The Value of the Computer in Learning Algebra Concepts

The BackgroundThe problems and difficulties which many secondary schoolchildren have withalgebra (generalised arithmetic) are well known and have been the subject ofmuch research investigation. Many of these relate to the conventions of thenotation and the inability of children to interpret the meaning of the use ofletters (Booth 1983a). Faced with a new and daunting cognitive situation,many fall back on their previous experience and make use of a one-to-onecorrespondence between the natural numbers and the letters of the alphabet (egWagner 1977), feeling a strong need for a numerical ‘answer’. Booth (1983b)reported encouraging success using an imaginary ‘Maths Machine’ which thechildren had to ‘program’ to produce answers. The value of computerprogramming in understanding algebra has already been shown (see, forexample, Tall 1983) and the natural extension of Booth’s work was to providethe children with actual ‘maths machines’ to program.The psychological framework of the research is based on constructivistPiagetian theory, with its idea of abstraction from experience, Ausubel’stheory of meaningful learning, and the relational understanding of Skemp. Allthese theories emphasise the importance of the ‘framework of knowledge’which the individual constructs in any cognitive area, and the need to build onthe existing knowledge structures of the child by conceptual rather than rotemeans.The experimenta) equipmentTo enable the children to construct a mental model for a variable in algebra,and the manner in which it is manipulated, a concrete model was providedconsisting of a ‘box’ containing the current numerical value of the variable andan attached label with the variable name (figure 1). Although this model doesnot fulfil all the mathematical uses of the concept of variable (see e.g. Wagner1981), it proved to be of great value to the children.