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.

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).

Teacher to Teacher: Playing around with Mono-pi-ly

2006 ◽  
Vol 11 (6) ◽  
pp. 294-297
Author(s):  
Cindy Kroon
Keyword(s):  
South Dakota ◽  
Three Dimensional ◽  
Department Of Education ◽  
School Mathematics ◽  
Mathematics Students ◽  
Measurement Standard ◽  
Three Dimensional Objects ◽  
Principles And Standards

According to the geometry standard in Principles and Standards for School Mathematics, “In grades 6–8, all students should precisely describe, classify, and understand relationships among types of two- and three- dimensional objects” (NCTM 2000, p. 232). The Measurement Standard goes on to state, “In grades 6–8, all students should develop and use formulas to determine the circumference of circles” (NCTM 2000, p. 240). In addition, South Dakota's Measurement Standard for Grade 7 delineates what mathematics students should know, such as “Given the formulas, find the circumference, perimeter, and area of circles” (South Dakota Department of Education 2004).

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 Case of Units

2003 ◽  
Vol 9 (7) ◽  
pp. 397-399
Author(s):  
Christopher M. Kribs-Zaleta ◽  
D'Lynn Bradshaw
Keyword(s):  
Young Children ◽  
Learning Opportunities ◽  
School Mathematics ◽  
Learning Potential ◽  
Mathematical Development ◽  
Great Learning ◽  
The World ◽  
Principles And Standards ◽  
Children’S Work

Young children learn by playing, and they first learn mathematics through exploration that develops naturally from their curiosity and experiences. They count, build, draw, model, and measure the world around them. The informal origins of their first mathematical insights remain an important link to the role of context in learning at any age. It is especially important for teachers to know this, in order to be alert to learning opportunities that arise. By paying attention to the details in students' conversations, we can develop the habit of listening to their mathematical discoveries. Encouraging and focusing these discoveries often releases the great learning potential inside students. Principles and Standards for School Mathematics (NCTM 2000) elaborates on the idea of play being children's work by observing, “Adults support young children's diligence and mathematical development when they direct attention to the mathematics children use in their play, challenge them to solve problems, and encourage their persistence” (p. 74).

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.

Selecting High-Quality Mathematics Textbooks

2006 ◽  
Vol 12 (1) ◽  
pp. 50-54
Author(s):  
James E. Tarr ◽  
Barbara J. Reys ◽  
David D. Barker ◽  
Rick Billstein
Keyword(s):  
Mathematics Learning ◽  
High Stakes Testing ◽  
School Personnel ◽  
Learning Opportunities ◽  
School Mathematics ◽  
High Quality ◽  
High Stakes ◽  
Principles And Standards ◽  
Curricular Materials ◽  
Silver Bullet

In this era of high-stakes testing and public accountability, school personnel are scrambling for ways to improve mathematics learning opportunities for all students. Although there is no single silver-bullet solution, Principles and Standards for School Mathematics (NCTM 2000) provides guidelines for designing high-quality school mathematics programs. One avenue for strengthening programs is through selecting and implementing high-quality curricular materials (textbooks).

Prisms and Pyramids: Constructing Three-Dimensional Models to Build Understanding

2003 ◽  
Vol 9 (8) ◽  
pp. 436-442
Author(s):  
Beverly A. Koester
Keyword(s):  
Three Dimensional ◽  
School Mathematics ◽  
Plane Geometry ◽  
Elementary Grades ◽  
Two Dimensional ◽  
Rich Variety ◽  
Dimensional Models ◽  
Principles And Standards ◽  
Three Dimensional Models

The Geometry Standard of NCTM's Principles and Standards for School Mathematics (2000) describes the study of both two- and three-dimensional shapes. In the elementary grades, plane geometry often receives more emphasis than does three-dimensional geometry. In many classrooms, students actively explore two-dimensional shapes using a rich variety of materials, including tangrams, geoboards, and pattern blocks. Materials and lessons for exploring three-dimensional shapes are not as prevalent.

What influence will the new Principles and Standards for School Mathematics (2000) have?

2000 ◽  
Vol 31 (4) ◽  
pp. 394-395
Author(s):  
Judith T. Sowder
Keyword(s):  
Annual Meeting ◽  
Research Community ◽  
School Mathematics ◽  
The Public ◽  
Principles And Standards

The new NCTM Principles and Standards for School Mathematics (2000) were presented to the public with great fanfare at the NCTM Annual Meeting in Chicago in April of this year. The mood was celebratory, perhaps even more so than when the 1989 Standards were presented. How will these new Principles and Standards be accepted? What influence will they have? Are there messages here to which the research community ought to be attending?

Bringing Dynamic Geometry to Three Dimensions

2015 ◽  
pp. 68-99
Author(s):  
Nicholas H. Wasserman
Keyword(s):  
Teaching And Learning ◽  
Spatial Reasoning ◽  
Mathematics Classroom ◽  
Three Dimensional ◽  
Dynamic Geometry ◽  
State Standards ◽  
Three Dimensions ◽  
Two Dimensional ◽  
The Common ◽  
K 12

Contemporary technologies have impacted the teaching and learning of mathematics in significant ways, particularly through the incorporation of dynamic software and applets. Interactive geometry software such as Geometers Sketchpad (GSP) and GeoGebra has transformed students' ability to interact with the geometry of plane figures, helping visualize and verify conjectures. Similar to what GSP and GeoGebra have done for two-dimensional geometry in mathematics education, SketchUp™ has the potential to do for aspects of three-dimensional geometry. This chapter provides example cases, aligned with the Common Core State Standards in mathematics, for how the dynamic and unique features of SketchUp™ can be integrated into the K-12 mathematics classroom to support and aid students' spatial reasoning and knowledge of three-dimensional figures.

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