Taking Stock: Summary of a Workshop (1997)

reform.” Robert Floden, who looked at the role standards actually play in American mathematics classrooms, reinforced this point in the next discussion.

Permeating the discussion throughout the workshop was a sense of the importance of teachers. Several participants pointed out that teachers are cast in a variety of sometimes conflicting roles when standards are discussed. Critics have cast them as both targets who are accountable for students' failure to achieve high standards of performance and obstacles to the kinds of reforms that high standards will require. Others have described teachers as coaches who can help students achieve goals that are established outside the school walls. Many have commented on the vital importance of including teachers in the process of developing standards, not only so that the standards will benefit from teachers' wisdom, but also so that teachers will truly understand and support the standards. But most important is the recognition that teachers are vital to the successful implementation of any education standards.

Robert Floden examined that point in detail. He argued that regardless of the quality and content of any standards document that is adopted, the standards actually in use are those that exist in teachers' minds (Floden, 1996). Floden reviewed a variety of research from the past 20 years that has explored the relationship between the practices of mathematics teachers and the materials and goals that are meant to guide them. Researchers in one of the earliest studies he discussed, conducted in the 1970s, identified four basic decisions that teachers make about what they will teach. Their point was that these decisions effectively constitute the implementation of any set of content and performance standards for students:

What topics will I include?

How much time will I spend on each topic?

To whom will I teach each of these topics?

What level of mastery of each topic will I expect from my students?

These four decisions are influenced by the content of standards documents, assessments, textbooks, parental expectations, a teacher's own background and experience, the students' prior instructional experiences, as well as other factors, but they are decisions that teachers must make, whether or not they receive clear guidance on how to make them. Floden's point was that standards alone, even standards that are closely aligned with assessments and other aspects of the education system, cannot do the job of reforming educational practice. For anyone involved in attempting to raise content and performance standards, an understanding of the standards in use, and of how their use is determined, is crucial.

In general, Floden reported, mathematics teachers were not teaching to formally established standards 20 years ago, and, by and large, they are not doing so today. He noted that the impetus behind one study of this issue conducted in the 1970s was a concern that children were being held to de facto standards established by assessment companies and textbook manufacturers. The hypothesis this study explored was that the content of elementary mathematics classrooms was being routinized by the existence of norms established without public scrutiny or input. The study found that the reverse was true: the content of tests and texts was by no means consistent. Teachers were receiving conflicting messages from various sources about what content ought to be covered or emphasized, and they were making their own judgments. The result was that even in a subject that many lay people would consider straightforward—elementary school mathematics—there were dramatic differences in the topics covered, the time spent on topics, and even in the total time spent on mathematics instruction.

More current findings look extremely similar, Floden reported. The National Council for Teachers of Mathematics (NCTM) has developed coherent standards in mathematics that have been widely espoused. The movement for systemic reform has encouraged people to focus on the alignment of assessments with the NCTM standards and the use of textbooks that are similarly aligned. Nevertheless, even recent studies of classroom practice show that teacher behavior is frequently not in line with the goals of the NCTM standards, though it is moving in that direction. Floden was quick to point out that the explanation for the gap does not lie in a resistance on the part of teachers to change. He cited a variety of data indicating that teachers are willing to follow guidance if the guidance is consistent, and that they are very open to incorporating new content and strategies into their practice.

One problem, however, is that teachers are generally not inclined to discard anything from their existing curricula in order to make room for the new. The result—and this conclusion was generally reinforced by the findings of the curriculum study that was part of The Third International Mathematics and Science Study (TIMSS) (see box on p. 3)—is that teachers have too many topics and themes crammed into their schedules. Choices still need to be made about allocating time to various topics and about reorganizing instruction, and standards documents generally provide very little guidance for these choices. A criticism of many standards documents has been that they are long and detailed enough to serve as textbooks. To have an impact on teachers' choices, they may need to incorporate more decisions about priorities.²

