Arithmetic Operations and Attention in Children with Intellectual Disabilities

Education and Training in Autism and Developmental Disabilities, 2011, 46(2), 214 –219 © Division on Autism and Developmental Disabilities Arithmetic...
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Education and Training in Autism and Developmental Disabilities, 2011, 46(2), 214 –219 © Division on Autism and Developmental Disabilities

Arithmetic Operations and Attention in Children with Intellectual Disabilities Aleksandra Djuric-Zdravkovic, Mirjana Japundza-Milisavljevic, and Dragana Macesic-Petrovic University of Belgrade Abstract: This paper is aimed at depicting the quality of functions of some of the aspects of attention in children with mild intellectual disabilities and their influence on the mastering of arithmetic operations, including addition and subtraction. The sample used in this study encompasses 60 pupils, both males and females. The criteria used in the selection of examinees included the IQ level of the students which ranged from 50 – 69, calendar age from 12 to 14 years, school age which involved the inclusion of pupils attending grades five to seven of primary school in Serbia. To evaluate the quality of attention in our study we used the Trail Making Test form A and the Double Letter Cancellation Test, whilst a Criterion-referenced test was used to evaluate how well the specified body of knowledge, in this case arithmetic operations i.e. addition and subtraction were learned by the pupils. The implications of the study pertain to the proposal of implementing specific, creative activities and exercise during play, concrete contents, demonstration, experiments and teaching resources susceptible for teaching arithmetic. The unsatisfactory results achieved by pupils during the assessment of their knowledge of mathematics at all levels of education, demonstrate a need for continuous examination of parameters that can influence the process of its comprehension (OECD, 2006). Throughout the world, at the beginner level of mathematical education at school age, children most often begin with learning addition and subtraction and continue with this concept to the end of primary school, building on their knowledge (Canobi, 2004). Addition and subtraction represent the building blocks of the majority of future mathematical notions and for this reason it is important for a child to understand their basic concepts (Robinson & Dube, 2009). Addition, as an arithmetic operation, should be understood by a child as the process of accumulation of certain elements, while the arithmetic operation subtraction is presented

Correspondence concerning this article should be addressed to Aleksandra Djuric-Zdravkovic, Department of Oligofrenology, University of Belgrade, Faculty for Special Education and Rehabilitation, 2 Visokog Stevana, Belgrade, SERBIA. Email: [email protected]



to the child as the separation of elements (Gilmore & Spelke, 2008; Nunes, Bryant, Hallett, Bell, & Evans, 2009). Children with mild intellectual disabilities (MID) have difficulties in utilizing arithmetic operations, involving addition and subtraction, even once they comprehend their fundamental concepts. For example, because of difficulties in the generalization process, these children cannot apply the learnt arithmetic knowledge if the question is set up differently from the conditions given in those questions that were practiced (Butler, Miller, Lee, & Pierce, 2001). In children with MID the importance of mastering fundamental mathematical knowledge is emphasized, including the ability to utilize arithmetic operations involving addition and subtraction to resolve a series of problems in everyday situations. Taking into consideration the importance of socialization for children with MID the application of addition and subtraction enables shopping (price comparison, understanding of weights and measurements, value of money) and later on household budget management (planning, saving), etc. (Rosenberg, Westling, & McLeskey, 2008).

Education and Training in Autism and Developmental Disabilities-June 2011

One of the most relevant neuropsychological functions important for successful mastering of program content for mathematics is surely attention (Djuric-Zdravkovic, 2006; Japundza-Milisavljevic, 2009). The study of attributes pertaining to the attention of children with MID is inflicted by its manifestative signs, which are particularly emphasized in the teaching process. In children with MID various attention functions are disturbed. It is characterized by short-livedness, it is unselective and distinctively oscillatory. Attention deficits in children with MID, are amongst other things, considered fundamental cognitive deficits, which hinder the quality of adoption of mathematical knowledge (Macesic-Petrovic, 1998; according to Djuric-Zdravkovic, 2006). In that sense, the aim of this paper is to give an overview of the quality of function of some of the components of attention in children with MID and their influence on the mastering of the content of arithmetic operations, including addition and subtraction. Apprehension of the characteristics of cognitive organization and more accurate determination of the primary deficit of attention with the purpose of improving the adoption of arithmetic knowledge would lead to the individualization of the approach taken in working with this population of children. The results obtained in this study should represent a basis for planning and appropriate directing of the educational process. Planning and organization of individual educational programs in working with these children, regardless of the variety of their forms and modalities, must be founded on the knowledge of the developmental rhythm of certain structures and functions and they must be harmonized with that rhythm. Method Participants The sample used in this study consisted of 60 pupils of both sexes. The criteria used in selecting the examinees included the intelligence quotient of the pupils which ranged from 50 to 69, that was assessed using the WISC scale for the assessment of intellectual capabilities, the calendar age involved exam-

inees from 12 to 14 years of age, and the school age which encompassed pupils attending grades 5 to 7 at primary schools in Serbia. Within the aforementioned age group we evaluated arithmetic operations: addition and subtraction up to one thousand and one million (thirty pupils were assesses from each calendar age group), they showed no evidence of neurological, psychological, sensory, distinct emotional and combined disturbances. In the sample there were a somewhat larger number of male pupils (56.7%) in relation to the female examinees (of which there were 43.3%).

