Apply the Curriculum Standards with Project Questions

1993 ◽  
Vol 86 (8) ◽  
pp. 686-689
Author(s):  
Richard T. Edgerton
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Organizing Principles

A goal of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) is faci litating “mathematical power” in students. The curriculum standards use problem solving, communication, reasoning, and connections as organizing principles. One way to apply these principles in the classroom is with the use of “project questions.”

Implementing The Standards: Evaluation: A New Vision

1991 ◽  
Vol 84 (4) ◽  
pp. 276-284
Author(s):  
Frank K. Lester ◽  
Diana Lambdin Kroll
Keyword(s):  
Instructional Practices ◽  
Evaluation Process ◽  
School Mathematics ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Evaluation Program ◽  
Testing Procedures ◽  
Mathematics Program ◽  
New Vision

Teaching according to the vision of the NCTM's Curriculum and Evaluation Standards will involve numerous changes in the content and instruction of the school mathematics program. Moreover, this vision will also require a change in testing procedures and methods for evaluating the effectiveness of instructional practices (Clarke, Clarke, and Lovitt 1990; EQUALS and California Mathematics Council 1989; NAEP 1987; NCTM 1989). As is pointed out in NCTM's curriculum standards, an evaluation program that is properly aligned with the proposed curriculum standards can no longer use only written tests. Calculators, computers, and manipulatives must be included in the evaluation process.

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.

Implementing the Standards: Uses of Technology in Prealgebra and Beginning Algebra

1990 ◽  
Vol 83 (3) ◽  
pp. 194-198
Author(s):  
M. Kathleen Heid
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Classrooms ◽  
Beginning Algebra ◽  
Grade Levels ◽  
Mathematical Connections

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Stan dards) (1989) designates four standards that apply to all students at all grade levels: mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. These and NCTM's other standards are embedded in a vision of technologically rich school mathematics classrooms in which students and teachers have constant access to appropriate computing devices and in which students use computers and calculators as tools for the investigation and exploration of problems.

Problem Solving With Discrete Mathematics

1996 ◽  
Vol 2 (7) ◽  
pp. 426-431
Author(s):  
Louis M. friedler
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Discrete Mathematics ◽  
Evaluation Standards

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1981) calls for an emphasis on problem solving at all levels and recommends introducing discrete mathematics topics. In fact, the first standard for grades K-4 states that “the study of mathematics should emphasize problem solving …” (p. 23).

Problem Solving: Is More Than Solving Problems

1998 ◽  
Vol 4 (1) ◽  
pp. 20-25
Author(s):  
Michael G. Mikusa
Keyword(s):  
Problem Solving ◽  
Correct Answer ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Students First ◽  
Mathematics Class ◽  
General Goals ◽  
Problem Solvers

The curriculum and evaluation Standards for School Mathematics (NCTM 1989) states that one of its five general goals is for all students to become mathematical problem solvers. It recommends that “to develop such abilities, students need to work on problems that may take hours, days, and even weeks to solve” (p. 6). Clearly the authors have not taught my students! When my students first encountered a mathematical problem, they believed that it could be solved simply because it was given to them in our mathematics class. They also “knew” that the technique or process for finding the solution to many problems was to apply a skill or procedure that had been recently taught in class. The goal for most of my students was simply to get an answer. If they ended up with the correct answer, great; if not, they knew that it was “my job” to show them the “proper” way to go about solving the problem.

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.

Exploring Patterns, Relations, and Functions

1992 ◽  
Vol 39 (9) ◽  
pp. 19-21
Author(s):  
Charles P. Geer
Keyword(s):  
Problem Solving ◽  
Cognitive Skills ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
First Century ◽  
Evaluation Standards ◽  
Learning Mathematics ◽  
New Knowledge ◽  
Paper And Pencil ◽  
Twenty First Century

As teachers use NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) to develop programs that will prepare students for the twenty-first century, some are discovering that mathematics instruction is going to be very different in the 1990s. Many previous programs placed a heavy emphasis on paper-and-pencil proficiency with computational skills and learning mathematics by memorizing rules. Because of advances in technology, new knowledge about how learning occurs, and the changing needs of business and industry, future programs will focus on mathematics with meaning, problem solving, and higher-level cognitive skills.

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.

Developing a Problem-Solving Lesson

1989 ◽  
Vol 37 (2) ◽  
pp. 14-19
Author(s):  
Pamala Byrd Cemen
Keyword(s):  
Elementary School ◽  
Problem Solving ◽  
Elementary School Teachers ◽  
Lesson Plans ◽  
School Mathematics ◽  
School Teachers ◽  
Evaluation Standards ◽  
Mathematical Abilities ◽  
Cognitive Levels

Problem solving is one of the most important mathematical abilities that teachers can foster in students, as evidenced by its prominent role in NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and An Agenda for Action (1980). Because of the increased availability of calculators and computers, knowledge of which computations are necessary is more important than proficiency in carrying out those computations. As a result, elementary school teachers are being encouraged and entreated to teach problem solving. However, teaching such a topic at higher cognitive levels is far from easy; the key is to be able to ask good questions. Because excellent problem-solving questions are seldom created “on the spot,” teachers will benefit from writing lesson plans that include questions they can ask at crucial moments, keeping in mind they may not need the questions at all.

Thematic Webbing and the Curriculum Standards in the Primary Grades

1994 ◽  
Vol 41 (6) ◽  
pp. 294-298
Author(s):  
Jenny A. Piazza ◽  
Margaret M. Scott ◽  
Elizabeth C. Carver
Keyword(s):  
Instructional Practices ◽  
Mathematical Knowledge ◽  
Mathematical Thinking ◽  
Primary Grades ◽  
School Mathematics ◽  
National Council ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Curricular Content

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) reflects the importance of understanding the development of knowledge at the K-4 level. The standards document recognizes that current instructional and curricular content must focus on students' active construction of mathematical knowledge. Instructional practices need to be conceptually oriented, involve children actively, emphasize the development of mathematical thinking and application, and include a broad range of content.

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