Common Difficulties with Probabilistic Reasoning

1983 ◽  
Vol 76 (8) ◽  
pp. 565-570
Author(s):  
Jack A. Hope ◽  
Ivan W. Kelly
Keyword(s):  
Probabilistic Reasoning ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
National Council ◽  
The Past ◽  
Probability And Statistics ◽  
Modern Mathematics

In the past two decades several influential organizations, including the National Council of Supervisors of Mathematics (1978), NACOME (1975), UNESCO (1972), CEEB (1959), and the Cambridge Conference on School Mathematics (1963), have acknowledged the role that probability and statistics play in our society. Consequently, each has recommended that probability and statistics be included as part of the modern mathematics curriculum.

Developing Spatial Thinking In The Middle Grades: Designing A Space Station

1990 ◽  
Vol 37 (6) ◽  
pp. 59-63
Author(s):  
Barbara Moses
Keyword(s):  
Elementary School ◽  
Mathematics Curriculum ◽  
Space Station ◽  
Physical World ◽  
School Mathematics ◽  
Spatial Thinking ◽  
National Council ◽  
Elementary School Mathematics ◽  
Geometric Figures ◽  
Spatial Sense

The recently published Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, Commission on Standards for School Mathematics 1989, 21) clearly states that educators should devote less attention to “ complex paper-andpencil computations” and “rote memorization of rules.” The time currently spent in the elementary school mathematics curriculum on these topics should instead be devoted to other areas, such as geometry and problem solving. Students should “visualize and represent geometric figures with special attention to developing spatial sense” and learn to appreciate “geometry as a means of describing the physical world” (p. 112). But elementary school mathematics textbooks typically contain few activities that deal with the development of spatial sense.

Welcome to Our Focus Issue on Problem Solving

2003 ◽  
Vol 96 (8) ◽  
pp. 529
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Word Problems ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
National Council ◽  
Seminal Work ◽  
Strong Case ◽  
School Mathematics Curriculum

THE CALL FOR THIS FOCUS ISSUE BEGAN BY reminding readers that in 1980, the National Council of Teachers of Mathematics made a strong case for including problem solving in the mathematics curriculum. Problem solving was not a new topic at that time—after all, George Pólya published his seminal work, How to Solve It, in 1945. However, the 1980 Agenda for Action publication marked the beginning of a period in mathematics education when the processes of problem solving received specific attention in the school mathematics curriculum. Problem solving became much more than solving word problems.

Building the Mathematics and Literature Connection through Children's Responses

2004 ◽  
Vol 10 (6) ◽  
pp. 328-333
Author(s):  
Jeffrey C. Shih ◽  
Cyndi Giorgis
Keyword(s):  
Elementary Mathematics ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
The Past ◽  
And Mathematics

The Connections Standard in Principles and Standards for School Mathematics makes the significant observation that “the opportunity for students to experience mathematics in a context is important” (NCTM 2000, p. 66). Literature provides such a contextual base by embedding the meaning of the mathematics in situations to which children can relate. In this regard, the use of literature in the elementary mathematics curriculum has steadily increased over the past few years. The publication of books that specifically feature mathematics, as well as a deeper understanding by teachers of how to integrate literature and mathematics topics, has aided this increase. This article builds on the premise that educators want children to recognize and respond to the mathematics that may be evident or embedded in literature.

Guiding Young Children in Successful Problem Solving

1982 ◽  
Vol 29 (5) ◽  
pp. 15-17
Author(s):  
Kil S. Lee
Keyword(s):  
Problem Solving ◽  
Young Children ◽  
Conference Report ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Skills ◽  
The Past ◽  
Mathematics Educators ◽  
Mathematics Curricula

In the past twenty years, problem solving has received much attention from mathematics educators. Inclusion of imaginative problems in school mathematics curricula was recommended in the 1963 Cambridge Conference report. Problem solving was the first of the ten basic mathematical skills identified by the National Council of Supervisors of Mathematics in 1976 and the position of the NCSM was endorsed by the National Council of Teachers of Mathematics in 1978. “That problem solving be the focus of school mathematics in the 1980s” is the first of eight recommendations expressed in An Agenda for Action: Recommendations for School Mathematics of the 1980s published by the NCTM.

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.

Activities for Students: Transformations on Data Sets and Their Effects on Descriptive Statistics

2005 ◽  
Vol 99 (3) ◽  
pp. 208-217
Author(s):  
Thomas B. Fox
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Descriptive Statistics ◽  
Data Sets ◽  
National Council ◽  
Data Set ◽  
Scale Change ◽  
School Mathematics Curriculum

The development of concepts in statistics and functions is an important part of the school mathematics curriculum. Also important is the formulation and verification of mathematical conjectures (National Council of Teachers of Mathematics 2000). This activity asks students to examine the effects on the descriptive statistics of a data set that has undergone either a translation or a scale change. They make conjectures relative to the effects on the statistics of a transformation on a data set. Students then defend their conjectures and deductively verify several of them.

Mathematical Roots: The Other Life of Florence Nightingale

2002 ◽  
Vol 7 (6) ◽  
pp. 337-339
Author(s):  
Christine Annette Franklin
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
The Other ◽  
German Mathematician ◽  
Florence Nightingale ◽  
Probability And Statistics ◽  
Bell Shaped Curve ◽  
School Mathematics Curriculum

Probability and Statistics are important parts of the school mathematics curriculum. Many students believe that these areas are recent additions to the field of mathematics. Probability and statistics, however, have been actively studied for more than three hundred years. James Bernoulli (1654–1705), a Swiss mathematician, developed important probability concepts. Johann Carl Friedrich Gauss (1777–1855) was a German mathematician who studied the distribution that takes on the famous bell-shaped curve. Another statistician from England, R. A. Fisher (1890–1962), argued for the importance of randomness when designing an experiment. All these men are well-known statisticians who made important contributions to the field of statistics. An individual who is not commonly discussed as an early contributor to the study of statistics is the famous English nurse Florence Nightingale (1820–1910).

Preparing prospective teachers of elementary school mathematics

1968 ◽  
Vol 15 (7) ◽  
pp. 643-651
Author(s):  
W. Robert Houston
Keyword(s):  
Elementary School ◽  
Prospective Teachers ◽  
Human Learning ◽  
School Mathematics ◽  
Elementary School Mathematics ◽  
The Past ◽  
The Future ◽  
Younger Generation ◽  
Modern Mathematics

During the past decade, major changes have occurred in mathematics in the elementary school, both in content and approach. Indeed, “modern mathematics” has become a household term epitomizing the radical changes in today's curriculum which separate the younger generation from their parents. Parents complain they can no longer understand, much less help their children with mathematics. Innovations in experimental programs, technical advancements, and new insights into human learning promise even greater changes in the future.

Focal Point: The Cambridge Conference on School Mathematics

1964 ◽  
Vol 11 (3) ◽  
pp. 207-210
Author(s):  
J. Fred Weaver
Keyword(s):  
Mathematics Education ◽  
Significant Influence ◽  
Mathematics Curriculum ◽  
Focal Point ◽  
School Mathematics ◽  
The Past ◽  
The Subject

Within the past year a potentially significant influence on the mathematics curriculum and on mathematics education has become the subject of much interest and discussion. We refer to that which is known simply as “The Cambridge Conference on School Mathematics.”

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