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This study focuses on the undergraduate mathematics students' perceptions and applied techniques for the preparation for their final examination in Abstract Algebra. The results of this study suggest that the revision for the final examination involves, firstly, the review of the lecture notes, followed by the solution of the coursework together with the use of model solutions and the solution of the past papers. The order of the last two activities varies. An often-occurring revision technique involves, instead of a linear succession of the aforementioned activities, a 3-dimensional spiral approach towards revision, with the three activities interchanging until the students who apply it feel that they have achieved adequate object-level and metalevel learning.

This paper reports on the use of lesson study as a professional development tool. In particular the paper focuses on the way in which the teachers increased their understanding of how tasks, classroom activity and teacher actions scaffolded student learning of early algebraic reasoning of equivalence and the commutative principle. Teacher voice is used to illustrate how lesson study cycles caused the teachers to reflect and review their own understandings of early algebraic concepts and how their students considered the concepts.

In recent years there has been an increased emphasis on algebraic reasoning in primary school classrooms. This includes introducing students to the mathematical practices of making conjectures, justifying and generalising. Drawing on findings from a classroom-based study, this paper explores one teacher's journey in shifting her task design and enactment to develop a "conjecturing atmosphere" in the classroom. The findings affirm the important role of the teacher in introducing mathematical practices. Careful task design and enactment, teacher questioning, and noticing and responding to student reasoning were important elements in facilitating conjecturing, justifying and generalising.

Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic understanding of subgroup's definition, and the inaccurate application of the relevant metarules. For the purposes of this study there has been used the Commognitive Theoretical Framework.