This is an intercession survey that aimed at look intoing the effectivity of utilizing computing machine engineering and manipulatives in heightening kindergartners ‘ command of numbering accomplishments. The targeted accomplishments were frontward numbering, figure after, figure before, numbering backward, skip numeration, one-one correspondence rule, cardinality rule, production of sets, and comparing measures. A sum of 48 kids were recruited for the survey from one kindergarten in Al-Ain City, United Arab Emirates. Two integral subdivisions of 24 kids each served as experimental and control groups. The control group was taught in the traditional manner while the experimental group was taught with the usage of computing machine engineering and manipulatives for one semester. Datas were collected through single interviews with kids before and after intercession. Interview inquiries involved points that addressed each of the above mentioned accomplishments. Consequences revealed that kids in both groups have improved in all numeration accomplishments. However, the experimental kids outperformed their opposite numbers in the control group in all these accomplishments. Deductions for mathematics direction in kindergarten are discussed.

Introduction

Increased attending is being given to set uping a foundation in mathematics in kindergarten old ages in many states such as the European states and the United States of America ( Kaufmann, Delazer, Phol, Semenza, & A ; Dowker, 2005 ; Aubrey, 2003 ; Kilpatrick, Swafford, & A ; Findell, 2001 ; Department of Education and Employment [ DfEE ] , 1999 ) . When speech production of mathematics in preschool, numbering comes to the forepart. From a developmental position, numbering is of particular involvement because it is the first formal computational system to be learned by kids. Harmonizing to Gelman and Galistell ( 1978 ) , there are five conceptual rules that govern numbering. Those rules are:

The stable order rule: figure words must be used in a fixed order in numeration.

The one-one-correspondence rule: every figure word is assigned to one object in the counted set.

The cardinality rule: the value of the last figure word in the numeration sequence represents the measure of the counted objects.

The abstraction rule: any type of objects can be counted.

The order-irrelevance rule: the numbering consequence does non depend on the order in which the objects are counted.

The first three rules are viewed as the indispensable rules because they represent the footing for kids ‘s cognition of numeration ( Geary, 2004 ; Gelman & A ; Meck, 1983 ) . Violating any of these rules will needfully ensue in wrong numeration. For illustration, go againsting the stable order rule will ensue in saying figure words randomly which of class is wrong. The same is true when go againsting the one-one-correspondence rule or the cardinality rule.

The other two rules viewed as inessential because go againsting any of them will non impact the truth of numeration ( Briars & A ; Siegler, 1984 ) . These two rules are used by kids along with the indispensable rules in their early development of numbering cognition but kids discard the inessential rules over clip ( Stock, Desoete, & A ; Roeyers, 2009 ) .

Harmonizing to Butterworth ( 2004 ) , kids do non get the hang all indispensable rules at the same clip. The stable order rule is mastered foremost while the cardinality rule is mastered last. In a recent survey, Le Fevre, Smith-Chant, Fast, Skwarchuk, Sargla, Arnup, et Al. ( 2006 ) found that kids ‘s cognition of the stable order rule was really good in kindergarten and equal to grownups ‘ cognition in first class. They besides found similar consequences in respect to the one-one-correspondence rule. Similarly, Birars and Siegler ( 1984 ) found that kids had good apprehension of the one-one-correspondence rule at the age of five and that this understanding improved with age.

The command of the cardinality rule is much debated excessively. Some research workers found that the rule is mastered at the age of three ( Gelman & A ; Meck, 1983 ) . Some others argued that the apprehension of the rule begins at the age of three and a half ( Wynn, 1992 ) . Yet, some other research workers found that kids could non find measures before the age of four and a half and that principled apprehension of cardinality does non look before the age of five ( Freeman, Antonucci & A ; Lewis, 2000 ) .

Baroody and Coslick ( 1998 ) sort numbering accomplishments into two chief classs, unwritten numeration and object numeration. Oral numbering involves mentioning the figure words. Normally kids learn foremost the forward numbering sequence ( one, two, three, aˆ¦ ) and this enables them subsequently from mentioning the figure after and figure earlier. In add-on, experience with numbering frontward helps them with numbering backward. Then kids become able to utilize skip numeration by 2, fives, and 10s.

Object numeration is more than mentioning the Numberss as it involves numbering, cardinality rule, and production of sets. Enumerating a aggregation of objects requires ( a ) cognizing the needful part of the go oning sequence, ( B ) adhering to the stable order rule ( degree Celsius ) adhering to the one-one correspondence rule, and ( vitamin D ) maintaining path of counted objects. Production of sets involves numbering a subset of a set of objects. Resnick and Ford ( 1981 ) see this accomplishment to be harder than numbering because it requires the kid to retrieve how many objects are requested and to halt numeration when making that figure.

