In this article, examples are shown to demonstrate how open-ended mathematical activities can be used in the classroom. Open-ended activities give students opportunities to apply their understanding in unfamiliar contexts without the pressure of finding one perfect solution.

The authors define two mathematical cognitive verbs which are fundamental to the development of mathematical thinking and reasoning. They distinguish between 'describing' and 'explaining' in relation to doing mathematics, rather than using them interchangeably.

In this article, we consider how assessment might reinforce New Zealand curriculum goals of knowing and doing in science for active and informed participation in societies that rely on scientific knowledge to guide decision making. This focus constitutes an orientation towards "sustainable assessment". Sustainable assessment encompasses…

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…

Reflexivity refers to the capacity for individuals to understand the cultural system and manage their own position within it. Reflexivity is a key concept in the understanding of intercultural communication, particularly in recognising the ability for individuals to understand and adapt to new cultural contexts. However, the prevailing methods…

In this paper, we present a novel approach to defining, teaching, and assessing creativity by examining its origins and delineating the processes involved. The rationale for introducing this framework developed from studying existing thinking and questioning the current metrics for measuring creativity, which we posit are unfit for purpose. We…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

According to Lev S. Vygotsky (1896-1934), the highest levels of abstract thinking and self-regulation in preschool development are established in "pretend play using object substitutions." An extensive research literature supports Vygotsky's empirical model of the internalization of self-guiding speech (social speech > private speech…

This is a position paper in the field of Engineering Education, which is at the very beginning in Europe. It relates challenges in the new field to the emerging technology of (Computer) Theorem Proving (TP). Experience shows, that "teaching" abstract models, for instance the wave equation in mechanical engineering and in electrical…

It is commonly accepted in the academy that developing a critical thinking capacity and related capabilities will make students more effective thinkers and writers, and that these are desirable traits for graduates to have no matter what path they take after graduation. While most academics agree that critical thinking is an essential component of…

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…

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

This paper is an attempt to reconstruct how C.V. Raman, a peripheral scientist in the early 20th century colonial India, managed to develop a research programme in physical optics from his remote colonial location. His attempts at self-training and self-education eventually led him to the discovery of the Raman Effect and to the Nobel Prize in…

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…