Some
of the activities in this program involve recognizing and continuing a pattern
or numerical sequence. In some cases there may be more than one solution
to a problem. Teachers should be careful not to jump to conclusions about
a particular solution or technique. Students will often present innovative
solutions that involve very creative strategies and these approaches may
have merit.
|
Visualization
and imagery are extremely important components of a person's general problem
solving ability. Because these components are often neglected in the regular
curriculum, students often experience difficulty when faced with problem
solving situations which require that these skills be employed. Teachers
who strive to provide students with an opportunity to develop visual thinking
skills will see dramatic improvements in problem solving skills. The activities
in this program can serve as models for teacher-developed activities which
can provide further work in visualization, visual thinking and imagery.
|
Many of
the problems presented in this program are open for elaboration. For example
a field trip may provide students with an excellent opportunity to look
for geometric shapes and to find visual patterns in both the natural environment
and as a part of man-made creations. Architecture is often rich in visual
patterns. If students look closely at a building they will often find many
interesting patterns which can be studied and copied. Photographs from magazines
can provide a rich source of visual patterns. During the investigation students
should be encouraged to look for examples of symmetry, congruence and rotation.
Ample opportunity should be provided for students to create their own examples
of designs which are based on geometric relationships, since this type of
activity serves to increase a student's enjoyment of mathematics.
|
Logic
is often a difficult skill for students who have not had much practice.
Some problems can be very challenging and then suddenly will seem simple
once the secret is known. Teachers need to be careful to not make problem
solving too frustrating. By providing model solutions for those who need
it, teachers can help students develop a greater sense of confidence in
their ability. It is helpful for teachers to show students how to organize
the information given in a problem and how to formulate an approach to the
solution. Some logic problems involve specific principles and have a structure
which is similar to other problems. A problem that may seem so complex that
it is overwhelming can be simplified by breaking it down into smaller components.
By taking one step toward a solution at a time, students will come to the
realization that problem solving is often more perserverence than inspiration.
|
| Success
is an important ingredient to building a sense of confidence in each student's
problem solving ability. The repeated experience of success will encourage
students to attempt even more difficult challenges. The puzzles in Puzzle
Logic vary in difficulty and teachers should realize that no harm will result
from assigning puzzles that are too easy but if difficult puzzles are assigned
before students are ready frustration may result. Success can be fostered
by assigning students to work in small groups and thereby observe the problem
solving strategies employed by others. After working in groups, eventually
students will want to try to solve puzzles by themselves. When this occurs
teachers will be proud to know that they have contributed to the process
every individual must go through in order to become a proficient problem
solver and critical thinker. |