The ability to compare measures is a natural consequence of the ability to number objects and numbering experiences in general. Two rules – if discovered – aid kids win in comparing measures: the same figure rule and the telling – Numberss principle ( Baroody & A ; Coslick, 1998 ) . The first rule suggests that if two or more aggregations show the same figure name, so they are equal regardless of how they look or what they contain. The 2nd rule suggests that later Numberss in the numeration sequence are larger than earlier Numberss ( e.g. five is larger than four because it follows four ) . Of class, harmonizing to this rule, if a figure comes “ much later ” than another figure in the numeration sequence so it is much larger than that figure ( e.g. 14 is much larger than 2 because it comes much later than 2 in the numeration sequence ) .

Count AND NUMBER CONCEPT DEVELOPMENT

There were two positions sing the development of figure construct, the logical-prerequisites position and the numeration position ( Baroody & A ; Coslick, 1998 ) . The first position was adopted by Piaget who believed that numbering accomplishments were terribly learned and they had nil to make with assisting kids understand Numberss ( Piaget, 1965 ) . Piaget believed that figure construct depended on logical thought and that kids should trust on matching, non numbering, to set up equality and in-equivalence.

Harmonizing to the 2nd position, nevertheless, numbering is the key to understanding figure constructs and arithmetic ( Baroody & A ; Coslick, 1998 ) . Many research workers agree that kids construct basic figure and arithmetic constructs bit by bit from experiences that mostly involve Numberss ( Baroody & A ; Coslick, 1998 ; Fuson, 1988 ; Gelman & A ; Gallistel, 1978 ; Baroody, 1987 ) . By and large, mathematics pedagogues agree that kids ‘s success in mathematics in early classs depends mostly on their numeration accomplishments. Baroody and Coslick ( 1998 ) suggest that troubles in numbering might earnestly blockade kids ‘s advancement in mathematics. Stock, Desoete, and Roeyers ( 2009 ) found that command of numbering rules in kindergarten predicted arithmetic abilities one twelvemonth subsequently in the first class. Therefore, they asserted that bettering arithmetic abilities is a developmental procedure that starts before formal schooling.

Some research workers confirmed the function of numbering abilities in the automatisation of arithmetic facts ( Aunola, Leskinen, & A ; Nurmi, 2004 ; Van de Rijt & A ; Van Luit, 1999 ) . Beyond the automatisation of arithmetic facts, a plentifulness of surveies confirmed the relation between command of numeration and success in school arithmetic ( Blote, Lieffering, & A ; Quwehand, 2006 ; LeFevere et al. , 2006 ; Stock, Desoete, & A ; Roeyers, 2007 ) . A recent survey ( Stock, Desoete, & A ; Roeyers, 2009 ) that involved 423 kids investigated the relationship between the command of numbering rules and arithmetic abilities. The consequences revealed that more than 50 % of kids did non get the hang the three indispensable numbering rules by the terminal of kindergarten and that get the hanging the numeration rules in kindergarten predicted arithmetic abilities in first class one twelvemonth subsequently.

Johansson ( 2005 ) conducted two surveies to look into the function of number-word sequence accomplishment in arithmetic public presentation. In one survey, he asked kids between 4 and 8 old ages old to number frontward and rearward on the figure sequence and work out arithmetic jobs. The consequences of the survey revealed that public presentation on figure word sequence predicted public presentation on arithmetic jobs every bit good as schemes used in work outing arithmetic jobs.

In another survey, he found that “ work outing doubles ( e.g. 2 + 2 = ? ) served as a nexus between the number-word sequence accomplishment and the figure of arithmetic jobs solved ” ( p. 157 ) . Johansson concluded that “ numbering on the number-word sequence may be an early solution process and that, with increasing numeration accomplishment, the kid may observe regularities in the figure word sequence that can be used to organize new and more accurate schemes for work outing arithmetic jobs. ” ( p. 157 ) .

The accomplishment of numbering frontward from an arbitrary point was found to foretell the usage of numbering on process for add-on jobs ( Secada, Fuson, and Hall, 1983 ) and public presentation on linear composing of figure jobs ( Martins-Mourao & A ; Cowan, 1998 ) . Besides, it was found that the length of numbering forward sequence correlated with apprehension of adolescent measures and work outing simple add-on jobs ( Ho & A ; Fuson, 1998 ) .

