Over the last few years, several systematic reviews have examined the complex relationship
between teacher practice and learner achievement; see, for example, Ingvarson, Beavis,
Bishop, Peck, and Elsworth (2004) in Australia and Hiebert and Grouws (2007) in the USA.
A typical review of this form, conducted in New Zealand, identified ten principles that underpin
pedagogical practices shown to facilitate students’ mathematical competence and dispositions (Anthony & Walshaw, 2009). Among these principles, in addition to ensuring an appropriate
teacher knowledge base, are the importance of building on students’ thinking, facilitating
mathematical communication, encouraging the development of mathematical language,
employing worthwhile mathematical tasks, making appropriate mathematical connections,
assessing formatively and selecting appropriate tools and representations.