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The relation between frequently exposed context in the early childhood settings’ mathematical activities and arithmetic skills: A cross-cultural comparison of 6-year-old children in Singapore and Japan

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Abstract

In this study, the authors explored the relation between the types of contexts which young children were frequently exposed to in their early childhood setting’s mathematical activities and their arithmetic skills. Addition test was administered to 35 Japanese young children (Mean age: 6 years 1 months) and 35 Singaporean young children (Mean age: 6 years 3 months) in two contexts: Written Arithmetic (WA) and Oral Arithmetic (OA). The WA problems were presented to the children on an A4-sized cardboard whereas the OA problems were read out to the children. The statistical results showed that Japanese children were more proficient in solving arithmetic by aurally instead of visually, whereas Singaporean children exhibited the opposite tendency. The authors suggested that this difference between both countries’ young children was likely due to the different contexts of mathematical activities which they were frequently exposed to in their early childhood settings.
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The relation between frequently exposed context in the early childhood settings’
mathematical activities and arithmetic skills: A cross-cultural comparison of
6-year-old children in Singapore and Japan
Name : Marcruz Yew Lee Ong
Institution : Hokkaido University, Graduate School of Education
Occupation : PhD Student
Email : marcruzong@edu.hokudai.ac.jp
Tel : +81-080-3951-8255
Address : 060-0811 Japan Hokkaido Sapporo City North Ward North 11 West 7
Graduate School of Education Hokkaido University
Name : Manabu Kawata, PhD
Institution : Hokkaido University, Research and Clinical Center for Child Development
Address : 060-0811 Japan Hokkaido Sapporo City North Ward North 11 West 7
Graduate School of Education Hokkaido University
Name : Mayumi Takahashi
Institution : Fuji Women’s University
Address : 001-0016 Japan Hokkaido Sapporo City North Ward North 16 West 2
Fuji Women’s University
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Abstract
In this study, the authors explored the relation between the types of contexts which young children
were frequently exposed to in their early childhood setting’s mathematical activities and their
arithmetic skills. Addition test was administered to 35 Japanese young children (Mean age: 6 years
1 months) and 35 Singaporean young children (Mean age: 6 years 3 months) in two contexts:
Written Arithmetic (WA) and Oral Arithmetic (OA). The WA problems were presented to the
children on an A4-sized cardboard whereas the OA problems were read out to the children. The
statistical results showed that Japanese children were more proficient in solving arithmetic by
aurally instead of visually, whereas Singaporean children exhibited the opposite tendency. The
authors suggested that this difference between both countries’ young children was likely due to the
different contexts of mathematical activities which they were frequently exposed to in their early
childhood settings.
Keywords: arithmetic, mathematical activities, frequently exposed context, early childhood
settings
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1. Introduction
Even before formal schooling, children participate in a variety of mathematical activities in their
everyday lives. Since the goals and the types of mathematical activities vary across cultures,
children participate in these activities in their own culturally valued way (Saxe, 1991; Guberman,
2004). Related studies have shown that as children frequently exposed to a specific context in their
mathematical activities, they developed familiarity and later expertise in solving arithmetic related
to this familiar context (Saxe and Esmonde, 2005; Taylor, 2013). For example, Taylor (2013),
explored the relationship between participation in tithing (giving 10% of one’s earnings to a church)
and children’s arithmetic skills. The results revealed that children’s frequent problem solving in the
context of tithing could have served as a foundation for understanding operations with rational
numbers. For example, using 1/10 or 10% as a basis for working out other percentages such as 5%
or 20%. As a result, the children tend to solve arithmetic problems presented in the context of
tithing successfully but not those in non-tithing contexts. In other studies, Brazilian candy child
sellers who engaged in retail sales in their everyday lives performed better when solving arithmetic
involving currency values. However, they did poorly in arithmetic presented in writing context,
which was unfamiliar to them (Nunes, Schliemann, and Carraher, 1993, Rogoff, 2003; Saxe, 1991).
It is of particular interest to note that the development of arithmetic skills among these children
might be limited to the context that they are frequently exposed to, but the same form of
development may not be reciprocated in an unfamiliar context.
