“COGNITIVE AND
PHONOLOGICAL SKILLS IN CHILDREN WITH ARITHMETICAL LEARNING DISABILITIES” Peake, C., Jiménez, J. E., Villarroel, R., García, E. & Rodríguez, C. Universidad de La Laguna, Canary Islands, Spain
INTRODUCTION: Different variables have been identified because its influence in arithmetic calculation (AC) and solution of arithmetical word problems (AWP). Working memory seems to be a strong indicator for the achievement in mathematical processing, independently to phonological processing (PP) [1], despite of different theoretical models have shown the influence of PP in arithmetical skills, specifically, in recalling of numerical facts [2], [3], [4]. Other models emphasize the syntactic component to process quantities and for calculation [5]. On the other hand, it is possible that low achievement of AC and solution of AWP could be due to comprehension difficulties, particularly in the case of word problem solution.
OBJECTIVE: This research examined the influence of different phonological and cognitive variables in arithmetic calculation and solution of arithmetic word problems. Three groups were selected in accordance with their achievement in AC and AWP. We studied whether there were significant differences between groups in the performance on non-word reading, working memory, syntactic awareness and listening comprehension. RESULTS
METHOD 2nd
COGNITIVE SKILLS
5th
Participants: A sample of 205 children from to grade of elementary school participated in this study. Next table show age and mean scores for final sample:
-Numerical Working Memory (NWM): F(2, 202) = 3,354. p<0,05. η² = 0,032. Low Achievement group in solving Arithmetical Word Problems had lower performance than control group. -Syntactic Awareness (SA): F(2, 202) = 9,993. p<0,001. η² = 0,09. Both Low Achievement groups scored below control group .
Table 1. Age scores for each group. LAC = Low Achievement in Arithmetic Calculation. LAWP = Low Achievement in Solving Arithmetic Word Problems . AAG = Average Achievement Group.
Materials: - PCA (Arithmetic Calculation Test, Jiménez & Artiles, 2009). - PVA (Arithmetic Word Problems Test, Jiménez & Artiles, 2009). - Spanish Oral Cloze Task (Jiménez, Siegel, Mazabel, & O’Shanahan, 2008). - Numerical Working Memory (García & Jiménez, 1997, adapted from Case, Kurland & Golberg, 1982). - PROLEC-R. Subtests: Non-Words Reading and Oral Comprehension. (Cuetos, Rodríguez, Ruano & Arribas, 2007). Procedures: Arithmetic skills tests were administered, and 3 groups were formed based on their performance in Arithmetic Calculation and Solution of Arithmetic Word Problems. -Children with a percentile score below 25th in PCA and average scores in PVA were selected for group 1 (Low Achievement in Arithmetic Calculation - LAC). - Children with a percentile score below 25th in PVA and average scores in PCA were selected for group 2 (Low Achievement in Solving Arithmetic Word Problems - LAWP). - Children with average scores in both tests (above percentile 50th) were selected for group 3 (Average Achievement Group - AAG).
-Oral Comprehension (OC): F(2, 202) = 56,623. p<0,001. η² = 0,142. Both Low Achievement groups performed below control group . Low achievement group in solving AWP scored below Low Achievement group in Arithmetic Calculations . Figure 1. Group Differences in: NWM = Numerical Working memory; SA = Syntactic Awareness; OC = Oral Comprehension.
PHONOLOGICAL SKILLS
These groups were administered phonological and cognitive tasks (see Materials section above). Statistical Analysis: Analysis of Variance for one factor (LAC vs LAWP vs AAG) for phonological or cognitive skill were performed, and their respective post-hoc comparisons.
each
REFERENCES [1] Swanson, H. L. & Beebe-Frankenberger, M. (2004) The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology, 96, 471-491. [2] Deheane, S. & Cohen, L. (1995) Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83-120. [3] Geary, D. C. (1993) Mathematical disabilities: cognitive, neurpsychological, and genetic components. Psychological Bulletin, 114, 345-362. [4] Geary, D. C. (2004) Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15. [5] McCloskey, M., Caramazza, A. & Basili, A. (1985) Cognitive mechanisms in number processing and calculation: evidence from dyscalculia. Brain and Cognition, 4, 171-196. [6] Siegel, L. S. & Ryan, E. B. (1988) Development of grammatical-sensitivity, phonological, and shortterm memory skills in normally and learning disabled children. Developmental Psychology, 24, 28-37.
ACKNOWLEDGEMENTS This research was supported by a grant from CajaCanarias for Postgraduate Students (2009)
Figure 2 and 3. Group Differences in: N-WR A = Non-Word Reading Accuracy. N-WR T = Non-Word Reading Time.
- Non-Word Reading Accuracy (N-WR A): F(2, 202) = 7,448. p<0,001. η² = 0,069. Both Low Achievement groups scored below control group.
- Non-Word Reading Time (N-WR T): F(2, 202) = 6,751. p<0,001. η² = 0,063. Low Achievement in Arithmetic Calculations group scored below Low Achievement in solving AWP and control group. CONCLUSIONS
Difficulties in arithmetic could be addressed to many causes. In this study two groups with different types of arithmetical difficulties have been compared in cognitive and phonological tasks. Both groups with lower achievement performed below control group in syntactic awareness (SA) and non-word reading accuracy (N-WR A). Syntactic awareness, in contrast to what other studies have demonstrated [6], can be explaining low achievement in arithmetical performance, such as calculation and solving word problems. Failing syntactic process in representing numerical information, can result in problems in arithmetical performance [5]. In this study, both low achievement groups showed poorer syntactic awareness than control participants. Both low achievement groups performed below control group when measuring accuracy in reading non-word task. This phonological process is implicated in mathematical cognition, specifically in representing quantities and in calculation performance [2]. Moreover, low achievement group in arithmetic calculations showed a severe deficit in phonological skills than the other two groups, in spite of low performance of children with problems in solving AWPs. These findings agree with some researches [2], [3], [4] who argued that phonological processing is implicated in recovering numerical facts, and therefore in arithmetical calculation. Low achievement group in solving AWPs showed poorer performance in NWM task. This process seems to be underlying these arithmetical difficulties, as have been showed in several studies ([1] and others). Children who performed poorer in arithmetical calculation did not differ from control group in NWM, this finding does not agree with literature, what makes it a merely topic for further research. Children who solved arithmetical word problems (AWP) worse than the other two groups, showed poorer performance in oral comprehension. In this study, AWPs were administered orally. It is possible that this comprehension deficit can be underlying their difficulties in solving AWPs. 19th Annual World Congress on Learning Disabilities. New Jersey, USA. October 21, 22, & 23. 2010