Mathematical tasks in tests are central to students’ learning.Research shows that there is a significant gap between mathematical tasks in national tests and teacher-made tests.In this pilot study we examineeighteenSwedish and Chinese teachers’ viewsonwhat constitutes of a good mathematicaltesttaskat thelowersecondary school level. E-Mail Interviewing is conducted by presenting sevenmathematical tasks from national tests inSweden and China, respectively. The preliminary results show that Swedish and Chinese teachers hold some common viewsonthecharacteristics of good mathematical test tasks, but they also show different viewson the cognitively demanding tasks. Implications of the results and the methodology informed by the pilot study are discussed.

The aim of the presented case study is to investigate how coherent analytical instruments may guide the a priori and a posteriori analyses of a didactical situation. In the a priori analysis we draw on the notion of affordances, as artefact-mediated opportunities for action, to construct hypothetical trajectories of goal-oriented actions that have not yet been initiated by an actor. These hypothetical action trajectories guide the design of a didactical situation, involving trigonometry in triangles and on the unit circle, for the specific purpose of illuminating how students in Swedish upper secondary school handle conceptually challenging tasks without making use of calculators. The a posteriori analysis puts corresponding focus on the actions that students have actually engaged in with respect to the available artefacts. We conclude that affordances, when embedded in the presented methodological framework, may be considered as a scientifically valid instrument for designing and evaluating didactical situations in mathematics.

In this paper, we report on an on-going study of novice university students in mathematics and the secondary-tertiary transition. A total of 146 novice mathematics students from three Swedish universities were given a questionnaire in the beginning of the semester. The aim was to characterize them as learners of mathematics. The results were summarized with descriptive statistics and Principal Component Analysis (PCA) was used to look for correlations. The results show that the teacher and the textbook play a crucial role in their learning of mathematics. Further more, the students can be characterized as either individual or interactive learners, which relates to students’ grades.

This paper reports on a study about the secondary-tertiary transition in mathematics from a student perspective. Using an empirically grounded definition of the transition as a point of departure, Schoenfeld’s methodological scheme for empirical research was employed and data were analysed with methods inspired by grounded theory. Three relationally defined categories describing students’ learning were generated; mathematical learning objects, mathematical resources and students’ actions as learners. The transition can be understood and described in terms of inter-relational changes between these categories. 

The aim of this paper is to examine the relationship between mathematical knowledge for teaching (MKT) and teachers’ actions when teaching mathematics, based on a qualitative case study of a novice mathematics teacher. The empirical data consist of interviews and an observed mathematics lesson during his first year of teaching mathematics. These data have been analysed by coordinating theories on teachers’ goal-oriented actions, action levels and MKT. The results show that at a classroom level, the lesson provides opportunities for using the whole spectrum of MKT. However, in the different situations the teacher mainly draws on common content knowledge (CCK) and aims at maintaining control over the situation.

In this paper, I present a theoretical model of students’ mathematical learning in a specific setting with regard to their previous experiences. Learning difficulties and special needs in mathematics is a complex issue. To reduce the complexity, researchers and educators tend to pre-define the character of the issue. I suggest another approach, which takes students’ perspective as a starting point. By focusing students as active learners, we can observe their mathematical learning objects and mathematical resources to identify learning difficulties and needs. This can serve as a starting point for pedagogical development and for further research.