The above mentioned studies are some of the studies that focused on children’s
out-of-school mathematical activities to examine links between the familiar contexts in these
activities and their arithmetic skills (Nunes et al., 1993; Taylor, 2013). While much is now known
about the influences of out-of-school mathematical activities on children’s arithmetic skills, the
topic of mathematical activities in early childhood settings has rarely been the issue of similar
investigation. However, for two reasons we feel this issue should not be overlooked and it is worth
investigating.
Firstly, the nature of mathematical activities in early childhood setting is very different from
those of out-of-school mathematical activities. In fact, most of the activities in early childhood
settings are designed with goals that are more geared towards developing and nurturing children’s
cognitive development. Besides that, young children usually only interact with their teachers or
peers, guidance and assistance are often provided by the teachers to help them to achieve the
different learning goals through these activities. On the other hand, out-of-school mathematical
activities placed emphasis on task accomplishment in their daily lives instead of learning of
mathematics. For these reasons, the findings and explanations on children’s mathematical
development in studies that centered on out-of-school mathematical activities might not be
applicable to those young children in early childhood settings.
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Secondly, early childhood setting is one of the most important platforms where children
construct and develop their foundational mathematical knowledge. It is common to see young
children learning and using different cultural tools such as mathematical symbols, and concrete
artefacts as they participate in activities with their teachers and peers in early childhood settings. In
the recent work, it has been reported that the experiences from these activities play an extremely
vital role in young children’s mathematical development as they form the foundation of their
mathematical learning in later stage (Claessens, and Engel, 2013; Jacobi-Vessels, Todd Brown,
Molfese and Do, 2016; Jordan, Kaplan, Ramineni, & Locuniak, 2009; Manfra, Dinehart, &
Sembiante, 2014), and these experiences vary across cultures because even in early childhood
settings young children often engage in mathematical activities which are valued by their own
cultures (Tobin, Hsueh, & Karasawa, 2009). Therefore, we suggest that they are likely to go
through different trajectory of mathematical development which result their mathematical cognition
to situate in a specific and familiar context.
2. Mathematical activities in early childhood settings– Singapore and Japan
Now that we have established most children are exposed to mathematical activities in early
childhood settings which will impact their arithmetic skills, we want to investigate this issue further
by conducting a cross-cultural comparison study of Singaporean and Japanese young children.
Interestingly, while Singapore and Japan seem to differ greatly in terms of the context of early
childhood activities for mathematics (Ikeda, & Yamada, 2006), both countries share many
similarities in terms of economic status, social issues, and the quality of education, which help to
minimize confounding effects. In addition, both countries’ children are often been ranked as one of
the few top performers for mathematics in OECD Programme for International Student Assessment
(PISA). Therefore, all these factors provide good grounds for a cross-cultural comparison study.
Singapore, a highly competitive society, places very strong emphasis on educational
qualifications. Formal lessons are commonly conducted in early childhood settings to prepare young
children for their elementary school education (Ikeda, & Yamada, 2006). Given that Singapore’s
educational system places a great emphasis on the assessment of learning and written assessment, it
has influenced the pedagogy of mathematics teaching towards written arithmetical teaching and
learning. Mathematical activities in early childhood settings, therefore also often revolve around
paper-and-pencil tasks, written numerals on textbooks, and workbooks (Ikeda, & Yamada, 2006),
suggesting that Singaporean young children might be more immersed in the written arithmetic
context in these settings.
On the contrary, in Japan, mathematical activities in early childhood settings can be very
diverse. For instance, mathematical concepts were embedded in activities such as taking attendance,
cleaning up and playing games, and thus considered as mathematical activities (Sakakibara, 2006,
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2014). Although there was a great diversity of mathematical activities, most of them appeared to
take place in an oral arithmetic context. For instance, a teacher would ask the children for the
number of boys and girls that were absent, and they verbally added up the total number of absentees.
In another activity, before a drawing session, the teacher asked the children to verbally add up all
the pink papers that she had counted and those remaining on the table (Sakakibara, 2006, 2014).
