The Effectiveness of Teaching Geometry to Enhance Mathematical Understanding in Children with Down Syndrome

ABSTRACT

It is widely known that people with Down syndrome have difficulties transitioning from a basic understanding of counting and cardinality to more advanced arithmetic skills. This is commonly addressed by resorting to the mechanical use of algorithms, which hinders the acquisition of mathematical concepts. For this reason some authors have recently proposed a shift in the focus of learning from arithmetic to more fertile fields, in terms of understanding. In this paper we claim geometry fits this profile, especially suited for initiating children with Down syndrome into mathematics. To support this we resort to historical, epistemological, and cognitive reasons: the work of Séguin and his intuition on the central role of geometry in the development of abstract thinking in the so-called idiot children, the ideas of René Thom about the role of continuum intuition in the emergence of conscious thinking, and finally the two strengths people with Down syndrome display: visual learning abilities and interest in abstract symbols. To support these ideas we present the main findings of qualitative research on elementary mathematics teaching to a group of seven children (3–8) with Down syndrome in Spain. The didactic method used, naturally enhance their naïve geometrical conceptions.

KEYWORDS:

• Abstract thinking
• Down syndrome
• geometry
• intellectual disabilities
• mathematics
• mimesis

Acknowledgments

Thanks to Ana Millán Gasca who offered her advice in the application of her work for infant and preschool mathematics to young children with trisomy 21, and for the interpretation of the results. Thanks to the team of volunteer teachers and students of Primary Education degrees who have supported the research from the beginning and are essential for its success. Thanks to the young teachers who initially developed activities with the proposed approach for children without any kind of disability. Thanks to the children and parents, and the local association they belong to, who have trusted us and participated in the educational experience this research has become. We have learned while they have learned and this has opened the path for future work with other children with Down syndrome.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. We have chosen to use the term Down syndrome instead of Trisomy 21 throughout this article because of its wider meaning.

2. These notes have to do with what Séguin called following diary (1839), useful for recording the progress of the child. It allows one to evaluate the degree of achievement of the objectives proposed, while at the same time serving as a basis for raising new challenges.

Additional information

Funding

Both authors are supported, since September 2018 by the Erasmus+ Programme no. 2018-1-ES01-KA203-050986 (Strategic Partnership ANFoMAM) funded by the European Commission.