Research in Developmental Disabilities 32 (2011) 1822–1828

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Research in Developmental Disabilities

The effectiveness of Korean number naming on insight into numbersin Dutch students with mild intellectual disabilities

Johannes E.H. Van Luit a,*, Mariet J. Van der Molen b

a Utrecht University, Heidelberglaan 1, 3584 CS Utrecht, The Netherlandsb University of Amsterdam, Roetersstraat 15, 1018 WB Amsterdam, The Netherlands

A R T I C L E I N F O

Article history:

Received 4 March 2011

Received in revised form 15 March 2011

Accepted 16 March 2011

Available online 16 April 2011

Keywords:

Mild intellectual disabilities

Number naming

Intervention

Number insight

Place value

A B S T R A C T

Children from Asian countries score higher on early years’ arithmetic tests than children

from Europe or the United States of America. An explanation for these differences may be

the way numbers are named. A clear ten-structure like in the Korean language method

leads to a better insight into numbers and arithmetic skills. This assumption forms the

basis of the current study. Examined is whether an intervention with number naming in

the Korean way influences number awareness of students with mild intellectual

disabilities (N = 70; mean age: 9.0 years). The results indicate a positive effect of this

alternative method of number naming on the insight into numbers up to 20. However, the

effect did not generalize to insight into numbers 21–100. The Korean method of number

naming seems to be a promising way to teach students with mild intellectual disabilities

insight into numbers.

� 2011 Elsevier Ltd. All rights reserved.ICATE

1. Introduction

Passing through the arithmetic process and accompanying thinking actions, requires particular knowledge, skills andperseverance (Van Luit & Naglieri, 1999). For many children this is a substantial problem. Kroesbergen and Van Luit (2003)cite several factors that seem to contribute to the problems experienced by many arithmetically weak children. Theymention child factors, such as intellectual functioning, motivation, problem solving skills, memory capacity, strategyacquisition and the application of skills. In addition, didactical aspects seem to matter (Timmermans, 2005). From the firstgrade in primary school the arithmetic curriculum focuses on arithmetic skills such as learning multidigit addition,subtraction, multiplication and division. Insight into the ten-structure (knowing that a number consists of tens and ones) andunderstanding place value (with two digit numbers, the tens comes first and the ones on the second place) is essential indeveloping these skills (Jordan, Mulhern, & Wylie, 2009). According to Miura and Okamoto (1989) the way in which numbersare named, influences children’s developing insight into numbers. Research shows that Asian children more easilyunderstand and integrate the place value of each digit within a number than American or European children. Maybe partlybecause of this Chinese, Japanese and Korean children obtain higher scores on arithmetic tests than their American andEuropean peers (Towse & Saxton, 1998).

Counting, understanding of numbers, as well as insight into numbers, require the use of a number system. The Arabicnumber system is the most commonly accepted system throughout the world. In nearly all cultures Arabic notation is used,however, the way in which the numbers are named differs in each language. Evidence from a variety of research areasindicates the involvement of language in mathematical cognition (Donlan, Cowan, Newton, & Lloyd, 2007). In the Dutch

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* Corresponding author. Tel.: +31 30 2534614; fax: +31 30 2537731.

E-mail addresses: J.E.H.vanLuit@uu.nl (Johannes E.H. Van Luit), M.J.vanderMolen@uva.nl (M.J. Van der Molen).

0891-4222/$ – see front matter � 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ridd.2011.03.014

J.E.H. Van Luit, M.J. Van der Molen / Research in Developmental Disabilities 32 (2011) 1822–1828 1823

language the number 27, for example, is pronounced as ‘zeven en twintig’ (7 and 20). Conversely, languages based on the old-Chinese language, such as the Korean language, pronounce the number 27 as ‘two-ten-seven’. In the latter way of numbernaming the ten-structure clearly emerges; the place value of each digit within a number is evident (Andersson, 2008). Incontrast to, for example, Dutch-speaking and English-speaking children, Asian children do not have to know the differentnames of the numbers between 10 and 20, such as ‘eleven’ or ‘eighteen’, rather they learn numerals by the same regular andlogical system: ‘one-ten-one’ or ‘one-ten-eight’. Because of this children are able to integrate the ten-structure easily andquickly (Miura & Okamoto, 1989). Asian students do show superior early math achievement than Western students, whichseems to be related to the regularity of number words in (East) Asian languages (Suk-Han Ho & Fuson, 1998).

