This article examines the mathematics learning experiences in proportional reasoning I created for pre-service teachers in my teacher education course in Canada. The approach aimed to enable pre-service teachers to work on and with their prior mathematics understandings, make connections that were particular to what emerged during group work, and…

Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…

Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…

In our work in environmental education (EE) as part of formal schooling we partnered with local schools to explore the practice of embedding, or integrating EE within formal school curriculum using inquiry-based pedagogies. In this paper we report on and discuss our growing understanding of the practice of pedagogical documentation and the…

There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. "Reducing abstraction" is a theoretical framework that examines learners' behavior in terms of coping with abstraction level. This article extends the scope of applicability of this…

If British Columbia education policy wanted to promote growth in numeracy and mathematics, the curriculum would provide opportunities to use mathematical concepts in social situations and give students time to move from concrete to abstract thought. Instead, the curriculum emphasizes extensive mechanical understanding and algorithmic manipulation…

The generic skills studies in Canada have as their objectives the formulation of generic skills, the identification of their uses for certain occupational groups, and the preparation of specifications for instructional modules in an attempt to provide greater flexibility to workers, employers, and vocational training programs. Another objective of…