There is a concerning question nowadays in Australia which started as a debate of University lecturers who said high school physics is at a very low level of quality and focused on the history of physics at the expense of rigorous mathematical analysis and problem-solving. As a result, they said, students often arrive at university with a distorted view of what physics is and whether they are good at it.
To define the goals of mathematics teaching, it is necessary to consider what mathematics is and does and what might be the purposes for teaching mathematics to school students. The basic argument is that the emphasis in school mathematics should be predominantly on practical and useable mathematics that can enrich not only students’ employment prospects but also their ability to participate fully in modern life and democratic processes.
The Goals of Mathematics Teaching
There is a broad consensus among policy makers, curriculum planners, school administrations and business and industry leaders that mathematics is an important element of the school curriculum. Rubenstein (2009), for example, offers a compelling description of the importance of mathematics from the perspective of mathematicians, as well as the challenges Australia is facing due to the decline in mathematics enrolments in later year university mathematics studies.
Part of the context in which this debate is being conducted is that schools are confronting the serious challenge of disengaged students. In their report on the national Middle Years Research and Development Project, Russell, Mackay and Jane (2003) made recommendations for reform associated with school leadership and systematic school improvement, especially emphasising the need for more interesting, functionally relevant classroom tasks which can enhance engagement in learning. Additionally, there is said by some to be a serious decline in the number of students completing later year university level mathematics studies, thereby threatening Australia’s future international competitiveness and capacity for innovation. These claims feed calls for more mathematical rigour at secondary level, as preparation for more advanced learning in mathematics. Unfortunately, these claims are presented by the protagonists as though teachers must adopt one perspective or the other.
In one of the major presentations at the Teaching Mathematics? Make it count conference, Ernest (2010) delineated both perspectives. He described the goals of the practical perspective as follows: students learn the mathematics adequate for general employment and functioning in society, drawing on the mathematics used by various professional and industry groups. He included in this perspective the types of calculations one does as part of everyday living including best buy comparisons, time management, budgeting, planning home maintenance projects, choosing routes to travel, interpreting data in the newspapers, and so on. Ernest also described the specialised perspective as the mathematical understanding which forms the basis of university studies in science, technology and engineering.
A necessary corollary to incorporating these dual perspectives in mathematics teaching and learning in pedagogy is a consideration of the ways that teachers might engage their students in more productive learning. The research strongly suggests that teachers incorporate both types of mathematical actions in tasks for their students to undertake when learning mathematics.
 Peter Sullivan, Australian Education Review – Teaching Mathematics: Using research-informed strategies, 2011.