THE ROLE OF MANIPULATIVES AND COMPUTERS IN LEARNING MATHEMATICS

Young kids learn best by researching their milieus, largely through playing, during which they construct mental representations of the universe ( Hengeveld, et Al, 2007 ) . Prior to Piaget ‘s formal operational phase, immature kids need concrete, hands-on experiences instead than abstract constructs to larn, develop, and think ( Marshall, 2007 ) . Learning with manipulatives was found to correlate positively with the development of mental mathematics ( Gravemeijer, 1990 ) , and bring forth better accomplishment, and conceptual apprehension than do traditional instruction techniques ( Sowell, 1989 ; Fuson & A ; Briars, 1990 ; Chassapis, 1999 ) .

Computer assisted direction ( CAI ) has been widely used in instruction ( McKethan, Everhart, & A ; Sanders, 2001 ) . Some of the chief advantages of CAI is the presentation of the lesson in assorted ways [ text, sound and artworks ] and interactivity ( Vernadakis, Avgerinos, Tsitskari, & A ; Zachopoulou, 2005 ) . These characteristics help doing computing machine an interesting and effectual acquisition tool. Fletcher-Flinn and Gravatt ( 1995 ) reported positive consequence of the usage of CAI as the CAI group outperformed the traditional direction group in a broad scope of accomplishments in mathematics, scientific discipline, art, reading, and composing.

Elliot and Hall ( 1997 ) reported that kids who used CAI based activities, scored significantly higher on the Trial of Early Mathematical Ability ( TEMA2 ) than their opposite numbers who did non utilize such activities. More recent surveies besides showed that the usage of CAI had positive consequence on kids ‘s acquisition ( Chera & A ; Wood, 2003 ; Segers and Verhoeven, 2002 ) . On the other manus, other surveies revealed no differences in the development of mathematical accomplishments by computing machine usage as opposed to traditional methods ( Din & A ; Calao, 2001 ; Moxley et al. , 1997 ; Reitsma & A ; Wesseling, 1998 ) . This was explained partially by the deficiency of adulthood in kids of this age at being able to develop mathematical thought ( Shute & A ; Miksad, 1997 ) .

A survey by Shute and Miksal ( 1997 ) revealed an of import determination sing the usage of computing machines in preschool and that was the increased attending span of kids while larning with the usage of computing machine. Klein, Nir-Gal, and Darom ( 2000 ) studied the consequence of the adult- kid mediation in a computing machine larning environment. The consequences indicated significantly higher accomplishments for preschool pupils who interacted with grownups who were trained as go-betweens within the computing machine environment.

STATEMENT OF THE PROBLEM

Based on the treatment above, it is clear that numbering accomplishments play a cardinal function in later development of arithmetic. Therefore, it is of high importance to assist kids get the hang these accomplishments before come ining first class. While a plentifulness of research surveies have been conducted on measuring kids ‘s command of numbering accomplishments, really few have intervened with kids to better these accomplishments. The writers of this survey provided kids with a learner-centered plan to assist them construct strong numeration accomplishments through purposeful and meaningful direction with the aid of computing machine and manipulatives. In order to measure the effectivity of our intercession, we used a quasi experimental design with pre and station appraisals. Our chief research inquiry was: are at that place important differences between kids ‘s public presentation on forward numeration, figure after, figure before, numbering backward, skip numeration, numbering, cardinality rule, production of sets, and comparing measures due to intervention?

Context OF THE STUDY

Early on childhood instruction in the United Arab Emirates ( UAE ) consists of two class degrees, kindergarten 1 ( KG1 ) and kindergarten 2 ( KG2 ) with one academic twelvemonth for each degree. Normally, kids enter KG1 at the age of four. The purpose of these two degrees is to fix kids for first class. In respect to mathematics, kids are expected to number till 30 by the terminal of KG2. No accent is placed on accomplishments beyond numbering to 30 such as add-on, and minus. Children are besides expected to acknowledge and pull basic geometric forms such as square, trigon, rectangle, and circle.

