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This study examines relationships between mathematical problem-solving performance (in terms of strategies used and accuracy) and the main cognitive domains associated with mathematical learning (i.e. executive functions, verbal comprehension and social perception) of children with and without autism spectrum disorder (ASD and non-ASD resp.). The study involved 26 ASD and 26 non-ASD children without intellectual disabilities, between 6 and 12 years old, matched by sex, age and school (grade and classroom). The results show a higher percentage of ASD children with problem solving difficulties than non-ASD (57% vs. 23% resp.). Poor performing ASD children showed comparatively lower scores in inhibition, theory of mind and verbal comprehension. Implications for the design of mathematical interventions for ASD students are discussed.
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Background & aims: In recent years, there has been an increased interest in analyzing the mathematical performance of students with learning difficulties in order to provide them with teaching methods adapted to their needs. In particular, the importance of studying the type of informal strategy that students use when solving problems has been highlighted. Observing how these strategies emerge and develop in children with learning difficulties is crucial, as it allows us to understand how they develop a subsequent understanding of arithmetic operations. In this paper we study the effect of explicit instruction in addition strategies, focusing on the minimum addend strategy, and analyze the difficulties that arise during this process. Methods: An adapted multiple-probe design across students with a microgenetic approach was employed to assess the effectiveness of the teaching instruction and the acquisition of the minimum addend strategy while solving addition word problems. The participants were three primary-school children (two boys and one girl) with learning difficulties, one of them diagnosed with autism spectrum disorder. The instruction on the minimum addend strategy was sequenced into levels of abstraction based on the addends represented with and without manipulatives. Results: The results show that the three participants were able to acquire the minimum addend strategy and transfer it to two-step problems. They all showed difficulties during the instructional process, with quantity comparison difficulties predominating. The instruction provided to address these and other difficulties is detailed for each participant. Conclusions: The teaching of the minimum addend strategy has proven effective, and all three students acquired it throughout the instruction. The results concerning the student diagnosed with autism spectrum disorder are especially interesting given the lack of studies that focus on the strategies employed by students with this disorder to solve arithmetic problems. In this sense, the use of the microgenetic approach was especially useful to observe the type of spontaneous strategies used by this participant, and how they varied in response to the instruction. Implications: Each study participant faced different difficulties and needed different periods of time to assimilate the new strategy. Conclusions are drawn for educators to help children with learning difficulties advance to more sophisticated strategies, so they can acquire these and subsequent mathematical concepts.
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RESUMEN: En los últimos años ha aumentado notablemente el interés por analizar el rendimiento académico de los estudiantes con trastorno del espectro autista (TEA). Entre las materias escolares, las matemáticas son uno de los grandes obstáculos que encuentran estos estudiantes. Por consiguiente, es fundamental mejorar nuestro conocimiento sobre el modo en que los estudiantes con TEA aprenden diferentes conceptos matemáticos para luego proporcionarles métodos de enseñanza adaptados a sus necesidades. Este documento explora las estrategias y los errores que un estudiante de 11 años diagnosticado con TEA muestra al resolver problemas aritméticos verbales de división. Se diseñó una secuencia de enseñanza compuesta por problemas en dos formatos diferentes: con y sin material manipulativo. Se recogieron datos durante 15 sesiones de una hora en las cuales el estudiante resolvió un total de 49 problemas. Los resultados muestran una clara preferencia por la estrategia de reparto por múltiplos para los problemas en los que dispone de material manipulativo, mientras que recurre principalmente a la estrategia de reparto uno a uno cuando no dispone de material. Se identifica un conjunto de errores relacionados con los significados de las nociones de partición, equidad y representatividad, necesarios para resolver con éxito problemas aritméticos verbales de división partitiva.
ABSTRACT: In recent years there has been an increasing interest in studying the academic performance of students with Autism Spectrum Disorder (ASD). Among school subjects, mathematics is one of the great obstacles that face students with ASD. It is therefore crucial to go in depth into the understanding that they develop on mathematical concepts, to later provide learning instructions adapted to their needs. This paper explores the strategies and errors that an 11-year old student diagnosed with ASD shows when solving partitive division word problems. A teaching sequence has been designed that includes problems in two different formats: with and without support material. The data was collected during 15 one-hour sessions in which the student solved a total of 49 problems. Results show a clear preference for the one-to-many correspondence strategy in the problems with support material whereas the student mainly resorted to the sharing one-by-one strategy when he did not have the material. A list of errors has been identified related to the meaning of the notions of partition, equity and representativeness, required in partitive division word problems.