the current findings, this might be particularly so for theories on the development of children's object counting, their understanding of number order and their knowledge of Arabic numerals, all of which have been identified as critical predictors of children's subsequent mathematics achievement in primary school as well as risk factors for the development of mathematical learning difficulties (e.g., Geary et al., 2018;Geary & VanMarle, 2016;Göbel et al., 2014;O'Connor et al., 2018). ...
There are massive developments in children’s early number skills in the ages 4- to 6-year old during which they attend preschool education and before they transition to formal school. We investigated to which extent these developments can be explained by children’ schooling experiences during preschool or by chronological age related maturational changes. In a secondary data-analysis of an existing longitudinal dataset, we compared children who were similar in age but different in the amount of preschool education (Old Year 2, n = 104, Mage = 62 months SDage 0.9 months vs. Young Year 3, n = 71, Mage = 65 months, SDage = 1.5 months) as well as children who were similar in the amount of preschool experience but differed in age (Young Year 3, n = 71, Mage = 65 months, SDage = 1.5 months vs. Old Year 3, n = 104, Mage = 74 months, SDage = 1.1 months). All children completed measures of numbering (verbal counting, dot enumeration, object counting), relations (number order, numeral identification, symbolic comparison, nonsymbolic comparison) and arithmetic operations (nonverbal calculation). We observed effects of preschool on object counting, numeral recognition and number order. There were also effects of chronological age on verbal counting, number order, numeral recognition and nonverbal calculation. The current data highlight which early number skills may be particularly malleable through schooling. They provide a more careful characterization of the potential factors that contribute to children’s early numerical competencies.
... Diversos autores están focalizando sus investigaciones en el impacto que tiene la ordinalidad sobre la adquisición del sistema simbólico y su impacto posterior sobre la habilidad de cálculo. Se ha visto que la capacidad para ordenar series de símbolos arábigos está directamente relacionada con la adquisición del sistema numérico simbólico (Lyons, Vogel, y Ansari, 2016) y que además ésta es un predictor muy potente de la habilidad aritmética posterior (Goffin y Ansari, 2016;Lyons, Price, Vaessen, Blomert, y Ansari, 2014;O'Connor, Morsanyi, y McCormack, 2018). Lyons, et al., (2014) encontraron que el valor predictivo de la ordinalidad aumento durante la enseñanza básica, llegando a ser, incluso, el predictor más potente en 6º básico de entre todos los que se habían evaluado. ...
Full-text available
Numerical ability is developed in the early years of age and is the basis for later learning mathematics, as well as academic and work success in adulthood. Initial mathematics education has traditionally focused on the teaching of general processes, seeking the development of logical-mathematical thinking and mathematical language. This article seeks to think about the importance of training specific numerical cognitive processes, based on the findings in cognitive psychology. Thus, in this work the latest empirical evidence is reviewed, based on recent studies with behavioral approaches in numerical cognition, focused on the development of early numerical skills. For this, the main milestones of numerical development in relation to the acquisition of later arithmetic are reviewed, taking into account the intrinsic and extrinsic influences on the individual during the first years of age.
Full-text available
Students’ motivation and perception are important factors to consider in online learning. This study determined the students’ level of motivation in instructional materials and perception in synchronous classroom learning at Misamis University for the academic year 2021-2022. The researchers used the descriptive-correlational research design. The respondents of the study were the 138 Junior High School students chosen through purposive sampling technique. The gathering of data was done by the use of the Instructional Materials Motivation Survey (IMMS) and Synchronous Classroom Learning Survey (SCLS) as instruments. Mean, Standard Deviation, Pearson r, and Stepwise Regression Analysis were the statistical tools employed in the data analysis. Results revealed that students' level of motivation in instructional materials used by teachers was high, and students' perception of synchronous classroom learning was good. This indicates that students who find the learning materials appealing are more likely to perform well in Mathematics. Teachers needed to be comfortable using technology to produce classes, interactive activities, assessments, projects, and other responsibilities to boost their creativity in creating instructional materials to increase students' satisfaction in the classroom. Future researchers should look into other factors contributing to students' academic performance in synchronous classroom learning.
Mathematics skills are associated with future employment, wellbeing and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.
