Teaching Mathematics

There is a need for new approaches to teaching mathematics. This is due, in part, to the vast amounts of research that have been generated since mathematics education became recognised as a discipline. Wide changes are occurring rapidly in societies nationally, internationally and globally. Change impacts upon students, mathematics education and schools.

The mathematics curriculum encountered in the pre-1960s period focused on arithmetic and operations. Most of the mathematics education developed after that in Western countries arose post-Sputnik, when the race to the moon became a race for intellectual superiority; and mathematics was seen to be the linchpin for success. The 'New Mathematics' contributed to a lock-step approach to teaching mathematics, with hierarchies in orders and sequences of teaching. The 1970s witnessed a boom in the ways in which mathematics curricula were organised, most of which were not research-based but influenced by arguments of logic and reason.

In more recent times, there has been a growing awareness that such approaches are not resulting in positive learning outcomes. Indeed, as Clements (1989) argued, all students learn from 10 years of compulsory schooling (and in most countries this may be extended to 12- 13 years) is that they can't do mathematics! Not all countries have bought into this approach to teaching. Research emanating from these countries, particularly the Netherlands, has strongly focused on developing new methods and approaches to teaching mathematics.

These twin movements have conjointly emerged as it is being recognised that many of the old methods of teaching mathematics are failing too many students. This has made the time ripe for identifying more valid methods for teaching mathematics, and many countries, states and provinces are now adopting new methods for mathematics teaching and learning.

Contemporary approaches to teaching mathematics need to encourage two aspects: content and pedagogy.

Content is the intellectual integrity of the subject where students learn, apply and appreciate mathematics and where deep learning and deep knowledge are paramount to learning experiences. Importantly, students are able to make connections between the mathematics they learn and other curriculum areas and the world beyond schools. It is important for them to develop an appreciation of how mathematics is an informing discipline that has importance and relevance to many spheres of life.

Many of the issues not taught explicitly to students. They are expected to be learnt through a process of osmosis. This results in some students cracking the code of classroom literacies and others making little sense of the game being played. Unfortunately, failure to 'crack the code' can have serious consequences. For ethical teaching, teachers need to be aware of the ways in which language is implicated in teaching mathematics and make the game explicit to their students.

When introducing new approaches to teaching mathematics -groupwork, open-ended tasks, investigations- spend time explaining or modelling to students the nuances of the approaches so they are not expected to second-guess what is expected from them. This is particularly important when the approach being used is very different from the usual classroom practices.

Countries such as Japan which scored highly on the test were more likely to use problems or investigations. This data support a common belief that the review - and - revise format may not be the best method for teaching mathematics- particularly new concepts.