The Dutch language gives no clarity concerning the ten-structure. Furthermore the spoken order of the numbers in theDutch and, for example, also in the German language does not match the written form, unlike the English language (Miura,Kim, Chang, & Okamoto, 1988). The Dutch pronunciation ‘zestien’ (sixteen) for the number ‘16’ implies that the writtennumber begins with the six and continues with the ten. For several children this causes written and/or interpretationerrors, such as ‘61’ or ‘610’. In addition to the lack of a clear structure and notation, Dutch number naming makes anincreased demand on memory. In the Korean language, for example, a child only has to memorize ten basic numbers andlarger numbers can be derived on the basis of simple rules (Miura & Okamoto, 1989; Miura et al., 1994). In contrast, in theDutch number naming not only the first ten numbers have to be remembered, but also the equivalents for the various tens(Miller & Stigler, 1987). Moreover, in naming a number like ‘thirty’ a clear match with respectively ‘three’ and ‘ten’ ismissing.

The assumption that number naming influences insight into numbers and arithmetic skills, has led Karen Fuson andcolleagues (Fuson, Perry, & Kwon, 1994; Fuson, Smith, & Lo Cicero, 1997; Fuson & Wearne, 1997) to carry out interventionsusing an alternative method of number naming with English-speaking arithmetically weak children. In these interventions,students with arithmetic problems are taught, alongside the existing method of number naming, an alternative methodbased on the Korean language. The interventions lead to positive results with regard to insight into the ten-structure and onarithmetic achievement.

The Dutch number naming system contains even more irregularities than the English one. The number naming system inDutch differs from English starting with 21 up to 100. In English ‘21’ is named ‘twenty one’ and in Dutch it is ‘een en twintig’(one and twenty). So, an alternative method of number naming with a clear ten-structure, place value and notation of digitsmay be the solution for arithmetically weak children. Especially for those who experience problems with unclear processing,the irregularity of the (Dutch) number naming system seems to hinder the development of a correct insight into numbersand consequently the development of arithmetic skills (Kroesbergen & Van Luit, 2003).

As far as we know, the influence of an alternative method of number naming on number awareness is never examined inchildren with mild intellectual disabilities (MID; IQ score 50–79), who do show difficulties in mathematics (e.g. Gronna,Jenkins, & Chin-Chance, 1998; Lancioni, Smeets, & Oliva, 1987). The current research aims to examine whether anintervention, in which numbers between 10 and 20 are taught by means of the structure of the Korean number namingsystem, leads to improvement in the insight into numbers of these children. A similar intervention has been examined in astudy involving 52 typical developing children in regular primary education (Van Luit, 2007). This research showed that theintervention of a number naming system with a ten-structure, like the Korean system, had a significant effect on numbernaming and number representation up to 20 of arithmetically weak Dutch children in first grade. However, there was hardlyany transfer as the intervention had only a weak effect on mental knowledge about numbers up to 100, which contradictedresults from earlier research (Luijs, 2004). An explanation for this finding is possibly that the trained children had too littleproblems with the regular Dutch number naming to be able to take any real advantage of the alternative method of numbernaming.

The results above have led to the following two research questions:

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- W

hat is the influence of the alternative method of number naming on the insight into numbers of arithmetically weakchildren with mild intellectual disabilities (MID)? This question concerns insight in numbers up to 20. Whencompared to the usual number naming system, this way of naming is expected to result in an improved insight intonumbers.

U

- T o what extent are children, who have insight into the number naming up to 20, able to apply this knowledge to numbers

up to 100? Considering the univocal structure of the alternative number naming system, we expect these students to beable to apply this structure to larger numbers, in the same way as their Korean peers. However, a contraindication is thatchildren with MID rarely show generalized knowledge (Van Luit & Van der Aalsvoort, 1985).

2. Method

2.1. Participants

A group of 70 students with MID (range IQ-score 50–79 on the WISC-III, Kort et al., 2005) from five schools for specialprimary education in 2 states out of 12 in the Netherlands (i.e., North-Brabant and South-Holland) were randomly recruitedfor this research by means of a cluster sample. Sixty-two of them had the Dutch nationality, one was Moroccan, five wereTurkish and two were Antillean.

