Numeracy and Learning Difficulties: Approaches to Teaching and Assessment

Until fairly recent times the term OCynumeracyOCO was usually taken simply to mean adequate competence in applying the basic skills of arithmetic necessary for coping with everyday situations. More recently, although retaining the same OCyeveryday functional useOCO connotation, the concept of numeracy has been expanded considerably. Numeracy isnOCOt just possessing some mechanical facility with numbers: it also embraces the notion of being able to communicate effectively with others through the basic language of mathematics, to interpret everyday quantitative information, and to have a repertoire of strategies and OCynumber senseOCO to deal with problems that may arise (Willis 1998). Numeracy includes not only an understanding of and competence with basic number and measurement, but also skills and confidence in the handling and interpretation of quantitative data (Peach 1998). Steen (1997, p. xvii) describes numeracy as OCyquantitative literacyOCO, and by doing so implies that it is as important for an individual to be numerate in todayOCOs world as it is to be able to read and write proficiently. In Australia, as in other countries, the development of numeracy skills is being given high priority in the school curriculum. Ellison (1998, p. 27) states that, OCyA high standard of numeracy is vital if our young people are to operate effectively in a complex technological society and realise their goals and potentialOCO. It is an unfortunate fact, however, that too many of our students experience difficulty in learning basic mathematics. For them, a satisfactory level of numeracy is an unattained goal. This is not a book about identifying students with learning difficulties in basic mathematics and removing them from class for intensive OCyremediationOCO (although such intervention will be necessary for a few students). It is a book that argues for high-quality OCyfirst teachingOCO to prevent students failing in the initial acquisition of numeracy skills. While many of the teaching and assessment strategies described are equally applicable to small group work and to individual tuition, the aim is actually to explore and encourage more effective classroom teaching. The argument put forward is that the most effective approach is one that combines important and successful aspects of direct teaching with the most meaningful and motivating components of student-centred, constructivist approaches. It is true that in the past, at all age levels, mathematics was taught through predominantly didactic methods, with too much emphasis placed on rote memorisation of rules and OCytricksOCO to obtain the OCyrightOCO answers. The studentsOCO learning was much too procedural rather than conceptual, hence the call for a reform in the teaching of mathematics. The widely advocated solution is for a shift toward constructivist, student-centred, enquiry-based approaches, in the belief that students understand best the knowledge they acquire through their own activity and exploration. These constructivist approaches are being advocated so strongly that there is a real danger that the educational pendulum will swing so far in the opposite direction that teachers will feel that they must abandon all forms of direct teaching. The argument presented in Numeracy and Learning Difficulties is that, for effective acquisition of numeracy skills, a balanced approach is required, combining the best of the new knowledge about studentsOCO learning with the best of traditional pedagogy."