Implementing the Professional Standards for Teaching Mathematics: Analyzing Teaching and Learning: The Art of Listening

1996 ◽  
Vol 89 (4) ◽  
pp. 326-329
Author(s):  
Bridget Arvold ◽  
Pamela Turner ◽  
Thomas J. Cooney
Keyword(s):  
Teaching And Learning ◽  
Mathematical Concept ◽  
Point Of View ◽  
Professional Standards ◽  
Mathematical Tasks ◽  
Teaching Mathematics ◽  
Mathematics Section

The visions of teaching set forth in the Professional Standards for Teaching Mathematics (NCTM 1991) do not, in themselves, ensure that we can successfully teach all students mathematics. To reach all students, we must understand how students think and then develop instruction compatible with their thinking. To begin to understand, we must observe, listen, and gather a variety of evidence of what and how students are learning. Although we might view a mathematical concept or algorithm as simple, it is “a mysterious, almost inexplicable phenomenon from the point of view of the outsider” (Davis and Hersh 1981, 43). Examining students' thinking through their interactions with mathematical tasks can help unlock a bit of the mystery. This process of analysis is the amalgamating item in the “Standards for Teaching Mathematics” section of the Professional Standards for Teaching Mathematics and emphasizes the need to listen carefully to our students.

Using Problems to Implement the NCTM's “Professional Teaching Standards'

1994 ◽  
Vol 87 (1) ◽  
pp. 5-7
Author(s):  
Millard E. Showalter
Keyword(s):  
Teaching And Learning ◽  
Professional Standards ◽  
Mathematical Tasks ◽  
Teaching Mathematics ◽  
Mathematical Ideas ◽  
Teaching Standards ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Professional Teaching Standards ◽  
Professional Teaching

As set forth in the Professional Standards for Teaching Mathematics (NCTM 1991), a primary goal for teaching and learning mathematics is the development of mathematical power for all students. To accomplish this goal, the teaching standards document recommends that teachers select interesting and intellectually stimulating mathematical tasks, present opportunities for students to deepen their understanding of mathematics and its applications, promote the investigation of mathematical ideas, use technology to pursue these investigations, find connections to previous and developing knowledge, and employ cooperativelearning experiences (NCTM 1991, 1).

Implementing The Professional Standards for Teaching Mathematics: Linking Teaching, Learning, and Assessment

1994 ◽  
Vol 41 (9) ◽  
pp. 550-552
Author(s):  
Jeane M. Joyner
Keyword(s):  
Learning Environment ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Other Information ◽  
Teaching Learning ◽  
Analysis Of Teaching

The sixth standard in the Professional Standards for Teaching Mathematics (NCTM 1991) focuses on analyzing and interconnecting teaching and learning. The standard calls for the analysis of teaching and learning to be ongoing by “[o]bserving, listening to, and gathering other information about students to assess what they are learning.” Teachers examine the “[e]ffects of the tasks, discourse, and learning environment on students' mathematical knowledge, skills, and dispositions.”

Implementing the Professional Standards for Teaching Mathematics: Focusing on Worthwhile Mathematical Tasks in Professional Development: Using a Task from the National Assessment of Educational Progress

1998 ◽  
Vol 91 (2) ◽  
pp. 156-161
Author(s):  
Glendon W. Blume ◽  
Judith S. Zawojewski ◽  
Edward A. Silver ◽  
Patricia Ann Kenney
Keyword(s):  
Professional Development ◽  
Classroom Practice ◽  
Mathematical Reasoning ◽  
Professional Standards ◽  
Mathematical Tasks ◽  
Problem Solver ◽  
Teaching Mathematics ◽  
National Assessment ◽  
Mathematical Ideas ◽  
Solution Methods

Worthwhile mathematical tasks engage the problem solver in sound and significant mathematics, elicit a variety of solution methods, and require mathematical reasoning. Such problems also prompt responses that are rich enough to reveal mathematical understandings. Just as good classroom practice engages students in worthwhile mathematical tasks, sound professional development does the same with teachers. Providing teachers with opportunities to engage in worthwhile mathematical tasks and to analyze the mathematical ideas underlying those tasks promotes the vision of the Professional Standards for Teaching Mathematics (NCTM 1991).

Standards-Based Teaching: Alive and Well in Portugal

2001 ◽  
Vol 6 (9) ◽  
pp. 538-542
Author(s):  
Iris DeLoach Johnson
Keyword(s):  
Mathematics Teaching ◽  
Teaching Practices ◽  
Teaching And Learning ◽  
Large Scale ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematics Reform ◽  
Reform Movements ◽  
Mathematics Teaching And Learning ◽  
Principles And Standards

NCTM'S Professional Standards for Teaching Mathematics (1991) emphasizes that teachers are “the key” to changing mathematics teaching and learning. Given that mathematics reform movements have never brought about “large-scale changes in teachers' behavior and teaching practices” (Hitch 1990, p. 2), Willis (1992) lamented that “whether the standards will actually produce sweeping changes in the way mathematics is taught and learned in U.S. classrooms remains to be seen” (p. 1). With Principles and Standards for School Mathematics (NCTM 2000), we continue to ask the vital question, How can we induce teachers to implement the Standards?

