**Colección:**La Educación

**Número:**(119) III

**Año:**1994

**NCTM’S**

*Professional Teaching Standards*NCTM, in

*Curriculum and Evaluation Standards for School Mathematics,*paints a vision of school mathematics classrooms that is very different from the current norm. A basic premise to their position “... is that

*what*a student learns depends to a great degree on

*how*he or she has learned it” (NCTM 1989, 5). Thus, in addition to suggesting changes in the content of the school mathematics curriculum, the

*Curriculum and Evaluation Standards*also posit the need for changes in the way that mathematics is taught in schools. Clearly, the latter point has profound implications for the education of both preservice and inservice teachers of mathematics.

In an attempt to explicate some of those implications, in 1991, NCTM released

*Professional Standards for Teaching Mathematics.*These

*Professional Teaching Standards*are organized around four major themes: standards for the teaching of mathematics, standards for the evaluation of the teaching of mathematics, standards for the professional development of teachers of mathematics, and standards for the support and development of mathematics teachers and teaching. Those standards most relevant to the present discussion are the set of standards for the professional development of teachers of mathematics, as well as two of the standards for the support and development of mathematics teachers and teaching: responsibilities of colleges and universities and responsibilities of professional organizations.

In the remainder of this section, we describe, in some detail, those aspects of the

*Professional Teaching Standards*that are most relevant to the preparation of preservice teachers of mathematics.

*The Professional Development of Teachers of Mathematics*

NCTM notes that five assumptions underpin the professional development standards:

- The professional development standards are based upon the vision of
school mathematics presented in the
*Curriculum and Evaluation Standards*. - Teachers are influenced by the teaching they see and experience.
- Learning to teach is a process of integrating theory with practice.
- The education of teachers is an ongoing process.
- There are level-specific needs for the education of teachers of mathematics. (NCTM 1991, 124-125)

*Experiencing good mathematics teaching.*This standard basically suggests that mathematics and mathematics education faculty in preservice teacher education programs need to model good mathematics teaching. The suggestions in this standard, therefore, mirror the first five standards for the teaching of mathematics: posing worthwhile mathematical tasks; establishing mathematical discourse, so as to foster a mathematics community in the classroom; and creating learning environments conducive to the development of students’ mathematical power.

*Knowing mathematics.*What is perhaps most striking about the standard on knowing mathematics is the focus on mathematics as a way of thinking. Thus, although some specific mathematics content is suggested, the intent is clearly for the development of: mathematics concepts and procedures that are connected, multiple means of mathematical representation, mathematical reasoning, and mathematical communication. Of course, it is no coincidence that mathematical communication, connections, reasoning, and representations form much of the basis of the

*Curriculum and Evaluation Standards*.

The specific recommendations on content suggest a broad background in mathematics, the depth of which should vary according to the level of prospective teaching: grades K-4, 5-8, or 9-12. In particular, it is suggested that

*all*teachers of mathematics have a background in foundational mathematics that includes number systems and number sense, geometry, measurement, statistics and probability, and functions and their uses. In addition, the preparation of prospective teachers of mathematics at grades 5-8 should include a background in algebraic structures and concepts of calculus, as well as deeper understandings in the areas listed for the preparation of all teachers of mathematics. Finally, it is recommended that the preparation of teachers of mathematics for grades 9-12 should include a background in number theory, linear algebra, and discrete mathematics, as well as greater depth in all of the areas previously mentioned.

It is also suggested in this standard that the above breadth and depth cannot be attained with less than:

- 9 semester hours of content mathematics in the preparation of mathematics teachers of grades K-4, assuming a foundation of three years of college preparatory mathematics in high school as a prerequisite.
- 15 semester hours of mathematics content in the preparation of mathematics teachers of grades 5-8, assuming a foundation of four years of college preparatory mathematics in high school as a prerequisite.
- The equivalent of an undergraduate major in mathematics as content preparation for mathematics teachers of grades 9-12, again assuming a foundation of four years of college preparatory mathematics in high school as a prerequisite.

*Knowing students as learners of mathematics.*This standard notes, from the onset, that “the study of general principles of teaching and learning is insufficient for teachers of mathematics because it does not include consideration of the nature of mathematics and of current research on children’s mathematical thinking and its implications for instruction” (NCTM 1991, 144). Thus, all of the recommendations in this standard refer explicitly to the learning of

*mathematics*.

Specifically, it is suggested that the preservice preparation of teachers of mathematics provide knowledge of and multiple perspectives on:

- research on how students learn mathematics;
- the effects of students’ ages, abilities, interests, and experiences on their learning of mathematics;
- the influences of linguistic, ethnic, racial, socioeconomic, and gender differences on students’ learning of mathematics; and
- ways to affirm and support full participation and continued study of mathematics by all students.

