Implications for Mathematics Education Policy of Research on Algebra Learning
Stacey, Kaye, MacGregor, Mollie, Australian Journal of Education
The teaching of algebra in Victorian secondary schools has changed substantially in the last decade. Here we present implications for curriculum policy arising from research into students' algebra learning in Years 7 to 11. Data were collected from approximately 3000 students in 34 schools. Information about programs offered was obtained from teachers, by textbook analysis and by some lesson observation and teaching interventions. Performance varied considerably between schools and classes. Some differences are attributable to teaching methods, the content taught, and the arrangement of the curriculum. Subtle reductions in goals and the isolation of topics in the curriculum were disturbing trends. We discuss findings that have important implications for mathematics education policy Australia-wide.
Over the six years 1991-96, we have studied the learning of school algebra, with particular focus on the causes of common misunderstandings and low attainment. In the course of this research, we tested and talked to students, observed teaching, discussed approaches with teachers, and analysed textbooks and curriculum documents. Readers will find details of the data collection and specific findings in our research reports and articles (see Stacey & MacGregor, 1997c). In this article, we discuss the `broad brush' issues and the implications for curriculum policy that arise from them. We intend that our discussion and analysis will stimulate and inform debate on issues such as whether algebra as currently being taught is achieving its purpose for various groups of students, the levels of achievement that we expect, and the quantity and quality of instruction needed to reach such levels.
The first section of this article places algebra in context in the secondary school mathematics curriculum and summarises our research procedure and findings. The subsequent sections highlight aspects of the findings relating to the issues above.
School algebra and students' achievement
Place of algebra in the mathematics curriculum
Algebra is one of the five strands of content in A national statement on mathematics for Australian schools (Australian Education Council, 1991) and the Curriculum and standards framework: Mathematics (Board of Studies, 1995). As highlighted in the National statement, ideas essential for learning algebra have a place in the primary curriculum, but only in secondary school do students begin formal algebra, which for us is signified by the use of letters to denote unknown or variable quantities. This late introduction reflects the special role of algebra as a gateway to higher mathematics. Algebra is the language of higher mathematics and is also a set of methods to solve problems encountered in professional, rather than everyday, life.
Some algebra is taught to all junior secondary students in normal Victorian (and Australian) schools. This is done for two reasons. First, some familiarity with algebra is considered to be important for informed participation in a democratic society, and therefore all students should learn about its key concepts. Secondly, since algebra is important for further mathematics, on grounds of equity no student should be denied access to it. The inclusion of algebra in a common curriculum for all secondary school students is not universal, however. In the United States, for example, a different curriculum structure means that many students never take the one-year algebra course that is a prerequisite for subsequent mathematics courses. There is at present a campaign for all students to take this course, so that decisions about future access to mathematics are not made so early. In Australia, since all students have the opportunity to learn some algebra in every year level, the questions that must be asked about `algebra for all' are `What type of algebra?' and `How much for whom?'. These are important questions.
In recent years, there have been substantial changes in the way algebra is taught, in Australia and in other countries, at least as indicated in curriculum documents and textbooks. …