Written for pre-service and in-service educators, as well as parents of children in preschool through grade five, this book connects research in cognitive development and math education to offer an accessibly written and practical introduction to the science of elementary math learning. Structured according to children's mathematical development, How Children Learn Math systematically reviews and synthesizes the latest developmental research on mathematical cognition into accessible sections that explain both the scientific evidence available and its practical classroom application. Written by an author team with decades of collective experience in cognitive learning research, clinical learning evaluations, and classroom experience working with both teachers and children, this amply illustrated text offers a powerful resource for understanding children's mathematical development, from quantitative intuition to word problems, and helps readers understand and identify math learning difficulties that may emerge in later grades. Aimed at pre-service and in-service teachers and educators with little background in cognitive development, the book distills important findings in cognitive development into clear, accessible language and practical suggestions. The book therefore serves as an ideal text for pre-service early childhood, elementary, and special education teachers, as well as early career researchers, or as a professional development resource for in-service teachers, supervisors and administrators, school psychologists, homeschool parents, and other educators.
Ordinal processing plays a fundamental role in both the representation and manipulation of symbolic numbers. As such, it is important to understand how children come to develop a sense of ordinality in the first place. The current study examines the role of the count-list in the development of ordinal knowledge through the investigation of two research questions: (1) Do K-1 children struggle to extend the notion of numerical order beyond the count-list, and if so (2) does this extension develop incrementally or manifest as a qualitative re-organization of how children recognize the ordinality of numerical sequences. Overall, we observed that although young children reliably identified adjacent ordered sequences (i.e., those that match the count-list; ‘2-3-4') as being in the correct ascending order, they performed significantly below chance on non-adjacent ordered trials (i.e., those that do not match the count-list but are in the correct order; ‘2-4-6’) from the beginning of kindergarten to the end of first grade. Further, both qualitative and quantitative analyses supported the conclusion that the ability to extend notions of ordinality beyond the count-list emerged as a conceptual shift in ordinal understanding rather than through incremental improvements. These findings are the first to suggest that the ability to extend notions of ordinality beyond the count-list to include non-adjacent numbers is non-trivial and reflects a significant developmental hurdle that most children must overcome in order to develop a mature sense of ordinality.
Full-text available
Digit order processing is highly related to individual differences in arithmetic performance. To examine whether serial scanning or associative mechanisms underlie order processing, order tasks (i.e. deciding whether three digits were presented in an order or not) were administered in two experiments. In the first experiment, digits were presented in different directions namely ascending, descending and non-ordered. For each direction, close and far distance sequences were presented. Results revealed reversed distance effects for ordered sequences, but ascending sequences elicited faster performance and stronger reversed distance effects than descending sequences, suggesting that associative mechanisms underlie order processing. In the second experiment, it was examined to which extent the relation between order processing and arithmetic is number-specific by presenting order tasks with digits, letters and months. In all order tasks similar distance effects were observed and similar relations with arithmetic were found, suggesting that both general associative mechanisms and number-specific mechanisms contribute to arithmetic.
Full-text available
Recent evidence has highlighted the important role that number ordering skills play in arithmetic abilities (e.g., Lyons & Beilock, 2011). In fact, Lyons et al. (2014) demonstrated that although at the start of formal mathematics education number comparison skills are the best predictors of arithmetic performance, from around the age of 10, number ordering skills become the strongest numerical predictors of arithmetic abilities. In the current study, we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was partially mediated by number ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor which included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.
Full-text available
Cognitive models of magnitude representation are mostly based on the results of studies that use a magnitude comparison task. These studies show similar distance or ratio effects in symbolic (Arabic numerals) and non-symbolic (dot arrays) variants of the comparison task, suggesting a common abstract magnitude representation system for processing both symbolic and non-symbolic numerosities. Recently, however, it has been questioned whether the comparison task really indexes a magnitude representation. Alternatively, it has been hypothesized that there might be different representations of magnitude: an exact representation for symbolic magnitudes and an approximate representation for non-symbolic numerosities. To address the question whether distinct magnitude systems exist, we used an audio-visual matching paradigm in two experiments to explore the relationship between symbolic and non-symbolic magnitude processing. In Experiment 1, participants had to match visually and auditory presented numerical stimuli in different formats (digits, number words, dot arrays, tone sequences). In Experiment 2, they were instructed only to match the stimuli after processing the magnitude first. The data of our experiments show different results for non-symbolic and symbolic number and are difficult to reconcile with the existence of one abstract magnitude representation. Rather, they suggest the existence of two different systems for processing magnitude, i.e., an exact symbolic system next to an approximate non-symbolic system.
