Spotlight on the Principles/Standards: Building Mathematically Powerful Students through Connections

2002 ◽  
Vol 7 (9) ◽  
pp. 484-488
Author(s):  
Christine Thomas ◽  
Carmelita Santiago
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematical Tasks ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Natural Inclination ◽  
Points Of View ◽  
Principles And Standards

Connections in mathematics can be implemented in ways that create excitement in the classroom, develop in students a love for doing mathematics, and foster students' natural inclination for pursuing mathematical tasks. According to the Curriculum and Evaluation Standards for School Mathematics, “If students are to become mathematically powerful, they must be flexible enough to approach situations in a variety of ways and recognize the relationships among different points of view” (NCTM 1989, p. 84). Principles and Standards for School Mathematics (NCTM 2000) further asserts that students develop a deeper and more lasting understanding of mathematics when they are able to connect mathematical ideas. The 1989 and 2000 Standards clearly delineate the power and importance of connections in the mathematics curriculum. This article examines and compares curricular recommendations for connections in the two documents.

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.

On My Mind: Not All Manipulatives and Models Are Created Equal

2007 ◽  
Vol 13 (1) ◽  
pp. 6-9
Author(s):  
Sally K. Roberts
Keyword(s):  
Mathematics Instruction ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematical Ideas ◽  
Mathematics Knowledge ◽  
Proof Techniques ◽  
Reasoning And Proof ◽  
Principles And Standards

The vision of the mathematics curriculum articulated in Principles and Standards for School Mathematics (NCTM 2000) calls for students to construct their own understanding of mathematical ideas by making, refining, and exploring conjectures based on evidence and use of a variety of reasoning and proof techniques (p. 3). For many of us who struggled to learn mathematics through a chalk-and-talk, do-it-my-way approach to mathematics instruction, the notion of using models and manipulatives to help the learner construct mathematics knowledge is both refreshing and exciting.

Photographs and Committees: Activities That Help Students Discover Permutations and Combinations

2000 ◽  
Vol 93 (2) ◽  
pp. 93-96
Author(s):  
Jennifer Earles Szydlik
Keyword(s):  
Mathematics Curriculum ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematical Connections ◽  
Problem Situations ◽  
Guiding Principles ◽  
Support Students

The vision of Mathematics Curriculum promoted by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) is based on two guiding principles: “First, activities should grow out of problem situations; and second, learning occurs through active as well as passive involvement with mathematics” (1989, 9). In particular, curriculum should be designed to support students in constructing their own mathematical ideas and connections. Students should solve problems, communicate ideas both orally and in writing, engage in mathematical reasoning, and search for mathematical connections.

One Point of View: Reclaiming School Mathematics

1990 ◽  
Vol 37 (8) ◽  
pp. 4-5
Author(s):  
Portia Elliott
Keyword(s):  
Mathematics Education ◽  
Mathematics Curriculum ◽  
Point Of View ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Design Change

The framers of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) call for a radical “design change” in all aspects of mathematics education. They believe that “evaluation is a tool for implementing the Standards and effecting change systematically” (p. 189). They warn, however, that “without changes in how mathematics is assessed, the vision of the mathematics curriculum described in the standards will not be implemented in classrooms, regardless of how texts or local curricula change” (p. 252).

Transition Boards: A Good Idea Made Better

1991 ◽  
Vol 38 (5) ◽  
pp. 4-8
Author(s):  
John T. Sutton ◽  
Tonya D. Urbatsch
Keyword(s):  
Conceptual Understanding ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Addition And Subtraction ◽  
School Mathematics Curriculum

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) recognizes that addition and subtraction computations remain an important part of the school mathematics curriculum and recommends that the emphasis be shifted to the understanding of concepts. Transition boards are simple devices to aid students' conceptual understanding.

Technology Tips: When Is a Good Fit Not a Good Fit? Dynamic Regression with the TI-Nspire Graphing Calculator

2008 ◽  
Vol 102 (4) ◽  
pp. 300-305
Author(s):  
Michael Edwards ◽  
Michael Meagher ◽  
S. Asli Özgün-Koca
Keyword(s):  
Graphing Calculator ◽  
School Mathematics ◽  
Mathematical Education ◽  
National Council ◽  
Mathematics Textbooks ◽  
Multiple Points ◽  
Complex Concept ◽  
Mathematics Classrooms ◽  
Points Of View ◽  
Principles And Standards

In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics (NCTM) acknowledges the importance of exploring mathematical ideas from multiple points of view: “Different representations often illuminate different aspects of a complex concept or relationship…. The importance of using multiple representations should be emphasized throughout students' mathematical education” (2000, p. 68). In particular, NCTM notes that the introduction of technology in school mathematics classrooms provides new ways for teachers and their students to explore connections among representations: “Computers and calculators change what students can do with conventional representations and expand the set of representations with which they can work” (2000, p. 68). In this article, we discuss an interesting finding that our students made as they explored linear regression with a teacher-constructed TI-Nspire calculator document. The calculator's capability to link variables across two or more pages in the same document led students to findings that are important yet rarely discussed in school mathematics textbooks.

Implementing the Standards: Building key Concepts for Calculus in Grades 7–12

1990 ◽  
Vol 83 (7) ◽  
pp. 532-540
Author(s):  
Elizabeth A. Jockusch ◽  
Patrick J. Mcloughlin
Keyword(s):  
Conceptual Understanding ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Key Concepts ◽  
Natural Extensions

The NCTM'S Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) recommends that the mathematics curriculum should include informal explorations of calculus concepts. These concepts can be developed as natural extensions of topics that students have already encountered. The approach should focus on exploring concrete problems in a way designed to build conceptual understanding of key ideas and to offer an introduction to some interesting applications.

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.

Felix Klein and the NCTM's Standards: A Mathematician Considers Mathematics Education

2000 ◽  
Vol 93 (8) ◽  
pp. 714-717
Author(s):  
Kim Krusen McComas
Keyword(s):  
Mathematics Education ◽  
School Mathematics ◽  
Rote Learning ◽  
German Mathematician ◽  
Evaluation Standards ◽  
10Th Anniversary ◽  
Felix Klein ◽  
Look Back ◽  
Principles And Standards ◽  
Year 2000

The year 1999 marked the 10th anniversary of the NCTM's Curriculum and Evaluation Standards for School Mathematics. It also marked the 150th anniversary of the birth of German mathematician Felix Klein, who lived from 1849 to 1925. Although the relation between these two anniversaries may not be obvious, the connection is that Klein, were he still alive today, would probably support the NCTM's Standards. As the year 2000 brings us NCTM's Principles and Standards for School Mathematics, let us look back to the year 1900 and find Felix Klein at the forefront of a movement to reform mathematics education from rote learning to more meaningful mathematical learning.

Technology Tips: Using a Graphing Utility as a Catalyst for Connections

1997 ◽  
Vol 90 (1) ◽  
pp. 50-56
Author(s):  
Charles Vonder Embse ◽  
Arne Engebretsen
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Evaluation Standards

One of the most important ideas expressed in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) is that of connections. The Standards document recommends that “the mathematics curriculum should include investigation of the connections and interplay among various mathematical topics and their applications … ”

Sign in / Sign up

Export Citation Format

Share Document