Abstract: Stumbles, Robert The foundation of geometric knowledge and understanding starts in primary school, and in contemporary mathematics education there is an emphasis on identifying learning progressions and trajectories as a way of moving students forward. The van Hiele (1986) theory is well-documented and provides insights into the progression and differences of individuals' geometric thinking. Van Hiele's theory significantly influences geometry curricula worldwide and contains teaching phases that can help all teachers understand developmentally appropriate ways to facilitate their students' geometric thinking. This article considers previous work by presenting dynamic geometry software (DGS) as a tool for a teaching sequence that is embedded within the van Hiele Teaching Phases and links theory and practice within a primary mathematics classroom
Abstract: Hurst, Chris Evidence suggests that some students have learned procedures with little or no underpinning understanding while others have a much more connected and conceptual levels of understanding. An analogy is drawn with Charles Dickens' character, Mr Thomas Gradgrind, who would have endorsed procedural teaching and abhorred teaching that encouraged understanding
Abstract: West, John The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The openended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning
Abstract: Livy, Sharyn; Muir, Tracey; Sullivan, Peter Challenging mathematical tasks can be designed to allow students of all abilities to experience productive struggle. It is important for teachers to communicate with students that productive struggle is important and it is what mathematicians do.
Abstract: Seah, Rebecca Geometry, from Greek meaning 'earth measure', is a formal study of the properties of shape and objects and their relative position in space. Geometric knowledge is the key to succeeding in science, technology, engineering, and mathematics disciplines (Wai, Lubinski, & Benbow, 2009). It is also needed when pursuing leisure activities such as designing a garden, engaging in craft work, comprehending maps, and making decisions involving measurement situations. An important benefit of learning geometry is the ability to support visualisation, spatial reasoning, critical thinking and deductive reasoning (Jones, 2002). In a world that is bombarded by images, being able to reason spatially and critically is essential to navigate the space we live in and engage in civic affairs. As reflected in The Australian Curriculum: Mathematics (Australian Curriculum Assessment and Reporting Authority (ACARA), n.d), numeracy is no longer confined to having number sense but includes data, spatial and measurement sense. This article explores some of the key ideas involved in learning about two dimensional shapes and discusses how materials can be used to support learning.
Abstract: Hilton, Annette; Hilton, Geoff Proportional reasoning involves relative thinking: the ability to think about multiple quantities simultaneously, and in relative terms as opposed to absolute terms (Ontario Ministry of Education, 2012). Concepts related to relative and absolute thinking and the ability to think relatively and multiplicatively are essential to understanding proportionality (Hilton, Hilton, Dole, & Goos, 2015). It takes time for students to develop proportional reasoning and without targeted teaching, many students fail to develop the important skills and conceptual understanding that underpins it (Bangert- Drowns, Hurley, & Wilkinson, 2004; Kastberg, D'Ambrosio, & Lynch-Davis, 2012; Lamon, 2012). Proportional reasoning is essential for students to succeed in many mathematical areas, including ratio and proportion, measurement and unit conversions, geometry, and probability. It is also necessary in other subjects, such as geography and science (Akatugba & Wallace, 2009). In fact, scale and proportion have been identified as crosscutting concepts fundamental to understanding and reasoning in science (National Research Council, 2012).
Abstract: Attard, Catherine A case study from a Year 6 classroom involved in an action research project based around MoneySmart and the Framework for Engagement with Mathematics is described. The process for developing a new unit of work in financial literacy is explained
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