Page 153 - 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. 153
Fostering Mathematically Gifted Students with Complex Fields of Problems
Introduction into the problem
Essential information
Restrictive examples
First question
Further questions
Open problem-solving process
Generalisations
Following problems
Figure 1 Hourglass Model of Progressive Research Problems
All students get the same problem. A fitting level of work is not defined by
a teacher but rather by the way students work on the question. This avoids a
mismatch between the given task and the potential of a student. To work on
the problems need more time than students are used to. So, to support the
endurance we start with an easy question at the beginning. Thus, every child
gets access to the mathematical core of the problem and can be successful.
Especially because the problems are complex working on them needs more
time than the problems usually given in classroom. Thus, motivation at the
beginning is important and also motivation by a sense of success during the
problem solving process. This is an important aspect to support the devel-
opment of endurance and volition. After this guiding step students can con-
tinue working the way they like. Working on the problems, children use dif-
ferent level of strategies. Some of them see a kind of ramp while working on
the problem and with this enlarge the mathematical content to connected
problems. The students are supported by teachers using scaffolding and fad-
ing strategies (Mason, Burton, & Stacey, 2010). Here the main idea is to help as
much as necessary and as little as required. In plenary discussions different
ways of working on the problems, different answers and in general different
ideas are discussed.
Example: Starting part of the natural numbers (Nolte, 1999). The following
problem was presented to eight to ten-year-old children. Taking the first
starting parts of the natural numbers (every number is used exactly once)
it is possible to calculate either 1 or 0 by using the operations ‘addition’ and
151
Introduction into the problem
Essential information
Restrictive examples
First question
Further questions
Open problem-solving process
Generalisations
Following problems
Figure 1 Hourglass Model of Progressive Research Problems
All students get the same problem. A fitting level of work is not defined by
a teacher but rather by the way students work on the question. This avoids a
mismatch between the given task and the potential of a student. To work on
the problems need more time than students are used to. So, to support the
endurance we start with an easy question at the beginning. Thus, every child
gets access to the mathematical core of the problem and can be successful.
Especially because the problems are complex working on them needs more
time than the problems usually given in classroom. Thus, motivation at the
beginning is important and also motivation by a sense of success during the
problem solving process. This is an important aspect to support the devel-
opment of endurance and volition. After this guiding step students can con-
tinue working the way they like. Working on the problems, children use dif-
ferent level of strategies. Some of them see a kind of ramp while working on
the problem and with this enlarge the mathematical content to connected
problems. The students are supported by teachers using scaffolding and fad-
ing strategies (Mason, Burton, & Stacey, 2010). Here the main idea is to help as
much as necessary and as little as required. In plenary discussions different
ways of working on the problems, different answers and in general different
ideas are discussed.
Example: Starting part of the natural numbers (Nolte, 1999). The following
problem was presented to eight to ten-year-old children. Taking the first
starting parts of the natural numbers (every number is used exactly once)
it is possible to calculate either 1 or 0 by using the operations ‘addition’ and
151
