Designing learning environments for developing understanding of geometry and space

By Chris Donlan. 2000

185 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b473d28f5295e68c246ecd98a2695c0b583310c3

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In Education

Citations in the corpus

Dynamic Geometry Environments as a Source of Rich Learning Contexts for the Complex Activity of Proving (2000, background): “The set of papers illustrate the variety of functions and roles of proof which have been made explicit in previous theoretical frameworks (Balacheff , 1987; de Villiers, 1998; Hanna and Jahnke, 1996).”
The fundamental cycle of concept construction underlying various theoretical frameworks (2005, background): “Subsequently, Pegg (1992) and Pegg and Davey (1998) revealed examples of at least two UMR cycles in the concrete symbolic mode, where the relational level response in one cycle evolves to a new unistructural level response in the next cycle within the same mode.”
Preservice Elementary Teachers' Conceptual and Procedural Knowledge of Mean, Median, and Mode (2006, background): “Several studies have pointed out that the entire SOLO taxonomy can be discussed entirely in terms of unistructural-multistructural-relational (UMR) cycles (Pegg & Davey, 1998; Watson, Collis, & Moritz, 1997; Watson & Moritz, 1999).”
Conceptual Limitations in Curricular Presentations of Area Measurement: One Nation’s Challenges (2016, background): “…may overgeneralize “length times width” as the meaning of area (Schifter & Szymaszek, 2003); produce area measures by additively combining lengths, widths, or heights (Lehrer et al., 1998; Zacharos, 2006); or simply answer questions about areas with numbers without units (Clements & Sarama, 2009).”
The Process of Probability Problem Solving: Use of External Visual Representations (2010, background): “These researchers have suggested that the tool is useful because it makes the geometric diagrams the central focus of the problem-solving process and allows students to explore the diagrams dynamically, altering points, lines, and arcs (Olive, 1998).”
The Teaching of Proof (2003, background): “Q uestion G 1 in both Year 8 and Year 9 (see Fig 1),is concerned with how farstudentsuse geom etricalreasoning to m ake decisionsin geom etry and how far they sim ply argue from the basis ofperception orwhat ‘it lookslike’(see Lehrer and Chazan,1998;Hareland Sowder,1998).”