Variables in "Bbuilding up Mathematics" textbooks and students' understanding of this concept (At pre-high school levels)

النوع : Mémoire

This study applied content analysis to investigate the way variables are introduced and treated in the “Building up Mathematics” textbook series for grades six, seven, eight and nine. It also investigated the existence of support for teachers regarding the concept of variables in the teachers’ editions of these textbooks. Besides, it documents the curriculum objectives regarding variables in mathematics. In addition, it examined students’ understanding of variables at these grade levels using a diagnostic test designed for this purpose. Findings from content analysis of the textbooks revealed that these textbooks did not provide any historical information or formal definitions of variables yet still, they applied different types of variables in different proportions. The most used types of variable in these textbooks as a whole were abstract symbols and constants whereas the least used types were parameters and generalized numbers. Also, considering the textbooks as a whole, the type of variable encountered most in algebra was the abstract symbol. Constants were dominant over other uses of variables in plane geometry, trigonometry and space whereas varying quantities were most dominant in analytic geometry. In real life situations, labels are encountered more than other types of literal symbols. Besides, the teacher’s editions of the textbooks provided no guidance for them on how to enact variable ideas. A diagnostic test was designed to investigate pre-high school students’ understanding of variables and to specify the common misconceptions they had regarding this concept. Results revealed that students had a hard time dealing with variables. Common wrong answers were documented and analyzed to determine the possible misconceptions resulting in them. Some of these misconceptions were not attaining the ability to determine the role of the variable, assuming that a literal symbol stood for a single value, defining variables nominally not quantitatively, not attaining the meanings of basic expressions, such as 2x and 3x2. In addition, the possible links between the percentage a type of variable was used in the textbooks and students’ understanding of this specific type of variable were studied. The linear correlation between them was studied and the obtained results implied an almost strong positive which means that as the first increased, the second tended strongly to increase; yet further statistical studies need to be done regarding this issue.