Becoming Flexible with Functions: Investigating United States Population Growth

1996 ◽  
Vol 89 (5) ◽  
pp. 414-418
Author(s):  
Barry E. Shealy
Keyword(s):  
Mathematical Modeling ◽  
United States ◽  
Real World ◽  
Core Curriculum ◽  
National Council ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Problem Situations ◽  
United States Population ◽  
Real World Problem

Real-world contexts are appearing more often in international curricula, and the arguments for using modeling and applications are broadening (Blum and Niss 1991). The National Council of Teachers of Mathematics, in its Curriculum and Evaluation Standards for School Mathematics (1989), suggests that modeling is a great context for developing problem-solving and reasoning skills. These types of experiences promote communication and allow students to make connections among mathematical ideas and between mathematics and other disciplines. Modeling activities are also consistent with the concept of a core curriculum, offering contexts for a variety of types and depths of problems. It is not surprising that the Curriculum and Evaluation Standards points out that students should be able to “apply the process of mathematical modeling to real-world problem situations” (NCTM 1989, 137)

Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum

1991 ◽  
Vol 84 (5) ◽  
pp. 358-365
Author(s):  
Frank Swetz
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Original Problem ◽  
Problem Situation ◽  
Multistage Process ◽  
Problem Solving Skills ◽  
Evaluation Standards ◽  
Problem Situations ◽  
Real World Problem ◽  
The Impact

In suggesting plans of action for the reform of mathematics education in North America, NCTM reports have focused strongly on the need to improve problem-solving skills and the need to “do” mathematics. Most recently, these goals have been reiterated and clarified in Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). In discussing the impact of Standard 1: Mathematics as Problem Solving on students in grades 9-12, the report notes that students should be able to “apply the process of mathematical modeling to real-world problem situations” (p. 137). By using the phrase “apply the process of mathematical modeling,” the authors of this standard were most precise in their language. Mathematical modeling is a process and must be taught as a process. Certainly mathematical modeling involves problems, but it should not be considered as merely a collection of interesting problems and solution schemes. More important, modeling is a multistage process that evolves from the identification and mathematical articulation of a problem through its eventual solution and the testing of that solution in the original problem situation. The challenge for teachers is to understand this process of mathematical modeling and to apply it effectively in problem solving.

Technology Tips: A Mathematical Look at a Free Throw Using Technology

1996 ◽  
Vol 89 (9) ◽  
pp. 774-779
Author(s):  
Charles Vonder Embse ◽  
Arne Engebretsen
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematics Curriculum ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Free Throw ◽  
Problem Situations ◽  
Real World Problem

Technology can be used to promote students' understanding of mathematical concepts and problem-solving techniques. Its use also permits students' mathematical explorations prior to their formal development in the mathematics curriculum and in ways that can capture students' curiosity, imagination, and interest. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recommends that “[i]n grades 9–12, the mathematics curriculum should include the refinement and extension of methods of mathematical problem solving so that all students can … apply the process of mathematical modeling to real-world problem situations” (p. 137). Students empowered with technology have the opportunity to model real-world phenomena and visualize relationships found in the model while gaining ownership in the learning process.

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.”

Analyzing Energy and Resource Problems: An Interdisciplinary Approach with Mathematical Modeling

1993 ◽  
Vol 86 (8) ◽  
pp. 628-633
Author(s):  
Joseph Fishman
Keyword(s):  
Mathematical Modeling ◽  
Real World ◽  
Core Curriculum ◽  
Data Gathering ◽  
Interdisciplinary Approach ◽  
School Students ◽  
Evaluation Standards ◽  
Problem Solving Strategies ◽  
Different Levels ◽  
Real World Problems

The Curriculum and Evaluation Standards (NCTM 1989) recommends that students learn to recognize and formulate problems, develop problem-solving strategies, and apply the process of mathematical modeling to real-world problems. It recommends that secondary school students have the opportunity to experience the pervasiveness of functions through real-world relationships and sketching graphs of data. Gathering and analyzing data and developing models can generate interest among students at different levels of mathematical abilities and facilitate cooperative learning-important aspects of the core curriculum advocated in the curriculum standards.

