The Learning and Teaching of Geometry in Secondary Schools: by Pat Herbst, Taro Fujita, Stefan Halverscheid, Michael Weiss PDF

By Pat Herbst, Taro Fujita, Stefan Halverscheid, Michael Weiss

IMPACT (Interweaving arithmetic Pedagogy and content material for educating) is a thrilling new sequence of texts for instructor schooling which goals to improve the training and instructing of arithmetic by way of integrating arithmetic content material with the wider learn and theoretical base of arithmetic education.

The studying and instructing of Geometry in Secondary Schools stories prior and current learn at the educating and studying of geometry in secondary colleges and proposes an procedure for layout learn on secondary geometry instruction.

Areas coated include:

  • teaching and studying secondary geometry via history;
  • the representations of geometric figures;
  • students’ cognition in geometry;
  •  teacher wisdom, perform and, beliefs;
  • teaching concepts, educational development, and school room interventions;
  • research designs and difficulties for secondary geometry.

Drawing on a group of foreign authors, this new textual content should be crucial interpreting for knowledgeable academics of arithmetic, graduate scholars, curriculum builders, researchers, and all these attracted to exploring scholars’ learn of geometry in secondary schools.

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Additional resources for The Learning and Teaching of Geometry in Secondary Schools: A Modeling Perspective

Example text

H. Moore suggested in an address to the American Mathematical Society in 1902, the potential of concrete material for geometry: “The drawing and the paper folding must lead on directly to systematic study of intuitional geometry” (Trafton & LeBlanc, 1971, p. 17). Dienes (1969) pled for sys­ tematic use of things—that is, physical objects—in the learning of mathematics. The examples for geometry in primary school range from the use of mirrors, to chal­ lenging partitions of the cube, to paper folding.

From a cognitive point of view, construction tasks combine tactile manipulation with processes of visualization and reasoning (Duval, 1998). Roberts (2014) described the history of tools and technology in mathematics education with special regards to geometry. We return to some of these themes below, in our discussion of dynamic geometry software (DGS). In addition to being recognized for the influence of his geometry research pro­ gram, Felix Klein is regarded as the founder of mathematics education as a field of study at German universities.

Special features: Most DGS systems include the ability for a user to create and save macros so as to be able to repeat constructions on different sets of prim­ itives; they also permit tracing points as their position continuously varies in dragging mode; these are features that do not exist in paper-and-pencil constructions (Sträßer, 2002). Thus in DGS, the diagram represented on screen at any given moment is only a single representative of an entire class of equivalent diagrams that can be con­ tinuously varied.

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