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.

We, as a culture, tend to lump students into broad categories to describe their relationships with mathematics, such as ‘good at math’ or ‘hates math.’ This study focuses on five students each of whom could be considered ‘good at math,’ and shows how the beliefs that make up their mathematical identities are actually significantly different. The study examined eight beliefs that affect a student's motivation to do mathematics: confidence, anxiety, enjoyment of mathematics, skill level, usefulness of mathematics, what mathematics is, what it means to be good at mathematics, and how one learns mathematics. These five students' identities, which seemed to be very similar, were so intrinsically different that they could not be readily ranked or compared on a one-dimensional scale. Each student had a unique array of beliefs. For example, the students had strikingly different ideas about the definition of mathematics and how useful it is to the world and to the individual, they had varying amounts of confidence, different aspects that cause anxiety, particular facets that they enjoy and different ways of showing enjoyment. Their commonly held beliefs also varied in specificity, conspicuousness, and importance. Recognizing that there are such differences among seemingly similar students may help teachers understand students better, and it is the first step in knowing how teachers can improve student's relationships with mathematics.

Lärare i Sverige använder i stor utsträckning matematikböcker i matematikundervisningen. Hur lärares uppfattningar påverkar deras undervisning är dock debatterat. Denna studie undersöker därför sambandet mellan lärares användning av matematikböcker och deras uppfattningar om matematik, matematikundervisning och lärande i matematik. Först fick åtta lärare i årskurs 1-3 besvarade en enkät om uppfattningar, och om användning av matematikböcker och sedan intervjuades tre av dem. Resultatet visar att lärarna i olika grad kan ha både en dynamisk och statisk syn på matematik som ämne, och både en konstruktivistisk och traditionell syn på undervisning och lärande i matematik. Resultatet visar även att den lärare som i minst utsträckning tar uppgifter från matematikboken är den lärare som i störst utsträckning visar på en konstruktivistisk syn, medan den lärare som i störst utsträckning tar uppgifter från matematikboken är den lärare som i störst utsträckning visar på en dynamisk och problemlösande syn. Den lärare som befinner sig i mitten vad gäller vart uppgifterna tas ifrån är den lärare som i störst utsträckning håller med om en statisk och platonistisk samt instrumentalistisk syn. Ses uppfattningar om undervisning och lärande i matematik och uppfattningar om matematik som ämne däremot som en enhet går det inte att påvisa ett samband till användningen av matematikböcker. / Swedish teachers tend to use mathematics textbooks in their teaching to a large extent. How teachers’ beliefs impact their teaching is however, debated. Therefore, this study investigated the relationship between teachers’ use of mathematics textbooks and their beliefs about mathematics, mathematics teaching and learning mathematics. Eight 1-3 grade teachers completed a questionnaire measuring their use of mathematics textbooks and their beliefs, three of these were interviewed. The results indicate that the teachers can agree with both a dynamic and a static view of the nature of mathematics, and both a constructivist and traditional view of mathematics learning and teaching. The results also show that the teacher that uses the least amount of tasks from mathematics textbooks is the teacher that to the largest extent holds a constructivist view, while the teacher that uses the most amount of tasks from mathematics textbooks is the teacher that to the largest extent holds a dynamic and problem solving view. The teacher that’s in between the other teachers when it comes to where the tasks are taken from is the teacher that to the largest extent holds a static, platonist and instrumentalist view. However, if beliefs about mathematics, mathematics teaching and learning mathematics are seen as a unit there is no correlation between the use of mathematics textbooks and beliefs.