It's numbers and that's it: An exploration of children's beliefs about mathematics through their drawings and words
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Children’s beliefs about mathematics involve epistemological beliefs about the subject, its nature and how it works, as well as beliefs about who can and cannot do mathematics. While children’s beliefs about mathematics have been linked to their achievement in mathematics, there is little research that explores beliefs about mathematics in the New Zealand context. A general concern is that students do less well than they could at mathematics; hence many people give up on and disengage from mathematics.
This study explores children’s and their teachers’ beliefs about mathematics and is set against a backdrop of prevailing achievement discourses, both in New Zealand and abroad, that define people’s perceived abilities as usually based on ethnicity and gender. It also considers the multiple worlds of the child, the worlds of mathematics beliefs and of doing school mathematics, the child’s relationships with these worlds and with others who inhabit them.
The study combines complementary theories and methods to examine espoused and enacted mathematics beliefs by adopting a predominantly sociocultural perspective and including a combination of constructivist and pragmatic theories as well as multiple methods of accessing and analysing beliefs. In order to develop a picture of mathematics beliefs, I collected data from a number of sources: mathematics beliefs questionnaires from 823 children at 17 schools, drawings from 180 children at two focus schools, video recordings of multiple mathematics lessons in two focus classrooms and observations. The following year, I revisited, observed and interviewed nine focus children and their teachers. I applied multiple analysis ‘frames’ to the data: factor analysis, adapted visual frameworks, metaphors and themes.
By combining a variety of methods and applying a number of different analysis perspectives, this study exposed a rich and complex landscape of beliefs about mathematics. In particular, the children’s drawings communicated mathematics beliefs by using metaphors such as ‘maths as problem solving’, ‘maths as useful’, ‘maths as life’, and ‘maths as brain burn inducing’. The children and teachers exhibited a range of beliefs about the world of mathematics and who belongs to this world by positioning certain people as good at mathematics, not good at mathematics, or in certain cases, both positions depending on the context. In terms of assigned mathematics identities, both children and teachers refer to the ‘Asian as good at maths’ discourse but do not position Māori and Pasifika as weak; gender was not viewed as important. On the other hand, the children’s responses were influenced by their ethnicities, gender, socioeconomic status and mathematics achievement levels. The implications for primary school mathematics relate to the powerful influence of how mathematics is done, taught and learnt within the dominant context of the Numeracy Projects which governs ability groupings, the dance of the mathematics class, the ascendency of strategy over algorithm, and the notion that there are multiple ways to solve problems. In particular, the implications of inequality inherent in mathematics ability grouping warrants addressing.