The linguistic communication of direction in public kindergartens is Arabic which is the official linguistic communication in the UAE. Language and number-naming systems were shown to play a function in kids ‘s mathematical acquisition ( Alsawaie, 2004 ; Miura, Okamoto, Chungsoon, Steere, Fayol,1993 ; Saxe, 1982 ) . Like English, the Arabic figure calling system places pupils at disadvantage in larning Numberss, which necessitates supplying pupils with excess aid ( Alsawaie, 2004 ) . For illustration, Numberss 11 and 12 in Arabic seem to be arbitrary. One is spoken as wahed and 2 is spoken as ithnan, 11 is spoken as ahada-ashar and 12 is spoken as ithna-ashar. As for Numberss 13 to 19, Arabic replaces asharah ( 10 ) by ashar, similar to replacing 10 with “ adolescent ” in English. So 13, for illustration, is spoken as thalathata ashar. It is besides of import to observe that thalathah ( 3 ) has become thalathata in 13. This is the instance for all Numberss 3 to 9. In English, 3 becomes “ thir- ” in 13 and 5 becomes “ fif- ” in 15. Similarly, the figure of 10s is non made explicit in the decennaries ( Ishroon, 20 ; Thalathoon, 30 ; arba’oon, 40 ; khamsoon, 50 ; … ; tess’oon, 90 ) . Except ishroon ( 20 ) , in which ithnan ( 2 ) is non at that place at all, all other decennaries are made by adding “ oon ” ( tantamount to “ -ty ” in English ) to the individual figure Numberss after doing some accommodation on them ( thalath alternatively of thalathah, 3 ; arba alternatively of arba ‘ah, 4 ; khams alternatively of khamsah, 5, and so on ; see Table 1 ) .

Table 1

Number Names in English and Arabic

Numeral

English

Arabic

1

One

Wahed

2

Two

Ithnan

3

Three

Thalathah

4

Four

Arba’ah

5

Five

Khamsah

6

Six

Settah

7

Seven

Sab’ah

8

Eight

Thamaniyah

9

Nine

Tess’ah

10

Ten

Asharah

11

Eleven

Ahada-ashar

12

Twelve

Ithna-ashar

13

Thirteen

Thalathata-ashar

14

Fourteen

Arba’ata-ashar

19

Nineteen

Tess’ata-ashar

20

Twenty

Ishroon

21

Twenty one

Wahed-wa-ishroon

29

Twenty nine

Tess’ah-wa-ishroon

100

One hundred

Me’ah

## THE INTERVENTION PROGRAM

The intercession plan aimed at heightening kids ‘s accomplishments in the undermentioned countries: ( 1 ) Forward numeration, ( 2 ) Number after and figure before, ( 3 ) Counting backward, ( 4 ) Skip numeration, ( 5 ) Enumeration, ( 6 ) Cardinality rule, ( 7 ) Production of sets, and ( 8 ) Comparing measures. Following are some illustrations of the types of activities used.

Forward numbering

As for Numberss 1-13, utilizing power point, we had a sketch character ( CC ) count and the kids counted after him. Children so were asked to number separately or as a whole category. Some Arabic vocals were besides utilized to further memorising the numeration sequence. In other activities the CC made some errors in numeration and the kids were asked to observe his errors.

For Numberss 14 to 29, two CCs modeled the use of the form and the kids were asked to make the same. For illustration, the first CC says: Arba’ata ( 4 ) and the 2nd says: ashar ( adolescent ) . Then both of them say: Arba’ata ashar ( 14 ) . The same process is done for Numberss 15 to 19. The intent of this activity was to demo kids that numbering from 14 to 19 is non something new. They merely need to state the Numberss 4 to 9 adding the word ashar ( adolescent ) . The same was done for Numberss 21 to 29 where the first CC says the figure in the 1s digit [ wahed ( 1 ) for illustration ] and the 2nd CC says wa-ishroon ( and 20 ) , and so on. Again, mistake sensing activities were utilized.

Except ishroon ( 20 ) which has to be memorized, decennaries in Arabic parallel the 1s and are made by replacing “ ah ” in the 1s by “ oon ” . For illustration, thalathoon ( 30 ) is thalathah ( 3 ) with “ ah ” replaced by “ oon ” . So, we utilized this form in learning decennaries to kids. As with the ashar ( adolescent ) Numberss, the CCs modeled the use of form in larning these decennaries.

Number after and numbered before

Using numbered blocks, kids played figure after and figure before games. Numbered regular hexahedrons were made available to kids. The game starts by holding each participant draw a die. The participant with the larger figure starts the game by choosing a regular hexahedron with a certain figure and inquiring for a figure after or before. The undertaking of the other participant ( s ) is to seek for the figure after or before it as determined by the first participant. To do the game more ambitious, the 2nd participant has to happen the targeted regular hexahedron before the first participant completing numeration to 10 or 5. The game is flexible in footings of the figure of participant.

Counting backward

On PowerPoint, the CC promises the kids of demoing them his friend after a figure of seconds. He asks them to number rearward get downing from that figure. After making figure 1, his friend appears. Besides, kids played the telling blocks game. The game asks kids to order numbered blocks frontward and rearward. The fastest kid wins. The game is besides utile for numbering frontward. Further, a CC counted backward and the kids ( in groups ) detected his errors.

Skip numeration

A figure of objects ( apples, marbles, aˆ¦etc. ) is shown one by one on the computing machine. The kids count with the CC. Then the same objects are shown in 2 and once more the kids count with the CC. Using concrete stuffs, kids experienced skip numeration purposefully and meaningfully through games or job resolution activities.

