Bergqvist, Ewa

Bergqvist, Tomas

Hultdin, Ulrika Wikström

Vingsle, Lotta

Österholm, Magnus

English

Repositorio Institucional de la Universidad de Alicante

HOW TEXTBOOKS IN DIFFERENT SCHOOL YEARS GIVE MEANING TO MATHEMATICAL SYMBOLS Ewa Bergqvist, Lotta Vingsle, Magnus Österholm, Tomas Bergqvist, and Ulrika Wikström Hultdin Department of Science and Mathematics Education, Umeå University Research shows that natural language (for example English) is central to students’ meaningful understanding of mathematical symbols. For example, natural language can be important as a starting point for the learning of the symbolic language (Caspi & Sfard, 2012). However, longitudinal studies are missing. This ongoing study is part of a larger project concerning the role of natural language when learning the mathematical symbolic language, including how progression in the use of natural language can relate to advancements in the use and understanding of the symbolic language. Here we focus on textbooks, with the aim to answer the research question: How is meaning given to mathematical symbols through the use of natural language in mathematics textbooks in different school years? In the analyses, we used a set of categories that describe different ways of using natural language to give meaning to symbols. Giving meaning to symbols can be done by specifying a referent to mathematical symbols (Hiebert, 1988). We delimit this study to situations when some (property of a) referent is specified through natural language. One of our categories includes situations when a symbol is defined or explained in very explicit language. For example, the category includes statements as “x is a number”, which specifies a referent (number), or “13 is odd”, which specifies a property (being odd) of the referent. Other categories describe situations when information is given in more implicit and indirect manners. We analysed three different textbook series commonly used in Sweden, from school years 2, 5, and 8, and we randomly selected 20 pages from each of the nine textbooks. Analyses are ongoing, but preliminary results show the fraction of analysed situations that explicitly describe a (property of) a referent, in the different school years: 6.5% in year 2, 9.2% in year 5, and 7.2% in year 8, among a total of 1283 units of analysis. There is no statistically significant difference between the school years, showing that the more explicit focus on the meaning of symbols is equally common across school years. Continued analyses will examine if there are any qualitative differences. References Caspi, S., & Sfard, A. (2012). Spontaneous meta-arithmetic as a first step toward school algebra. International Journal of Educational Research, 51-52, 45-65. Hiebert, J. (1988). A theory of developing competence with written mathematical symbols. Educational Studies in Mathematics, 19, 333-355. 4 - 178 2022. In C. Fernández, S. Llinares, A. Gutiérrez, & N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, p. 178). PME.

How textbooks in different school years give meaning to mathematical symbols

http://rua.ua.es/dspace/bitstream/10045/126728/1/proceedings-pme45-vol4-034.pdf

How textbooks in different school years give meaning to mathematical symbols

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Repositorio Institucional de la Universidad de Alicante