Factores que afectan el clima laboral

The nation can adopt rigorous standards, set forth a visionary scenario, compile the best research about how students learn, change textbooks and assessment, promote teaching strategies that have been successful with a wide range of students, and change all the other elements involved in systemic reform—But without professional

development, school reform and improved achievement for all students will not happen. Unless the classroom teacher understands and is committed to standards-based reform and knows how to make it happen,

the dream will not be realized.

—Principles for Professional Development, American Federation of Teachers, 2002, p. 2

Teachers matter. A variety of recently published documents support the notion that the key to in-creasing students’ mathematical knowledge and to closing the achievement gap is to put knowledge-able teachers in every classroom. For example, in a survey designed by Lou Harris and undertaken in 1998 by the Recruiting New Teachers organization, a carefully chosen sample of a cross-section of U.S.

adults was questioned about how to improve Amer-ica’s schools (Haselkorn & Harris, 1998). Of the 2525 people interviewed, an overwhelming majority agreed that “improving the quality of teaching is the most important way to improve public education”

(p. 1). Other documents essentially repeating this message include the 1998 report Every Child Math-ematically Proficient: An Action Plan from the Learn-ing First Alliance, the 2000 report Before It’s Too Late:

A Report to the Nation from the National Commis-sion on Mathematics and Science Teaching for the 21st Century as requested by the U.S. Department

of Education, the 1996 and 2003 reports What Mat-ters Most: Teaching for America’s Future and No Dream Denied from the National Commission on Teaching and America’s Future, the 2000 report The Mathe-matical Education of Teachers (MET) from the Confer-ence Board of the Mathematical SciConfer-ences, the 2001 act No Child Left Behind from the U.S. Department of Education (2002), and the 2003 report Mathematical Proficiency for All Students from the RAND Mathemat-ics Study Panel.

The purpose of this chapter is to address what it means to prepare teachers of mathematics and to provide them, while they progress in their careers, with the professional learning opportunities they need to lead their students to succeed in learning mathematics.

In this chapter I attempt to answer, as much as is possible on the basis of theory and research evidence, the following questions:

1. Why has professional development become a priority in realizing current goals for mathematics education?

2. What are the goals of professional development?

3. What principles can be used to guide the design of professional development?

4. How do teachers learn what they need to know for teaching mathematics?

5. How do teachers learn from their professional communities about teaching mathematics?

6. What can teachers learn by investigating their own teaching of mathematics?

7. What can be learned from research on teacher change?

8. What can be learned from research about the preparation of teachers to teach mathematics?

9. What do researchers know about issues that affect professional development, such as support and accountability, preparing teacher leaders, evaluating professional development, and policy issues?

10. Where do we stand now, and what comes next?

In the ten major sections of this chapter, I address these ten questions.

Before beginning to address these questions, I raise six caveats that will clarify some decisions I made in organizing and writing this chapter. First, because this volume also contains chapters on teacher knowl-edge, teaching, and teacher beliefs, I address these topics only to the extent needed to provide a basis for much of the ensuing discussion. Second, the more general literature on professional development and teacher education provides a context from which to interpret the literature within mathematics educa-tion. Thus, the two bodies of literature are intermin-gled in this chapter. Third, many of the claims made by authors and quoted here are based on reviews of literature, and, thus, for understandable reasons, the original literature on which they base their claims is not usually included here. Fourth, much of the re-search discussed here could easily fit under more than one heading; that is, the categories I use are not dis-joint. My placement decisions are apt to be different from those of some readers. Fifth, some authors make distinctions among teacher education, professional development, and teacher change. For example, Ler-man (2001) and Ponte (2001) associated teacher ed-ucation with preservice teacher preparation, that is, courses and experiences designed for students

prepar-ing to be teachers, whereas professional development and teacher change are linked to in-service programs and teachers’ changing roles and could occur in tak-ing courses, complettak-ing projects, readtak-ing, reflecttak-ing, sharing experiences, and so on. That distinction is not always made here because much of what is true for pro-fessional development is also true for teacher prepara-tion. For example, an inquiry approach can be used in both; strategies such as focusing on children’s think-ing or studythink-ing cases can be used in both; changes of beliefs about mathematics and about learning mathe-matics can be expected from both, even though these approaches are discussed in sections on professional development. Likewise, topics such as mentoring are discussed within the section on teacher preparation.