These are some of the many mathematical activities in Japanese early childhood settings that
require young children to rely greatly on their speech and hearing, suggesting that they were more
likely to expose to the oral arithmetic in these settings.
In view of these considerations, this study seeks to explore whether the contexts of
mathematical activities which both countries’ young children are frequently exposed to in their early
childhood settings influence their arithmetic skills differently.
3. Methodology
3.1 Participants
There were two groups of participants - first group comprised 35 Japanese young children (19 boys,
16 girls, Mean age: 6 years 1 month) and second group comprised 35 Singaporean young children
(17 boys, 18 girls, Mean age: 6 years 3 months). These participants were selected through
convenience sampling from four typical early childhood settings in Singapore and Japan.
Both informed consent from parents and assent from children before the study. In order to
remove any potential stress in children, procedures and items in this study were slightly modified.
Furthermore, all children were given the opportunity to withdraw from the study at any time, and all
their information were treated confidentially.
3.2 Materials
A total of 24 arithmetic items - addition questions in two types of contexts (WA: Written
Arithmetic; OA: Oral Arithmetic) with sums less than 100 were selected. Half of the items were
presented in the WA format, and the remaining half in the OA format. Each WA item was printed
on an A4-sized card, and displayed to the children. Whereas, OA items were read out to the
children.
With reference to LeFevre, DeStefano, Coleman, & Shanahan (2005), each context was
categorized into four levels (A to D) of three items each. Slight modifications were made to the
complexity and structure of the items to suit the learning age of the children. The items were
administered in English and Japanese languages, which are the first languages for the children in
Singapore and Japan, respectively. Much attention was placed on the question techniques to ensure
that the tests were parallel when presented in English and Japanese languages. In order to eliminate
experimenter bias, the same researcher was deployed to conduct the experiment in both settings.
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Details of WA and OA items are shown in Table 1.
The two types of items were counterbalanced across children. The design of this study was a
2 (Countries: Singapore and Japan) × 2 (Contexts: WA and OA) × 4 (Levels: A, B, C, and D)
mixed factor design.
3.3 Independent variables
Three independent variables- participants’ test scores, problem solving time, and strategies used
were assessed in this study.
Firstly, total test scores of WA and OA problems for each child were measured. One point
was awarded for each correctly solved item, with a maximum of 12 points for each context.
Secondly, the solving time of each correctly solved item was measured in seconds by the
researcher. He started the stopwatch when he presented an item and stopped it when the child
answered. According to Bull and Johnston (1997), one is likely to take a shorter time to solve
arithmetic that were presented in familiar context than those of other contexts.
Thirdly, with reference to Bisanz, Sherman, , & Ho (2005), we categorized the solving
strategies into two main types - the overt and covert strategies. If the children used concrete
referents such as their fingers or circular cards, as support while solving the items, they were coded
as overt strategies. In contrast, solving the items without any use of concrete referents was classified
as covert strategies. And children are more likely to use covert strategies on easy or familiar
problems than on difficult problems (Bisanz et al 2005).
In sum, Singaporean children are expected to employ more covert strategies and utilize a
shorter time to solve more WA than OA items. Conversely, Japanese children are expected to
employ more convert strategies and utilize a shorter time to solve more OA than WA items. In
addition, Japanese children tend to be more proficient in solving OA items than Singaporean
children whereas Singaporean children are expected to perform better in WA items than Japanese
children.
3.4 Procedure
The children were tested individually by a researcher. A pretest was administered to all the children
to verify their understanding of Arabic numerals and the addition ‘+’ sign. Those who did not meet
the requirement were excluded from the main task.
During the main task, a paper, pencil, and 100 circular cards (3cm in diameter) were
available on the table. A blank A4 double sided printed response sheet was distributed to each child
for them to fill in their answers.
WA and OA items were presented one at a time to the children starting from Level A. The
task stopped once the children failed to solve or wrongly answered two items in a row. The children
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were encouraged to solve the items using whichever strategy was easiest for them.
