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The aim of the study was to explore pre-service primary school teachers' motivational beliefs about mathematics in the light of the expectancy-value theory. We wanted to find out to what extent the motivational beliefs of pre-service teachers are related to their previous experiences in mathematics and to their engagement in learning mathematics and mathematics anxiety. The participants were 237 pre-service primary school teachers in their first year of study. They completed a mathematics exam and a questionnaire on their motivational beliefs (self-efficacy and subjective value), previous experiences in mathematics (level of high school math program, mathematics competencies, epistemic beliefs and achievement goals during high school), engagement and mathematics anxiety. The results of hierarchical regression analyses show that previous experiences with mathematics are important predictors of self-efficacy and subjective value. Furthermore, motivational beliefs are significant predictors of the pre-service teachers' engagement in learning mathematics and mathematics anxiety, along with their previous experiences with mathematics. The results are in line with the expectancy- -value theory and indicate that it is important to foster the development of adaptive beliefs about mathematics during the initial education of pre-service teachers.

Different kinds of resources, material and non-material, are used and developed with the aim of being part of an effective mathematics education. As a non-material resource, time seems to be of great importance to teachers and students. The aim of the present study is to focus on teachers’ views about time as a resource and its interactions with other resources in mathematics education. For this purpose, a large-scale examination of teachers’ opinions was undertaken, combining qualitative and quantitative methods, and involving teachers from different school levels. The results show that teachers highly value time as a resource, although with clear differences among primary, middle, and higher grade teachers. The participants of all levels complained to a great extent about not having as much time as they need for geometry topics, problem solving, and teamwork. On the other hand, the results show that textbooks and technology as material resources save teachers and students time, making lesson preparation and enactment more efficient, particularly in lower grades. The insight gained into teachers’ views about time, together with the literature review, indicate the importance of non-material resources within the discussion of resources.

Abstract. We use combinatorial description of bases of FeiginStoyanovsky's type subspaces of standard modules of level 1 for affine Lie algebras of types A to obtain character formulas. These descriptions naturally lead to systems of recurrence relations for which we also find solutions.