Flying through Graphs: An Introduction to Graph Theory

2001 ◽  
Vol 94 (8) ◽  
pp. 680-688
Author(s):  
Amy Roth McDuffie
Keyword(s):  
Graph Theory ◽  
Problem Solving ◽  
Computer Technology ◽  
School Curriculum ◽  
Discrete Mathematics ◽  
National Council ◽  
High School Curriculum ◽  
Problem Situations ◽  
Education Community ◽  
Solution Methods

The mathematics education community has called for changes in the high school curriculum to increase the emphasis on meaningful problem solving and on topics in discrete mathematics (National Council of Teachers of Mathematics 1989, 1991, 2000). This recommendation resulted from changes in knowledge and revisions in problem-solving needs because of advances in such fields as information processing and computer technology. Including graph theory in the curriculum is one way to meet these goals. Graphs present an opportunity to model and analyze such problem situations as networks and circuits. This activity incorporates basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel.

A Problem-solving Component for Junior High School Mathematics

1986 ◽  
Vol 34 (2) ◽  
pp. 14-17
Author(s):  
Roger P. Day
Keyword(s):  
High School ◽  
Problem Solving ◽  
Junior High School ◽  
Junior High ◽  
Eighth Graders ◽  
School Curriculum ◽  
School Mathematics ◽  
High School Mathematics ◽  
High School Curriculum ◽  
Mind Set

While teaching junior high school mathematics at the Stavanger American School in Norway. I sensed the need to challenge the students' perceptions of mathematics. The seventh and eighth graders seemed most concerned with producing correct answers. They saw little need for questioning, evaluating, checking, and comparing. They simply wanted to be shown “how to do it.” I set out to implement a problem-solving component within the structure of the junior high school curriculum that would alter this. “right-wrong-produce an anwer” mind set. This article reports my experience and sets forth ideas that may work for you.

Three Methods of Attacking Problems in Discrete Mathematics, Part 1

1987 ◽  
Vol 80 (3) ◽  
pp. 224-230
Author(s):  
Jan Mansheim ◽  
Phyllis Baldridge
Keyword(s):  
High School ◽  
Junior High ◽  
School Curriculum ◽  
Discrete Mathematics ◽  
High School Curriculum ◽  
Mathematical Techniques

We are concerned about how we will meet the challenge of introducing our students to those topics usually listed under the heading of “discrete mathematics.” We agree with those authorities who, like Schoen (1986), maintain that this subject should be an integral part of the junior high and high school curriculum. Since many students find problems in discrete mathematics rather difficult, we think that these should be approached from various avenues. A variety of approaches will make the problems more understandable and increase the students' skill in the use of diverse mathematical techniques.

Activities: From Graphs to Matrices

1990 ◽  
Vol 83 (2) ◽  
pp. 127-134
Author(s):  
Peter Lochiel Glidden ◽  
Robert A. Laing ◽  
Dwayne E. Channell
Keyword(s):  
Secondary School ◽  
Recurrence Relations ◽  
Discrete Mathematics ◽  
National Council ◽  
Matrix Representations ◽  
School Students ◽  
Evaluation Standards ◽  
Finite Graphs ◽  
Problem Situations ◽  
Discrete Structures

Introduction: The NCTM's curriculum and evaluation standards call for topics from discrete mathematics to be included in the 9–12 curriculum so that all students can “represent problem situations using discrete structures such as finite graphs, matrices, sequences, and recurrence relations; [and] represent and analyze finite graphs using matrices …”(National Council of Teachers of Mathematics, Commission on Standards for School Mathematics 1989, 176). This activity is offered as an example of how matrices can be introduced informally from finite graphs and how finite graphs can be analyzed by examining their matrix representations. Because this introduction to matrices is concrete and requires only marginal computational proficiency, it makes matrices accessible to the majority of middle and secondary school students.