4. Findings
4.1 Test Scores
Singaporean children scored an average of 8.8 out of a total of 12 for WA items, and an average of
6.6 out of a total of 12 for OA items. Conversely, Japanese children performed better in OA items
than WA items, with an average score of 8.0 and 4.7 respectively (Figure 1). Two way factorial
analysis of variance (ANOVA)’s results showed that there was a significant Country Groups’ test
scores × Context interaction, F (1, 68) = 98.39, p< .05. In addition, simple main effect tests were
also performed to determine whether the test score of Singaporean children and Japanese children
differed in each of the two contexts. In these two contexts there was a significant effect of country
group’s test scores: OA items, F (1,68)=4.45, p< .05and WA items, F (1,68)=57.73, p< .01.
4.2 Problem Solving Time
Singaporean children took an average of 7.89 seconds and 5.26 seconds to solve OA and WA items
respectively. In contrast, Japanese children solving time for OA and WA items were 5.18 seconds,
and 6.72 seconds respectively (Figure 2). Two-way factorial analysis of variance (ANOVA) was
conducted, and there was a significant Country Groups solving time × Context interaction, F (1,
68) = 8.32, p< .05. In order to determine whether both countries’ children’s solving time differed
across the two contexts, simple main effect tests were also conducted. There was a significant effect
of country group’s solving time found for the OA problems: F (1, 68) =5.22, p< .05, but not for the
WA items.
4.3 Strategy use
A chi-square test was performed to determine the strategy used by the children during problem
solving across the two contexts. The test did not show any significant relationship between the
children’ strategy use and the contexts, except for OA’s Level C (χ2(1) = 5.307, p<.05). In other
words, only at OA’s level C, were Japanese children more likely to use covert strategies than overt
strategies (Table 2). Whereas, Singaporean children showed an opposite tendency. We excluded
Level D in our analysis as very few children managed to solve Level D items.
5. Discussion
This study is the first of its kind to examine and reveal the contexts which Singaporean and
Japanese young children were frequently exposed to in their early childhood settings’ mathematical
activities were likely to cause their arithmetic skills to differ not only from each other but also vary
across the WA and OA contexts.
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For instance, Singaporean children were more likely to be exposed to written arithmetic
context in early childhood settings as their mathematical activities often revolved around written
numerals on textbooks, and workbooks (Ikeda, & Yamada, 2006). The claim that children developed
expertise in solving arithmetic in the context of their frequently participated mathematics activities
(Ong, 2016; Rogoff, 2003; Taylor, 2013) was evident in this study as Singaporean children
performed better in WA items, than OA items and the WA items by their counterparts (Figure 1).
Conversely, most of the mathematical activities in the Japanese early childhood settings tend to
require young children to rely greatly on their speech and hearing (Sakakibara, Hatano, & Inagaki,
2001). Therefore, Japanese children performed better in OA items, than WA items and the OA items
by Singaporean children.
Similar to the above reason of the frequent exposure to written arithmetic context,
Singaporean children, on average, took a shorter time to solve WA items, than OA items and the WA
items by Japanese children. On contrary, Japanese children took a shorter time to solve OA items,
than WA items and the OA items by their counterparts (Figure 2). Since solving arithmetic items
requires one to correctly identify, and transfer the information from the stimulus to the working
memory for processing (DeStefano, & LeFevre, 2004), this finding suggests that Singaporean
children correctly identified and processed visually presented problem information faster than
aurally presented information, whereas, Japanese children tend to exhibit the opposite tendency.
Next, prior to the experiment, we expected Singaporean children to use more overt strategies
to solve OA items and more covert strategies for WA items, while Japanese children will exhibit the
opposite tendency. Unexpectedly, young children in both countries used more covert strategies than
overt strategies to solve both OA and WA items at Level A and B. This could be due to the fact that
both levels of problems are easy to solve for a six-year-old child, and easy problems are usually
solved by covert strategies (Bisanz et al 2005).
The only distinct difference between these groups of young children was at Level C’s OA
items where the problems became more challenging hence children used a different approach to
resolve this. Japanese children who were more proficient with OA items used more covert strategies
than overt strategies, whereas, Singaporean children took the reverse strategy by using more overt
strategies instead.