Combinatorics Connections: Playoff Series and Pascal's Triangle

1992 ◽  
Vol 85 (7) ◽  
pp. 532-535
Author(s):  
Bonnie H. Litwiller ◽  
David R. Duncan
Keyword(s):  
Real World ◽  
School Mathematics ◽  
Discrete Mathematics ◽  
National Council ◽  
Major Theme ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Pascal’S Triangle ◽  
Pascal's Triangle ◽  
The Relationship

One major theme of the National Council of Teachers of Mathematic's Curriculum and Evaluation Standards far School Mathematics (1989) is the connection between mathematical ideas and their applications to real-world situations. We shall use concepts from discrete mathematics in describing the relationship between sports series and Pascal's triangle.

Implementing the “Curriculum and Evaluation Standards”: Ladders and Saws

1993 ◽  
Vol 86 (6) ◽  
pp. 510-513
Author(s):  
Debra Tvrdik ◽  
Dave Blum
Keyword(s):  
Real World ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
School Year ◽  
Real World Applications ◽  
Geometry Class

How many of our students begin the school year apprehensive and fearful of their geometry class? They enter the room having heard all sorts of horror stories about the dreaded two-column proof and all those theorems. Too often, geometry is taught mechanically with an emphasis on recalling facts. The NCTM's Curriculum and Evaluation Standards (1989) calls for a move away from geometry as a tour through a collection of predetermined Euclidean theorems and their proofs. Instead, they advocate greater attention to approaches using coordinates and transformations, to real-world applications and modeling, and to investigations leading to student-generated theorems and conjectures, with supporting arguments expressed orally or in paragraph form. As teachers, we search for activities that will involve our students in the study of geometry and help them to understand the “whys” behind the facts. The following activity employs several strategies to enable students to make conjectures, construct mathematical ideas, and use mathematics as a tool to communicate with others.

Coordinate Geometry: A Powerful Tool for Solving Problems

1990 ◽  
Vol 83 (4) ◽  
pp. 264-268
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematics Standards ◽  
Problem Situations ◽  
Coordinate Geometry

In calling for reform in the teaching and learning of mathematics, the Curriculum and Evaluation Standards for School Mathematics (Standards) developed by NCTM (1989) envisions mathematics study in which students reason and communicate about mathematical ideas that emerge from problem situations. A fundamental premise of the Standards, in fact, is the belief that “mathematical problem solving … is nearly synonymous with doing mathematics” (p. 137). And the ability to solve problems, we are told, is facilitated when students have opportunities to explore “connections” among different branches of mathematics.

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.

Analyzing Data from the Olympic Games for Trends and Inferences

1996 ◽  
Vol 89 (5) ◽  
pp. 370-372
Author(s):  
Richard T. Edgerton
Keyword(s):  
Real World ◽  
Olympic Games ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Problem Situations ◽  
Real World Problems ◽  
The Olympic Games

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) emphasizes classroom mathematics that engages students in meaningful activities through which they construct their own understanding of important concepts. Students' investigations are derived from problem situations that arise from real-world contexts. The Olympic Games furnish ample data for students to connect meaningful mathematics with real-world problems.

Promising Research: The World's Largest Math Event: Promoting Mathematical Thinking

1999 ◽  
Vol 5 (7) ◽  
pp. 430-432
Author(s):  
Daniel J. Brahier ◽  
Melfried Olson
Keyword(s):  
United States ◽  
Real World ◽  
Mathematical Thinking ◽  
The United States ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The World

The Great Sphinx in Egypt is about 73.2 m (240 ft.) long, including the paws, which are each 15.3 m (50 ft.) long. Would one of its paws fit in a typical classroom? Would it fit in the school hallway? If the 90 800 kg (200 000 lbs.) of copper sheeting that make up the Statue of Liberty were melted down into pennies, how many pennies could be produced? How high would the pennies stand if they were stacked on one another? In which city and state would you find the world's largest ball of twine? Where would you find the world's largest catsup bottle? Such questions were the focus of the World's Largest Math Event 4— Landmarks: Seeing the World by Numbers— in April 1998. All over the United States and throughout the world, tens of thousands of students, from kindergarten through college, participated in the event. With the emphasis that the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) places on having students use real-world phenomena as a context for the study of mathematics, the World's Largest Math Event is a popular program.

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