*Knowing mathematical pedagogy.*In this standard, mathematical pedagogy is described as “... the ways in which teachers help their students come to understand and be able to do and use mathematics” (NCTM 1991, 151). Thus, it is suggested that the preservice preparation of teachers of mathematics develop knowledge of and the ability to use and evaluate:

- instructional materials and resources, including calculators and computers with appropriate software;
- multiple ways of representing mathematical concepts and procedures;
- instructional strategies;
- classroom organizational models;
- ways to foster mathematical discourse; and
- means of assessing students’ understandings of mathematics.

*Developing as a teacher of mathematics.*It is in this standard that the very heart of teaching, a reflective practice, is addressed. Because the development of a teacher should be a lifelong process, it is suggested that “it is the practice of teaching, the growing sense of self as teacher, and the continual inquisitiveness about new and better ways to teach and learn that serve teachers in their quest to understand and change the practice of teaching” (NCTM 1991, 160).

In this vein, the recommendations for the preservice preparation of teachers of mathematics include opportunities to:

- examine and possibly revise assumptions about the nature of mathematics, its teaching, and its learning;
- observe and analyze a range of teaching styles;
- work with a diverse range of students in close collaboration with mathematics teacher educators and teachers in the field;
- analyze and evaluate their own work; and
- develop a positive attitude toward teaching mathematics.

*Teacher’s role in professional development.*Rather than waiting for professional development opportunities to come to them, it is suggested that teachers take a more proactive role in that development.

Teachers’ professional development, within and outside their classrooms, is a product of reflectiveness and participation in educational opportunities that will enhance and extend their growth and development. As professionals, teachers [should] take responsibility for their own growth and development. (NCTM 1991, 168)

Among the means suggested by which a teacher might do so are experimenting in the classroom, reflecting on their work, participating in workshops or other professional development opportunities, reading, and discussing issues with colleagues. While the need for schools and school districts to support and encourage teachers in this regard is acknowledged, the writers of this standard clearly posit that the genesis of such proactivity lies in teacher education programs.

*Responsibilities of Colleges and Universities*

This standard recognizes that what happens in colleges and universities “... is fundamental to successful mathematics teaching” (NCTM 1991, 184). It calls for college and university administrators to establish means of support that encourage faculty to:

- spend time in schools working with teachers and students;
- collaborate with schools and teachers in the design of preservice and inservice teacher education programs;
- conduct and interpret mathematics education research, especially that which is school-based;
- offer appropriate graduate level courses and programs for experienced teachers of mathematics;
- articulate the K-16 mathematics curriculum, in cooperation with precollege educators; and
- recruit and retain teacher candidates of quality and diversity.

*Responsibilities of Professional Organizations*

This standard acknowledges the work of NCTM in the preparation of the two

*Standards*documents, as well as the work of MAA in developing recommendations for the mathematical preparation of teachers of school mathematics (Leitzel). These efforts are seen as prototypical of the activities needed to develop a professional consensus regarding the aspects of a discipline.

The explicit suggestions for ways that the professional organizations might support teachers of mathematics in schools include:

- providing professional development opportunities;
- focusing the attention of mathematics and mathematics education communities on contemporary issues in the teaching and learning of mathematics;
- recognizing the achievements of exemplary mathematics teachers and programs; and
- initiating political efforts in support of mathematics education.

*Summary*

In this section, we have noted that, whereas in

*Curriculum and Evaluation Standards for School Mathematics*, NCTM presented a broad vision of what school mathematics education might be like, a vision whose realization will require significant changes in the practice of mathematics teaching. In

*Professional Standards for Teaching Mathematics*, NCTM outlines the sorts of changes that will be required in the preparation of teachers of mathematics, if the vision is to be made real. As would be expected, these two NCTM documents complement one another. The explicit recommendations call for a more thorough background in mathematics content for prospective teachers of mathematics at all levels, a knowledge of students as learners of mathematics, a knowledge of and the ability to use a variety of aspects of mathematics pedagogy, and a lifetime of reflective practice. There is also an implicit call for greater cooperation and collaboration between mathematics educators in schools and faculty in colleges and universities, as well as between mathematics faculty and mathematics education faculty.

**[INDEX] [SUMMARY] [INTRODUCTION] [PURPOSE] [MAA'S A CALL FOR CHANGE] [NCTM'S PROFESSIONAL TEACHING STANDARDS] [COMPARISON OF RECOMMENDATIONS AND STANDARDS] [CONCLUSION] [RESUMEN] [RÉSUMÉ] [RESUMO] [REFERENCES]**