As for Level C’s WA problems, Singaporean children who were more proficient with WA
items used covert strategies more than overt strategies. Unexpectedly, although Japanese children
were less proficient with WA items, they used more covert strategies instead of overt strategies.
During the study, many reported that they might get teased by their peers for using fingers or
circular cards to count (overt strategies), therefore they tried to avoid using overt strategies even
though concrete referents are helpful as a form of support to solve difficult WA items. This therefore
led them to make more mistakes when solving those items. This unexpected finding could also
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suggest that besides arithmetical abilities, social factors such as peer pressure might also influence
the types of strategies a child chooses to solve the arithmetic problems.
6. Implication
In this study, we administered the addition tests to the young children visually and aurally in order
to determine how their arithmetic skills fare in each context. Taking into consideration all the data
from both countries’ preschoolers, there was concrete evidence that Singaporean children were
more proficient in solving arithmetic visually instead of aurally, whereas Japanese children
displayed the opposite tendency. These findings are beneficial for Singaporean and Japanese early
childhood educators and also elementary school teachers because we had identified which context
the children were less proficient or more proficient when dealing with arithmetic. Since WA and OA
are two of the most basic and important contexts in which children learn mathematics in schools,
being less proficient in any one of the contexts is likely to hinder children’s learning of mathematics.
Therefore, in order to ensure both countries’ preschoolers become equally proficient in both
contexts as they proceed to elementary school, early childhood educators can integrate more
elements related to the less proficient context into their mathematical activities with the children. In
addition, elementary school teachers can make the mathematical content easier to understand when
teaching in the less proficient context.
Next, although this study centered on Singaporean and Japanese children, the findings can
also be beneficial for other early childhood educators in countries where their early childhood
education systems share similar frameworks with those of Singapore and Japan.
Furthermore, through this study, it is advantageous for other countries’ early childhood
educators to understand that the context and also the types of mathematical activities which their
young children were frequently exposed to in their early childhood settings, may also influence the
children’s arithmetical competencies. This may help to raise an even higher awareness level among
early childhood professionals on the importance of their roles in designing of mathematical
activities and supporting young children in these activities.
7. Limitation and Future research directions
Firstly, as with other studies, this study also had some limitations. For instance, data was collected
from a relatively small number of young children in Singapore and Japan, and therefore, it was not
possible to generalize the results. A much larger sample size of young children would be required.
In addition, it might be more insightful and interesting if other countries’ young children are also
included as participants for investigation in future studies.
Secondly, this study suggested that the contexts of mathematical activities which
Singaporean and Japanese young children were frequently exposed to in their early childhood
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settings influence their arithmetic skills differently. However, in order to further strengthen the
above findings, future study that investigates the degree of exposure to the written and oral
arithmetic contexts by both countries’ children in their early childhood setting’s mathematical
activities is required. For instance, future study might want to expand their area of investigation
beyond arithmetic to other aspects of mathematics, such as counting, measurement, geometry, and
pattern since young children do not only deal with arithmetic in their mathematical activities.
Another area which is worth investigating to strengthen the above outcome is the issue on
the link between young children’s mathematical development and their social interaction with
teachers and peers in early childhood settings. Although Vygotskian theory holds that children’s
development is shaped by social interactions with others and how children co-construct their
knowledge through symbols, and artefacts with the guidance from the adults (Carruthers &
Worthington, 2006; Ong, 2016; Rogoff, 2003), little is known about the process of how young
children’s social interactions in early childhood settings influence their mathematical development.
As we look deeper into this progressive issue, it leads us to ponder upon a number of key questions,
such as how do these young children learn and share meanings of mathematical symbols and
artefacts during their engagement in joint mathematical activities with teachers or peers, and how
does this process shape the way young children construct their mathematical knowledge in their
own culturally valued way. In order to advance our understanding of young children’s mathematical
development, especially in the context of early childhood settings, it is therefore crucial to answer
these key questions in future studies.
Finally, we believe work addressing early childhood settings still plays a very important role
in contributing evolving, exceptional and progressive insights into the discussion of young
children’s mathematical development. This topic continues to leave lots of room for researchers,
teachers, and other education stakeholders to debate further.
