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.”

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.

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)

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.

What Is in the Daily News? Problem-Solving Opportunities!

1999 ◽  
Vol 5 (7) ◽  
pp. 390-394
Author(s):  
Robyn Silbey
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Daily News ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
The Everyday ◽  
Everyday World ◽  
Real World Problems

In An Agenda for Action, the NCTM asserted that problem solving must be at the heart of school mathematics (1980). Almost ten years later, the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) stated that the development of each student's ability to solve problems is essential if he or she is to be a productive citizen. The Standards assumed that the mathematics curriculum would emphasize applications of mathematics. If mathematics is to be viewed as a practical, useful subject, students must understand that it can be applied to various real-world problems, since most mathematical ideas arise from the everyday world. Furthermore, the mathematics curriculum should include a broad range of content and an interrelation of that content.

Integrating Manipulatives and Computers in Problem-Solving Experiences

1990 ◽  
Vol 38 (2) ◽  
pp. 8-10
Author(s):  
Sue Brown
Keyword(s):  
Problem Solving ◽  
Group Work ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Good Mathematics Instruction ◽  
K 12

In 1980, the National Council of Teachers of Mathematics stated that “problem solving must be the focus of school mathematics.” In 1989 the Council reaffirmed that belief with the Curriculum and Evaluation Standards for School Mathematics (Standards). Standard 1 for grades K–12 is “Mathematics as Problem Solving.” The Standards also asserts that “a computer should be available in every classroom for demonstration purposes, and every student should have access to a computer for individual and group work.” Also according to the Standards, “manipulative materials are necessary for good mathematics instruction.” In a typical classroom, problem solving may be taught, manipulative materials may be used, or students may be working at a computer. These functions, however, are usually completed as disjoint activities. Integrating these activities is possible, and this article illustrates how it can be done.

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.

Implementing the Standards: Developing Communication Skills in Mathematics for Students with Limited English Proficiency

1991 ◽  
Vol 84 (3) ◽  
pp. 186-189
Author(s):  
Gilbert J. Cuevas
Keyword(s):  
Problem Solving ◽  
Communication Skills ◽  
Limited English Proficiency ◽  
English Proficiency ◽  
Mathematical Understanding ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Listening And Speaking

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) emphasizes the need to address communication skills. These skills, including reading, writing, listening, and speaking, enhance mathematical understanding and problem-solving ability. Moreover, to communicate effectively, one must be able to interpret and analyze mathematical ideas. The curriculum and evaluation standards recommend that opportunities be afforded students to “use language to communicate their mathematical ideas” (NCTM 1989, 78). Although these recommendations are valuable, teachers may find them difficult to implement with students who are not proficient in English.

A Popcorn Project for All Students

1997 ◽  
Vol 90 (3) ◽  
pp. 194-200
Author(s):  
Lydotta M. Taylor ◽  
Joann L. King
Keyword(s):  
Problem Solving ◽  
Cooperative Learning ◽  
Real World ◽  
Data Gathering ◽  
School Mathematics ◽  
Combine Data ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematical Connections ◽  
Reasoning Problem

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) encourages teachers to include activities that help students “construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations” (p. 167) and “express mathematical ideas orally and in writing” (p. 140). The following activities combine data gathering and analysis with cooperative learning, mathematical connections, reasoning, problem solving, and communication.

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.

Power On!: Learning Statistics with Technology

1994 ◽  
Vol 1 (2) ◽  
pp. 130-136
Author(s):  
Gary Kader ◽  
Mike Perry
Keyword(s):  
Problem Solving ◽  
Mathematics Curriculum ◽  
Real Data ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Problem Solving Process ◽  
K 12

In its Curriculum and Evaluation Standards for School Mathematics (1989), the National Council of Teachers of Mathematics recommends that the K-12 mathematics curriculum be broadened and designates statistics as an area deserving increased attention. The standards document promotes the concept that statistics be learned through the study of real problems with real data collected by the students. Rather than focus on developing formulas from which answers are simply computed, teachers should present statistics in a coherent fashion and develop the topic as a whole problem-solving process.

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