A related problem is that the NCTM standards are often not completely understood either by the teachers who are attempting to incorporate them or by the administrators who are advocating them. As LeMahieu and Bickel found in their study, educators tend to show relatively less support than do other groups for implementing new standards, not because they question the value of standards, but because they believe high standards are already in place. Ninety-five percent of mathematics teachers surveyed in TIMSS reported that they were familiar with the NCTM standards. In general, the teachers surveyed believed that their practice was in line with those standards, but these same teachers' responses to specific questions about their practice do not support their beliefs (National Center of Education Statistics, 1996:4–5). The disjuncture suggested by these reports, and by Floden's observations may be explained by the fact that the NCTM standards are not simply a new prioritization of existing mathematics topics. Rather, they reflect a fairly profound rethinking of mathematics education. Consequently, a teacher who has not had the opportunity to study and truly digest them may not recognize the ways in which they are at odds with many traditional methods. An often-cited example is that of problem solving. The NCTM standards ask teachers to incorporate the view of mathematics as a tool for realworld problem solving throughout their practice. Floden has found, however, that many teachers have not absorbed what is conceptually new in this familiar-sounding language, and they believe they can meet that standard by assigning more story problems.

Teachers' decisions about what content to emphasize are also affected by both their perceptions about their students' backgrounds and abilities and their own knowledge of the subject, Floden reported. Naturally enough, teachers were generally found to be less comfortable teaching material they themselves had not studied and were consequently more likely to omit or downplay it. Teachers clearly need the opportunity to learn new content before they can teach it. To the extent that the NCTM standards call for a true rethinking of mathematics instruction, this may be a particularly urgent need right now.

Although Floden's conclusion is that standards by themselves will do little to improve student performance, he had several specific suggestions about ways to enhance their effectiveness. Primarily, he stressed that rather than simply creating financial or other practical incentives for teachers to comply with higher standards, education leaders should find ways to engage them with the content of the standards. He stressed that for standards to be effective, they must be internalized by teachers. In particular, teachers need the opportunity—especially time in their schedules—to really

learn what the standards are about. In many cases, as noted above, they need the opportunity to learn new content, and as one administrator pointed out to Floden, this generally requires more than a weekend workshop. Teachers also need opportunities to interact with other professionals who know the standards well, have used them, and are in a position to share ideas about implementing them.

For all of these things to occur, public support for professional development is crucial. One participant asked whether Floden considered it a good idea to require teachers to pass assessments tied to new, higher standards in order to remain in their jobs. Floden acknowledged the appeal of this idea as a common-sense method of ensuring that teachers have the minimum qualifications to implement new standards, but he pointed out the risk in setting teachers up for a humiliating public failure. A more constructive strategy, he suggested, might be to use the existence of new standards to build public support for providing the time and funds for whatever training teachers need to enable them to implement the high standards the community has adopted.

Looking at the long term, Floden also pointed out that the many policies that send messages to teachers about what to teach are not consistent. Picking up on that notion, Andrew Porter made the more general point that although excellent standards documents have been developed for the major academic disciplines in the United States, there are few supports in place to facilitate their implementation. In particular, he noted, there could be assessments, materials (textbooks and the like), and teacher education, both preservice and ongoing professional development, that are all in sync with the standards.

A number of participants also raised the point that incentives can play a key role in implementation of standards-based programs. As noted above, many countries have tied high performance standards to specific and serious consequences at various points in a student's career. Though Floden agreed that penalizing teachers would not be constructive, positive incentives can work. Alan Ruby explained that in Australia, universities have been given incentives to develop courses specifically for practicing teachers who need to update their discipline knowledge. These courses offer the teachers a credential that can be tied to promotion or other benefits; to obtain the credential, teachers must demonstrate not only mastery of the content, but also the ability to present it in a lesson.

Several participants took up this point, noting that schools of education are not necessarily offering the material that will best prepare beginning teachers to make use of the NCTM standards. This is partly because in the United States colleges and universities have little incentive to pay attention to the specific credentials that beginning teachers might need. Floden noted that prestigious universities

are the least likely to be concerned about these credentials. The relatively low status that teaching has traditionally suffered in comparison with other professions is part of the reason. Prestigious universities are perfectly willing to ensure that students are offered the courses that will prepare them for careers in law or medicine, for example. A formal system of licensure and professional development for teachers that is both coherent and rigorous is an obvious solution. Under such a system teachers would be expected to update their knowledge, and, like physicians, would be supported in doing so. The National Board for Professional Teaching Standards has been working since 1987 to develop assessments for experienced teachers that could complement and reinforce academic standards: eventually the board plans to offer certificates in approximately 30 subject areas. The board awarded its first certificates to 81 teachers in 1995. A similar effort has been undertaken by the Interstate New Teacher Assessment and Support Consortium (INTASC) which is working to develop an assessment system that can be used to license beginning teachers.