8. Acknowledgements
I would like to extend my deepest gratitude to Dr. Kawata Manabu, who has been my advisor and
mentor since my Masters degree course. Without his guidance and persistent help this work would
not have been possible.
I would also like to thank Dr Ito Takashi, Dr Kato Hiromichi, and Mrs Takahashi Mayumi
for their continuous support and guidance.
In addition, I also express my sincere appreciation to Sister Jessie Blakely, who assisted in
the proof-reading of this work, and provided me with many valuable advices about writing and
early childhood education.
Last but not least, a big thank to my beloved family who is always there for me.
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Table 1.
Descriptions of the WA and OA problems
Table 2.
Frequency and Percentage of Covert and Overt strategies
Level Written Arithmetic (WA) Oral Arithmetic (OA) Details
A 3+4, 7+1, 2+6 2+3, 5+1 3+6 Single digit operands, sum less than 10
B 5+10, 9+10, 10+12 2+10, 10+8, 14+10 At least one operand which is 10
C 16+12, 13+11, 21+17 12+13, 17+11, 23+14 Absence of carrying operations
D 17+16, 23+19, 36+28 15+17, 25+16, 33+29 Presence of carrying operations
OA WA
Japan Singapore Japan Singapore
Level A
Covert Strategy 78 69 70 88
(%) (75.73) (72.63) (77.78) (86.27)
Overt Strategy 25 26 20 14
(%) (24.27) (27.37) (22.22) (13.73)
Total 103 95 90 102
(%) (100.00) (100.00) (100.00) (100.00)
Level B
Covert Strategy 70 57 46 79
(%) (73.68) (67.06) (76.67) (79.80)
Overt Strategy 25 28 14 20
(%) (26.32) (32.94) (23.33) (20.20)
Total 95 85 60 99
(%) (100.00) (100.00) (100.00) (100.00)
Level C
Covert Strategy 44 19 9 50
(%) (70.97) (46.34) (64.29) (66.67)
Overt Strategy 18 22 5 25
(%) (29.03) (53.66) (35.71) (33.37)
Total 62 41 14 75
(%) (100.00) (100.00) (100.00) (100.00)
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Figure 1.
Test scores over the two contexts
Figure 2.
Solving time over the two contexts
0.00
4.00
8.00
12.00
OA WA
Test Scores
Contexts
Japan
Singapore
0.00
4.00
8.00
12.00
16.00
OA WA
Solving time (Seconds)
Contexts
Japan
Singapore
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... Mullis et al. 2012;OECD 2016). In our recent cross-national study (Ong, Kawata, and Takahashi 2016), we found out that on average, both the Japanese and Singaporean kindergarteners solved up to two-digit addition (e.g. 16 + 12, 23 + 14) in oral and written forms. ...
... Differences: written numeral vs. oral numeral context Our previous study (Ong, Kawata, and Takahashi 2016) reported that on average, 6-yearold Japanese and Singaporean kindergarteners were able to solve up to two-digit addition, but they tended to fare better in one of the modalities than the other, and their performances were contrary to each other. Specifically, Japanese kindergarteners performed well in those addition problems presented in oral numeral than those in written form, whereas their Singapore counterparts displayed a contrary pattern. ...
... Each WA problem was printed on an A4-sized card and displayed to the participants, whereas OA problems were read out to them. These problems were the same as those used in our previous study (Ong, Kawata, and Takahashi 2016). Papers, pencils, and 100 circular cards (3 cm in diameter) were provided as an aid in computation. ...
