Treating Arithmetical Text Problem Solving in a Child with Intellectual Disability: An Observative Study

Abstract

In this single case study we analyze the treatment focused on arithmetical text problems with a multiplicative structure that was offered to Lu., a 7.8-years-old child who had been diagnosed with mild mental retardation and a genetic anomaly (cariotype 47 XYY) associated with learning disabilities and language delay. Our main aim is to analyze the longitudinal learning profile of our target child in order to identify both the major sources of difficulties interfering with effective learning and the internal cognitive constructions linked to his acquisitions. We deploy qualitative observations tracking the longitudinal changes in the procedures that Lu. applied to the tasks and in adult-child interactive talk. We identified three types of cognitive difficulties interfering with effective learning of solving arithmetical text problems: sensitivity to interference effects in verbal working memory, difficulties with complex coordination of sequential actions, slow automatization. The longitudinal analysis of the adult-child interactive talk showed that the child's talk changed from being almost exclusively focused on giving simple answers, to producing descriptions and anticipation of computations or procedures. It is likely that this use of language provided Lu. with an abstract representational format that triggered an internal reorganization and conceptualisation of the acquired problem-solving procedures. In this study we maintain that treatments for children with cognitive deficits should be devised answering three crucial questions. The first is how, in each specific domain (e.g. language, numerical cognition) children can be helped to represent and memorise basic input data and to organize procedures. Asking such question leads us to assess [1], treat or compensate the processing (e.g. selective attention) and the output mechanisms (e.g. inhibitory control) enabling the individual to encode visual, auditory, tactile information and to build procedures exploiting such information. The second question, rooted to a developmental construc-tivist framework [2], is how children can be helped to build internal representational changes allowing them to expand functional uses of their knowledge. A change from implicit, sometimes holistic, procedurally encapsulated representations to analyzed, explicit representations may enhance generalizations from one micro-domain to another, allow children to access knowledge in a more flexible way, and create strategies to cope with new unfamiliar tasks. For instance, re-describing the perceptual image of a zebra as a "striped animal" [2] allows the cognitive system to understand the analogy between the zebra and the "zebra crossing" sign. Karmiloff-Smith [2] hypothesizes that re-describing in different representational formats the information acquired in a specific domain is an intraindividual, endogenous process. The use of language and other symbolic codes within the rehabilitation context might provide, however, a crucial environmental factor triggering such endogenous process in the child. Describing actions, anticipating their goals, explaining their outcomes, spatially and visually representing linguistic information or arithmetic procedures can provide multiply encoded knowledge. Such multiple encoding can promote the conceptualization of the relationships among internal components of the procedures that the child might have mastered through modelling or other types of teaching practices. The third question is how to address the children's emotional problems that are associated to their cognitive deficits. Such question may be interpreted in a rather decontextual-ized way, considering the child's attachment bonds with his parents, and how these bonds contributed to the child's emotional development. We think that such more general approach to emotions can be useful in some cases of children with cognitive deficits and obviously requires a close collaboration between parents, clinical psychologists or psychotherapists on one hand and cognitive rehabilitators on the other. More specific questions, however, should be addressed by cognitive rehabilitators. Which emotions are related to certain strategies the child has built to compensate his deficit? In a complex system [3] the alterations of one part of it are likely to be reflected in a change in behaviour of the other parts. For instance, a child with cognitive delays might overuse previously acquired routines as a strategy to decrease the fear of failure in difficult tasks. He may also prefer giving chance answers rather than saying "I do not know". The diagnosis of mental retardation may induce re-habilitators to interpret the child's incorrect answers in terms of "weak reasoning abilities". This interpretation, in turn, makes the rehabilitator deploy suggestive questions or direct modelling in order to overcome the child apparent lack of learning progress. Detecting the emotional aspects of the child's wrong answers and the emotional response and attri-butions that these answers elicit in the rehabilitator is likely to result in adult-child interaction patterns that can enhance the child's sense of self-efficacy and agentivity [4].