Enumeration ( numbering objects )

The CC tells kids that he needs 9 apples for illustration and asks them for aid by look intoing if the apples he has are plenty. Because maintaining path of the objects is frequently a job for kids, PowerPoint characteristics were used to get the better of the job by altering the colour of the objects after being counted. Some other times, the counted object was marked by X. Further, kids had ample chances for numbering carnal playthings, regular hexahedrons, flowers, and other concrete stuffs and pictural objects.

Cardinality rule

After numbering a set of objects, the CC asks kids: how many objects do I hold? In other activities, the CC tells kids that his friend claims that he has a certain figure of objects and asks them to verify his claim. The instructor besides implemented similar activities utilizing manipulatives.

Production of sets

Two CCs have a heap of objects and inquire kids to assist them in acquiring a figure of objects for each. The instructor implements this activity in 3 different ways: ( 1 ) Children do that utilizing the mouse, ( 2 ) the instructor has a set of concrete objects and asks the kids to bring forth sets, ( 3 ) the instructor gives kids worksheets with pictural objects and asks the kids to circle a figure of objects.

Comparing measures

Two CCs ask the kids to assist them make up one’s mind who of them has more marbles. Alternatively, each group of kids chooses a colour. Then a screen with sets of marbles of different colourss appears. The group with more marbles wins. So, kids compare the sets of marbles by numbering to make up one’s mind which group wins.

Some activities were used to intentionally assist kids detect the same figure rule and the telling – Numberss principle ( Baroody & A ; Coslick, 1998 ) . First, kids were asked to ( a ) count a figure of organized objects ( concrete or pictorial ) and the same figure of scattered objects and compare the two measures, ( B ) count a figure of flowers for illustration and the same figure of coneies and compare the two measures. Second, to assist kids understand that ulterior Numberss in the numeration sequence are larger than earlier Numberss, many activities were utilised. Here are some illustrations: ( 1 ) utilizing concrete stuffs to compare little measures and so larger measures, ( 2 ) comparison ages, ( 3 ) utilizing figure lines, and ( 4 ) utilizing computing machine.

For illustration, kids compared numbered objects organized in rows. Of class, shorter rows contain fewer objects. On the computing machine, a CC made tonss of different Numberss of regular hexahedrons ( e.g. 2, 3, 9, and 15 ) . After doing each stack, the CC shows some marks of fatigue that addition with the figure of regular hexahedrons used. Children discussed the grounds and engaged in comparings.

## Method

## Sample

Forty eight KG2 kids ( 21 male childs, and 27 misss ; average age before intercession = 62.19 months ; SD = 2.27 ) were recruited from one kindergarten in Al-Ain City, UAE.. All kids belong to the in-between socio-economic category harmonizing to the life criterions of the UAE. The kids were in two subdivisions, one subdivision was indiscriminately assigned to the experimental group ( EG ) and the other to the control group ( CG ) . The EG had 11 male childs and 13 misss while the CG had 10 male childs and 14 misss.

## Data Collection and analysis

Datas were collected through single interviews with kids. Through the interview, kids were tested on 9 accomplishments. Except for numbering frontward, numbering backward and skip numeration, kids were tested on 5 points for each accomplishment. Cronbach ‘s alpha for the trial was found to be ( 0.87 ) bespeaking an acceptable grade of internal consistence. The trial was judged by 8 experts in mathematics instruction and early childhood instruction as a valid instrument. Detailss for each accomplishment follow.

Counting forward:

Children were tested on their truth in numbering frontward till 15 in the pretest, and till 30 in the station trial. One point was deducted for each error the kid made ( maximal mark is 15 in the pretest and 30 in the station trial ) .

Counting backward:

Children were tested on their truth in numbering backward from 15 to 1 in the pretest, and from 30 to 11 in the station trial. One point was deducted for each error the kid made ( maximal mark is 15 in the pretest and 20 in the station trial ) .

Number After:

This portion included 5 points inquiring kids to find the figure after a figure written on a brassy card. The Numberss ranged between 1 and 14 in the pretest and between 12 and 29 in the station trial. Each right response was granted one point.

Number before:

Lapp as in figure after except that kids were asked to find the figure before. The Numberss ranged between 1 and 15 in the pretest and between 12 and 30 in the station trial.

Skip numeration:

Children were asked to number by 2 from 2 to 14 in the pretest and from 2 to 30 in the station trial. Therefore, the maximal mark for the pretest was 7 and for the posttest was 15. One point was deducted for each error the kid made ( maximal mark is 7 in the pretest and 15 in the station trial ) .

