## Knowledge and Knowing in Mathematics and Pedagogy: A Case Study of Mathematics Student Teachers’ Epistemological Beliefs

Source: *Teachers and Teaching: theory and practice, Vol. 21, No. 5*, 527–542, 2015.

(Reviewed by the Portal Team)

The current study examines the challenges that students experience in the consolidation of knowledge in mathematics and education.

**Methods**

The participants were three mathematics student teachers in a Finnish mathematics subject teacher programme.

The authors chose field-specific problem-solving tasks, interviews and video-stimulated recall as methods.

The findings reveal that the epistemological beliefs of the three students differed between the two disciplines.

The authors argue that all the students tended to regard mathematical knowledge as certain and coherent in nature. For instance, the authors found that the students usually relied on a memorised algorithm or formula in the mathematical tasks. In education, however, they relied more on personal opinions and experiences as sources and justifications of knowledge.

The authors also identify six main areas that can challenge the consolidation of mathematical and pedagogical knowledge. Three of these areas are related to the students’ mathematical thinking: (1) the students held formalistic beliefs about mathematics. they relied on memorised formulas for mathematical problem-solving; (2) the students were performance-orientated in their problem-solving; and (3) they relied on authority as a source and justification for knowledge.

The obstacles to the students’ pedagogical thinking were threefold as well: (1) the students mostly held the belief that pedagogical knowledge is relative in nature; (2) the students’ knowledge of methods of inquiry and theoretical concepts was rather weak; and (3) the students were unable to relate theoretical pedagogical knowledge to practice.

The obstacles identified appear to clash with the aims of developing pedagogical thinking in the curriculum, i.e. developing reflection skills, mastering theoretical knowledge, possessing the ability to connect theory and practice, and developing the ability to evaluate research-based knowledge in educational sciences.

The authors conclude that the epistemological beliefs that emerged in the study are problematic from the perspective of mathematics didactics. The authors argue that pedagogical knowledge is essential in order for the mathematics teacher to solve the empirical ‘problem’ of how to teach mathematics. As part of their teacher education, students conduct a small-scale investigation. In engaging in this activity, students are taking responsibility for the construction of knowledge and evaluating that knowledge which should help them to understand to grasp how pedagogical knowledge is created and justified. A stronger focus on the exploration of educational research methods in teacher education could be helpful.