It is almost taken for granted that school mathematics would benefit from having more mathematically trained teachers in schools. However, when making this assertion important research has been missed out. For instance, research on teachers’ implicit and scientific theories of intelligence suggest that such theories strongly influence curriculum development and teaching design and evaluation, approaches to assessment and, subsequently, also pupil learning, that some theories have negative effects and some positive, and that trained maths teachers seem to adopt negatively correlating theories (Jonsson et al, 2008a, b). Implicit theories are also called naïve or lay theories. They can be of one of two forms, with some space for eventual hybridised positions. They can be entity theories, where intelligence is explained as a fixed, unchangeable entity that is not under the subject’s control, or incremental theories, where intelligence is seen as malleable, changeable and subject to interaction effects (Jonsson et al, 2008a, b). It matters which of these theories future teachers conform to as an entity theory of intelligence promotes learning less effectively than an incremental theory does. In the present paper these issues are considered in relation to previous research and ethnographic data from investigations in Swedish secondary and upper-secondary schools Beach, 1999, 2003). The paper uses quantitative data to examine relationships between the theories of learning and intelligence teachers have, their education background and training and their understandings about pupil performance and what can change performance levels and lead to learning improvement. These investigations have been done amongst qualified, practicing teachers and student-teachers in initial teacher education. Comparisons have been made between individuals who are specialised in, or are specialising in, mathematics on the one hand and social sciences on the other. In addition ethnographic data is presented on how teachers have expressed themselves about pupil intelligence, capacity and performance and engaged in everyday interaction to open up different subject possibilities for learners, that influence how they learn, what they learn and how they understand themselves as learners. The data from the two parts of the research have led to the following question being posed: Do we really need more maths trained teachers in our elementary schools? This question is posed because of the way entity theories of intelligence seem to correlate with mathematic subject identities and how mathematics teachers have engaged in teaching and evaluation in ways that often influence pupil learning negatively.

Relationships between implicit theories of intelligence have been found between 1) what feedback praise (person, process or product) a teachers, 2) how credible they believe different scientific theories of intelligence to be (specifically the Cattell-Horn-Carrol Theory, Sternberg’sTriarchic Theory of Intelligence, Gardner’s Theory of Multiple Intelligences and the Socio-Cultural Theory of Thinking that has developed from Vygotsky), 3) whether they see competition as beneficial for learning. The present paper has drawn upon data of both quantitative and qualitative character in order to analyse these relationships and their possible effects on student learning further. Ethnographic participation in education maths and other teaching and learning contexts in six educational settings (3 secondary and 3 upper-secondary) has also been involved. This research has been longitudinal, from 1998 onwards. Most of the data for the present analyses come from the later part of this period, from two Swedish Research Council projects.

The results show that a naïve theory of intelligence as an entity is very prevalent amongst teachers of math and that exposure to maths teaching/learning in schools and higher education (and clearly in teacher education) generally raises beliefs in an entity theory of intelligence, which is also, according to previous research, negative for learning outcomes for the majority of pupils and perhaps particularly those from the lower-socio economic class/classes.