Number words and Arabic numerals
Intermodal integration and its relationship to the development of mathematical performance
Summary
Theoretical background:
The integration of number words and Arabic numerals is largely unexplored, but represents an interesting predictor for the successful development of mathematical skills. Previous studies have mainly used single-digit numbers to assess numerical knowledge. However, according to recent findings, understanding the place value of multi-digit numbers in particular is likely to have an influence on children's further arithmetic development. The sequence of numbers poses a particular challenge when writing numbers in German. The number "fifty-four", for example, is written as 54. In contrast to the Arabic number, in the spoken number word the ones comes first and then the tens. This is a peculiarity that only occurs in a few languages and is known as inversion. In English, the order of the number word corresponds to the written number: 54 is read as "fifty-four". Initial studies have shown that language-specific rules influence early numerical knowledge on the one hand and can have an impact on subsequent numeracy skills on the other.
Objectives:
In this project, we investigated the extent to which the efficient integration of number words and Arabic numerals is a reliable indicator of mathematical development in elementary school. The developmental course of the integration of number words and Arabic numerals as well as the role of language-specific factors in the integration process were to be investigated. For this purpose, data was collected in the two languages English and German, whose number words are very similar but differ in the critical feature of the decade–unit inversion. The aim was to develop a differentiated model of the integration of number words and Arabic numerals, which also enables the early identification of risk factors for problems in the development of mathematical performance.
Method:
The research initiative was conducted transnationally with project partners from York (England). This made it possible to compare developmental steps in a language with inversion and a language without inversion. In a three-year longitudinal study, children in the UK and Austria were followed in their number processing and mathematical development from school entry to the end of Year 3 (summer semester 2017, 2018, 2019). Among other things, the children were asked to write down multi-digit numbers, assign number words to Arabic numbers, read multi-digit numbers aloud and solve short arithmetic problems. Tasks were also carried out on logical thinking, memory and speech sound processing. The data collected was anonymized and included in our analysis.
In a second line of research, detailed experimental and neurophysiological (EEG) paradigms on numerical processing were carried out cross-sectionally with children in the 2nd and 4th grades and with adults in the two languages.
Results of the German-language survey:
There is a high correlation between number reading and number writing. Children who were able to write many numbers correctly also performed well in number reading. As the results for number reading and number writing are very similar, we will focus on number writing in the following.
We were able to confirm that number reading and number writing performance in both first and second grade is related to numeracy performance. Uncertain performance in number writing was associated with weaker numeracy performance.
Our analysis of written and read numbers confirmed previous studies that many German-speaking children in first grade have difficulties with one-to-ten inversion. Inversion can also affect the writing of three- and four-digit numbers, as children overgeneralize their learned knowledge. This means that they not only transpose the tens and ones, but also the hundreds and thousands and the dictated number "three hundred and twenty-six" is written as 263 instead of 326, for example.
We also investigated whether the length of a number and/or its structure have an influence on the level of difficulty. We came to the conclusion that it is the number structure rather than the size of a number that determines the degree of difficulty. For example, we were able to show that the number 8000 (X000) was much easier to write than the smaller number 870 (XX0). This result was observable in both first and second grade. The structure of a number is therefore more important than its size.
These findings are important to the extent that children can be given even more targeted support in learning numbers in future, particularly by focusing on apparently more difficult number structures.
Cooperation partner: Dr. Silke Göbel, University of York
Duration: 01.04.2017 - 30.09.2021
Publications:
Banfi, C., Clayton, F.J., Steiner, A.F., Finke, S., Landerl, K., & Göbel, S.M. (2022). Transcoding counts: Longitudinal contribution of number writing to arithmetic in different languages. Journal of Experimental Child Psychology, 223, 105482. https://doi.org/10.1016/j.jecp.2022.105482
Finke, S., Vogel, S.E., Freudenthaler, H.H., Banfi, C., Steiner, A.F., Kemény, F., Göbel, S.M., & Landerl, K. (2022). Developmental trajectories of symbolic magnitude and order processing and their relation with arithmetic development. Cognitive Development, 64, 101266. doi. org/10.1016/j.cogdev.2022.101266
Steiner, A.F., Finke, S., Clayton, F.J., Banfi, C., Kemény, F., Göbel, S.M., & Landerl, K. (2021). Language Effects in Early Development of Number Writing and Reading. Journal of Numerical Cognition, 7(3), 368-387. https://doi.org/10.5964/jnc.6929
Steiner, A.F., Banfi, C., Finke, S., Kemény, F., Clayton, F.J., Göbel, S.M., & Landerl, K. (2021). Twenty-four or four-and-twenty: Language modulates cross-modal matching for multidigit numbers in children and adults. Journal of Experimental Child Psychology, 202, e104970. https://doi.org/10.1016/j.jecp.2020.104970
Finke, S., Banfi, C., Freudenthaler, H.H., Steiner, A.F., Vogel, S.E., Göbel, S.M., & Landerl, K. (2021). Common and distinct predictors of non-symbolic and symbolic ordinal number processing across the early primary school years. PLoS ONE, 16(10), e0258847. https://doi.org/10.1371/journal.pone.0258847
Finke, S., Kemény, F., Clayton, F.J., Banfi, C., Steiner, A.F., Perchtold-Stefan, C.M., Papousek, I., Göbel, S.M., & Landerl, K. (2021). Cross-format integration of auditory number words and visual-Arabic digits. An ERP study. Frontiers in Psychology, 12, e765709. https://doi.org/10.3389/fpsyg.2021.765709
Clayton, F.J., Copper, C., Steiner, A.F., Banfi, C., Finke, S., Landerl, K., & Göbel, S.M. (2020). Two-digit number writing and arithmetic in Year 1 children: Does number word inversion matter? Cognitive Development, 56, e100967. https://doi.org/10.1016/j.cogdev.2020.100967
Finke, S., Freudenthaler, H.H., & Landerl, K. (2020). Symbolic processing mediates the relationship between nonsymbolic processing and later arithmetic performance. Frontiers in Psychology, 11, e549. https://doi.org/10.3389/fpsyg.2020.00549