Indeed, the National Science Foundation now uses the term professional development to refer both to teach-er preparation and to the development of practicing teachers. That said, some issues, such as the effects of methods courses and field experiences, relate to teacher preparation but not to professional develop-ment of practicing teachers. For this reason, I devote a section to only the preparation of teachers. And, sixth, although the term reform has been both over-used and often abover-used, it so thoroughly permeates the literature that I realized that I could not completely avoid its use here. When possible, however, I use the term principled knowledge in the manner articulated by Spillane (2000) as a way of thinking about the goals of school mathematics reform:

Reformers want principled mathematical knowledge, as distinct from procedural knowledge, to receive more attention in school work. Whereas procedural knowledge centers on computational procedures and involves memorizing and following predetermined steps to compute answers, principled knowledge focuses on the mathematical ideas and concepts that under-gird mathematical procedures. Procedural knowl-edge has dominated the K through 12 curriculum.

Reformers also propose that students develop a more sophisticated appreciation for doing mathematics in-cluding framing and solving mathematical problems, articulating conjectures, and reasoning with others about mathematical ideas: Students need to appreci-ate mathematical activity as more than computation.

(p. 144)

In this chapter I focus on what researchers can tell us about teaching mathematics for principled knowledge and the implications this information has for the design of programs of teacher education and development. Changing the focus from procedural

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to principled knowledge is a new frontier for many teachers, administrators, and policy makers. The knowledge demanded is not an add-on; for many, this change can mean a complete reconceptualization of such fundamental questions as: What does it mean to teach mathematics? What is mathematics? What math-ematics is important for teachers to know and why?

What does teaching mathematics entail? How does one acquire knowledge? How can teachers produc-tively assess that knowledge and use assessment data to plan instruction? The answers to all these questions change from those that underlie teaching for proce-dural knowledge.

ADDRESSING QUESTION 1:

WHY HAS PROFESSIONAL DEVELOPMENT BECOME A PRIORITY IN REALIZING CURRENT

GOALS FOR MATHEMATICS EDUCATION?

The standards movement of the 1990s coupled with a call for school reform, both set against a backdrop of performance-based accountability demands that in-clude high-stakes testing, conspire to change the ways in which schools operate. The standards movement was heralded by the publication of the Curriculum and Evaluation Standards for School Mathematics by the Na-tional Council of Teachers of Mathematics (NCTM) in 1989; this document set the stage for standards in other K–12 disciplines. NCTM, too, continued to pub-lish standards for teaching mathematics (1991) and assessing mathematics learning (1995) and in 2000, published the Principles and Standards for School Mathe-matics. States have also developed standards for teach-ing mathematics, some based on the NCTM Standards and some not.

The accountability movement is more recent and results from recognition that all students have the ability to learn—and to learn more than they are cur-rently learning—even while the student population becomes more diverse. To some, accountability means that all should know their basic skills, but others rec-ognize that “the future of education clearly presses be-yond the basics to more demanding forms of academ-ic learning” (Sykes, 1999, p. 153). The accountability movement is perhaps best represented in the United States by the 2001 No Child Left Behind Act, which, by law, calls for vast changes that are intended to result in all children’s becoming proficient in key areas.

Education reformers realize that instructional improvement and increased student achievement

depend on the professional development of teach-ers and administrators (e.g., Ball & Cohen, 1999; El-more & Burney, 1999; Nelson & Hammerman, 1996;

Sykes, 1999; C. L. Thompson & Zeuli, 1999). Hawley and Valli (1999) provided evidence from a number of sources that “one of the most persistent findings from research on school improvement is, in fact, the symbi-otic relation between professional development and school improvement efforts” (p. 129). Sykes (1999) noted that the view that professional development can act as a “significant lever for education improvement”

(p. 151) is fairly recent and has occurred as the result of three major societal changes: systemic reform ef-forts, new research knowledge about instruction, and the escalation of the commitment to quality educa-tion for all. Systemic reform has been a major policy influence.

