Mathematics Education
http://hdl.handle.net/10587/1241
Thu, 16 Nov 2017 07:57:32 GMT2017-11-16T07:57:32ZElementary Student Teachers Practising Mathematical Enquiry at their Level: Experience and Affect
http://hdl.handle.net/10587/1222
Elementary Student Teachers Practising Mathematical Enquiry at their Level: Experience and Affect
Knoll, Eva
From the time of publication of Polya’s “How to Solve It” (1954), many researchers and
policy makers in mathematics education have advocated an integration of more problem
solving activities into the mathematics classroom. In contemporary mathematics
education, this development is sometimes taken further, through programmes involving
students in mathematics research projects. The activities promoted by some of these
programmes differ from more traditional classroom activities, particularly with regards
to the pedagogic aim. Several of the programmes which can claim to belong to this trend are designed to
promote a less static view of the discipline of mathematics, and to encourage a stronger
engagement in the community of practice that creates it. The question remains,
however, about what such an experience can bring the students who engage in it,
particularly given the de-emphasis on the acquisition of notional knowledge. In the
study described in this thesis, I investigate possible experiential and affective outcomes
of such a programme in the context of a mathematics course targeted at elementary
student teachers.
The study is composed of three main parts. Firstly, the theoretical foundations of the
teaching approach are laid down, with the expressed purpose of creating a module that
would embody these foundations. The teaching approach is applied in an elementary
teacher education context and the experience of the participating students, as well as its
affective outcomes, are examined both from the point of view of authenticity with
respect to the exemplar experience, and for the expected–and unexpected–affective
outcomes. Both of these examinations are based on the establishment of a theoretical
framework which emerges from an investigation of mathematicians’ experience of their
research work, as well as the literature on affective issues in mathematics education.
Thu, 28 Feb 2013 00:00:00 GMThttp://hdl.handle.net/10587/12222013-02-28T00:00:00ZPolyhedra, Learning by Building: Design and Use of a Math-Ed. Tool.
http://hdl.handle.net/10587/1218
Polyhedra, Learning by Building: Design and Use of a Math-Ed. Tool.
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.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10587/12182000-01-01T00:00:00ZExperiencing research practice in pure mathematics in a teacher training context
http://hdl.handle.net/10587/1217
Experiencing research practice in pure mathematics in a teacher training context
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.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10587/12172004-01-01T00:00:00ZDiscussing the challenge of categorizising mathematical knowledge in mathematics research situations
http://hdl.handle.net/10587/1216
Discussing the challenge of categorizising mathematical knowledge in mathematics research situations
Knoll, Eva; Ouvrier-Buffet, Cécile
Starting with a quotation describing mathematical research, this paper presents ways
of providing students with comparable experiences in mathematical research, in the
classroom. The paper focuses on the benefits and implications for the students of
such experiences. “Real mathematics research-situations” are defined, and the
didactical goals of these situations, as they are experienced are elaborated on. These
elements are presented through examples, looking at similar situations (research situations)
in two contexts and using different theoretical frameworks.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10587/12162005-01-01T00:00:00Z