TASKS INVOLVING PERIMETER AND AREA OF PLANE FIGURES: ANALYSIS OF A MATHEMATICAL TEXTBOOK

The aim of this study is to know what a mathematics teacher can do in the class to vary the type of language used in the textbook. The methodology was qualitative (case study). Data were collected from the written registers of a group of students with four elements (aged 11-13), the teacher’s notes and the textbook used in their school. We characterized the 84 tasks (total of 96 questions) presented in their textbook related to the notions of perimeter and area of plane figures in middle school (6th grade). The results showed that the questions of the tasks had a statement which involved verbal and visual language types (62/96); a statement with verbal language (25/96), a statement with three types of languages (8/96) and a statement with verbal and symbolic language (1/96). We found 81 transformations limited to the same language: symbolic language (53/81), visual (22/81) and verbal (6/81). Transformations which involved two language types were found as following: (i) from visual to symbolic (56/88); (ii) from verbal to symbolic (17/88); (iii) from visual to verbal (7/88); (iv) from verbal to visual (7/88); and (v) from symbolic to verbal (1/88). Among the analysed tasks, 65% of the questions contained a verbal and visual statement which required symbolic language answers. In general, in these transformations the answers are few. We considered this as a limitation because there are no multiple representations for the same mathematical object. To overcome this limitation, the teacher needs to have the intention to recreate the tasks and has to persuade the students to do the same. We concluded that this textbook does not reflect an equal importance on the different types of language, giving more importance to the symbolic representations and conversions from visual to symbolic language. However, if the teacher values all types of language one must recreate the textbook tasks as students carryout their tasks.