Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules for endorsement and rejection of mathematical statements. In this study, we investigate newcomers' learning of these rules when being taught them explicitly. Our data come from academically motivated…

Engaging students in mathematical justification is extremely important from a learning-focused and a disciplinary perspective. Prior research has commonly found that middle grades students struggle to produce viable justifications, arguments, and proofs, yet these studies often consider students' justification in only one modality (oral or…

Teachers are continually in search of tasks that balance the dual priorities of rigorous thinking and fluency development. These often-competing priorities are emphasized by national-level organizations as well as by state-level standards and assessments. The National Council of Teachers of Mathematics (NCTM) calls for school mathematics…

The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at building the pattern of a structure sense as a profile of the structure sense in group property. Using a qualitative study, the structure sense of group property was explored through lecturing activity of…

Students who engage in mathematical arguments in classrooms take part in an important practice involving reasoning and justification. As a mathematical practice, argumentation involves using both conceptual and procedural reasoning to justify a claim. Even though argumentation can occur in discussions where one asserts and defends their claim…

Writing in mathematics can improve procedural knowledge and communication skills and may also help students better understand and then remember problems. The majority of mathematics teachers know that they ought to include some writing assignments in their instructional plans, but the challenge of covering the curriculum and the time required to…