On My Mind: Classroom Realities We Do Not Often Talk About

1998 ◽  
Vol 3 (5) ◽  
pp. 330-331
Author(s):  
Steven J. Leinwand
Keyword(s):  
Teaching And Learning ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Diverse Schools ◽  
Analysis Of Teaching

After spending time in diverse schools, I often return to the Professional Standards for Teaching Mathematics (NCTM 1991) to help sort through what I have seen and heard. I use the Standards document to track the gap between our vision and the day-to-day realities I observe. A well-worn touchstone is Standard 6: Analysis of Teaching and Learning, which states the following (p. 63):

Implementing the Professional Standards for Teaching Mathematics: Beyond the Classroom

1995 ◽  
Vol 1 (8) ◽  
pp. 494-497
Author(s):  
Nancy Nesbitt Vacc ◽  
Criss Ervin ◽  
Sue Travis
Keyword(s):  
Learning Environment ◽  
Teaching And Learning ◽  
First Grade ◽  
Professional Standards ◽  
Fifth Grade ◽  
Teaching Mathematics ◽  
Mathematical Learning ◽  
Mathematical Connections ◽  
Grade One ◽  
Analysis Of Teaching

To present a mathematical learning environment in which students are challenged by worthwhile activities that stimulate them to make mathematical connections, that promote communication about mathematics, and that offer opportunities for ongoing analysis of teaching and learning, try combining one first grade, one fifth grade, measurement activities, and gorillas.

Implementing the Professional Standards for Teaching Mathematics: Teaching Patterns, Relationships, and Multiplication as Worthwhile Mathematical Tasks

1995 ◽  
Vol 1 (7) ◽  
pp. 446-450
Author(s):  
Barbara E. Armstrong
Keyword(s):  
Mathematics Teaching ◽  
Professional Standards ◽  
Mathematical Tasks ◽  
Teaching Mathematics ◽  
Complex Task ◽  
Instructional Activities

The goal of presenting students with worthwhile tasks that enable them to make connections is to ensure the development of mathematical insights. Determining instructional activities that meet this goal, however, can be a complex task in itself.

Implementing the Professional Standards for Teaching Mathematics: Teacher as Architect of Mathematical Tasks

1995 ◽  
Vol 1 (5) ◽  
pp. 296-299
Author(s):  
Barbara J. Reys ◽  
Vena M. Long
Keyword(s):  
Mathematics Teacher ◽  
Professional Standards ◽  
Mathematical Tasks ◽  
Teaching Mathematics

The first standard presented in the Professional Standards for Teaching Mathematics (NCTM 1991) highlights the importance of choosing and using worthwhile mathematical tasks. Teachers are curriculum architects charged with ensuring the quality of the mathematical tasks in which their students engage.

Using Games to Meet the Standards for Middle School Students

1993 ◽  
Vol 40 (9) ◽  
pp. 499-503
Author(s):  
Lisa M. Leonard ◽  
Dyanne M. Tracy
Keyword(s):  
Middle School Students ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
National Council ◽  
Teaching Behaviors ◽  
School Students ◽  
Evaluation Standards ◽  
Broad Framework

It is evident that our society as a whole needs to take a new look at the way mathematics is taught. The National Council of Teachers of Mathematics (NCTM) has publ ished documents to establish a broad framework that will lead to the transformation of the teaching and learning of mathematics. The Curriculum and Evaluation Standards (1989) calls for a reform in school mathematics based on societal and economic needs. The Professional Standards for Teaching Mathematics (1991) makes suggestions for teachers about ways to change their mathematics teaching behaviors on the basis of the curriculum standards. It will take time to educate teachers and administrators about both documents.

Mathematical Tasks as a Framework for Reflection: From Research to Practice

1998 ◽  
Vol 3 (4) ◽  
pp. 268-275 ◽  
Author(s):  
Mary Kay Stein ◽  
Margaret Schwan Smith
Keyword(s):  
Professional Development ◽  
Learning Environment ◽  
Professional Growth ◽  
Professional Standards ◽  
Primary Factor ◽  
Mathematical Tasks ◽  
Teaching Mathematics ◽  
Research To Practice ◽  
Classroom Experiences ◽  
Learning And Teaching

According to the professional Standards for Teaching Mathematics (NCTM 1991), a primary factor in teachers' professional growth is the extent to which they “reflect on learning and teaching individually and with colleagues” (p. 168). Reflecting on their classroom experiences is a way to make teachers aware of how they teach (Hart et al. 1992) and how their students are thriving within the learning environment that has been provided. Although all teachers think informally about their classroom experiences, cultivating a habit of systematic and deliberate reflection may hold the key to improving one's teaching as well as to sustaining lifelong professional development.

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