Page 155 - 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. 155
Fostering Mathematically Gifted Students with Complex Fields of Problems
How do you get such an arithmetic problem for a given n?
In classroom students can work about a small given number. They can use
trial and error to find the results. Working like this they do many calculations
and train their calculation capabilities. At the same time they can recognize
patterns and structures like the sequence of results of succeeding numbers:
1, 1, 0, 0, 1, 1, 0, 0, . . . . A deeper insight lies in grouping four succeeding num-
bers like Simon did; and some of the students are able of generalize and
proof their hypotheses. This problem can be extended (Kießwetter, 2006).
One question lies in the effects of using e.g. odd or even numbers.
Teachers who use problems like this in a sensible way so that all students
are encouraged to express their ideas have the opportunity to recognize high
potential in students. While working on these kinds of problems students
unfold their competencies in problem solving processes.
Potentials of progressive research problems (PRP, see Nolte, 2012):
– Enable working together on a shared mathematical object and to learn
from each other (e.g. to learn and reflect different approaches),
– Support the learning of heuristics;
– Contribute to the development of problem solving competences and
the ability of reasoning (especially regarding the construction of hy-
potheses and proving);
– Stimulate first processes of theory building and generalization;
– Provokes (written) formulation of considerations and reasoning;
– help to ensure that especially children with special gifts are challenged;
– support the recognition of special interests and talents of children;
– enable the continuation of its application at various ages.
‘We define children as mathematically gifted when they are able to work
on complex problems. In this learning environment they recognize patterns
and structures. They are able to exploit these patterns and structures while
working the problem. They can work on a high level of abstraction. They con-
struct superordinate structures and gasp coherences. They are able to gener-
alize their findings. So when children show special patterns of action in chal-
lenging and complex fields of problems we suppose high mathematical tal-
ent’ (Nolte, 2012, p. 157).
References
Aßmus, D. (2007, March). Merkmale und Besonderheiten mathematisch po-
tentiell begabter Grundschüler: aktuelle Forschungsergebnisse [Charac-
teristics and peculiarities of mathematically potentially talented primary
school students: Current research results]. Paper presented at the 41.
153
How do you get such an arithmetic problem for a given n?
In classroom students can work about a small given number. They can use
trial and error to find the results. Working like this they do many calculations
and train their calculation capabilities. At the same time they can recognize
patterns and structures like the sequence of results of succeeding numbers:
1, 1, 0, 0, 1, 1, 0, 0, . . . . A deeper insight lies in grouping four succeeding num-
bers like Simon did; and some of the students are able of generalize and
proof their hypotheses. This problem can be extended (Kießwetter, 2006).
One question lies in the effects of using e.g. odd or even numbers.
Teachers who use problems like this in a sensible way so that all students
are encouraged to express their ideas have the opportunity to recognize high
potential in students. While working on these kinds of problems students
unfold their competencies in problem solving processes.
Potentials of progressive research problems (PRP, see Nolte, 2012):
– Enable working together on a shared mathematical object and to learn
from each other (e.g. to learn and reflect different approaches),
– Support the learning of heuristics;
– Contribute to the development of problem solving competences and
the ability of reasoning (especially regarding the construction of hy-
potheses and proving);
– Stimulate first processes of theory building and generalization;
– Provokes (written) formulation of considerations and reasoning;
– help to ensure that especially children with special gifts are challenged;
– support the recognition of special interests and talents of children;
– enable the continuation of its application at various ages.
‘We define children as mathematically gifted when they are able to work
on complex problems. In this learning environment they recognize patterns
and structures. They are able to exploit these patterns and structures while
working the problem. They can work on a high level of abstraction. They con-
struct superordinate structures and gasp coherences. They are able to gener-
alize their findings. So when children show special patterns of action in chal-
lenging and complex fields of problems we suppose high mathematical tal-
ent’ (Nolte, 2012, p. 157).
References
Aßmus, D. (2007, March). Merkmale und Besonderheiten mathematisch po-
tentiell begabter Grundschüler: aktuelle Forschungsergebnisse [Charac-
teristics and peculiarities of mathematically potentially talented primary
school students: Current research results]. Paper presented at the 41.
153
