Soundoff!–Teaching Applications: Will the Pendulum of Reform Swing Too Far?

1996 ◽  
Vol 89 (6) ◽  
pp. 450-451
Author(s):  
Peter L. Glidden
Keyword(s):  
High School ◽  
School Mathematics ◽  
Recent Experience ◽  
Mathematics Reform ◽  
Evaluation Standards ◽  
New Math ◽  
The Way

Before getting to the main point of this article, I need to make a confession: I am a product of the “new math.ȝ I had the “new math” from kindergarten all the way through high school. The “new math” influenced my understanding of what mathematics is and what doing mathematics means. Most of the time I am not conscious of this influence, but a recent experience made me nostalgic for two, interrelated ideas of the “new math.” I believe that these ideas are just as valid today as they were thirty years ago. More important, as the pendulum of school mathematics reform swings toward the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and away from any residual legacy of the “new math,” we need to retain these two ideas.

On My Mind: The Standards—Some Second Thoughts

1996 ◽  
Vol 2 (1) ◽  
pp. 8-11
Author(s):  
Stephen S. Willoughby
Keyword(s):  
Mathematics Education ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Professional Educators ◽  
The Way

Members of the National Council of Teachers of Mathematics can be proud of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). Not only has the Standards document set the course for improving mathematics education, but it has been imitated by virtually every other content-oriented teachers' organization. Thus, as well as recasting mathematics education, the NCTM has led the way toward recasting education generally. However, professional educators have an obligation to reconsider and reflect on the Standards themselves and any other recommendations made by responsible educators and organizations.

Students Generating Test Items: A Teaching and Assessment Strategy

1998 ◽  
Vol 91 (3) ◽  
pp. 198-202
Author(s):  
Victor U. Odafe
Keyword(s):  
Learning Process ◽  
Teaching And Learning ◽  
School Mathematics ◽  
Mathematics Reform ◽  
Evaluation Standards ◽  
Assessment Strategy ◽  
Test Items

The more students invest in their own learning process, the more they will learn. This widely documented view is supported by publications from the mathematics-reform community. For example, the National Research Council's (NRC) Moving beyond Myths (1991) and Everybody Counts (1989) and NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) have called for changes in the teaching and learning of mathematics.

Prove It

1998 ◽  
Vol 91 (8) ◽  
pp. 726-728
Author(s):  
Amy A. Prince
Keyword(s):  
High School ◽  
School Mathematics ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry

Ask anyone who has taken high school geometry, and he or she will have a notion of a proof— generally, a two-column proof of statements and reasons. The two-column proof has fallen out of favor in such reform documents as the NCTM's Curriculum and Evaluation Standards for School Mathematics, which seeks to emphasize “deductive arguments expressed orally or in sentence or paragraph form” (NCTM 1989, 126). The two-column proof is a somewhat rigid form, yet it demonstrates to the students that they may not just give statements or draw conclusions without sound mathematical reasons.

One Point of View: The Dangers of Implementing the Standards; or, When Bad Things Happen to Good Ideas

1992 ◽  
Vol 40 (1) ◽  
pp. 8-9
Author(s):  
David J. Whitin
Keyword(s):  
Mathematics Education ◽  
Whole Language ◽  
Writing Process ◽  
Language Education ◽  
Point Of View ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The Way

A trhough I embrace the vision that the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) sets for us in the field of mathematics education, I am already worried about the way many people have begun to interpret it. My concerns echo those in the field of language education who fear the same fare for the writing process and whole language movement. Bad things can happen to good ideas, including the curriculum and evaluation standards, unless we are clear about what that document is and is not.

International Mathematical Education: High School Mathematics Reform in Greece

1966 ◽  
Vol 59 (7) ◽  
pp. 671-674
Author(s):  
C. B. Glavas
Keyword(s):  
High School ◽  
School Mathematics ◽  
Mathematical Education ◽  
Mathematics Reform ◽  
High School Mathematics ◽  
International Mathematical

In this article the school mathematics reform in Greece is examined. The exposition is on the present phase of the reform, which is limited to the lower cycle of the high school (ages twelve to fifteen).

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.

Connecting Research to Teaching: Mathematics as Reasoning

1995 ◽  
Vol 88 (5) ◽  
pp. 412-417
Author(s):  
Peter Galbraith
Keyword(s):  
High School ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematical Quality

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) defines a role for reasoning in school mathematics that is far different from the norm of recent practice. Until recently, the study of mathematical reasoning was largely confined to high school geometry. Further, as Schoenfeld (1988) pointed out, the approach used in geometry was often so rigid that it conveyed the impression that the style of the response—for example, the two-column-proof format—was more important than its mathematical quality. The Standards document notes that reasoning is to have a role in all of mathematics from the earliest grades on up and that the form of justification need not follow a pre scribed format. Indeed, students are encouraged to explain their reasoning in their own words. Teachers are asked to present opportunities for students to refine their own thoughts and language by sharing ideas with their peers and the teacher.

Using The Geometer's Sketchpad to Visualize Maximum-Volume Problems

2000 ◽  
Vol 93 (3) ◽  
pp. 224-228 ◽  
Author(s):  
David C. Purdy
Keyword(s):  
High School ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Geometer's Sketchpad ◽  
Maximum Volume ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Traditional Courses

An underlying tenet of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and other movements toward reform in school mathematics is breaking down content barriers between traditional mathematical topics, with the goal of teaching mathematics as a logically interconnected body of thought. As teachers move toward integrating the various areas of mathematics into traditional courses, problems that were once reserved for higher courses, for example, precalculus and calculus, now surface earlier as interesting explorations that can be tackled with such tools as the graphing calculator. One such problem is the well-known maximum-volume-box problem. Although this problem and related optimization questions have been common in advanced algebra, precalculus, and calculus textbooks, they have only recently found their way into high school geometry textbooks, including Discovering Geometry: An Inductive Approach (Serra 1997).

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?

Aligning Assessment with the NCTM's Curriculum Standards

1993 ◽  
Vol 86 (9) ◽  
pp. 722-725
Author(s):  
Cathy G. Schloemer
Keyword(s):  
High School ◽  
School Mathematics ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Ideal Situation ◽  
The Ideal

I recently found myself in the ideal situation of wanting to integrate the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) more fully into my teaching and, at the same time, being enrolled in a class that required me to research some aspect of assessment and then engage in a practical assessment project. As a result, I decided to find out more about standardsaligned assessment and then see if could use it with my high school precalculus students.

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