Recognition of the need to change the way in which mathematics is taught and learned is interna-tional in scope—“Across the world, . . . mathematics teacher education programmes are preparing teach-ers to work with and promote reform in the practice of school mathematics” (Adler, 2000, p. 205). Inter-national researchers view teachers as the key figures on which the success of current reforms depends (Ponte, 1994). In the United States, the escalation of the commitment to providing quality education to all students, at a time when the student population grows more diverse, has led to higher demands on teachers, who in turn need the support provided through ap-propriate professional development. In mathematics education, “mathematics for all” has been a founda-tion for all volumes of NCTM Standards (1989, 1991, 1995, 2000).

Even with increased recognition that teacher professional development must be a priority, the pro-fessional development offered in mathematics often does not meet teachers’ needs. According to Ball and Cohen (1999), most professional development fund-ing is spent on

sessions and workshops that are often intellectually su-perficial, disconnected from deep issues of curriculum and learning, fragmented, and noncumulative (Cohen and Hill, 1997; Little, 1994). Rarely do these in-services seem based on a curricular view of teachers’ learning.

Teachers are thought to need updating rather than op-portunities for serious and sustained learning of cur-riculum, students, and teaching. (pp. 3–4)

In many school districts a “one size fits all” mentality limits the type of professional assistance teachers re-ceive (Lord, 1994). Some frame the issue even more

dramatically—Miles (1995) called current profes-sional development a “joke”—“pedagogically naive, a demeaning exercise that often leaves its participants more cynical and no more knowledgeable, skilled, or committed than before” (p. vii). Others (e.g., Elmore, 2002a; Hargreaves, 1995; Middleton, Sawada, Judson, Bloom, & Turley, 2002) have been milder in stating their criticism of current professional development efforts but, nonetheless, have found them to be inef-fective in terms of current reform and accountability demands.

The confirmation of the belief that much con-ventional professional development is ineffective and wasteful was found by Hawley and Valli (1999) to be one of four converging developments that ap-peared to provide a consensus among stakeholders that major changes in how professional develop-ment is conceptualized and conducted are needed.

A second development they noted was the body of research that showed how change is related to pro-fessional development. Schools cannot change un-less teaching is improved. And schools will not be improved for children unless schools also become places for teachers to learn. A third development was a “growing agreement that students should be expected to achieve much higher standards of per-formance, which include a capacity for complex and collaborative problem solving” (p. 128). The view of teaching as transmission of knowledge is at odds with the type of performance now expected of children.

The fourth development they noted was that the re-search on how people learn leads to strategies for teaching and assessment that differ from those most commonly used. Many of teachers’ core beliefs need to be challenged before change can occur.

Case studies have become a useful way to under-stand and evaluate the effectiveness of professional development or intervention into the teacher prepa-ration process. Large-scale research projects in which professional development has been a major factor of-ten use case studies as a means to study the effects of the professional development on individual teachers.

The results can be dismaying, as exemplified in a case study by D. K. Cohen (1990). His portrayal of Mrs. Ou-blier has attained the status of a study that can be used as a generic description of a class of teachers who have misinterpreted the principles underlying the profes-sional development they received. Mrs. Oublier, an elementary school teacher in California, willingly par-ticipated in professional development that included familiarization with the 1985 Mathematics Framework for California Public Schools (California Department of Education), a framework much different from Cali-fornia’s current framework. She eagerly adopted new

curriculum materials and activities introduced to her during professional development in which she partici-pated. She believed that she had revolutionized her practice. Cohen noted that she had simply adapted these new materials and activities to her traditional teaching style. She continued to teach mathematics as though there were only right and wrong answers, and she discouraged exploration that would reveal students’ understanding. Cohen observed many ten-sions that lay beneath the surface of the work in Mrs.

