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.

Implementing The Standards: Evaluation: A New Vision

1991 ◽  
Vol 84 (4) ◽  
pp. 276-284
Author(s):  
Frank K. Lester ◽  
Diana Lambdin Kroll
Keyword(s):  
Instructional Practices ◽  
Evaluation Process ◽  
School Mathematics ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Evaluation Program ◽  
Testing Procedures ◽  
Mathematics Program ◽  
New Vision

Teaching according to the vision of the NCTM's Curriculum and Evaluation Standards will involve numerous changes in the content and instruction of the school mathematics program. Moreover, this vision will also require a change in testing procedures and methods for evaluating the effectiveness of instructional practices (Clarke, Clarke, and Lovitt 1990; EQUALS and California Mathematics Council 1989; NAEP 1987; NCTM 1989). As is pointed out in NCTM's curriculum standards, an evaluation program that is properly aligned with the proposed curriculum standards can no longer use only written tests. Calculators, computers, and manipulatives must be included in the evaluation process.

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.

Thematic Webbing and the Curriculum Standards in the Primary Grades

1994 ◽  
Vol 41 (6) ◽  
pp. 294-298
Author(s):  
Jenny A. Piazza ◽  
Margaret M. Scott ◽  
Elizabeth C. Carver
Keyword(s):  
Instructional Practices ◽  
Mathematical Knowledge ◽  
Mathematical Thinking ◽  
Primary Grades ◽  
School Mathematics ◽  
National Council ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Curricular Content

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) reflects the importance of understanding the development of knowledge at the K-4 level. The standards document recognizes that current instructional and curricular content must focus on students' active construction of mathematical knowledge. Instructional practices need to be conceptually oriented, involve children actively, emphasize the development of mathematical thinking and application, and include a broad range of content.

Implementing the Professional Standards for Teaching Mathematics: Sharing, Supporting, Risk Taking: First Steps to Instructional Reform

1992 ◽  
Vol 85 (6) ◽  
pp. 466-470
Author(s):  
Steven J. Leinwand
Keyword(s):  
Risk Taking ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Curriculum Standards ◽  
Instructional Reform ◽  
Evaluation Standards ◽  
Teaching Standards

For many of us, the Professional Standards for Teaching Mathematics (NCTM 1991) represents a much scarier and much more intimidating vision of school mathematics than its predecessor, the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). Accordingly, implementing the teaching standards will require different strategies from those being used or proposed to implement the curriculum standards.

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.

Sharing Teaching Ideas: A Mathematical Investigation of Quality Control

1995 ◽  
Vol 88 (3) ◽  
pp. 200-202
Author(s):  
Richard T. Edgerton
Keyword(s):  
Quality Control ◽  
Real World ◽  
School Mathematics ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Mathematical Investigation ◽  
Teaching Ideas ◽  
Real World Problems

One way to apply the principles of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) is to use real-world problems. The curriculum standards are enacted as students develop “mathematical power” while they communicate, reason, and make connections within and outside mathematics.

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?

Teaching Mathematics with Technology: Exploring Geometry with The Geometer's Sketchpad

1992 ◽  
Vol 40 (3) ◽  
pp. 187-191
Keyword(s):  
Middle School ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Geometer's Sketchpad ◽  
Curriculum Standards ◽  
Older Students ◽  
Evaluation Standards ◽  
Geometric Objects ◽  
Elementary And Middle School

Have you ever thought of exploring geometric relationships on the computer? The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) challenges us to pay increased attention to “developing an understanding of geometric objects and relationships” and “using geometry in solving problems” (p.70). The document also advises placing decreased emphasis on memorizing geometric vocabulary, facts, and relationships. This article describes several geometric investigations that were developed in the spirit of the curriculum standards and are appropriate for use at advanced elementary and middle school levels, as well as with older students. They encourage exploration, creativity, and discovery.

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