Abstract:

Statistical tables are often included in the study of mathematics and other subjects to represent, summarize and communicate information, and are also used for data analysis. In everyday contexts, tables also appear, for example, on television, the news, in advertising and on the Internet. Consequently, citizens need to read and construct statistical tables in order to function in the information society, where statistical knowledge is essential in making better decisions.

The study of the tables involves a variety of types and different uses, which are accompanied by a series of cognitive demands involved in their understanding. Research on tables is scarce, and little explored. Some authors argue that the apparent facility of tables is a fallacy, because the variety of types of tables imply that they should be read differently. Despite the fact that students use tabular representations in different mathematical topics, or in other subjects, researches warn that this use involves a special difficulty.

The curricular guidelines of various countries explicitly incorporate the study of statistical tables beginning in the first years of primary education. Along the primary and secondary education different types of tables, such as data tables, distribution of frequencies of one-dimensional variables, and contingency tables appear, which are distinguished according to the mathematical objects they incorporate, such as, for example, the types of frequencies (absolute, relative, cummulative), the variable values and the possibility of using data grouped in intervals.

Our research is focused on analyzing the algebraic activity required in the study of statistical tables in a sample of textbooks along the final years of primary education. In the work with statistical tables not only statistical and arithmetic knowledge is applied, but algebraic reasoning is also initiated. Therefore, we analyze the types of algebraic objects and levels of reasoning that emerge in activities involving statistical tables.

The analysis of the tasks is based on the four initial levels of algebraization described by Godino and his collaborators. These levels are defined by taking into account the activity performed by the subject who solves a mathematical task and the degree of generality of the objects used, in addition to the mathematical processes involved and the type of language used.

The following algebraic objects are considered to differentiate the algebraic levels: binary relations (equivalence and order), operations performed on the elements of a set and their properties, functions and objects involved in them (formulas, variables, representations) and algebraic structures. In addition, the levels involve characteristics of algebraic activity, such as the processes of generalization, particularization and representation.

This algebraic activity should be recognized, as it can contribute to the introduction of early algebra into the school curricula, and, as such, this introduction could be beneficial to students. In addition, analyzing algebraic levels in statistical tables is a useful tool for teachers to assess the difficulty and algebraic activity required by their students.

Keywords:

Statistical tables, Levels of algebraization, Textbooks.