TITLE: Problem Solving---A Part of Everyday Thinking
AUTHOR: Octaviano Garcia, Cuba Elementary School,
Cuba, NM
GRADE LEVEL/SUBJECT: (4-12)
OVERVIEW: Many students view problem solving, its process,
and necessary skills as that task assigned by the teacher on
Monday between the hours of 9:15 and 10:15 A.M. and to be
completed with this set time or suffer the consequences---
gradewise. They have not gotten into the habit of critically
reviewing every recommendation and decision they make before
executing on it. Therefore, the act of critically thinking
through every significant idea that comes to mind is viewed
as playing a very minor role in their daily lives.
PURPOSE: The purpose of this activity, used as an
introduction to a course at the very beginning of the year
or an introduction to any unit of study, is to help students
master the process of applying critical thinking to each and
every problem/task that confronts them in their daily
undertakings. Further, this activity can serve as a base
reference and model for every problem/task assigned or any
problem that a student or students might bring up.
OBJECTIVE(s): As a result of this activity, each student
will:
1. Demonstrate her/his knowledge of the six basic steps to
problem solving by listing them or reciting them
orally.
2. Demonstrate his/her mastery of the six basic steps to
problem solving by actively applying them in problem
solving when the task lends itself to such a process.
3. Demonstrate her/his ability to apply these six basic
steps to problem solving by guiding other students in
the solution of a given problem or set of problems.
This activity works well as an introduction to a course, its
objectives, requirements, and expectations. The activity can
also serve to achieve the following secondary learning
objectives given that the necessary follow through is
provided during the course of the school year.
1. Demonstrate a high awareness of the need for the
application of critical thinking skills to everyday
problem solving.
2. Demonstrate an observable and measurable
improvement in his/her problem solving skills by way of
constantly and consistently applying this modeled
process.
3. Show his/her understanding and mastery of the
problem solving process by way of written or oral
explanation of the critical steps in problem solving
learned through this mode.
4. Show a marked improvement in the quality and
completeness of his/her written and oral responses to
other assigned, as well as, routine personal problems.
RESOURCES/MATERIALS: None are required if solution to the
problem is assigned individuals other than pencil and paper.
Large writing chart paper may be used for group work if
assigned to small groups. Overhead transparencies may be use
for easy viewing if the teacher works the solution through
with the total class.
ACTIVITIES AND PROCEDURES: Set the stage by explaining the
purpose of this story problem to the student. Orient
students as to the expectations. Review with the students
the basic strengths of a "good" problem solver. Emphasize a
student's ability to think critically; to identify, group,
and classify information in an order and form that makes it
relevant and applicable to a given solution. Alert them to
the fact that ones ability to solve daily problems,
simulated or real, depends on ones ability to separate
useful from useless information; separate necessary from
unnecessary information and then apply the pertinent
information to the problem/task at hand. Remind them that
their success in the course or unit of study heavily depends
on their attention and critical thinking skills/habits.
Tune-in; tune-out habits that will result in low quality
solutions to assigned tasks while critical listening,
critical thinking, and assertive problem solving processes
will result in high quality solutions to any problem they
solve. Tell them that the story problem you are about to
share with them contains many fabricated distractors
together with the pertinent and necessary information that
they will need for solving the problem that the story posts
for them as listeners.
The Story: The Shepherd and the Harvard Boys
A few years ago, not counting those that came later, two
Harvard sophomore students decided that they would spend
their summer break traveling across the United States of
North America, the same country that they had studied for
years in books. In preparation for this long journey they
were careful to pack the necessary credit cards, which their
generous parents provided for them, maps, some light casual
traveling clothes, and the friendliest Harvard smile they
could muster. Their mode of travel was to be by way of an
old 1961 Chevy panel truck that one of the boys had gotten,
as a gift, from an uncle upon graduating from high school.
The vehicle had made many trips between New Port,
Connecticut, their home town, and the Harvard campus in
Cambridge, Mass., therefore, the two agreed that the panel
truck would make it to the west coast and back. All due
caution was taken in preparing the vehicle for the trip
also. Once all of these preparations were in place their
journey was underway.
Traveling through the mid-west and southwestern states did
provide much in the way of entertainment or challenge to
their superior Harvard trained mind. The real fun began when
they reached the far west coast in California. They spent
four weeks in Hollywood, two weeks in the San Diego Zoo, a
few days in San Fransisco, and many days in Disney Land. All
too soon, it appeared, their summer had come to an end and
it was time for them to start back to more familiar
territory. So after picking up some supplies for the trip in
Sacramento they headed east on Interstate 80. On the second
day the panel truck made only 150 miles during a ten hour
day. Repairs had taken up most of that day. On the third day
the two decided to abandon the vehicle and hitch a ride home
after having to stop six times for repairs within a sixty
mile stretch of I-80.
