Problem solving in school mathematics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reston, Virginia
National council of teachers of mathematics
1980
|
| Series: | National Council of Teachers of Mathematics: Yearbook.
1980 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv, 241 Seiten Diagramme |
| ISBN: | 0873531620 |
Staff View
MARC
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| 245 | 1 | 0 | |a Problem solving in school mathematics |c Stephen Krulik ; 1980 Yearbook editor ; Temple University ; Robert E. Reys ; General yearbook editor ; University of Missouri |
| 246 | 1 | 3 | |a Problem solving in school mathematics |
| 264 | 1 | |a Reston, Virginia |b National council of teachers of mathematics |c 1980 | |
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| 490 | 1 | |a National Council of Teachers of Mathematics: Yearbook. |v 1980 | |
| 650 | 4 | |a Résolution de problème | |
| 650 | 4 | |a Problem solving | |
| 700 | 1 | |a Reys, Robert E. |0 (DE-588)1252405405 |4 aut | |
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Record in the Search Index
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| adam_text | Content*,
Foreword xi
Preface xiii
1. On Solving Mathematical Problems in High School 1
George Polya, Stanford University, Stanford, California
Polya emphasizes that much of students interest and motivation must stem
from mathematics itself—from certain intrinsic qualities inherent in mathe¬
matics and in the problem solving process. This essay indicates how a
teacher who has an appreciation of this point of view can teach mathe¬
matics in such a way that the student may experience the tension and en¬
joy the triumph of discovery.
2. Problem Solving as a Goal, Process, and Basic Skill 3
Nicholas A. Branca, San Diego State University, San Diego, California
Problem solving has many meanings. Three common interpretations of the
term problem solving are as a goal, as a process, and as a basic skill. Ex¬
amples of these different interpretations are given. Each interpretation is im¬
portant, and, taken both singularly and together, they have implications for
teaching mathematics.
3. Heuristics in the Classroom 9
Alan H. Schoenfeld, Hamilton College, Clinton, New York
Heuristics are general suggestions or strategies that better enable problem
solvers to approach problems, to understand them, and to solve them. This
essay describes a variety of heuristics and shows how they can be used in
problem solving. It also offers a sample discussion to show how the teacher
can lead a heuristic discussion in the classroom.
V
Vi CONTENTS
4. Posing Problems Properly 23
Thomas Butts, Case Western Reserve University, Cleveland, Ohio
Mathematics is problem solving. A primary source of motivation for solving
a problem is the manner in which that problem is posed. Different types of
mathematical problems are discussed, and many suggestions for improving
the art of posing problems are offered.
5. Untangling Clues from Research on Problem Solving 34
Marilyn N. Suydam, Ohio State University, Columbus, Ohio
The results of research on problems solving from the past decade are un¬
tangled, not merely to describe findings but also to call attention to direc¬
tions for classroom practice that may be indicated. Research about children
as problem solvers, about problems, and about problem solving strategies
are presented, with clues for teaching highlighted.
6. Opinions about Problem Solving in the Curriculum for the 1980s: • ,
A Report 51
Alan Osborne, Ohio State University, Columbus, Ohio
Margaret B. Kasten, Ohio State University, Columbus, Ohio ¦
Opinions of professional and lay samples about the curriculum for school
mathematics in the 1980s were surveyed by the NCTM PRISM Project. ;
Summary observations of the data about the preferred content and ap i
proaches to problem solving indicate support but little preference for ex¬
tremes in methodology or resources.
7. Pictorial Languages in Problem Solving 61
Joel Schneider, Comprehensive School Mathematics Program,
CEMREL, Saint Louis, Missouri
Kevin Saunders, Northern Michigan University, Marquette, Michigan
One approach to early teaching of problem solving is to provide a pictorial
language with which to record information. The availability of such a tool not
only encourages good habits but also allows individual freedom in ap¬
proaching problems. As students progress, pictorial languages may be an
effective support in the gradual introduction of symbolic languages. Two ex¬
amples of pictorial languages illustrate their application.
8. Polya Visits the Classroom 70
Linda J. DeGuire, University of Georgia, Athens, Georgia
Two classroom episodes are used to attempt to illustrate Polya s style of
teaching problem solving. The episodes are set in middle school class¬
rooms, one in fifth grade and one in eighth grade.