One-one-correspondence rule:

This portion included 5 points all inquiring for numbering random forms of drawings ( points, apples, pencils, birds, and diamonds ) . The Numberss of drawings ranged between 9 and 15 in the pretest and between 12 and 30 in the station trial. Each right response was granted one point.

The cardinality rule:

The “ how many ” undertaking ( Wynn, 1990, 1992 ) was used to prove this rule where the kid is presented with a set of objects and asked “ how many are at that place in entire? ” This undertaking included 5 points with the figure of objects presented runing between 9 and 15 in the pretest and between 12 and 30 in the station trial. Each right response was granted one point.

Production of sets:

This portion included 5 points. Children were presented with a set of objects ( ranged between 6 and 15 in the pretest and between 12 and 30 in the posttest ) and asked to do a group of objects. For illustration, showing kids with 15 apples and inquiring them to “ set 8 apples in a box. ” Each right response was granted one point.

Comparing measures:

Children were asked to compare between two sets of objects. This undertaking included 5 points with the figure of objects presented runing between 6 and 15 in the pretest and between 12 and 30 in the station trial. Each right response was granted one point.

Procedures

The control group was taught in the conventional manner followed in the kindergarten. The experimental group nevertheless was taught through a plan that involved computing machine and manipulatives. Both groups followed the same course of study and covered the same content. Teachers of both groups were judged by the principal of the kindergarten and their supervisor as equivalent. Both instructors have unmarried man ‘s grades in early childhood instruction from the same university ; the experimental instructor has 7 old ages of experience and the control instructor has 8 old ages of experience. Both instructors had an overall rating by the educational territory as excellent for the last three old ages.

The experimental instructor was familiarized with the plan through six 1-hour single preparation Sessionss conducted by one of the writers. Each two back-to-back Sessionss were separated with 3 to 5 yearss. After each session, the instructor reviewed what was learned at place and brought inquiries to the trainer in the following session. Further, this instructor was observed by the trainer during the execution of the intercession and given feedback on her public presentation. In the first month of intercession, the instructor was observed twice a hebdomad. After that, she was observed one time a hebdomad for 3 months.

The first stage of interviews was conducted in the first hebdomad of the 2nd semester ( Spring 2009 ) and the 2nd stage in the last hebdomad of the same semester. All interviews were conducted by one of the writers. The interviews took topographic point in a quiet room in the kindergarten. The interviewer started by giving the kid a small gift and speaking to him/her for approximately two proceedingss as an ice ledgeman. Then, she started to inquire kids to execute the undertakings. Undertakings were presented in the same order for all kids. Materials relevant to each undertaking were made available for the kid and so replaced by others depending on the type of the undertaking.

## Consequence

As shown in Table 2, tonss on all accomplishments seem to be tantamount in the pre phase. Both groups did reasonably good on numbering frontward but non on other accomplishments. Performances were low on figure before, cardinality rule, figure after, and production of sets. Independent sample t-test showed no important difference in the pre trial on any of the accomplishments due to group ( P & gt ; .05 ) , which assured that the two groups were tantamount before the start of the intercession plan.

Table 2

Descriptive statistics on the pre and station trials for each accomplishment by group

Experimental group

Control group

Skill

Time ( max. )

Meter

South dakota

Meter

South dakota

Counting forward

Pre ( 15 )

11.79

1.47

11.96

1.60

Post ( 30 )

28.38

1.47

26.17

2.33

Counting Backward

Pre ( 15 )

7.21

2.04

7.17

1.95

Post ( 20 )

18.38

1.61

13.96

2.03

Number After

Pre ( 5 )

2.13

.61

2.21

.93

Post ( 5 )

4.25

.61

3.13

.90

Number before

Pre ( 5 )

2.00

.78

2.00

.98

Post ( 5 )

4.13

.68

3.04

.86

Skip Counting

Pre ( 7 )

3.79

.78

3.75

.99

Post ( 15 )

13.75

1.45

10.50

1.69

One-one- correspondence

Pre ( 5 )

2.63

.65

2.63

.82

Post ( 5 )

4.79

.42

4.29

.81

Cardinality rule

Pre ( 5 )

2.08

.78

2.08

.83

Post ( 5 )

3.63

.77

3.00

.93

Production of Sets

Pre ( 5 )

2.13

.80

2.17

.76

Post ( 5 )

3.50

.72

2.88

.85

Comparing measures

Pre ( 5 )

2.96

.62

3.00

.72

Post ( 5 )

4.38

.50

3.50

.83

While the tonss on numbering frontward in the pre phase were reasonably high ( close to 80 % ) , they do non reflect really strong command of the stable order rule. Tonss on numbering backward were much less than those on numbering frontward. Low public presentation is besides clear on figure after, figure before, and skip numeration. Besides, tonss on one-one correspondence rule were so low reflecting low degree of command of this rule. Tonss on the cardinality rule were the lowest. Tonss were besides low on production of sets.