The emphasis on making sure teachers have the opportunity for professional development and collaboration was echoed in the panel discussion of the New Standards Project, which works with 17 states and seven large districts to set high academic standards and to develop a system of performance assessments to measure progress toward these standards (see box on p. 19). The New Standards Project has made a significant effort to collect and synthesize information about the standards used in other countries and to benchmark its standards to them.

The paper and presentation prepared by Kate Nolan for the workshop focused on the importance of using consensus and discussion to build a well-grounded notion of standards for a given academic area. Nolan described the dynamic in a typical standard-setting session run by New Standards. Participants would begin by looking at a sample of student work and would be asked to evaluate it. Invariably the discussion would quickly zero in on key questions, such as “what grade is the student in?” “What kinds of work have been done in this student's classroom?” In other words, the participants would find that there was no absolute “high” standard, but that the caliber of the performance could only be judged in the context of a set of specific expectations for students in a particular context.

Moreover, Nolan reported, the teachers who worked together to understand the standards by which they were to judge a particular body of student work came away with a far deeper understanding of both the evaluation criteria and the assumptions about the classrooms that produced the work than they could have developed by simply reading about the standards, or even attempting to apply them on their own. Similar experiences are often reported by teachers who have

participated in scoring open-ended exercises for assessments. Christopher Cross noted that Maryland teachers who had scored the state assessment not only found it an excellent professional development activity, but also became ambassadors for the program. Having had the opportunity to understand the assessment in some depth, they were able to explain it to others.

Nolan noted that language barriers are a major obstacle to attempting such collaboration internationally. While in a sense this is a technical obstacle, and one that has been addressed by international studies such as TIMSS, it raises the issue of culture and context. The example of TIMSS, in which the United States worked with Germany and Japan in an unprecedented effort to collect data about contextual factors and tie them to international achievement data, suggests that coordinating these different kinds of information is not a straightforward exercise. The study made innovative use of several different

methodologies and has little precedent to follow in bringing together and presenting the results from its different components (see National Research Council, 1997). Similarly, those involved in the New Standards Project have found that truly understanding what a particular standard means in its own setting requires a deep level of knowledge of that setting. This perspective could be seen as further reinforcing Ruby's point that a search for a specific international standard in a given subject may be less fruitful than incorporating international comparisons and perspectives into the process of tailoring standards to a particular context.

States have confronted the need to tailor standards directly since it is a variety of competing demands that have led them to develop standards in the first place. These demands include pressure from business interests to educate skilled workers for local employment as well as the reality that, in a mobile society, the students they are educating now may be employed all over the United States and the world. Local political concerns faced by state education policy makers might range from an industry-based need for particular skills or a governor's devotion to a particular subject to public pressure to align themselves with national discipline standards and national goals for public education.

A few states have made a deliberate effort to incorporate an international perspective into their standard-setting efforts, and one consortium of districts in Illinois has done so in a high-profile way by participating in TIMSS on its own (see box on p. 21). The vast majority of states are working on standards, and many have begun to collaborate and to pool some of their resources. One participant suggested that, as both state and national efforts begin to build on experience, the United States is slowly groping its way toward some national priorities for standards in “bottom-up” fashion. However, the three state representatives at the workshop—from among the very few states that have looked internationally in working on their standards—all stressed the value of the state's controlling the process.

Robert Rice of Maryland explained: “There is a value for us in doing it ourselves because teachers and communities buy into it. If a federal standard is handed to us, we would have a very different selling job.” Tom Kerins of Illinois made a very similar point: “Consensus was difficult enough for us as it was. Something from D.C. would be much harder. There is a lot of duplication; it's slow and laborious, but it has the best chance for affecting schools given the structure in this country.” Wayne Martin of Colorado echoed this sentiment and added: “It's the auxiliary things we need help with. For example there's a need for a literacy test for ESL [English as a second language] students in their native language. We need to find out if they are literate at all before we work on their knowledge of English.”

Another participant made the point that an international benchmark does not necessarily identify the highest standard—or one worthy of serving as a benchmark for others—citing the International