Hidden Behaviors in Graphs

1993 ◽  
Vol 86 (6) ◽  
pp. 466-468
Author(s):  
H. Edward Donley ◽  
Elizabeth Ann George
Keyword(s):  
Problem Solving ◽  
Instructional Methods ◽  
Graphing Calculators ◽  
Graphical Analysis ◽  
School Mathematics ◽  
Mathematical Ideas ◽  
Algebraic Analysis ◽  
New Approaches ◽  
Problem Solving Strategies ◽  
The Relationship

Through the use of graphing calculators or computers, instructors can expose students to richer examples in algebra and exploit the relationship between algebraic analysis and graphical analysis. The NCTM's Commission on Standards for School Mathematics (NCTM 1989) recommends incorporating this technology into the curriculum, thereby supplying students with new approaches in the investigation of mathematical ideas. Changes in both our curriculum and instructional methods are necessary to create an environment wherein students can develop the new problem-solving strategies that this technology makes possible.

Powers and Patterns: Problem Solving with Calculators

1982 ◽  
Vol 30 (2) ◽  
pp. 42-44
Author(s):  
Glenda Lappan ◽  
Elizabeth Phillips ◽  
M. J. Winter
Keyword(s):  
Problem Solving ◽  
Mathematical Concept ◽  
School Mathematics ◽  
Mathematical Idea ◽  
Wide Spread ◽  
Problem Solving Skills ◽  
Problem Solving Strategies ◽  
Paper And Pencil

With the publication of An Agenda for Action: Recommendations for School Mathematics of the 1980s, the NCTM has emphasized its support for helping students to develop and use problem-solving skills. The challenge for the teacher is to provide opportunities for the development of the e skill while teaching mathematical concept that comprise the basic curriculum. With the wide-spread availability of calculators, teachers have a tool that can be used to expand the study of many basic mathematical idea to include the development of problem-solving strategies. Calculations that would be so time consuming as to be impractical if they were done with paper and pencil, can be quickly done with a calculator.

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.

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.

Autobiographical memory and problem-solving strategies of parasuicide patients

1992 ◽  
Vol 22 (2) ◽  
pp. 399-405 ◽  
Author(s):  
J. Evans ◽  
J. M. G. Williams ◽  
S. O'Loughlin ◽  
K. Howells
Keyword(s):  
Problem Solving ◽  
Autobiographical Memory ◽  
Matched Control ◽  
Control Group ◽  
Clinical Implications ◽  
Memory Recall ◽  
Autobiographical Memories ◽  
Matched Control Group ◽  
Problem Solving Strategies ◽  
The Relationship

SYNOPSISRecent research has noted the tendency of parasuicide patients to retrieve over-general autobiographical memories. Separate studies suggest problem-solving deficits within this group.The present study was concerned first with replicating these findings and, secondly, with developing a model of the relationship between over-general memory recall and poor problem-solving abilities in parasuicide patients. Anger and hopelessness were measured as markers for mood.In line with the hypotheses, the parasuicide group (N = 12) produced significantly over-general memories in contrast to a matched control group (N = 12). This occurred significantly in relation to positive cues, and latency to first responses was significantly delayed in the parasuicide group. The parasuicide group also provided fewer and less-effective problem-solving strategies than the control group, and a significant association was found between low effectiveness of problem-solving strategies and over-general memory recall in the parasuicide group. Anger and hopelessness levels were significantly higher within the parasuicide group in line with previous findings.The clinical implications of these findings are discussed.

Investigating the Mathematical Process with Nonlinear Asymptotes

2008 ◽  
Vol 101 (8) ◽  
pp. 574-580
Author(s):  
Michael J. Bossé ◽  
Karen A. DeUrquidi ◽  
David L. Edwards ◽  
N. R. Nandakumar
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Multiple Representations ◽  
School Mathematics ◽  
School Students ◽  
Mathematical Ideas ◽  
Mathematics Educators ◽  
Algebraic Concept ◽  
Mathematical Process

Principles and Standards for School Mathematics (NCTM 2000) emphasizes having students experience mathematics as mathematicians do and demonstrates that the Process Standards—Problem Solving, Reasoning and Proof, Communication, Connections, and Representation—are not simply means through which mathematics is learned and taught; they are also the manner through which mathematics is done. This article presents an abbreviated version of the musings and methodologies experienced by mathematics educators through a genuine problemsolving investigation. This account will investigate dimensions of an algebraic concept known to many high school students and show how these lead to an intuitive understanding of the limit in calculus. Readers will experience and come to a deeper understanding of the Process Standards as well as experience the necessity of using multiple representations to make and solve mathematical conjectures. To accomplish these multidimensional goals, the authors describe a chronological development of mathematical ideas among themselves and invite readers to reason along with them in their actual investigations.

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.

News from the Net: Aunty Math's Challenges for Kids

1999 ◽  
Vol 5 (7) ◽  
pp. 420
Author(s):  
Beth Lazerick
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Web Site ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The Real ◽  
Problem Solving Strategies ◽  
The Web

Aunty Math, for students and their teachers, is a terrific site that emphasizes problem-solving strategies listed in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The site is designed for children; the layout is easy to use, and the graphics are inviting. Aunty Math's problems, called “challenges,” are set in stories about Aunty Math's nephews and niece. The real Aunty Math behind the Web site is an experienced, awardwinning teacher who is very involved in mathematics education.

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