Connections: A Lottery, a Computer, and the Number e

1993 ◽  
Vol 86 (8) ◽  
pp. 652-655
Author(s):  
Alfinio Flores
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematics Students ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Constant E ◽  
K 12 ◽  
Compound Interest ◽  
Probabilistic Context ◽  
Mathematical Constants

I mportant mathematical constants, like π and e. which are encountered first in specific contexts, appear throughout different branches of mathematics. Students are surprised to find rr, which they know as the ratio of the circumference to the diameter of a circle, in such a probabilistic context as Buffon's needle problem (Hirsch 1981). This article links Euler's constant e-the base of natural logarithms, which students usuaUy encounter in relation to compound-interest problems-with an experiment simulating a drawing. Establishing mathematical connections among different mathematical fields is one of the standards stressed throughout the K-12 mathematics curriculum in NCTM's Curriculum and Evaluation Standards for School Mathematics (1989).

Implementing The Standards: Students' Microcomputer-Aided Exploration in Geometry

1990 ◽  
Vol 83 (8) ◽  
pp. 628-635
Author(s):  
Daniel Chazan
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematical Structure ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Mathematical Connections ◽  
Teachers And Students ◽  
K 12

Four important themes presented in the K–12 Curriculum and Evaluation Standards for School Mathematics (Standards) (NCTM 1989) are mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. The high school component also stresses mathematical structure. Furthermore, the Standards calls for new roles for teachers and students and suggests that microcomputer technology can help support teachers and students in taking on these new roles.

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.

Young's Vision

1993 ◽  
Vol 86 (4) ◽  
pp. 330-333
Author(s):  
Sharyn L. Stein
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Dartmouth College ◽  
John Wesley ◽  
Underlying Assumption ◽  
Evaluation Standards ◽  
Grade Levels ◽  
Educational Pedagogy ◽  
K 12

The boxed paragraph's objective can also be considered one of the fundamental concepts found in NCTM's Curriculum and Evaluation Standards for School Mathematics, published in 1989. Making the underlying assumption that a metamorphosis was drastically needed in our nation's mathematics curriculum, the standards document thoroughly examined and analyzed all aspects of the current methods by which mathematics is presented at all grade levels (K–12), as well as what is considered to be essential material that must be presented to students. (For an overview of the Curriculum and Evaluation Standards, see Thompson and Rathmell [1988].) However, the succinct statement below is not the product of the NCTM's standards; rather it is the wisdom of Jacob William Albe1t Young (1865–1948), a tum-of-thecentury pioneer in the field of educational pedagogy. (J. W. A. Young is not to be confused with John Wesley Young, 1879–1932, a professor of mathematics at Dartmouth College during the same era.)

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.

Activities: Extending Problem-Solving Skills

1985 ◽  
Vol 78 (1) ◽  
pp. 36-44
Author(s):  
Robert A. Laing
Keyword(s):  
Problem Solving ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Problem Solving Skills ◽  
Technological Society ◽  
K 12

Introduction: Recognizing that the mathematics curriculum in grades K-12 must include more than the concepts and skills of mathematics to prepare students to be productive and contributing members of a rapidly changing technological society, the Agenda for Action (NCTM 1980, 3, 4) recommends that problem solving be the focus of school mathematics in the 1980s.

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.

Soundoff: Nctm's Standards, Curriculum Reform, And High School Mathematics Teachers

1990 ◽  
Vol 83 (7) ◽  
pp. 510-512
Author(s):  
William S. Hadley
Keyword(s):  
High School ◽  
Curriculum Reform ◽  
Mathematics Teachers ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Major Obstacle ◽  
Classroom Teachers ◽  
High School Mathematics ◽  
K 12 ◽  
High School Mathematics Teachers

With the release of NCTM's curriculum standards in the spring of 1989, emphasis on mathematics-curriculum reform at all levels K-12 has been renewed. Reform is obviously long overdue, but one major obstacle stands in the way of its achievement: the classroom teachers. Given t he proper opportunities, however, teachers can become the key to success.

Illustrating Mathematical Connections: Two Proofs That Only Five Regular Polyhedra Exist

1993 ◽  
Vol 86 (8) ◽  
pp. 657-661
Author(s):  
Peter L. Glidden ◽  
Erin K. Fry
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Mathematics Curriculum ◽  
Three Dimensional ◽  
Discrete Mathematics ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Regular Polyhedra ◽  
Real World Problems

The reforms proposed in the NCTM's Curriculum and Evaluation Standards (1989) call for specific changes in the grades 9-12 mathematics curriculum, as well as for general themes that should be emphasized throughout the curriculum. In particular, the standards document calls for including topics from discrete mathematics and three-dimensional geometry, and it calls for increased emphasis on paragraph-style proofs. Overall, these and other topics should be taught with the ultimate goals of illustrating mathematical connections and constructing mathematical models to solve real-world problems.

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