Writing to Learn Mathematics

1991 ◽  
Vol 84 (7) ◽  
pp. 516-521 ◽  
Author(s):  
L. Diane Miller
Keyword(s):  
School Mathematics ◽  
Writing To Learn ◽  
Content Area ◽  
Evaluation Standards ◽  
Learn Strategy ◽  
K 12 ◽  
Relevant Material

The use of the writing-to-learn strategy in mathematics classes is one way teachers can implement “Mathematics as Communication,” the second standard in NCTM's (1989) Curriculum and Evaluation Standards for School Mathematics. For students in grades K-12, writing is suggested as a means through which students should be able to communicate their understanding of mathematics and its applications. Using writing in a content area has earned the support of many educators. Emig (1977) believes that writing in a content area can cause students to analyze, compare facts, and synthesize relevant material. Writing about a topic requires students to think about the topic, focus on and internalize important concepts, and make those concepts to some degree their owu (Kennedy 1980).

Who's Winning at Monopoly Junior?

1999 ◽  
Vol 92 (3) ◽  
pp. 197-203
Author(s):  
Donald E. Hooley
Keyword(s):  
Modeling And Simulation ◽  
School Mathematics ◽  
Content Area ◽  
Real Problem ◽  
Evaluation Standards

A “real” problem for many students with younger siblings, in the spirit of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). This article also illustrates the use of modeling and simulation, which Burrill (1997) notes that mathematicians in industry report using more than any other content area.

Integrating Manipulatives and Computers in Problem-Solving Experiences

1990 ◽  
Vol 38 (2) ◽  
pp. 8-10
Author(s):  
Sue Brown
Keyword(s):  
Problem Solving ◽  
Group Work ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Good Mathematics Instruction ◽  
K 12

In 1980, the National Council of Teachers of Mathematics stated that “problem solving must be the focus of school mathematics.” In 1989 the Council reaffirmed that belief with the Curriculum and Evaluation Standards for School Mathematics (Standards). Standard 1 for grades K–12 is “Mathematics as Problem Solving.” The Standards also asserts that “a computer should be available in every classroom for demonstration purposes, and every student should have access to a computer for individual and group work.” Also according to the Standards, “manipulative materials are necessary for good mathematics instruction.” In a typical classroom, problem solving may be taught, manipulative materials may be used, or students may be working at a computer. These functions, however, are usually completed as disjoint activities. Integrating these activities is possible, and this article illustrates how it can be done.

Mathematical Modeling and the Presidential Election

1992 ◽  
Vol 85 (7) ◽  
pp. 520-521
Author(s):  
Joseph C. Witkowski
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Secondary Schools ◽  
Presidential Election ◽  
Presidential Elections ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Modeling Problem ◽  
Mathematical Sciences ◽  
K 12

In recent years, interest in problem solving and mathematical modeling has increased. In 1975, the Conference Board of the Mathematical Sciences issued its Overview and Analysis of School Mathematics K-12, which recommended the incorporation of mathematical applications and modeling into secondary schools. More recently the Curriculum and Evaluation Standards for School Mathematics (1989) formulated by the NCTM stressed the importance of mathematical modeling as a facet of problem solving. The purpose of this article is to look at an interesting mathematical-modeling problem regarding presidential elections.

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.

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?

NCTM's Standards for School Mathematics, K – 12

1988 ◽  
Vol 81 (5) ◽  
pp. 348-351
Author(s):  
Charles S. Thompson ◽  
Edward C. Rathmell
Keyword(s):  
Mathematics Education ◽  
School Districts ◽  
Mathematics Learning ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
State And Local ◽  
K 12 ◽  
National Tests ◽  
Local Levels

The National Council of Teachers of Mathematics is in the process of generating a set of Curriculum and Evaluation Standards for School Mathematics (Standards) (Commission on Standards of the NCTM 1987). NCTM has committed considerable resources to this project, anticipating that the Standards will have a pervasive effect on mathematics education during the next five to ten years. The expectation is that the Standards will influence curriculum writing at the state and local levels and that the resulting curricular changes will influence the content of textbooks adopted by states and school districts. Furthermore, the newly written curricula, together with the new Standards for the evaluation of mathematics learning, should influence the content and emphasis of local, state, and national tests.

Implementing The Standards: Teaching Informal Algebra

1991 ◽  
Vol 38 (9) ◽  
pp. 34-37
Author(s):  
James E. Schultz
Keyword(s):  
School Mathematics ◽  
Evaluation Standards ◽  
Early Grades ◽  
Formal Concepts ◽  
Algebraic Concepts ◽  
And Algebra ◽  
K 12

Algebra is described in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989, 150) as “the language through which most of mathematics is communicated.” For many years algebra has often referred to a single course or two featuring manipulative skills and punctuated by other courses called prealgebra or geometry. In the spirit of the Curriculum and Evaluation Standards, it is more appropriate to think of algebra as a cohesive body of concepts, closely connected to other branches of mathematics, in which manipulative skills play a supporting rather than star role. In this context, the distinction between prealgebra and algebra is less apparent. Rather, a gradual building from informal to formal concepts takes place over most of the K–12 curriculum. In the continuing series on implementing the Standards, this article presents suggestions for developing algebraic concepts beginning in the early grades.

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).

A Brief Look at the History of Probability and Statistics

1991 ◽  
Vol 84 (8) ◽  
pp. 623-630
Author(s):  
James E. Lightner
Keyword(s):  
Historical Development ◽  
Human Factor ◽  
School Mathematics ◽  
School Program ◽  
Evaluation Standards ◽  
History Of ◽  
Probability And Statistics ◽  
The Creation ◽  
K 12

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) includes concepts from probability and statistics throughout the school program, K- 12. Indeed, these areas of mathematics are listed as topics for increased attention in the curriculum. Because of this emphasis, all teachers should become more aware of the historical development of these areas of mathematics so we can incorporate historical topics for motivation and extension of the content and so we can show the very human factor in the creation of mathematics. Let us, therefore, trace the development of the areas of probability and statistics.

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