Principles and Standards (2002): April 2002

2002 ◽  
Vol 8 (8) ◽  
pp. 482-487
Author(s):  
James E. Tarr
Keyword(s):  
Data Analysis ◽  
Probability Learning ◽  
School Mathematics ◽  
Content Standards ◽  
Instructional Programs ◽  
Learning Expectations ◽  
Basic Concepts ◽  
Principles And Standards ◽  
K 12 ◽  
Standard States

NCTM's Principles and Standards for School Mathematics (2000) identifies Data Analysis and Probability as one of the five content standards for pre-K–12 mathematics and delineates learning expectations at each of four grade bands. This standard places much more emphasis on data analysis than on probability, particularly for grades pre-K through 5. Indeed, only one of the four goals in the standard directly addresses probability, and no probability learning expectations are explicitly stated for grades pre-K through 2. The standard states, however, that “instructional programs from prekindergarten through grade 12 should enable all students to understand and apply basic concepts of probability” (p. 48).

How Reform Secondary Mathematics Texts Stack Up against NCTM's Principles and Standards

2001 ◽  
Vol 94 (7) ◽  
pp. 540-589
Author(s):  
Tami S. Martin ◽  
Cheryl A. Hunt ◽  
John Lannin ◽  
William Leonard ◽  
Gerald L. Marshall ◽  
...  
Keyword(s):  
Secondary Mathematics ◽  
School Mathematics ◽  
Content Standards ◽  
Distinctive Features ◽  
Mathematics Curricula ◽  
Principles And Standards

This analysis of the five NSF–funded secondary mathematics curricula describes their alignment with the Process Standards and Content Standards in Principles and Standards for School Mathematics. Distinctive features and examples are included.

Writing About the Problem Solving Process to Improve Problem Solving Performance

2003 ◽  
Vol 96 (3) ◽  
pp. 185-187 ◽  
Author(s):  
Kenneth M. Williams
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
National Council ◽  
Instructional Programs ◽  
Principles And Standards ◽  
Problem Solving Process ◽  
Problem Solvers

Problem solving is generally recognized as one of the most important components of mathematics. In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics emphasized that instructional programs should enable all students in all grades to “build new mathematical knowledge through problem solving, solve problems that arise in mathematics and in other contexts, apply and adapt a variety of appropriate strategies to solve problems, and monitor and reflect on the process of mathematical problem solving” (NCTM 2000, p. 52). But how do students become competent and confident mathematical problem solvers?

Activities for Students: A Matter of Survival

2002 ◽  
Vol 95 (2) ◽  
pp. 100-112
Author(s):  
Victoria Young
Keyword(s):  
Data Analysis ◽  
School Mathematics ◽  
Medical Patients ◽  
Current Technology ◽  
Principles And Standards ◽  
Abundant Data ◽  
Analyze Data

The Data Analysis and Probability Standard of Principles and Standards for School Mathematics (NCTM 2000) urges students in all grades to devise ways to gather and analyze data. The vast quantities of data that will confront these future citizens, businesspeople, consumers, and medical patients will be overwhelming unless they have the tools that they need to interpret these data. Probability simulations offer ways to quickly gather abundant data, and current technology can readily support the accumulation of randomly generated results. This activity facilitates the implementation of these mathematical goals in an appealing way.

Principles and Standards: What is Algebra in Elementary School

2001 ◽  
Vol 8 (4) ◽  
pp. 196-200
Author(s):  
Jennifer M. Bay-Williams
Keyword(s):  
High School ◽  
Elementary School ◽  
School Children ◽  
Elementary School Children ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Early Mathematics ◽  
Principles And Standards ◽  
Abstract Content ◽  
K 12

Patterns have long been part of early mathematics experiences. The K–4 Patterns and Relationships Standard in Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) was replaced in Principles and Standards for School Mathematics (NCTM 2000) with a K–12 Algebra Standard. This Standard encompasses patterns, functions, and some topics that are beyond what traditionally was considered to be algebra. However, the word algebra, often associated with content covered in a traditional middle school or high school course, can evoke feelings of anxiety and raise questions of appropriateness when discussed in relation to elementary school children. What is algebra in elementary school if it is more than identifying and extending patterns in the early grades yet is not the abstract content of an algebra course?

A Look at the Development of Data Representation and Analysis in Curriculum Focal Points: A Quest for Coherence

2007 ◽  
Vol 13 (4) ◽  
pp. 208-210
Author(s):  
Jane F. Schielack ◽  
Cathy Seeley
Keyword(s):  
Data Analysis ◽  
Grade Level ◽  
Focal Point ◽  
Data Representation ◽  
School Mathematics ◽  
Descriptive Statistics ◽  
Focal Points ◽  
Principles And Standards ◽  
Grade 8 ◽  
Developing Knowledge