The hour was marching on to four o'clock in the afternoon
when they had bade their panel truck goodbye. Both boys were
silent for the first hour of walking but each was thinking
of the night ahead and having to round up a meal or go
without. The more timid of the two was re-experiencing fears
that he thought he had left behind at the age of twelve when
he was in seventh grade. He began envisioning attacks by
wild lions, tigers, panthers, and the like. When he spoke up
his first question to his partner was, "Where are we going
to sleep tonight and what are we going to eat?" "Fear not
my good friend," responded his partner, "I shall teach you
how the pioneers of the frontier survived in these desolate
plains long before there was even a highway through here.
Just keep your eyes alert for sheep and when you spot some
and hopefully their shepherd let me do the talking. For I
fear that in your condition you might jeopardize our chances
for an evening meal and perhaps even a bed to sleep in."
Our timid friend did not speak up but he did not much fancy
chasing and wrestling a sheep down for their dinner not to
mention having to butcher and prepare it over an open fire.
He was deep in his thoughts when his traveling companion's
shout of glee brought him back to reality. "There, there,
by those trees on that other slope!" he shouted as he
pointed with excitement at some white spots that, in Mr.
Timid's eyes looked like rocks. "Those are nothing but
rocks," he retorted with the air of certainty that he often
used on the Harvard campus. Nonetheless, he was very happy
to accept his error when they approached the white spots and
they turned out to be sheep as his companion had predicted
from the opposite side of the valley.
No sooner had they arrived at the herd's northern most edge
when out of a scrub oak thicket came two Australian Shepherd
dogs. Both stopped and assayed the valley for the
whereabouts of the shepherd and sure enough, from under the
tallest pine tree there emerged what looked like a person.
As they got closer they could recognize him as the lone
shepherd of this large herd. The man looked as if he had
needed a shave, a haircut, and probably a bath for several
weeks but they left all that aside and decided that here was
a good opportunity for them to cash in on that evening meal
they so badly needed and perhaps even a place to spend the
night if they applied their best manners and savvy.
Mr. Timid's partner took a quick glance over the entire herd
and in his mind made the best estimate of the number of
sheep in the herd that his bright mind could compute in the
time he had and when they were a dozen or so yards from the
shepherd he greeted him. "A very good afternoon to you Mr.
Shepherd of two thousand sheep," he offered, not knowing the
man's name. "Your greetings are kindly accepted my
traveling friends but you error Mr. Bright Boy. I am not the
shepherd of two thousand sheep. If I had that many sheep out
there plus another herd as large as that then again half as
many as I have out there I should be the shepherd of two
thousand sheep."
Mr. Timid immediately set his mathematical mind to the
problem and by the time they had arrived at the shepherd's
tent, which was a few hundred yards away he had figured out
how many sheep the shepherd actually had in that herd.
Problem and Solution:
Question to students: How many sheep were in this
shepherd's herd?
1. Direct the students to apply the six basic steps to
problem solving in solving this problem. To do so,
students must list each step and next to it or
immediately following they must list the information
from this story that applies and is pertinent to that
particular step. Remind students that at the out set
you warned them that the point of the story was to see
how well they can separate useful information from
useless information given a particular task/problem to
solve.
2. You may wish to accept a solution that is arrived by
guess and test (trial and error) method or you may
direct the students to apply their algebra skills and
produce an algebraic formula/equation:
Example: 1X + 1/2X = 2,000 sheep.
3. You may wish to have students attempt the solution to
this problem on an individual basis or on a small group
basis. If you feel the group is very unfamiliar with
the six basic steps to problem solving you may want to
use this story problem to establish familiarity with
these steps and do a total group problem solving
exercise. This problem lends itself well to any of the
above approaches in arriving at a solution.
4. A reward may be offered to the person or group that
produces the most complete and well formulated solution
first. Extra points is a good reward for this problem
or physical objects may also be offered.
TYING IT ALL TOGETHER:
1. Review by having students re-state and review the
purpose (objectives) associated with this story
problem.
2. Be sure to review the best solution (problem solving
process) with the students before this story problem is
set aside for the day or the week.
3. Remind students that there will be constant reference
made to the components of this problem and especially
the process followed in solving it as other problems of
similar character come up during the course of the year
or unit, whichever applies.
4. Encourage students to share the results of this
activity with their parents or guardian person(s).
5. Use this story problem to introduce or review the
problem solving process with any lesson, unit or
course. Remember you can vary it by level. Example: the
number of sheep that Mr. Bright Boy, as the shepherd
calls him, may be 20; 200; 2,000; etc.
Click here to return to OFCN's Academy Curricular Exchange
Click here to return to OFCN's Academy
Click here to return to OFCN's Main Menu
John Kurilecjmk@ofcn.org