9. Improving Story Problem Solving in Elementary School Mathematics 80
Edward J. Davis, University of Georgia, Athens, Georgia
William D. McKillip, University of Georgia, Athens, Georgia
Story problems are important because they are a major vehicle through
which we teach applications. Difficulties with story problems have caused
teachers and students to have negative attitudes toward them. This essay
addresses ways to overcome such attitudes and to improve students per¬
formance.
CONTENTS Vii
10. Textbook Problems: Supplementing and Understanding Them 92
Jeffrey C. Barnett, Fort Hays State University, Hays, Kansas
Larry Sowder, Northern Illinois University, DeKalb, Illinois
Kenneth E. Vos, College of Saint Catherine, Saint Paul, Minnesota
What can a teacher do in teaching story problems? Seek interesting con¬
texts, let the learners make up the problems, present the stories in pictures
or with objects. And, pay particular attention to reading factors that are es¬
pecially important in mathematics—the precise technical vocabulary and
the slower, more attentive readings necessary—with emphasis on keys to
the mathematical structure of the problem.
11. Teaching Problem Solving in the Elementary School 104
John F. LeBlanc, Indiana University, Bloomington, Indiana
Linda Proudfit, Valparaiso University, Valparaiso, Indiana
tan J. Putt, Townsville College of Advanced Education, Queensland,
Australia
This essay presents an instruction technique for teaching problem solving
that is based on Polya s four stage model of problem solving. This tech¬
nique emphasizes the teacher s role, particularly during the first stage (un¬
derstanding) and the final stage (reflecting on the solution). Examples deal¬
ing with a standard textbook problem and a process problem depict the
suggested technique in classroom terms.
12. Problem Solving Using the Calculator 117
Joan Duea, Price Laboratory School, University of Northern Iowa,
Cedar Falls, Iowa
George Immerzeel, Price Laboratory School, University of Northern Iowa,
Cedar Falls, Iowa
Earl Ockenga, Price Laboratory School, University of Northern Iowa,
Cedar Falls, Iowa
John Tarr, Price Laboratory School, University of Northern Iowa,
Cedar Falls, Iowa
There are advantages in using calculators in problem solving: (1) instruction
can focus on problem solving processes; (2) guess and test using a calcu¬
lator code and using tables become more meaningful strategies; (3) real
world problems are appropriate in classrooms; and (4) students are more in¬
volved through experimentation and data collection. The need for materials
to implement calculators in classroom problem solving can be met by modi¬
fying textbook problems, developing decks of problem cards, and building
a problem file. All are discussed in this paper.
13. Making Problem Solving Come Alive in the Intermediate Grades 127
Marilyn H. Jacobson, Montgomery County Community Schools
Corporation, Bloomington, Indiana
Frank K. Lester, Jr., Indiana University, Bloomington, Indiana
Arthur Stengel, Indiana University, Bloomington, Indiana
A way to get intermediate grade students actively involved in solving proc¬
ess oriented problems is described in this essay. Discussions of several
process problems are included.
Viii CONTENTS
14. Problem solving Strategies in School Mathematics 136
Gary L. Musser, Oregon State University, Corvallis, Oregon
J. Michael Shaughnessy, Oregon State University, Corvallis, Oregon
Some common strategies (heuristics) and illustrative problems are pre¬
sented together with classroom practices that successful teachers have
used to integrate problem solving into their curriculum.
15. Think of a Related Problem 146
Edward A. Silver, San Diego State University, San Diego, California
J. Philip Smith, Southern Connecticut State College, New Haven,
Connecticut
As an example of the kind of effort that is necessary to teach problem solv¬
ing strategies effectively, the authors discuss the advice, Think of a related
problem which is similar to the one you are now facing. Recent research
results are discussed, as are actual examples of students problem solving
behavior. The emphasis is on formulating strategies and advice for the
classroom teacher.
16. Risking the Journey into Problem Solving 157
Peggy A. House, University of Minnesota, Minneapolis, Minnesota
Engaging in open ended problem solving is one way of giving pupils valu¬
able experience in the process of mathematics, but such problem solving is
not the mathematics that pupils and teachers find most familiar. This essay
offers some practical hints to help teachers become more spontaneous
problem solvers and leaders of problem solving. Each is illustrated with a
concrete example taken from the actual experiences of classroom teachers.
17. Problem Solving through Recreational Mathematics 169
Kevin Gallagher, Northern Michigan University, Marquette, Michigan
The use of strategy games and mathematical puzzles is recommended to
provide problem solving experiences for high school students. A strategy
game and a mathematical puzzle are described in detail, demonstrating
how their use generates problem solving behavior. The question of transfer
is also discussed. For teachers who are unfamiliar with strategy games, sev¬
eral games are suggested for classroom use, and references are provided
for further information.