Materials and Procedure In the assessment of the quality of attention in our study we used the following: a) Trail Making Test - form A – the test measures the direction and sustainment of visual attention, visual processing speed, visuospatial and visuomotor competence of the examinees. In the study we assessed the processing speed and the number of mistakes made on the stimuli. This test was initially part of the Army Individual Test Battery (1944), and was afterwards incorporated into the Halstead-Reitan Battery (Reitan & Wolfson, 1985; Tombaugh, 2004). b) Double Letter Cancellation Test (Diller et al., 1974) – for the assessment of attention agility. The test involves discrimination of the letters E and C, which are distributed 105 times into six rows with 52 letters in one row (Wang, Huang, & Huang, 2006). In the study we assessed the processing speed and number of mistakes made. In the assessment of the knowledge of the content of arithmetic operations: addition and subtraction, we used the criterion referenced test, especially constructed for the requirements of this study. Pupils that were 12 years of age (attending grade 5 of primary school) solved questions involving arithmetic operations: addition and subtraction up to the number one thousand, whilst the pupils that are 14 years of age (grade 7 of primary school)

Arithmetic Operations and Attention



solved questions involving addition and subtraction up to the number one million. The results of the criterion referenced test were distributed into three categories: ● ● ●

Mastered the program requirements fully (⫹) Partially mastered the program requirements (⫹⫺) Did not master the program requirements (⫺)

The other data required for the study were gathered by analyzing the student records of the pupils involved in the study. The processing of the obtained data, entered into the database of SPSS, was completed using the descriptive and parameter statistic methods. Of the available statistical proceedings and measures we used: frequency, percentage, arithmetic mean, standard deviation, Student’s t-test, ␹2 test, Pearson’s Coefficient of Linear Correlation (r), contingency coefficient (c). The study was conducted on the territory of Belgrade, Serbia, at primary schools for children with mild intellectual disabilities. Testing was implemented in continuity, without time intervals, individually, with each student privately. At the end of the school year a criterion referenced test was issued, once all of the program content on arithmetic was presented in its entirety.

TABLE 1 Average Results by the Examinees on the Trail Making Test–form A

Time in Seconds AM SD min. max I (25%) II (50%) III (25%)

120.86 131.22 25 sec. 720 sec. 134–720 (n ⫽ 10) 51–133 (n ⫽ 40) 25–49 (n ⫽ 10)

Number of Mistakes 4.04 6.74 0 33 1–33 (n ⫽ 35) 0 (n ⫽ 25)

r ⫽ ⫹0.40 (level 0.01).

ber of mistakes) within the test there is no statistically significant correlation (see Table 2). Examinees were divided up into three categories for a better and easier overview of the results. The first category (I) includes the examinees with the worst results (25%), the second category (II) encompasses the examinees whose results fall into the intermediary values of our sample (50%), and the third category (III) encompasses the pupils who completed the test the quickest and with the least number of mistakes (25%). In analyzing Table 3, we observed that the examinees encompassed in our sample do not achieve the necessary 75% comprehension level of program content at any of the levels of education, which is necessary for the program

Results Table 1, shows there is a low level of positive correlation (r ⫽ ⫹ 0.40, level of 0.01) between the two variables (time of work and number of mistakes). Thus we can conclude with 99% certainty that the examinees that do their test quicker make fewer mistakes. In accordance with the given achievements, examinees are distributed into three categories: first category (I) encompasses examinees that obtained the worst results on the Trail Making Test (25%), second category (II) encompasses examinees whose results are found within the boundaries of intermediary values in our sample (50%), and the third category (III) is made up of examinees with the best results on the TMT - form A - (25%). Between the given variables (time and num-



TABLE 2 Average Results of the Examinees on the Double Letter Cancellation Test Double Letter Cancellation Test

AM SD min. max I (25%) II (50%) III (25%)

Time in Seconds

Number of Mistakes

206.52 122.74 49 sec. 800 sec. 228–800 (n ⫽ 10) 137–227 (n ⫽ 41) 49–134 (n ⫽ 9)

9.64 9.55 0 63 12–63 (n ⫽ 11) 4–11 (n ⫽ 31) 0–3 (n ⫽ 18)

No significant correlation.