In the station phase, both groups have improved on all accomplishments with the experimental group clearly bettering more. To prove whether the two groups have significantly improved on these accomplishments after one semester of direction, mated sample t-tests were carried out. Before transporting out the trials, pre tonss on numbering frontward, numbering backward, and skip numeration were converted such that the upper limits mark in both phases are the same. For illustration, the maximal possible mark on numbering forward was 15 in the pre phase and 30 in the station phase. Therefore, the pre tonss were multiplied by 2 before making the t-test. Consequences of the analyses ( see Table 3 ) revealed that both groups have significantly improved on all accomplishments back uping the claim that numbering accomplishments improve with age ( Birars & A ; Siegler, 1984 ) .

Table 3

Consequences of Paired samples t-tests for each accomplishment by group

Group

Skill

Mendelevium

T

df

Sig.

Control

Counting forward

2.25

3.23

23

.004

Counting Backward

4.40

8.49

23

.000

Number After

.92

7.70

23

.000

Number before

1.04

6.80

23

.000

Skip Counting

2.46

6.18

23

.000

One-one- correspondence

1.67

12.82

23

.000

Cardinality rule

.92

6.26

23

.000

Production of Sets

.71

5.56

23

.000

Comparing measures

.50

4.15

23

.000

Experimental

Counting forward

5.63

5.66

23

.000

Counting Backward

8.76

18.75

23

.000

Number After

2.13

23.22

23

.000

Number before

2.13

17.00

23

.000

Skip Counting

5.63

17.36

23

.000

One-one- correspondence

2.17

16.66

23

.000

Cardinality rule

1.54

12.84

23

.000

Production of Sets

1.38

13.62

23

.000

Comparing measures

1.42

13.78

23

.000

To prove whether the intercession had an advantage over the traditional manner of direction, independent samples t-test was done. Consequences showed that there were important differences in agencies on all 9 accomplishments prefering the experimental group ( see Table 4 ) . This indicated that the intercession was successful in better bettering kids ‘s numeration accomplishments.

Table 4

Consequences of independent samples t-tests for each accomplishment

Skill

Mendelevium

T

df

Sig.

Counting forward

2.21

3.92

46

.000

Counting Backward

4.42

8.35

46

.000

Number After

1.13

5.08

46

.000

Number before

1.08

4.85

46

.000

Skip Counting

3.25

7.14

46

.000

One-one- correspondence

.50

2.70

46

.01

Cardinality rule

.63

2.53

46

.015

Production of Sets

.63

2.75

46

.009

Comparing measures

.88

4.42

46

.000

Stock et Al. ( 2009 ) considered the cut-off for command of numbering rules to 3 out of 4. In this survey, we adopted a little more rigorous cut-off, 80 % . As shown in Table 5, really low per centum of kids mastered each accomplishment in the pre phase except for numbering frontward. About two tierces of the control group and a small less per centum of the experimental group mastered numbering frontward before intercession. Three kids ( 12.5 % ) of the control group and one kid ( 4.2 % ) from the experimental group mastered the one-one rule. Merely one kid from each group mastered the cardinality rule.

Table 5

Percentages of kids who mastered each accomplishment by group

Skill

Experimental group

Control group

Pre

Post

Pre

Post

Counting forward

58.3

100

66.7

79.2

Counting Backward

0

91.7

0

16.7

Number After

0

91.7

8.3

29.2

Number before

0

83.3

4.2

29.2

Skip Counting

0

91.7

4.2

33.3

One-one- correspondence

4.2

100

12.5

79.2

Cardinality rule

4.2

54.2

4.2

25.0

Production of Sets

0

45.8

0

20.8

Comparing measures

16.7

100

20.8

45.8

After intercession, the control group improved on all countries particularly on numbering frontward and one-one correspondence rule. Improvements on other accomplishments were non even comparable to those of the experimental group. One hundred per centum of kids in the EG mastered numbering frontward, the one-one correspondence rule, and comparing measures. However, merely a little more than half of them mastered the cardinality rule compared to one 4th of the CG kids.