18. The Theme of Symmetry in Problem Solving 178
Gerald A. Goldin, Northern Illinois University, DeKalb, Illinois
C. Edwin McClintock, Florida International University, Miami, Florida
The detection of hidden problem symmetry is frequently important to in¬
sightful problem solving. This essay examines problems having different
kinds of symmetry and discusses ways of detecting symmetry when it is
present in the structure of the problem.
19. Some Thoughts on Teaching for Problem Solving 195
Mary Grace Kantowski, University of Florida, Gainesville, Florida
This essay looks at problems, at what we teach, how we teach, and the role
of the teacher. It presents some characteristics of students at each level of
problem solving development.
CONTENTS IX
20. Measuring Problem solving Ability 204
John A. Malone, Western Australian Institute of Technology, Bentley,
Western Australia
Graham A. Douglas, University of Western Australia, Nedlands,
Western Australia
Barry V. Kissane, University of Western Australia, Nedlands,
Western Australia
Roland S. Mortlock, University of Western Australia, Nedlands,
Western Australia
The development of tests of problem solving ability that use a measurement
approach based on the work of Georg Rasch (1960) and that overcome
some of the traditional difficulties is discussed. A rationale for the use of the
Rasch model is presented; the model s characteristics are described along
with an outline of a procedure for the compilation of a problem pool and its
subsequent use in the construction of problem solving tests.
21. A New Approach to the Measurement of Problem solving Skills 216
Harold L. Schoen, University of Iowa, Iowa City, Iowa
Theresa Oehmke, University of Iowa, Iowa City, Iowa
The Iowa Problem Solving Project Test, a paper and pencil test that mea¬
sures a person s ability to understand a verbal problem, to carry out certain
problem solving strategies, and to vary conditions in a problem that has
been solved, is described. The test is designed for grades 5 8.
22. Problem Solving in Mathematics: An Annotated Bibliography 228
Sarah F. Mason, University of Georgia, Athens, Georgia
A sampling of materials on problem solving that are of primary interest to
teachers at all levels. The entries have been organized into six sections: (1)
Bibliographies; (2) General Works; (3) Suggestions for Teachers; (4) Puzzles
and Recreations; (5) Mathematical Discussions; and (6) Collections of Prob¬
lems.
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| physical | xiv, 241 Seiten Diagramme |
| publishDate | 1980 |
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| publisher | National council of teachers of mathematics |
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| series | National Council of Teachers of Mathematics: Yearbook. |
| series2 | National Council of Teachers of Mathematics: Yearbook. |
| spelling | Krulik, Stephen 1933- (DE-588)1084342901 aut Problem solving in school mathematics Stephen Krulik ; 1980 Yearbook editor ; Temple University ; Robert E. Reys ; General yearbook editor ; University of Missouri Problem solving in school mathematics Reston, Virginia National council of teachers of mathematics 1980 xiv, 241 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier National Council of Teachers of Mathematics: Yearbook. 1980 Résolution de problème Problem solving Reys, Robert E. (DE-588)1252405405 aut National Council of Teachers of Mathematics: Yearbook. 1980 (DE-604)BV002779092 1980 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004099610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krulik, Stephen 1933- Reys, Robert E. Problem solving in school mathematics National Council of Teachers of Mathematics: Yearbook. Résolution de problème Problem solving |
| title | Problem solving in school mathematics |
| title_alt | Problem solving in school mathematics |
| title_auth | Problem solving in school mathematics |
| title_exact_search | Problem solving in school mathematics |
| title_full | Problem solving in school mathematics Stephen Krulik ; 1980 Yearbook editor ; Temple University ; Robert E. Reys ; General yearbook editor ; University of Missouri |
| title_fullStr | Problem solving in school mathematics Stephen Krulik ; 1980 Yearbook editor ; Temple University ; Robert E. Reys ; General yearbook editor ; University of Missouri |
| title_full_unstemmed | Problem solving in school mathematics Stephen Krulik ; 1980 Yearbook editor ; Temple University ; Robert E. Reys ; General yearbook editor ; University of Missouri |
| title_short | Problem solving in school mathematics |
| title_sort | problem solving in school mathematics |
| topic | Résolution de problème Problem solving |
| topic_facet | Résolution de problème Problem solving |
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