Education and Training in Autism and Developmental Disabilities-June 2011

TABLE 3 Success of Examinees on the Test on the Level of Comprehension of Arithmetic Operations: Addition and Subtraction Arithmetic Operations: Addition and Subtraction Grade five (to 1000) Grade seven (to 1 000 000)

⫺ 29.44%


8.33% 62.23%

44.45% 19.44% 36.11%

to be considered appropriate and adapted to the capabilities of children with MID (Bojanin, 2002, according to Djuric-Zdravkovic, 2007). Testing of the correlation between the variables in Table 4 has shown a statistically significant difference of relations on the tests for assessing the quality of the developedness of attention and the comprehension of content of arithmetic operations involving addition and subtraction at the studied levels of education. Discussion Positive results at school by pupils can hardly be expected if we do not devote more attention to effectuating the conditions for adequate stimulation of attention development through its components, which lie at the basis of adopting arithmetic knowledge. The results of this study confirm the previously written fact, whilst the conclusions made in earlier studies in this field express similar views (Djuric-Zdravkovic, 2006; Japundza-Milisavljevic, 2009). Researchers are proving that chil-

dren with MID often have problems sustaining their attention whilst solving mathematical equations, which contributes to the difficulties arising in acquiring, recognizing and generalizing new arithmetic skills and knowledge (Heward, 2008). The results obtained in our study show that the examinees enrolled in grade 5 are most successful at completing tasks which require one-step adding of hundreds and tenths, while they are distinctly unsuccessful in solving textual problems where they are required to apply both arithmetic operations. Pupils in grade seven comprehend tasks which involve long addition over 1000, while they are quite unsuccessful in resolving problems which involve deciding on the use of one or both arithmetic operations. The data from this study that point to problems with mathematical conclusions and the application of concepts for resolving mathematical problems by children with MID to a great extent coincide with the data obtained in other studies (Butler et al., 2001; Heward, 2008). The focus of stimulating the development of attention in children with MID should be implemented through an effective teaching design where emphasis would be placed on strengthening the direction and sustainment of attention by way of specific, creative activities and exercises during play, arithmetic experiments, practical situations from everyday life and through various arithmetic problems (Geary, 2004; Heward, 2008; Rosenberg et al., 2008). Specific creative activities and exercises as outlined above would involve: directing attention, distinguish the important stimuli from the unimportant, indicating the significant details of an arithmetic problem, stimu-

TABLE 4 Correlation of the Quality of the Developedness of Attention with the Comprehension of the Content of Arithmetic Operations Involving Addition and Subtraction Comprehension of the Teaching Material on Addition and Subtraction Double Letter Cancellation Test/processing speed Double Letter Cancellation Test/accuracy Trail Making Test/processing speed Trail Making Test/accuracy

␹2 ␹2 ␹2 ␹2

⫽ ⫽ ⫽ ⫽

14.23 18.22 16.54 12.87

df df df df

⫽ ⫽ ⫽ ⫽

4c 4c 4c 2c

⫽ ⫽ ⫽ ⫽

⫹0.33 ⫹0.36 ⫹0.35 ⫹0.31

(level (level (level (level

Arithmetic Operations and Attention


0.01) 0.01) 0.01) 0.05)


lating to the end of the task, strengthening resistance to distractions, executive control, sustaining of attention, etc. When working with children with MID extra care should be taken that they are stimulated during exercises to resolve concrete problems from everyday life, whenever that is possible. In that way the pupils would gradually understand the role of mathematics. If possible, it would be a good idea to offer as many ways as possible to resolve the given tasks. Long-term studies of children with MID show that comprehension of the content of arithmetic operations including addition and subtraction had achieved the best possible results by way of the program Multisensory mathematics that engages all the senses. TouchPoints within the scope of this program familiarizes the pupils with MID with the fact that each number is a realistic value and that by manipulation including summation and dissociation, addition and subtraction are learned, as a representative quantity (Scott, 1993). Studies show a significant improvement in the quality of multiple capabilities and knowledge, amongst others attention and knowledge of arithmetic operations by children with MID, with the use of information technology and appropriate software which support the adoption of this type of program contents (Wehmeyer, Smith, Palmer, & Davies, 2004). With consideration for the specific needs of children with MID, in learning arithmetic operations there is mention of the possibility of activating numerous cognitive functions through the use of natural and manufactured objects, through various demonstrations, as well as the possibility of implementing “Cool Math” – an alternative method of learning mathematical content through the combination of fun, games, arts, etc (Whiten & Whiten, 2009). Finally, we can conclude that there is a prevailing viewpoint that one treatment approach cannot resolve the problem of a child with an attention deficit when attempting to comprehend mathematical content, thus the combination of various therapeutic methods is a necessity. It is useful to use all of the therapeutic methods in practice that have proven to be effective (Montague, 2008).



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Received: 8 February 2010 Initial Acceptance: 2 April 2010 Final Acceptance: 22 July 2010

Arithmetic Operations and Attention



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