Integrating Number and Algebra in The New Zealand Curriculum: Implications for teaching

Abstract

Introduction In 1993, The New Zealand Curriculum Framework (Ministry of Education, 1993) set out learning areas and strands to be covered in New Zealand schools. After consultation and revision, a newer version, The New Zealand Curriculum, was distributed to schools in 2007 (Ministry of Education, 2007). The learning area of Mathematics and Statistics was divided into three strands rather than previous six, with Number and Algebra being one strand. Why were previous strands of Number and Algebra put together? Was this just a matter of convenience, in order to simplify curriculum? If not, then what was basis for combining two strands? For many people, number appears to be concerned with computation, while algebra appears to be concerned with letters. The connections between these two parts of mathematics may not seem that obvious, and in order to appreciate them it is necessary to explore nature of both. Does, or should, reorganisation of curriculum have any implications for teaching? Are any number skills or knowledge prerequisites for learning algebra, or vice versa? What should we now be teaching at different levels of curriculum? Should teaching of number and algebra be integrated and does this vary with curriculum level? This article explores some of background to recent curriculum developments in mathematics in New Zealand, describes structure of Number and Algebra strand in The New Zealand Curriculum and provides some suggestions for integrating teaching of number with teaching of algebra, with particular emphasis on equations and expressions. Background The previous curriculum statement for mathematics in New Zealand schools (Mathematics in New Zealand Curriculum, Ministry of Education, 1992) was first that encompassed all years of schooling and that clearly specified outcomes for students. In 2007, in keeping with recommendations of Curriculum Stocktake Report (Ferguson, 2002), there were few major changes, but complexity of mathematics and statistics curriculum was simplified and number of strands reduced from six to three for levels 1-6. The strands are now Number and Algebra, Geometry and Measurement, and Statistics. This integration of number and algebra into one strand followed debate within mathematics education community in New Zealand, with many submissions made in response to The New Zealand Curriculum: Draft for Consultation 2006 (Ministry of Education, 2006). Collins Reference Dictionary of Mathematics defines algebra as the branch of elementary mathematics that generalizes by using variables to range over numbers,... in particular, use of symbols standing for unknown quantities in order to determine their value by elementary operations of arithmetic (Borowski & Borwein, 1989). This definition immediately emphasises use of symbols, and also links algebra to arithmetic. Many authors take a broad view of what constitutes algebra and make explicit links to arithmetic. Lee (2001), for example, suggested that algebra is generalised arithmetic, a language, a way of thinking, an activity, a tool and a culture. Kieran's (1992) view is that algebra is symbolising of general numerical relationships and mathematical structures, and operating on those structures. Again algebra is seen as having its foundation in number, but generalising from there to mathematical structures. Carraher and Schliemann (2007) also stressed continuity between and algebra and suggested that many problems that students experience with learning algebra are caused by earlier difficulties with arithmetic. Kaput (2008) saw traditional approach of teaching and algebra as separate subjects as being dysfunctional, because just focused on computation, while algebra was taught in a superficial way that led to teacher alienation and high student failure rates. …