An understanding of the equal sign is a fundamental concept for early algebra. While literature claimed that Chinese students commonly master the relational understanding of the equal sign in the elementary school, these claims are under-researched. This study used the Mathematics Equivalence Assessment with 237 Chinese Grade 5 students. The…

Fostering students' bidirectional conception of the equal sign (viewing the equal sign as indicating an equivalence of two sides rather than a 'show result' symbol) is challenging, and students' misconception of the equal sign is persistent. Some studies mention that in China, the pedagogical approach to introducing the equal sign supports…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

Growing from the commognitive framework, this study is concerned with objectification -- a special way of talking about mathematical objects, which is key to one's concept formation. The study explores how objectification can be manifested in the discourse on square roots that unfolds in writing. The data comes from a class in a foundation…

The Merriam-Webster dictionary defines "transition" as: (a) the passage from one state, stage, subject, or place to another: change; or (b) a movement, development, or evolution from one form, stage, or style to another. The word transition can refer to an active shift of the person in space and time or status, for example; it can also…

School and university mathematics: Do they speak the same language? Our university mathematics students come from amongst the successful school mathematics students, but what difficulties with symbols do their lecturers and tutors observe? In this paper, we report on data from interviews with 21 first-year lecturers and tutors from four…

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

Students develop understanding of mathematics when they translate between and within different mathematical representations. This paper explores a student-generated story and content descriptors from the Australian Curriculum: Mathematics to highlight how primary school students can represent mathematical concepts through exploring the links…

Despite an emphasis on manipulative algebraic techniques in secondary school algebra, many tertiary mathematics students have mastered these skills without conceptual understanding. A significant number of students with high tertiary entrance ranks enrolled in first semester university mathematics were found to have misconceptions relating to…

Changes to students' understanding of mathematical notation may be brought about by using technology within mathematics. Taking equality as a case study, the paper provides brief epistemological, historical, didactical, and computational reviews of its symbolic representation in pen-and-paper and technology-assisted mathematics, most especially in…