Mathematics Education

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https://hdl.handle.net/10587/1241
Materials authored by Dr. Eva Knoll pertaining to Mathematics Education.

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Browsing Mathematics Education by Subject "Elementary education"

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    Experiencing research practice in pure mathematics in a teacher training context
    (International group for the Psychology of Mathematics Education, 2004) Knoll, Eva; Morgan, Simon; Ernest, Paul
    This paper presents the early results of an experiment involving a class of elementary student teachers within the context of their mathematics preparation. The motivation of the exercise centred on giving them an experience with mathematical research at their own level and ascertaining its impact on their attitudes and beliefs. The students spent the first month working on open-ended geometrical topics. In the second month, working alone or in groups of up to four, they chose one or more of these topics then worked on a problem of their own design. The students spent the class time developing their ideas using strategies such as generating examples and nonexamples, generalising, etc. Reference to books was not accepted as a research tool, but the instruction team monitored student progress and was available for questions.
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    Polyhedra, Learning by Building: Design and Use of a Math-Ed. Tool.
    (Bridges: Mathematical Connections in Art, Music, and Science, 2000) Knoll, Eva
    This is a preliminary report on design features of large, light-weight, modular equilateral triangles and classroom activities developed for using them. They facilitate the fast teaching of three dimensional geometry together with basic math skills, and create a lasting motivational impact on low achievers and their subsequent performance in math and science. In directed discovery activities, lasting from 20 to 90 minutes, large models of basic polyhedra are made, enabling their properties to be explored. Faces, edges and vertices can all be counted and tabulated, providing opportunities to see number patterns and inter-relationships, to plot graphs, to extract algebraic relationships and to look for proofs of those relationships. These building activities can be kept central, under the teacher’s control for large classes with limited time, or building can be split out into groups of children where co-operative problem solving skills are also developed. In interviews, children have stressed the effectiveness of learning by building the shapes themselves. In classroom activities, it is clear to see that these triangles make children excited. Learning by building gives a concrete, active, authentic and personal experience of mathematics to children and teachers enabling them to feel the full excitement of the subject.
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    Preliminary Field Explorations in K-6 Math-Ed: the Giant Triangles as Classroom Manipulatives
    (Bridges: Mathematical Connections in Art, Music, and Science, 2002) Knoll, Eva; Morgan, Simon
    The present paper reports on children’s investigations using the giant equilateral triangles from the Geraldine Project2. It took place at the De Zavala Elementary School as the initial stage of a project in mathematics education. The triangles are a part of a modular construction kit made using kite technology. Their size, sturdiness and light weight make them ideal for in-class activities with children of all ages and stages of development. The school is located in a low socio-economic hispanic neighbourhood consisting of blue-collar families living in apartments and rental houses as well as small businesses and industries. Most of the students at the school are recent immigrants from Mexico or Central America or first generation born to immigrant families. Their parents have little or no education and are forced to work on jobs that entail long hours, frequently into the evening or night. This situation makes it difficult for parents to provide their children with appropriate support as students. At this stage, the structure of the activities that make up lessons emerged from the response of the children as the activities were tried. This approach, despite its unplanned nature, allowed for the introduction of much mathematical content, and the attention of the children was relatively easy to catch and hold. The activities successfully combined the play aspect of the giant triangles with the mathematical concept explorations that the instructors overlayed. In some cases the children were allowed to build their own shapes, which were then examined with them. The outcome of these trial activities was then used as a basis for lesson planning in later stages of the pilot project.