# Learning artificial number symbols: the role of ordinal and magnitude information

Numbers are everywhere and we use them constantly. Being numerate is essential to function in today’s society and failure to understand and use numbers is not only linked to mathematical (in)abilities, but also to success in employment, financial stability and health. Understanding how numbers are learned, how we attach meaning to these, is therefore a question of great importance. Research has investigated how numerical symbols gain meaning for decades, yet it is still unclear which types of semantic information are involved in this. This therefore warrants further investigation. The overarching aim of this thesis is to contribute to this by investigating what types of information can be used to give meaning to numerical symbols and what factors may influence numerical processing.

The numbers we mainly use, Arabic digits, always convey magnitude (i.e., the quantity of a set) as well as ordinal (i.e., the position of a number in relation to other numbers) meaning. I therefore focussed on investigating the role of these two types of semantic information. Specifically, I report a total of six empirical studies in which I trained adult participants, using ordinal and magnitude information, to learn the meaning of several artificially created number symbols. I then tested participants’ ability to compare and order the newly learned symbols based on their magnitude and ordinal meaning. The findings of Studies 1 – 3 indicated that both ordinal and magnitude information, as well as various combinations thereof, allowed participants to learn seven individual artificial symbols and to make relatively accurate ordinal and magnitude-based judgements about the symbols. Given that almost all numbers are part of a structured notational system, I shifted the focus of Studies 4 – 6 slightly, and looked at participants’ ability to learn and perform numerical tasks with the newly learned symbols, which are part of a structured symbol system. Similar to the first three studies, Studies 4 and 5 also showed that ordinal, magnitude and a combination of ordinal and magnitude information allowed participants to learn twelve artificial symbols, to make relatively accurate ordinal- and magnitude-based. judgements about the symbols, infer the meaning of and perform numerical tasks with symbols not encountered during the training phase, as well as to learn the underlying structure of the symbol systems to which the symbols belonged. Lastly, Study 6 indicated that ordinal information training allowed participants to learn the symbols as well as the underlying structure of both a place-value as well as a sign-value system.

Overall, I believe my results suggest that emphasising both ordinal and magnitude information best allows for the numerical meaning of number symbols to be learned. This may have important educational implications. Children start off by reciting the count sequence as an arbitrary list of words, and then they learn the absolute numerical values to those number words. Commonly, it is this magnitude meaning that is emphasised in order for children to learn to correctly use numbers, especially in an educational and mathematical context. Nevertheless, given the omnipresence of both ordinal and magnitude meaning of numbers, it may be beneficial to put somewhat more emphasis on the ordinal relations between numbers. With my thesis I contribute to the research on the symbol-grounding problem (i.e., how numerical symbols gain semantic meaning). I have shown that different types of semantic information can be used to attach meaning to novel artificial number symbols and what types of information can give rise to the commonly found behavioural effects of numerical processing.

## Funding

### Royal Society Grant [#RGF/EA/180254]

## History

## School

- Science

## Department

- Mathematics Education Centre