Teaching mathematics has evolved from the traditional instrumentalist view where the focus is on knowledge mathematical facts, rules and methods as independent concepts, to the more contemporary constructivist approach which focuses on building on prior knowledge and experiences incorporating mathematical facts, rules and methods to problem solve and investigate new mathematical concepts. This will in turn, enable students to apply concepts in real life situations. Teaching thematically is an approach which allows concepts to be applied to real life situations. While the benefits and success of the constructivist approach for long term learning are widely acknowledged, a teacher’s ability to engage with and implement this approach to teaching numeracy relies largely on their knowledge, experiences, attitudes and beliefs.
Ma (1999) explains that the understanding of elementary mathematical ideas in essence underpin the development of all mathematics. Ma (1999) further suggests that these elementary mathematical concepts establish the basis on which future mathematical thinking is constructed. Mathematics can often be taught in discrete and separate ways to cover a specific curriculum. However Richhart (1994) and Nodding (1993) imply that teachers should not simply cover the curriculum but rather uncover it. Booker (2010) supports these suggestions by explaining that mathematics needs to be viewed as a cohesive body of knowledge rather than as a series of fragmented ideas.
It is important for teachers to understand and foster new and ever evolving productive pedagogies. As previously briefly outlined, there has been a change in the way leading theorists believe to be the ideal way students should be taught for students to better learn and understand mathematics. Previously teachers would teach students with an instrumentalist view where mathematics is an accumulation of facts, rules and methods as separate entities. The more modern approach to teaching mathematics effectively, is the constructivist or problem solving view where mathematics is learnt through actively building on prior knowledge in a social and cultural context Ernest (1988). This constructivist theory has a emphasis on students constructing their mathematical meaning through dynamic problem solving activities and discussion.
The Australian Education Council [AEC], (1991); National Council of Teachers of Mathematics [NCTM], (2000) as cited in Nisbet, et al (2000) explains that the mathematics classroom environment should one where students are actively engaged in interpreting and making sense of their experiences, and the teacher is seen as the facilitator of learning. By incorporating this constructivist view on teaching mathematics, students will have a relational understanding where their mathematical knowledge is more adaptable to new concepts and contexts (Skemp, 1978). Booker et al (2010) explains that to acquire this way of thinking and understanding, it is fundamental...