Full-text available
Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non-symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta-analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17.201 participants. Effect sizes were combined by means of a two-level random-effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non-symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non-symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school aged children and adults.
The last several years have seen steady growth in research on the cognitive and neuronal mechanisms underlying how numbers are represented as part of ordered sequences. In the present review, we synthesize what is currently known about numerical ordinality from behavioral and neuroimaging research, point out major gaps in our current knowledge, and propose several hypotheses that may bear further investigation. Evidence suggests that how we process ordinality differs from how we process cardinality, but that this difference depends strongly on context—in particular, whether numbers are presented symbolically or nonsymbolically. Results also reveal many commonalities between numerical and nonnumerical ordinal processing; however, the degree to which numerical ordinality can be reduced to domain-general mechanisms remains unclear. One proposal is that numerical ordinality relies upon more general short-term memory mechanisms as well as more numerically specific long-term memory representations. It is also evident that numerical ordinality is highly multifaceted, with symbolic representations in particular allowing for a wide range of different types of ordinal relations, the complexity of which appears to increase over development. We examine the proposal that these relations may form the basis of a richer set of associations that may prove crucial to the emergence of more complex math abilities and concepts. In sum, ordinality appears to be an important and relatively understudied facet of numerical cognition that presents substantial opportunities for new and ground-breaking research.
Developmental dyscalculia is thought to be a specific impairment of mathematics ability. Currently dominant cognitive neuroscience theories of developmental dyscalculia suggest that it originates from the impairment of the magnitude representation of the human brain, residing in the intraparietal sulcus, or from impaired connections between number symbols and the magnitude representation. However, behavioral research offers several alternative theories for developmental dyscalculia and neuro-imaging also suggests that impairments in developmental dyscalculia may be linked to disruptions of other functions of the intraparietal sulcus than the magnitude representation. Strikingly, the magnitude representation theory has never been explicitly contrasted with a range of alternatives in a systematic fashion. Here we have filled this gap by directly contrasting five alternative theories (magnitude representation, working memory, inhibition, attention and spatial processing) of developmental dyscalculia in 9–10-year-old primary school children. Participants were selected from a pool of 1004 children and took part in 16 tests and nine experiments. The dominant features of developmental dyscalculia are visuo-spatial working memory, visuo-spatial short-term memory and inhibitory function (interference suppression) impairment. We hypothesize that inhibition impairment is related to the disruption of central executive memory function. Potential problems of visuo-spatial processing and attentional function in developmental dyscalculia probably depend on short-term memory/working memory and inhibition impairments. The magnitude representation theory of developmental dyscalculia was not supported.
Number skills are often reported anecdotally and in the mass media as a relative strength for individuals with autism, yet there are remarkably few research studies addressing this issue. This study, therefore, sought to examine autistic children's number estimation skills and whether variation in these skills can explain at least in part strengths and weaknesses in children's mathematical achievement. Thirty-two cognitively able children with autism (range = 8-13 years) and 32 typical children of similar age and ability were administered a standardized test of mathematical achievement and two estimation tasks, one psychophysical nonsymbolic estimation (numerosity discrimination) task and one symbolic estimation (numberline) task. Children with autism performed worse than typical children on the numerosity task, on the numberline task, which required mapping numerical values onto space, and on the test of mathematical achievement. These findings question the widespread belief that mathematical skills are generally enhanced in autism. For both groups of children, variation in performance on the numberline task was also uniquely related to their academic achievement, over and above variation in intellectual ability; better number-to-space mapping skills went hand-in-hand with better arithmetic skills. Future research should further determine the extent and underlying causes of some autistic children's difficulties with regards to number. Autism Res 2015. © 2015 International Society for Autism Research, Wiley Periodicals, Inc. © 2015 International Society for Autism Research, Wiley Periodicals, Inc.