## Discussion

This survey has contributed to the literature on kindergartners ‘ numeration accomplishments. It ‘s chief intent was to look into the effectivity of utilizing computing machine engineering and manipulatives in heightening kindergartners ‘ numeration accomplishments. The targeted accomplishments were frontward numbering, figure after, figure before, numbering backward, skip numeration, numbering, cardinality rule, production of sets, and comparing measures. Comparisons of public presentations of the EG and CG showed that EG kids outperformed their opposite numbers in the CG in all accomplishments. The two groups started the semester with tantamount accomplishments but after intercession, a well higher per centum of kids in the EG mastered numbering accomplishments than CG kids. These consequences support the determination of many old surveies that revealed advantages of utilizing computing machine ( Vernadakis, Avgerinos, Tsitskari, & A ; Zachopoulou, 2005 ; Chera & A ; Wood, 2003 ; Segers and Verhoeven, 2002 ; Elliot and Hall, 1997 ) and manipulatives ( Marshall, 2007 ; Hengeveld, et Al, 2007 ; Chassapis, 1999 ; Fuson & A ; Briars, 1990 ; Gravemeijer, 1990 ; Sowell, 1989 ) in learning mathematics.

Many characteristics of the plan led to these consequences. Most of the activities done through manipulatives took the signifier of playing which greatly helps kids maestro the intended accomplishments. This is consistent with what Hengeveld, et Al. ( 2007 ) suggested in that playing aid kids construct mental representations of the universe. Of class, playing with concrete stuffs was appropriate for the kids because they are categorized within Piaget ‘s preoperational phase ( Marshal, 2007 ) .

Using computer-based activities had many advantages that contributed to the consequences of the survey. Changing the presentation of the stuff utilizing text, sound and artworks made pupils interested and engaged in the lesson. The presence of the sketch characters besides attracted kids and increased their interaction with the lesson. Children ‘s battle and involvement were apparent in the experimental category as observed by one of the writers. Similar behaviours were observed in old surveies ( Vernadakis, Avgerinos, Tsitskari, & A ; Zachopoulou, 2005 ) . Further, one more of import factor of the effectivity of CAI is the addition of kids ‘s attending span which was confirmed by Shute and Miksal ( 1997 ) . While we did non officially mensurate the attending span of the EG kids, but the perceiver noticed that kids were engaged in the lesson all the clip and paid close attending to what was presented through the computing machine.

Other interesting consequences were besides revealed by the survey. These consequences support the thought that kids do non get the hang all indispensable rules at the same clip. Rather, the stable order rule is mastered foremost while the cardinality rule is mastered last ( Butterworth, 2004 ) . The consequences on the stable order rule and the one-one correspondence rule ( post phase ) are in understanding with those of Le Fever et Al. ( 2006 ) who found that kids ‘s cognition of these two rules was really good in kindergarten. However, the consequences disagree with Birars and Siegler ( 1984 ) who found that kids had good apprehension of the one-one-correspondence rule at the age of five because participants of this survey were more than five at the start of the intercession, yet their public presentation on the one-one-correspondence rule was excessively low but significantly improved after 4 months.

At the clip of the pretest, the average age of the take parting kids was more than 5 old ages ( 62.19 months ) , yet they did non look to get the hang the cardinality rule, merely 4.2 % of the kids did. Even after 4 months, merely 25 % of the CG kids mastered the rule. Some research workers argued that kids master the cardinality rule at the age of 3 old ages ( Gelman & A ; Meck, 1983 ) , or 3 old ages and a half ( Wynn, 1992 ) . However, Antonucci and Lewis ( 2000 ) found that principled apprehension of cardinality does non look before the age of five. Consequences of this survey are consistent with the ulterior determination. Further, the consequences of this survey support the determination that the apprehension of the cardinality rule is the most hard among the numeration rules ( Butterworth, 2004 ; Fuson, 1983 ) . Stock, Desoete, and Roeyers ( 2009 ) did non corroborate this determination. These fluctuations in consequences of different surveies show that it is difficult to find an exact age at which kids master the cardinality rule.

After intercession, kids in the EG performed rather good on comparing measures, numbering backward, figure before, figure after, and skip numeration but their opposite numbers in the CG did non even though they did good on numbering frontward. Baroody and Coslick ( 1998 ) suggested that experience with forward numbering leads to get the hanging the above mentioned accomplishments. Consequences of the CG on these accomplishments seem to connote that specific activities should concentrate on these accomplishments which was the instance with the EG in this survey.

By and large, the consequences of this survey show that with appropriate direction and wise usage of computing machine and manipulatives, kids can execute good on the indispensable numeration rules and other accomplishments before first class. These consequences every bit good as those of old surveies show that big differences exist among kids in get the hanging numeration accomplishments in preschool. Given that these accomplishments are indispensable for future success in mathematics, this issue must be extremely considered to avoid go forthing some kids at hazard.