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).

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).

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.

Geometric Patterns for Exponents

1992 ◽  
Vol 85 (9) ◽  
pp. 746-749
Author(s):  
Frances M. Thompson
Keyword(s):  
Visual Stimuli ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Geometric Models ◽  
Mathematical Ideas ◽  
Geometric Patterns

NCTM's Professional Standards for Teaching Mathematics suggests that “tasks that require students to reason and to communicate mathematically are more likely to promote their ability to solve problems and to make connections” with other mathematical ideas (1991, 24). Yet too frequently our classroom introductions to mathematics concepts and theorems demand little reasoning from students, leaving them unconvinced or with minimal understanding. Concrete, visual, or geometric models are seldom offered as aids, particularly when studying new numerical relations (Suydam 1984, 27; Bennett 1989, 130), even though many people depend heavily on visual stimuli for their learning, The challenge to the teacher is to select appropriate tasks and materials that will stimulate students to visualize and think about new mathematical concepts, thereby allowing them to develop their own understanding.

Implementing the Professional Standards for Teaching Mathematics: Learn from Your Students

1992 ◽  
Vol 85 (8) ◽  
pp. 656-659
Author(s):  
Margaret A. Farrell
Keyword(s):  
Professional Development ◽  
Classroom Instruction ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Teaching Standards ◽  
Professional Development Of Teachers ◽  
Professional Teaching Standards ◽  
Professional Teaching ◽  
Individual Commitment

The next four articles in this department address issues related to four of the six standards in the section of the Professional Teaching Standards (NCTM 1991) titled “Standards for the Professional Development of Teachers of Mathematics.” The series will pay particular attention to the ways in which these standards affect the in-service teacher of mathematics, whose ongoing professional development depends. to a large extent, on individual commitment, reflection, and action. We hope that these articles will furnish a basis from which teachers can begin to examine and improve their own classroom instruction.

Professional Development: Teachers' Communication and Collaboration Keys to Student Achievement

1995 ◽  
Vol 1 (6) ◽  
pp. 454-458
Author(s):  
Helene J. Sherman ◽  
Thomas Jaeger
Keyword(s):  
Professional Development ◽  
Student Achievement ◽  
Educational Reform ◽  
Mathematics Teaching ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Professional Satisfaction ◽  
Evaluation Standards ◽  
Instructional Changes

The curriculum and evaluation standards for School Mathematics (NCTM 1989) and the Professional Standards for Teaching Mathematics (NCTM 1991) have served as both stimuli for, and responses to, numerous formal and informal programs, conferences, and conversations calling for educational reform and improvement in mathematics teaching. After all the plans are drawn and all the objectives are written, however, reform is most likely to occur and make a lasting difference when teachers are aware of the need for improvement, have a voice in planning it, and derive a real sense of professional satisfaction from implementing the instructional changes.

A Teacher's Tryangles

2000 ◽  
Vol 6 (5) ◽  
pp. 299-302
Author(s):  
Connie H. Yarema ◽  
Rhonda H. Adams ◽  
Rachel Cagle
Keyword(s):  
Professional Development ◽  
Professional Standards ◽  
Teaching Mathematics

Describes a teacher's mathematics exploration in a professional development setting to exemplify the ideas of the Professional Standards for Teaching Mathematics.

Implementing the Professional Standards for Teaching Mathematics: Systemic Reform: A New Mantra for Professional Development

1996 ◽  
Vol 89 (7) ◽  
pp. 584-587
Author(s):  
Madeleine J. Long
Keyword(s):  
Professional Development ◽  
Decision Making ◽  
Educational Reform ◽  
Systemic Reform ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Educational Progress ◽  
New Ideas

Like a huge pendulum that indiscriminately sweeps aside everything in its path, educational reform sometimes adopts new ideas and approaches without fully understanding their implications for teachers, for programs, and, most important, for students. Too often, educators jump on the bandwagon, forgetting the complexities of educational progress and engaging in either-or thought and decision making.

From the Editorial Panel: A World of Ideas at Your Fingertips

1996 ◽  
Vol 89 (6) ◽  
pp. 454-455
Author(s):  
Roberta K. Koss
Keyword(s):  
Professional Development ◽  
Extracurricular Activities ◽  
Mathematics Teacher ◽  
Professional Growth ◽  
Active Role ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Student Activities ◽  
Professional Journals ◽  
Reading Professional

A teacher's workday is filled with so many tasks—planning and presenting lessons, giving help to individual students, contacting parents, acting as advisors for extracurricular activities, serving on committees, assessing students' work—that adding another responsibility seems impossible. However, professional development is a necessary task that affects all aspects of a teacher's work. The Professional Standards for Teaching Mathematics (NCTM 1991) calls for teachers to take an active role in their own professional development and lists “reading and discussing ideas presented in professional publications“ (p. 16g) as an activity that will enhance professional growth. The necessity of reading professional journals can be a blessing in disguise because teachers can gain myriad ideas to help with their work. I shall share a few of the ways in which I plan to use the 1996–1997 Mathematics Teacher to help me plan my lessons, prepare student activities, and grow professionally.

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.

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.

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