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Table 1

IQ-scores, age and didactical age.

IQ-score Age (months) Didactical age

(months)a

M SD M SD M SD

Experimental group (n = 32; 22 boys, 10 girls) 70 11.6 105 5.9 19 5.9

Control group (n = 38; 23 boys, 15 girls) 68 10.0 110 9.2 23 8.6a Didactical age: number of months a child attended special primary school from grade 1 (1 school year = 10 months).

J.E.H. Van Luit, M.J. Van der Molen / Research in Developmental Disabilities 32 (2011) 1822–18281824

The students were randomly assigned to the experimental or control condition. Table 1 contains data of these studentswith regard to gender, IQ-score, age and didactical age (number of months the students attended primary specialeducation). T-tests were used to examine to what extent the experimental and control group differed with respect to thecontrol variables of IQ-score, age and didactical age. The students in the experimental group were on average 4 months youngerthan the students in the control group, t(57) = 2.429, p = .02. IQ-score and didactical age (number of months attending school)did not significantly differ between both groups. A Chi-square test revealed that gender did not significantly differ between bothgroups.

2.2. Instruments

Insight into numbers was measured by means of the number insight test (NIT) that was developed for this study by or ownmath research group (Cronbach’s a = .84; Van Luit, 2007). The NIT is based on three relations important when assessingunderstanding of place value or insight into numbers (see Payne & Huinker, 1993): (1) spoken numbers and writtennumbers, (2) spoken numbers and quantities and, (3) written numbers and quantities. A generally accepted aim inarithmetic education, concerns learning how to make such relations (Fuson, Grandau, & Sugiyama, 2001). The items in theNIT correspond to the recommendations and examples found in earlier research (Fuson et al., 2001; Payne & Huinker, 1993).The test focuses on number cluster 1–10 and on number cluster 21–100 as well as on the three aforementioned relations.Fig. 1 shows some example items.

2.3. Intervention

The teachers had an important role in the execution of the intervention. They were responsible for a clear introduction ofthe concept and the method of number naming to the pupils. The teachers were free, however, to apply the alternativemethod of number naming in accordance with their own teaching practices. To prepare the teachers for the intervention, averbal explanation of number naming was given by the researcher to the teachers and to the internal coaches in the schools.The teachers and coaches were also given a manual containing important information about the intervention and itsapplication. The alternative method of number naming and its application were then discussed, demonstrated and practisedby the teachers and coaches, supported by the researcher. During the intervention period all of the numbers are named in theDutch way, with which the children are familiar. Directly thereafter the numbers were named in the alternative method (seeFig. 2). This method of number naming had to be applied actively during the intervention period by the teacher as well as thestudents.

2.4. Procedure

The NIT was administered within two weeks before the experimental group started receiving the intervention. Theintervention period lasted three months. Within two weeks after the end of the intervention period, all the participatingstudents were administered the NIT for the second time.

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[()TD$FIG]

Example 1: Spoken numbers and written numbers (NIT 21-100)

Write down the largest number: 25 or 32

Example 2: Spoken numbers and quantities (NIT 1-20)

Write down the number closer to 5: the number 4 or the number 9?

Example 3: Written numbers and quantities (NIT 1-20)

Order the numbers from small to large:

15 12 18 ___ ___ ___

Fig. 1. Example items of the number insight test.

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[()TD$FIG]

Number Dutch number

naming

Alternative number

naming

Number Dutch number

naming

Alternative number

naming

10 Ten One ten 20 Twenty Two tens

11 Eleven One ten and one 21 One and twenty Two tens and one

12 Twelve One ten and two 30 Thirty Three tens

13 Thirteen One ten and three 40 Forty Four tens

14 Fourteen One ten and four 50 Fifty Five tens

15 Fifteen One ten and five 60 Sixty Six tens

16 Sixteen One ten and six 70 Seventy Seven tens

17 Seventeen One ten and seven 80 Eighty Eight tens

18 Eighteen One ten and eight 90 Ninety Nine tens

19 Nineteen One ten and nine 94 Four and ninety Nine tens and four

Fig. 2. The alternative method of number naming.

