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The goal of this article is to introduce the revised Conceptual Understanding Weighting System (CUWS) Greene & Shorter (2012, Trans. Dial.), a tool for categorizing and weighting a mathematical task in order to identify the level of conceptual understanding being assessed by the task. In addition, there is discussion of how this weighting system relates to other frameworks that are currently used to classify mathematical tasks and student reasoning. Examples are provided to demonstrate how the revised CUWS can be used to calculate a conceptual understanding score for a particular exam, to create mathematical tasks that assess understanding at different levels and to analyse student understanding within those different levels. This in turn allows instructors to identify concepts with which students are struggling and quickly adapt classroom activities to improve students' understanding. The ability to use the CUWS to create mathematical tasks (not just categorize them) is one of the important goals of the CUWS and one that is not regularly emphasized when working with other frameworks to categorize mathematical tasks.

This study investigates the viewpoints of 20 preservice post-primary mathematics teachers taking a module of Group Theory in the final semester of their university teacher education programme. The purpose of the study was to investigate preservice mathematics teachers' perception of the value of studying a module in Group Theory and their perception of its relevance to the content they will teach at post primary school. The sample were surveyed again 12 months later, having taught at post primary level for almost a full academic year to see if their perspectives had changed. The findings are discussed in this paper. [ABSTRACT FROM AUTHOR]