ERG SES G 09, Mathematics and Education
Is the bar model approach sufficient, or does it form a necessary factor within a combination of other conditions, for autistic pupils to solve one-step, real-life mathematical word problems?
As the primary school curriculum evolves, and the government draw on international best practice, the bar modelling approach is becoming a more prominent tool in the teaching of mathematics. Coupled with the rise in numbers of students with autism in mainstream primary schools, the question is: Is this evolving curriculum inclusive to the needs of learners with autism?
According to Baron-Cohen (Baron-Cohen et al., 2009), approximately 1% of the population could be affected by autism spectrum disorder (ASD) and as educational practitioners, we have a responsibility to ensure that the provision within our schools ensures a fully accessible curriculum for these students.
As a primary school teacher (and head teacher) of thirteen years, I have witnessed first-hand the increasing number of students entering our education system with a diagnosis of ASD. In a recent primary school with 92 students on roll, two had an official diagnosis of ASD, representing 2.17% of the school’s population – more than double Baron-Cohen’s (2009) suggestion. With increasing pressure on schools to ensure that students are high levels of attainment by the end of year six, this study aims to explore the necessary and sufficient conditions required, with a focus on the Bar Model approach, for pupils with autism to learn and develop their mathematical skills and abilities in solving computational word problems to enable them to make expected or better progress in mathematics.
Aagten-Murphy et al., (2015) point out that further research is needed to determine the extent and underlying causes of some autistic children’s difficulties with regards to number, thus ultimately informing the practice of teachers for whom it is their role to ensure these students learn and develop their skills and abilities in line with their neurotypical peers.
Contrary to Baron-Cohen’s (2009) prediction, between 6% and 22% of autistic children and adolescents are reported to struggle with number and calculation, to an extent where their maths difficulties are incommensurate with their intellectual functioning (Aagten-Murphy et al., 2015). When it comes to solving mathematical word problems, Jitendra et al., (2007) in (Bae et al., 2015) point out, that there is a requirement for the integration of several cognitive processes.
This study uses Skemp's (1971) instructional and relational understanding as a theoretical framework,on which mathematical problem solving is explored and conceptulsied.
This study will use qualitative comparative analysis (QCA), as an evolving research design, to investigate whether the bar model method is necessary or sufficient for the development of problem solving skills for pupils with autism. The research question and research design will be addressed through a critical realist lens, which has become a more popular philosophical framework over recent years for research within the social sciences (A. J. Fletcher, 2017). From a critical realist perspective, there is a clear distinction between ontology and epistemology (ontological realism and epistemological constructivism) (Maxwell, 2012), where ‘ontology is not reducible to epistemology’ (A. J. Fletcher, 2017, p. 182).A further key feature of critical realism is that individual’s ideas and feelings are viewed as equally as real as physical, observable objects and processes. In line with this theory, it is argued that ‘there are often sufficient conditions for something to occur, but they are not necessary ones, except under specific circumstances, whereby the ‘natural necessity’ is actualised’ (Gerrits & Verweij, 2013, p. 171). Through the application of this view, it is recognised that the ability to solve real-life word problems in mathematics is influenced by a complex set of conditions. These conditions by themselves, may be sufficient, or form a necessary part of a more complex conjunction of events and conditions, to impact upon an individual’s ability to solve real-life word problems.
It is anticipated that this research will establish the effectiveness of the bar model approach to mathematical problem solving for pupils with autism. The intention is to explore whether this approach is sufficient, on its own to successfully support problem solving strategies for this population, or whether other key conditions are required to be present in order for the bar model approach to be an effective tool for problem solving.
Aagten-Murphy, D., Attucci, C., Daniel, N., Klaric, E., Burr, D. C., & Pellicano, E. (2015). Numerical Estimation in Children With Autism. Autism Research. Bae, Y. S., Chiang, H.-M., & Hickson, L. (2015). Mathematical Word Problem Solving Ability of Children with Autism Spectrum Disorder and their Typically Developing Peers. Journal of Autism and Developmental Disorders, 45(7), 2200–8. Baron-Cohen, S., Scott, F. J., Allison, C., Williams, J., Bolton, P., Matthews, F. E., & Brayne, C. (2009). Prevalence of autism-spectrum conditions: UK school-based population study. The British Journal of Psychiatry, 194(6), 500–509. Fletcher, A. J. (2017). Applying critical realism in qualitative research: methodology meets method. International Journal of Social Research Methodology, 20(2), 181–194. Gerrits, L., & Verweij, S. (2013). Critical Realism as a Meta - Framework for Understanding the Relationships between Complexity and Qualitative Comparative Analysis. Journal of Critical Realism, 12(2), 166–182. Maxwell, J., A. (2012). A Realist Approach for Qualitative Research. London: Sage. Skemp, R. (1971). The Psychology of Learning Mathematics. Harmondsworth: Penguin Books. Skemp, R. (1978). Relational Understanding and Instrumental Understanding. The Arithmetic Teacher, 26(3), 9–15
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