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It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral Arithmetic) with sums less than 100 were administered to 22 Japanese and 22 Singaporean 6-year-old kindergarteners. Our findings reveal that they were able to solve complex addition. For instance, Japanese kindergarteners tended to solve complex arithmetic using base-10 decomposition across the modality, whereas Singaporean kindergarteners used standard algorithms and basic counting to solve complex WA and OA problems, respectively. We speculate that Japanese kindergarteners might have a clearer understanding of the base-10 concept and were able to use this knowledge more readily than Singaporean kindergarteners. Mathematical experiences in kindergarten and number-naming systems have been put forward as two of the crucial contributors for such cross-cultural differences. This study also provides new directions for future research on the understanding of the base-10 concept and its application among young children. ARTICLE HISTORY
... Mullis et al. 2012;OECD 2016). In our recent cross-national study (Ong, Kawata, and Takahashi 2016), we found out that on average, both the Japanese and Singaporean kindergarteners solved up to two-digit addition (e.g. 16 + 12, 23 + 14) in oral and written forms. ...
... Differences: written numeral vs. oral numeral context Our previous study (Ong, Kawata, and Takahashi 2016) reported that on average, 6-yearold Japanese and Singaporean kindergarteners were able to solve up to two-digit addition, but they tended to fare better in one of the modalities than the other, and their performances were contrary to each other. Specifically, Japanese kindergarteners performed well in those addition problems presented in oral numeral than those in written form, whereas their Singapore counterparts displayed a contrary pattern. ...
... Each WA problem was printed on an A4-sized card and displayed to the participants, whereas OA problems were read out to them. These problems were the same as those used in our previous study (Ong, Kawata, and Takahashi 2016). Papers, pencils, and 100 circular cards (3 cm in diameter) were provided as an aid in computation. ...
... Mullis et al. 2012;OECD 2016). In our recent cross-national study (Ong, Kawata, and Takahashi 2016), we found out that on average, both the Japanese and Singaporean kindergarteners solved up to two-digit addition (e.g. 16 + 12, 23 + 14) in oral and written forms. ...
... Differences: written numeral vs. oral numeral context Our previous study (Ong, Kawata, and Takahashi 2016) reported that on average, 6-yearold Japanese and Singaporean kindergarteners were able to solve up to two-digit addition, but they tended to fare better in one of the modalities than the other, and their performances were contrary to each other. Specifically, Japanese kindergarteners performed well in those addition problems presented in oral numeral than those in written form, whereas their Singapore counterparts displayed a contrary pattern. ...
... Each WA problem was printed on an A4-sized card and displayed to the participants, whereas OA problems were read out to them. These problems were the same as those used in our previous study (Ong, Kawata, and Takahashi 2016). Papers, pencils, and 100 circular cards (3 cm in diameter) were provided as an aid in computation. ...
... Mullis et al. 2012;OECD 2016). In our recent cross-national study (Ong, Kawata, and Takahashi 2016), we found out that on average, both the Japanese and Singaporean kindergarteners solved up to two-digit addition (e.g. 16 + 12, 23 + 14) in oral and written forms. ...
... Differences: written numeral vs. oral numeral context Our previous study (Ong, Kawata, and Takahashi 2016) reported that on average, 6-yearold Japanese and Singaporean kindergarteners were able to solve up to two-digit addition, but they tended to fare better in one of the modalities than the other, and their performances were contrary to each other. Specifically, Japanese kindergarteners performed well in those addition problems presented in oral numeral than those in written form, whereas their Singapore counterparts displayed a contrary pattern. ...
... Each WA problem was printed on an A4-sized card and displayed to the participants, whereas OA problems were read out to them. These problems were the same as those used in our previous study (Ong, Kawata, and Takahashi 2016). Papers, pencils, and 100 circular cards (3 cm in diameter) were provided as an aid in computation. ...
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It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral Arithmetic) with sums less than 100 were administered to 22 Japanese and 22 Singaporean 6-year-old kindergarteners. Our findings reveal that they were able to solve complex addition. For instance, Japanese kindergarteners tended to solve complex arithmetic using base-10 decomposition across the modality, whereas Singaporean kindergarteners used standard algorithms and basic counting to solve complex WA and OA problems, respectively. We speculate that Japanese kindergarteners might have a clearer understanding of the base-10 concept and were able to use this knowledge more readily than Singaporean kindergarteners. Mathematical experiences in kindergarten and number-naming systems have been put forward as two of the crucial contributors for such cross-cultural differences. This study also provides new directions for future research on the understanding of the base-10 concept and its application among young children. ARTICLE HISTORY
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