Oublier’s classroom. Because her own understand-ing of mathematics was still superficial, she could not have been successful with the give and take of open discourse. Cohen reflected on his observations of Mrs.

Oublier, stating that the kind of change professional developers believe may be taking place is illusory.

The teachers and students who try to carry out such change are historical beings. They cannot simply shed their old ideas and practices like a shabby coat, and slip on something new. . . . As they reach out to em-brace or invent a new instruction, they reach out with their old professional selves, including all the ideas and practices comprised therein. The past is their path to the future. Some sorts of mixed practice, and many confusions, therefore seem inevitable. (p. 339)

Mrs. Oublier had little opportunity for sustained guidance and support. She had much to unlearn, but no one to help her do this unlearning. The lessons here for the need for sustained professional develop-ment and develop-mentoring are significant.

These developments and stories show that the quality of preparation and professional development of teachers must improve well beyond current levels if teachers are to become “capable of far more sophis-ticated forms of practice” (Sykes, 1999, p. 153). Ex-ploration of how this improvement can come about permeates the literature of teacher education.

ADDRESSING QUESTION 2:

WHAT ARE THE GOALS OF PROFESSIONAL DEVELOPMENT?

To teach mathematics for principled knowledge, teachers need an extensive knowledge base, techni-cal teaching skills, and epistemologitechni-cal stances that should all be goals of teacher preparation and profes-sional development programs (Elmore, 2002a; Sykes, 1999). To meet these goals, professional development must provide opportunities for professional growth on the part of teachers and motivate them to develop the knowledge, skills, and dispositions they need to

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teach mathematics well. Related outcomes of pro-fessional development include changing teachers’

understanding of how students learn mathematics and of the nature of mathematics, of mathematical knowledge, and of teaching mathematics well. Ideal-ly, this new understanding will result in mathematics teachers equipped to choose appropriate curricula, plan instruction, and organize their classrooms to promote and support learning for all the students they teach. Professional growth is thus marked by change in teachers’ knowledge, beliefs, and instruc-tional strategies. Professional development should be designed to address the needs of teachers so that they can teach for principled knowledge in a manner en-visioned by researchers and educators. Several edu-cators have addressed the issue of what these needs are. Ball and Cohen (1999) suggested that teachers need to become serious learners of practice rather than learners of strategies and activities. For teachers to become such learners would entail their coming to understand well the mathematics they teach and what it means to reason mathematically. They need to learn to attend to their students in insightful ways, a skill that “requires expertise beyond what one gathers from one’s own experience” (p. 9). They need to “de-velop and expand their ideas about learning, [which would require that] longstanding beliefs and assump-tions about learning would need to be examined” (p.

9). They would need to better understand pedagogy and how to establish a classroom culture that sup-ports learning goals. Ball and Cohen noted that even when these needs are addressed, the complexity of interactions and situations in classrooms also affect the ways in which teachers teach.

Borasi and Fonzi (2002) also identified several needs of teachers that could serve as a focus for pro-fessional development. In addition to the needs iden-tified by Ball and Cohen, they included the needs to develop a vision and commitment to school math-ematics reform, to become familiar with exemplary curriculum materials, to understand equity issues and their implications for the classroom, to cope with the emotional aspects of engaging in reform, and to de-velop an attitude of inquiry towards one’s practice.

In this section I address these teacher needs by first grouping them into six, sometimes overlapping, goals and then considering literature that informs and supports each goal. These goals are to develop (a) a shared vision for mathematics teaching and learning, (b) a sound understanding of mathematics for the level taught, (c) an understanding of how stu-dents learn mathematics, (d) deep pedagogical con-tent knowledge, (e) an understanding of the role of

equity in school mathematics, and (f) a sense of self as a mathematics teacher.

Goal 1. Developing a Shared Vision

When professional development providers plan, they themselves are guided by a vision of what they want teachers to know and be able to do. These visions will differ according to the providers’ views of the

When professional development providers plan, they themselves are guided by a vision of what they want teachers to know and be able to do. These visions will differ according to the providers’ views of the