Table 2

Scores on the NIT 1–20 (max. score = 29) and 21–100 (max. score = 11).

m SD t df p

Experimental group NIT 1–20 pre-test 16.7 3.8 3.744 31 .001

Post-test 19.3 4.4

NIT 21–100 pre-test 4.31 3.6 2.215 25 .036

Post-test 4.92 3.8

Control group NIT 1–20 pre-test 15.2 4.0 2.124 37 .040

Post-test 16.4 4.3

NIT 21–100 pre-test 4.07 2.6 1.304 28 .203

Post-test 4.55 2.6

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3. Results

3.1. Quantitative results

T-tests were used to examine whether the scores from the NIT of the two groups differed on the pre- and post-tests (seeTable 2) and Cohen’s d as indicator of the strength of the difference (effect size).1 We expect no significant differences andtherefore small effect sizes between both groups at pre-testing. On the other hand, we do expect significant differences andtherefore moderate to high effect sizes at post-testing.

The results showed that both the experimental and the control group made progress with respect to the NIT 1–20between the pre- and post-tests. The NIT 1–20 at pre-testing did not differ between both groups, t(1,68) = 1.62, p = .11,Cohen’s d = .39, but on post-testing the experimental group obtained a significant higher score, t(1,68) = 2.83, p = .006,Cohen’s d = .68, than the control group. In regard to the three relations on NIT, not on pre-testing, but on post-testing theexperimental group obtained a significant higher score, t(1,68) = 3.24, p = .002, Cohen’s d = .79, than the control group on‘‘Written numbers and quantities’. No other differences were observed.

Furthermore, in regard to the NIT 21–100 score, the experimental group showed a higher score on post-testing than onpre-testing (see Table 2), while this difference was not observed for the control group. Nevertheless, the progress of theexperimental group was not very large.

3.2. Qualitative results

Intervention observations were carried out during three arithmetic lessons for all participating classes. The followingfindings are based on these observations. First the consistency was examined on how the alternative method of number

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1 Cohen’s d interpretation .1–.3, small; .3–.5, moderate; .5–1.0, large.

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naming was applied opposed to the usual method of number naming. In the experimental classes 2 and 5 the teacher as wellas the students proved to be quite consistent in their application, whereas in the classes 1, 3 and 4 this was the case to a lesserextent. Furthermore in classes 2 and 5 the students’ participation in the alternative method of number naming wasconsiderably more frequent than in the other classes. In class 3 mainly the teacher applied the alternative method of numbernaming, whereas the children played a passive role. In classes 1 and 4 this was the case to an even greater extent.

Another marked difference between the five classes concerned the use of supporting material, based on suggestions in thecurriculum, which focused actively on the alternative method of number naming. In class 2 the ten-structure was illustratedby means of egg cartons of ten pieces. Through tokens the entities within the number were indicated. In class 5 teacher andstudents used a hundred bead-necklace, with in turn ten successive beads of a different colour (red or white). By listening toan alternative naming of a number, the students were able to indicate a number on the necklace with the help of steps of 10(10 red beads, ten white beads, three red beads: two tens and three). In classes 1, 3 and 4 the supporting material was hardlyused. Therefore the alternative method of number naming got no specific attention. However, it should be noted that the useof supporting materials as an aid in instruction was not specifically mentioned in the manual. Overall, both classes 2 and 5used the alternative number naming most consistently and intensively, whereas classes 1, 3 and 4 did not.

Evaluation with the teachers showed that the alternative method of number naming did have several effects on thestudents. The children for whom the structure of the number system was at the time of the study completely unclear, seemedto profit the most from the intervention. Children, who had already developed some insight, could however becomeconfused by the alternative method of number naming. An explanation for this was suggested by the teachers. They believedthat the students who had poor arithmetic skills had difficulty with switching from one system to another.

All five teachers of the experimental classes indicated to experience or yet to expect positive effects of the intervention onthe insight in numbers. Three out of the five teachers indicated that they would include the alternative method of numbernaming in their arithmetic lessons in the next school year. By implementing the alternative method of number naming rightfrom the start of the school year and over a longer period, they expected the intervention to have a greater influence.

