Several researchers, including Booth (1984, 1988), Greeno (1982), Kieran (1988, 1992), Lins (1990), and Matz (1980), attributed many of the fundamental difficulties experienced by beginning algebra students to their failure to identify equivalent forms of an algebraic expression. According to Kieran (1988), structural knowledge means being able to identify ‘all the equivalent forms of the expression’. Linchevski and Vinner (1990) argued that this definition should be modified to include the ability to discriminate between the forms relevant to the task – generally one or two forms – and all the others. Booth (1981, 1984, 1988) emphasized that students construct their algebraic notions on the basis of their previous experience in arithmetic. Thus, their algebraic system inherits structural properties associated with the number system they are familiar with. She suggests (Booth, 1988) that the students’ difficulties in algebra are in part due to their lack of understanding of various structural notions in arithmetic.
The above statement is part of the literature review in the paper Structure sense: the relationships between algebraic and numerical context by Liora Linchevski and Drora Livneh. They investigated the question: Do misinterpretations of the mathematical structure by beginning algebra students reflect difficulties they already have in arithmetic? And, if these difficulties do exist in arithmetic, are they systematic, or unsystematic?
Educational Studies in Mathematics 40: 173–196, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.