Investigations: Vehicles for Learning and Doing Mathematics

1996 ◽  
Vol 178 (2) ◽  
pp. 35-49 ◽  
Author(s):  
Carole Greenes
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Solution Method ◽  
Professional Organizations ◽  
Mathematical Concepts ◽  
Educational Benefits ◽  
Problem Situations ◽  
Mathematics Educators ◽  
Solution Methods ◽  
Problem Solving Strategies

Professional organizations of mathematics educators and mathematicians are calling for major reforms in the teaching and learning of mathematics. Among those reforms are a shift in emphasis in curriculum from mastery of lists of unrelated mathematical concepts and skills to exploration of rich mathematical topics and problem situations, and a shift in learning from memorizing and replicating algorithmic procedures to investigating and solving complex problems. To help students achieve proficiency in solving problems, the curriculum must focus on development of the major concepts of mathematics, the enhancement and enlargement of students' repertoires of problem-solving strategies and reasoning methods, and the refinement of communication and collaboration skills. Because they present intriguing problems whose solutions or solution methods are not immediately obvious, and require the application of concepts from different areas of mathematics, and, in some instances, knowledge from other content areas, investigations are powerful vehicles for helping students achieve expertise in solving problems. The nature of investigations and their educational benefits are described. Three types of investigations, whimsical, real, and mathematical, are defined and illustrated. For each investigation, the mathematical content and problem-solving strategies are identified, and a solution method is presented. The responsibilities of the teacher, before, during and after an investigation are described.

Discrete mathematics in the high school curriculum

2004 ◽  
Vol 36 (3) ◽  
pp. 105-116 ◽  
Author(s):  
Ian Anderson ◽  
Bram van Asch ◽  
Jack van Lint
Keyword(s):  
High School ◽  
School Curriculum ◽  
Discrete Mathematics ◽  
High School Curriculum

A Check List for Pre-Induction Mathematics

1944 ◽  
Vol 37 (6) ◽  
pp. 269-271
Author(s):  
Virgil S. Mallory
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
School Curriculum ◽  
National Council ◽  
Check List ◽  
Civilian Life ◽  
High School Curriculum ◽  
Army Service

In the October 1943 issue of The Mathematics Teacher a committee1 of the National Council of Teachers of Mathematics, working with the cooperation of the Civilian Pre-Induction Training Branch of the Army Service Forces and the U. S. Office of Education made a report on Essential Mathematics for Minimum Army Needs.2 The purposes of the report were to emphasize the needs of the inductee for certain minimum essentials in mathematics, to present a list of the essentials needed, to recommend placement in the high school curriculum of those essentials not already there, and to give some guidance for teaching them. Incidentally the report pointed out the value in civilian life of these same essentials.

Garbage Collection, Sunday Strolls, and Soldering Problems

1972 ◽  
Vol 65 (4) ◽  
pp. 307-309
Author(s):  
Walter Meyer
Keyword(s):  
High School ◽  
Graph Theory ◽  
Garbage Collection ◽  
Applied Mathematics ◽  
School Curriculum ◽  
High School Curriculum ◽  
Dual Nature ◽  
Practical Applications ◽  
Basic Ideas

Is there an area of mathematics that deals with garbage collection, Sunday strolls, and soldering problems all at once? Indeed there is, and it is called graph theory, a subject that considers the properties of configurations consisting of points and connecting lines such as the configuration shown in figure 2. (There is another meaning for the word graph, as in bar graph or graph of a function, which is not meant here.) The practical applications of graph theory are so widespread that this theory has become one of the most important and rapidly growing areas of applied mathematics in recent years. What is especially unique about it, however, is the extreme simplicity of the basic ideas. Because of this dual nature of practicality and simplicity, graphs have been creeping into the high school curriculum lately, often in the form of optional topics.

Creating Story Problems

1993 ◽  
Vol 41 (3) ◽  
pp. 140-142
Author(s):  
Donald M. Fairbairn
Keyword(s):  
Problem Solving ◽  
National Council ◽  
Story Problems ◽  
Evaluation Standards ◽  
Knowledge And Skills ◽  
Mathematical Ideas ◽  
Problem Situations ◽  
Wide Range

Much has been written concerning how to teach problem solving, going back to Póya's steps in problem solving (1957). The imponance of problem solving is also well documemed. Problem solving was made the “agenda for the eighties” by the National Council of Teachers of Mathematics (NCTM). The Curriculum and Evaluation Standards (NCTM 1989, 77) indicates that “problem situations can serve as a context for exploring mathematical ideas. Through these situations, students have opportunities to investigate problems, apply their knowledge and skills across a wide range of situations, and develop an appreciation for the power and beauty of mathematics.”

Sign in / Sign up

Export Citation Format

Share Document