One of the questions often raised with regard to NCTM's Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence is, “Where are data representation and analysis?” In this month's Focal Points feature, we take a look at an area of content—data representation and analysis—that is important enough to warrant a separate strand in Principles and Standards for School Mathematics (NCTM 2000) but that does not appear in the title of a content Focal Point until Grade 8. However, in the Appendix of Curriculum Focal Points, in comparison with Principles and Standards, it is clear that the content of the Data Analysis strand presented in each of the pre- K–2, 3–5, and 6–8 grade bands in the Standards is included in the specific grade-level descriptions in Curriculum Focal Points. Skills for data representation begin in prekindergarten and appear throughout later grades and are presented as connections to the concepts and skills involved in the Geometry and Measurement Focal Points. In Kindergarten through Grade 7, data representation and analysis in the Connections to the Focal Points sections also provide meaningful contexts as students apply their developing knowledge of number and operations. In Grade 8, the analysis of data through descriptive statistics becomes a Focal Point in itself.

Racing against Time: Using Technology to Explore Distance, Rate, and Time

2002 ◽  
Vol 8 (6) ◽  
pp. 322-347
Author(s):  
N. Kathryn Essex ◽  
Diana V. Lambdin ◽  
Rebecca H. McGraw
Keyword(s):  
Computer Technology ◽  
School Mathematics ◽  
Nonlinear Functions ◽  
Linear And Nonlinear ◽  
Principles And Standards ◽  
And Algebra ◽  
K 12

According to Principles and Standards for School Mathematics, one of the four major ideas permeating the study of patterns and algebra throughout grades pre-K–12 is analyzing “change in various contexts” (NCTM 2000, p. 37). Our focus in this article is on how computer technology can provide simple and motivating contexts for children's investigations of patterns of change and, in the process, help develop foundational ideas of algebra and calculus. We also offer brief explanations for teachers about how various patterns of change relate to such fundamental algebraic notions as linear and nonlinear functions; these same ideas collectively form the basis for an understanding of derivatives and integrals in calculus.

Understanding Transformations of Periodic Functions through Art

2001 ◽  
Vol 94 (8) ◽  
pp. 632-635
Author(s):  
Syrilda Miller
Keyword(s):  
Core Curriculum ◽  
School Mathematics ◽  
Professional Organizations ◽  
Content Standards ◽  
Periodic Functions ◽  
Curriculum Content ◽  
Principles And Standards

The use of interdisciplinary units can satisfy requirements found not only in the NCTM's Principles and Standards for School Mathematics (2000) but also in such state guidelines as New Jersey's Core Curriculum Content Standards. The secret to developing connected curricula is to use professional connections, which include many resources: professional organizations, teachers, and your own students.

Measurement: What's the Big Idea?

2004 ◽  
Vol 9 (8) ◽  
pp. 430-431
Author(s):  
Sherri Martinie
Keyword(s):  
Three Dimensional ◽  
Learning Opportunities ◽  
School Mathematics ◽  
Actual Performance ◽  
Principles And Standards ◽  
K 12

The value of building a strong understanding of measurement must not be underestimated. The skills of measurement are frequently encountered in realworld situations, from measuring the size of a room to measuring the time it takes to run a mile in gym class to the amount of water used when a faucet drips. Instruction involving measurement should focus on teaching students, K–12, to 'understand measurable attributes of objects … and apply appropriate techniques, tools, and formulas to determine measurements' (NCTM's Principles and Standards for School Mathematics, p. 44). These measurements may be one, two, or three dimensional and involve length, weight, capacity, time, or temperature. However, research on measurement reports that this concept harbors the largest discrepancy between learning opportunities and actual performance, meaning that although students are instructed in measurement skills in school, they cannot show that they have learned the concept.

Elastic, Cottage Cheese, and Gasoline: Visualizing Division of Fractions

2008 ◽  
Vol 14 (4) ◽  
pp. 208-212
Author(s):  
Sallie Peck ◽  
Japheth Wood
Keyword(s):  
School Mathematics ◽  
Cottage Cheese ◽  
Instructional Programs ◽  
Mathematical Representations ◽  
Division Of Fractions ◽  
Principles And Standards

Representation is one of the five Process Standards from Principles and Standards for School Mathematics. This Standard proposes that prekindergarten through grade 12 instructional programs should enable students to “select, apply, and translate among mathematical representations to solve problems” (NCTM 2000, p. 67). To implement a program that meets this Standard, teachers themselves must have attained this level of proficiency.

Activities for Students: Designing the Dynamic Domino Race

2002 ◽  
Vol 95 (7) ◽  
pp. 502-508
Author(s):  
Elizabeth George Bremigan
Keyword(s):  
Data Analysis ◽  
Mathematics Teachers ◽  
Olympic Games ◽  
Numerical Data ◽  
School Mathematics ◽  
Principles And Standards ◽  
The Olympic Games

Students of all ages are enthusiastic about the Olympic Games. Many mathematics teachers use this context as an opportunity for students to examine numerical data while they display and discuss the results of different events and the success of various countries during the Olympic Games. These discussions allow teachers to address several aspects of the Data Analysis and Probability Standard from Principles and Standards for School Mathematics (NCTM 2000).

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