Page 152 - 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. 152
ianne Nolte
Kießwetter defines as useful in solving mathematical problems successfully.
With their complexity the problems are an interesting challenge for chil-
dren with high mathematical potential. To work on them the usual knowl-
edge of students of that age level (class level) is sufficient. Because they
are self-differentiated they are also an adequate challenge for students of
different level of potential. (Progressive) research problems we use as these
kinds of problems support the development of capabilities which are needed
in mathematical research processes. The problems are challenging due to
their complexity. They are of mathematical relevance and allow stimulation
of mathematical thinking processes, problem solving competence, heuristic
strategies. The problems are open in a way that allows further leading ques-
tions and to open a ‘field of problems.’ Progressive research problems (PRP)
offer ‘a good chance to get a feeling of what science is and how one does
“good research”’ (Berman, Goldberg, & Koichu, 2005, p. 221). We do not ex-
pect an 8 year old to do scientific research! Nevertheless, we expect the child
to make first steps on his or hers way to do research! Due to the possibility
of working on the problems on different levels they are suitable for fostering
mathematically talented students on primary grade level and on secondary
level.
Progressive research problems . . .
– open age-appropriate complex mathematical problem areas,
– are of mathematical relevance (stimulation of mathematical thinking
processes, problem solving competence, heuristic strategies),
– start with a restricted question based on examples,
– enable a structured and quick access to the problem area,
– allow quickly success on different steps and level (providing process
motivation),
– allow different ways of working on the problem and different depth of
mathematical thinking processes,
– allow further leading questions (problem posing) to extend the math-
ematical context.
How to Work on Progressive Research Problems (PRP)
Due to the speed of grasping new ideas we present the problems at a low
level of redundancy. Nevertheless at primary grade level we introduce the
problems using examples. It is important for the children to be led to the
mathematical core of the problem. Similar to standardizes tests they should
not puzzle about the meaning of our questions.
150
Kießwetter defines as useful in solving mathematical problems successfully.
With their complexity the problems are an interesting challenge for chil-
dren with high mathematical potential. To work on them the usual knowl-
edge of students of that age level (class level) is sufficient. Because they
are self-differentiated they are also an adequate challenge for students of
different level of potential. (Progressive) research problems we use as these
kinds of problems support the development of capabilities which are needed
in mathematical research processes. The problems are challenging due to
their complexity. They are of mathematical relevance and allow stimulation
of mathematical thinking processes, problem solving competence, heuristic
strategies. The problems are open in a way that allows further leading ques-
tions and to open a ‘field of problems.’ Progressive research problems (PRP)
offer ‘a good chance to get a feeling of what science is and how one does
“good research”’ (Berman, Goldberg, & Koichu, 2005, p. 221). We do not ex-
pect an 8 year old to do scientific research! Nevertheless, we expect the child
to make first steps on his or hers way to do research! Due to the possibility
of working on the problems on different levels they are suitable for fostering
mathematically talented students on primary grade level and on secondary
level.
Progressive research problems . . .
– open age-appropriate complex mathematical problem areas,
– are of mathematical relevance (stimulation of mathematical thinking
processes, problem solving competence, heuristic strategies),
– start with a restricted question based on examples,
– enable a structured and quick access to the problem area,
– allow quickly success on different steps and level (providing process
motivation),
– allow different ways of working on the problem and different depth of
mathematical thinking processes,
– allow further leading questions (problem posing) to extend the math-
ematical context.
How to Work on Progressive Research Problems (PRP)
Due to the speed of grasping new ideas we present the problems at a low
level of redundancy. Nevertheless at primary grade level we introduce the
problems using examples. It is important for the children to be led to the
mathematical core of the problem. Similar to standardizes tests they should
not puzzle about the meaning of our questions.
150