4. Discussion and conclusion

The purpose of the current study was to examine whether an intervention, in which an alternative method of numbernaming was implemented in daily arithmetic lessons, influenced insight into numbers of a group of students with mildintellectual disabilities. The results indicated that application of this alternative method of number naming did indeedinfluence the insight into numbers of the participating students. After the intervention the experimental group showed agreater progress on insight into numbers than the control group. These results are consistent with similar research by Fusonand Wearne (1997) in typically developing American students. The results of the current study seemed to confirm thehypothesis that the method in which numbers are named influences children’s insight into numbers. The Korean number-naming system is relatively transparent, compared to English and especially compared to Dutch; in that number namestypically are directly indicative of the base-10 structure (Rasmussen, Ho, Nicoladis, Leung, & Bisanz, 2006).

When insight into numbers was further examined by means of the three relations of Payne and Huinker (1993), theintervention appeared to be effective on the relation ‘written numbers and quantities’. A possible explanation for this findingis that this relation is the most frequently taught and learned in early arithmetic and it makes fewer demands on memory,since the numbers are presented visually. Geary (1993) points out that arithmetically weak children often have problemswith working memory. The research of Passolunghi and Siegel (2004) further shows that students with arithmetic problemsrelated to numerical and verbal items (that is related to the two other relations named by Payne & Huinker, 1993), havedifficulty in selecting relevant information.

The univocal structure of the alternative method of number naming leads to an expectation that students will also be ableto apply this structure to numbers above 20 and with that show a deeper insight into the numbers. Nevertheless, research byCheng and Chan (2005) indicates that a good understanding of number naming does not automatically lead to an adequateunderstanding of the base-10 number system and place value. The results of our study are in line with this assumption. Thereappears to be no difference between the scores on the number insight test 21–100 for both groups. This means that nogeneralization of insight into numbers took place amongst these students. It seems that, in spite of a clear structure in theway numbers are named in this system, the difficulty with generalization prevails in arithmetically weak children (see VanLuit & Naglieri, 1999), and also characterises the learning of these students with MID (see Chung & Tam, 2005). However,some additional notes can be made with respect to this disappointing result. First, the number of items with which theinsight into numbers 21–100 was measured was considerably smaller than the number with which the insight in numbers1–20 was measured. Therefore the validity of the results on the generalization test was smaller than desired. A second noteconcerns the lack of concentration showed by many students during administration of the test. Several explanations can besuggested for this finding. First, the administration of the test appeared to be a little too long for the majority of the students.In spite of a short break the students had a great deal of difficulty to keep concentration on the test tasks. In addition theunfamiliarity with the numbers seemed to be an obstacle for most of the students. The number range above 20 had not yetbeen introduced in the students’ lessons not come up yet, as a result the children inhibited. Furthermore it is possible that theclass level administration of the test influenced the outcomes. Van Luit and Naglieri (1999) argue that, in particular, weakachievers are bothered by focusing their attention on realizing difficult tasks, if the setting invites to do other things. It couldalso be possible that the duration of the intervention was too short to bring about generalization. The subsequent discussions

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with the teachers show that a longer intervention period was desirable. This idea is supported by other research, whichshows that arithmetically weak children are slow in learning how to store knowledge (see Landerl & Kolle, 2009).

The current research demonstrated that an intervention, in which the numbers were named in an alternative method, sothat the ten-structure of the number clearly emerged, had a positive influence on students’ insight into the numbers 1–20.Several comments can be made about the intervention and the instruments. To determine with more certainty the influenceof an alternative method of number naming on the insight into numbers but also on arithmetic skills, further, long-termresearch is desirable. The positive remarks voiced by several teachers concerning the application of the alternative method ofnumber naming reinforce the desire for follow-up research.

Follow-up research should however pay greater attention to the specific characteristics of arithmetically weak children inspecial primary education. Researchers need to consider individual test administration on the solution processes of eachchild, shorter or more differentiated administration of tests and the inclusion of a wide range of control variables (Van derMolen, Van Luit, Van der Molen, Klugkist, & Jongmans, 2010). In addition a more structured implementation and applicationof the alternative method of number naming within this intervention, should make a better comparison betweenexperimental and control groups possible. In particular, it is suggested that the development and use of support materialmay be conducive to enhancing the intervention.

Conflicts of interest

There are no university restrictions or authors’ conflicts of interest regarding the publication of this study.

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