Title: Concept of place value in students with Down syndrome

Barbara Clarke. Monash University, Australia Top

Title: Assessing and Developing the mathematical understanding of young children with Down syndrome: Some Australian findings

Abstract: In this presentation work conducted with Dr Rhonda Faragher in Australia will be shared. A one-to-one mathematics task based interview was used with twelve young primary aged children with Down syndrome. The interview covered a range of mathematics content and was based on an instrument used extensively in the early years of school. Some results including some surprising responses will be presented. We will argue that a flexible methodology helped maximise the chances of children showing what they knew and could do mathematically.

Rhonda Faragher. University of Queensland, Australia Top

Title: Mathematics and the quality of life of people with Trisomy 21

Abstract: It has been known for some time that numeracy, the application of mathematics in daily life, is important for quality of life. Learners with Down syndrome have often been limited in developing numeracy because of what they have been taught. Many struggle with basic arithmetic and have been prevented from access to other mathematics as a result. Fortunately, this is changing with new understandings about the nature of mathematics and how it can be taught to learners with Down syndrome. The possibilities, then, are for dramatic changes in accomplishment of mathematics learning outcomes for students with Down syndrome. This impact is considered on Educational Quality of Life (EQoL), which is an emerging branch of the broader field of Quality of Life.
This presentation will explore the connection between mathematics, numeracy development and EQoL.

Karen Fuson. Northwestern University, USA Top

Title: Relating Words, Visual Images, and Math Symbols for Understanding and Competence

Abstract: I will briefly overview my research with young children in learning number by relating number words, research-based visual supports, and math symbols.  I will share what I have found to be productive learning activities and visual supports and discuss advantages and disadvantages of different supports.  I have found math drawings to be a key visual support that helps children transition to working meaningfully with symbols and words alone.

Elena Gil Clemente. Universidad de Zaragoza, España Top

Title: First steps in Mathematics for children with Trisomy 21: a Geometry-based study

Abstract: Mathematics is a basic discipline in education, not only because of its utilitarian nature, but above all because of the role they play in the development of abstract thinking and the ability to have a deeper knowledge of the world.
The difficulties with arithmetic observed in people with Trisomy 21 suggest the need to redirect the teaching of this basic discipline towards more fertile fields.
In this presentation we will discuss the role of geometry in child mathematical initiation. A role that the innovators of the nineteenth century already intuited and which is confirmed by the epistemology and the foundations of mathematics.
The analysis of the keys to the success of an experiment carried out in Zaragoza will lead us to rethink some ideas on the teaching of mathematics in general and on our conception of intellectual disability.

Ana Millán Gasca. Universidad Roma Tre, Italia Top

Title: Geometric intuition and mimesis in child’s introduction to Mathematics

Elisabetta Monari. Universidad de Padua, Italia Top

Title: The new Mathematics tree: beyond Arithmetic

Abstract: The key questions are: Is it true that persons with Down syndrome are hopeless at mathematics? Might it be possible that their difficulties are mainly restricted to some fields, such as numeracy and mental computation, but do not encompass the entire domain of mathematics? What can we say about the mathematical topics that emphasise logic over few numerical abilities? Is the use of a calculator recommended? Our experience is that these students can solve mathematical problems, though they may have very poor numeracy skills – in fact, a familiarity with algebraic computation and analytic geometry can help to raise their self-esteem and improve their numeracy too. Surprisingly, these students can learn and apply mathematical procedures such as those used to work with fractions, to solve equations, to solve problems with equations, to use equation formulas in a variety of other different contexts, and to work with Cartesian coordinates and formulas in analytic geometry, with the help of rulers, calculators, and other visual prompts that they learn to manage easily.
Some examples with adolescents included in Italian mainstream secondary schools will be reported. In fact, the role of the inclusion of every disabled student, regardless the severity of the disability, has been crucial for these results.

Jill Porter. University of Reading, Gran Bretaña Top

Title: Should we be fostering magnitude representation with children with Down syndrome?

Abstract: The focus of my presentation is on the earliest foundational skills of mathematics. I will look at what we know about children with Down syndrome’s understanding and knowledge of the procedures of counting, drawing on my own PhD research with 50 children with Down syndrome together with more recent research. These findings have led me to consider the role of magnitude representation (or numerosity) in supporting children at the earliest stages and the challenges of drawing firm conclusions from the literature. I will then report on some recent empirical data I gathered with 40 children with Down syndrome on their responses to an iPad game and a non-digital card game. This raised some interesting issues for me about pedagogy and the design and development of activities.

André Zimpel. Universität Hamburg, Alemania Top

Title: Abstract thinking in people with Trisomy 21

Abstract: In early reading, preschool children with trisomy 21 are interested in abstract, second-order supersigns. Many children with Down syndrom can already start learning to read at preschool age. Unfortunately, science still draws the wrong conclusions from this: one attributes visual strength to people with trisomy 21.
Our experimental findings from 1,294 people with trisomy 21 show a narrowing of the scope of attention to less than four units (chunks) simultaneously. As the results of our study demonstrate, the visual scope of attention of people with trisomy 21 is limited. Incidentally, this limitation also applies to the acoustic, haptic and kinesthetic scope of attention. These results suggest that visual, step-by-step and abstraction-avoidant classes at special needs schools take only little account of the neuropsychological features of people with trisomy 21.
In its original meaning, the word “abstraction” (derived from the Latin abstrahere for “draw away” or “detach”) describes the process of abstaining from seeing details or wholes. Pablo Picasso's drawings, which ingeniously omit many details, are a good example. Abstraction can, however, also elevate a detail, e.g., the maple leaf as a symbol for Canada.
There are brains in the neurodiversity spectrum for which arithmetic is particularly easy, e.g., some (a few) people in the autismspectrum. There are also people for whom it is less easy, e.g., people with trisomy 21. However, learning arithmetic is also particularly challenging for many neurotypical people. The decimal system and the power of five make it easier for many neurotypical people, but, by far, not for all. Taking the entire neurodiversity spectrum into account requires a diversity of learning pathways.

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