Page 151 - Kukanja Gabrijelčič, Mojca, and Maruška Seničar Željeznov, eds. 2018. Teaching Gifted and Talented Children in A New Educational Era. Koper: University of Primorska Press.
P. 151
Fostering Mathematically Gifted Students with Complex Fields of Problems
For constructing mathematical learning environments these aspects sho-
uld be complemented by components of mathematical thinking processes.
Kießwetter (1985) lists so called patterns of action which are advantageous in
problem solving processes (Kießwetter, 1985, 2006; Nolte, 1999):
– Organizing material in order to recognize (eventually different) pat-
terns;
– Developing and testing of hypotheses;
– Reduction of complexity through meta-symbolization (building super
signs (chunking)) recursion;
– Intuitive use of strategies already indicated or further heuristic strate-
gies;
– Finding connected problems.
There are similarities with the characteristics of giftedness described by
Krutetskii (1976) who lists as traits of mathematical giftedness e.g. the han-
dling of complex information, the capability of generalization, skipping of
steps in a solving process, the capability of reversion of thinking processes
(p. 107f ). His findings were confirmed for primary grade students (e.g. Aß-
mus, 2007; Aßmus & Förster, 2012; Käpnick, 1998). Although many authors
(e.g. Gavin et al., 2007) use Krutetskii’s idea of a ‘mathematical cast of mind’
as a trait of mathematical giftedness it should be taken into account that
the way teachers work on problems during the lessons shape the idea es-
pecially young students get of what is meant with mathematics. Therefore,
eventually students who orientate their behaviour on what they think is ex-
pected by the teacher, do not show the observed mathematical capabilities
(Nolte, 2018). ‘Early social and educational experiences may lead young girls
and boys to construct different beliefs about the system of mathematics and
their place in that system’ (Buchanan, 1987, p. 400).
Taken together, problems which are suitable to develop mathematical
competences should be complex and offer the possibility of generalization
and of further leading questions.
Progressive Research Problems
Based on these considerations we developed so called progressive research
problems (PRP), initially for students of our fostering program (PriMa). Fur-
thermore, we made investigations with students who were not identified as
mathematically gifted (Nolte & Pamperien, 2014, 2017). Progressive (research
problems) means that step by step students acquire patterns of action, which
149
For constructing mathematical learning environments these aspects sho-
uld be complemented by components of mathematical thinking processes.
Kießwetter (1985) lists so called patterns of action which are advantageous in
problem solving processes (Kießwetter, 1985, 2006; Nolte, 1999):
– Organizing material in order to recognize (eventually different) pat-
terns;
– Developing and testing of hypotheses;
– Reduction of complexity through meta-symbolization (building super
signs (chunking)) recursion;
– Intuitive use of strategies already indicated or further heuristic strate-
gies;
– Finding connected problems.
There are similarities with the characteristics of giftedness described by
Krutetskii (1976) who lists as traits of mathematical giftedness e.g. the han-
dling of complex information, the capability of generalization, skipping of
steps in a solving process, the capability of reversion of thinking processes
(p. 107f ). His findings were confirmed for primary grade students (e.g. Aß-
mus, 2007; Aßmus & Förster, 2012; Käpnick, 1998). Although many authors
(e.g. Gavin et al., 2007) use Krutetskii’s idea of a ‘mathematical cast of mind’
as a trait of mathematical giftedness it should be taken into account that
the way teachers work on problems during the lessons shape the idea es-
pecially young students get of what is meant with mathematics. Therefore,
eventually students who orientate their behaviour on what they think is ex-
pected by the teacher, do not show the observed mathematical capabilities
(Nolte, 2018). ‘Early social and educational experiences may lead young girls
and boys to construct different beliefs about the system of mathematics and
their place in that system’ (Buchanan, 1987, p. 400).
Taken together, problems which are suitable to develop mathematical
competences should be complex and offer the possibility of generalization
and of further leading questions.
Progressive Research Problems
Based on these considerations we developed so called progressive research
problems (PRP), initially for students of our fostering program (PriMa). Fur-
thermore, we made investigations with students who were not identified as
mathematically gifted (Nolte & Pamperien, 2014, 2017). Progressive (research
problems) means that step by step students acquire patterns of action, which
149
