Ideas for Developing Students’ Reasoning: A Hungarian Perspective

1998 ◽  
Vol 91 (8) ◽  
pp. 677-681
Author(s):  
Anita Szombathelyi ◽  
Tibor Szarvas
Keyword(s):  
Twentieth Century ◽  
Mathematics Education ◽  
Teaching Assistants ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Evaluation Standards ◽  
American University ◽  
Graduate Teaching ◽  
Reasoning Skills ◽  
End Results

As the end of the twentieth century approaches, we start to realize again the significance of proof in mathematics education. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) cautions against the tendency to completely abandon proofs and focus only on the end results and formulas. In this article, we reemphasize the importance of proofs in teaching by sharing some of our experiences as students and teachers in Hungary, in addition to our experiences as graduate teaching assistants at an American university. We offer examples and ideas that might help educators develop students' mathematical reasoning skills.

One Point of View: Reclaiming School Mathematics

1990 ◽  
Vol 37 (8) ◽  
pp. 4-5
Author(s):  
Portia Elliott
Keyword(s):  
Mathematics Education ◽  
Mathematics Curriculum ◽  
Point Of View ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Design Change

The framers of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) call for a radical “design change” in all aspects of mathematics education. They believe that “evaluation is a tool for implementing the Standards and effecting change systematically” (p. 189). They warn, however, that “without changes in how mathematics is assessed, the vision of the mathematics curriculum described in the standards will not be implemented in classrooms, regardless of how texts or local curricula change” (p. 252).

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.

Felix Klein and the NCTM's Standards: A Mathematician Considers Mathematics Education

2000 ◽  
Vol 93 (8) ◽  
pp. 714-717
Author(s):  
Kim Krusen McComas
Keyword(s):  
Mathematics Education ◽  
School Mathematics ◽  
Rote Learning ◽  
German Mathematician ◽  
Evaluation Standards ◽  
10Th Anniversary ◽  
Felix Klein ◽  
Look Back ◽  
Principles And Standards ◽  
Year 2000

The year 1999 marked the 10th anniversary of the NCTM's Curriculum and Evaluation Standards for School Mathematics. It also marked the 150th anniversary of the birth of German mathematician Felix Klein, who lived from 1849 to 1925. Although the relation between these two anniversaries may not be obvious, the connection is that Klein, were he still alive today, would probably support the NCTM's Standards. As the year 2000 brings us NCTM's Principles and Standards for School Mathematics, let us look back to the year 1900 and find Felix Klein at the forefront of a movement to reform mathematics education from rote learning to more meaningful mathematical learning.

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.

Soundoff: Where are the Counselors?

1992 ◽  
Vol 85 (7) ◽  
pp. 510-511
Author(s):  
Marla P. Peterson
Keyword(s):  
Mathematics Education ◽  
School Counselors ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Education Assessment ◽  
Education Profession

While reading the list of people who were involved in planning the 1991 National Summit on Mathematics Education Assessment, I noticed that no school counselors were included. However, individuals who have given excellent support to school counselors were represented. These National Summit representatives, along with others who are implementing and assessing the effectiveness of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989), need to encourage the mathematics education profession to solicit assistance from school counselors.

Implementing the “Curriculum and Evaluation Standards”: Recognizing and Recording Reform in Mathematics: New Questions, Many Answers

1994 ◽  
Vol 87 (3) ◽  
pp. 190-193
Author(s):  
Joan Ferrini-Mundy ◽  
Loren Johnson ◽  
James R. Smart
Keyword(s):  
Mathematics Education ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Anecdotal Evidence ◽  
Reform Effort ◽  
Evaluation Standards ◽  
Curriculum And Pedagogy ◽  
Standards Documents

NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and its Professional Standards for Teaching Mathematics (1991) lend possible direction and meaning to the reform effort in mathematics education that is sweeping the country. The documents have been widely disseminated and discussed, and anecdotal evidence indicates that teachers of mathematics are seeking ways to enact the ideas contained in the standards documents. These documents are also inspiring the development of standards in other disciplines. But a number of questions are being raised as schools, districts, states, and provinces attempt to incorporate these Standards in changing their curriculum and pedagogy.

Projects: Developing Modelers and Modeling Opportunities: The Stepping Stones Project

1997 ◽  
Vol 90 (8) ◽  
pp. 686-688
Keyword(s):  
Mathematical Modeling ◽  
Mathematics Education ◽  
Real World ◽  
Mathematical Knowledge ◽  
School Mathematics ◽  
Stepping Stones ◽  
Evaluation Standards ◽  
The Real ◽  
World Modeling

Mathematical modeling is an emerging theme in mathematics education. In addition to giving students a knowledge of the applications of mathematics and a process for applying mathematics in the “real” world, modeling offers teachers an excellent vehicle for introducing and developing students' mathematical knowledge. For these reasons, modeling occupies a prominent place in the recommendations of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).

Illustrating Mathematical Connections: A Geometric Proof of Euler's Theorem

1996 ◽  
Vol 89 (1) ◽  
pp. 62-65
Author(s):  
Erin K. Frye ◽  
Peter L. Glidden
Keyword(s):  
Mathematical Reasoning ◽  
School Mathematics ◽  
Geometric Proof ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Euler’S Theorem ◽  
Problem Solvers

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) calls for teachers to emphasize mathematical connections, promote mathematical reasoning, and help students become better problem solvers. If teachers are to achieve these goals, they need compelling examples, problems, and theorems that address all these elements.

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.

Sign in / Sign up

Export Citation Format

Share Document