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The section "Purpose of this work" alluded to the difficulties created by the variety of perspectives taken by various groups on the scope, purpose, and nature of standards. In order to develop an internally consistent model of standards and benchmarks, we address the significant problems that have resulted and describe our approach to their resolution. Here we consider four problems: (1) multiple documents, (2) varying definitions of standards, (3) differing types of content description, (4) differing grade ranges, and (5) varying levels of generality.
Science provides another example of multiple source documents. Three documents provide descriptions of essential student knowledge and skill in science as determined by three national organizations: the National Research Council, the American Association for the Advancement of Science, and the National Science Teacher's Association (see Section 2, Science, for a discussion). Additionally, a description of important science content also can be found in documents from NAEP, the International Baccalaureate Organization, the New Standards Project and the Council for Basic Education..
In most subject areas there exist different, and sometimes competing, views of what content is important; certainly no single document represents a comprehensive view of the content for a particular subject. Yet a comprehensive review is important for anyone who intends to identify important information and skills at the level of a school, district, or state. To address this need, we determined to identify the significant documents for each subject area and synthesize the content they address in a useful, comprehensive set of statements concerning what students should know and be able to do. At the end of the process, we had consulted 137 documents (listed in Appendix A), across 14 areas of study.
Varying Definitions of Standards
a. Students use estimation to check the reasonableness of results.These elements are presented as standards in the NCTM document but are very different in nature. Element a describes a skill or an ability a person might use to solve a real-life problem. For example, one might use estimation to determine whether the gas pump total generally squares with the price of a gallon of gas multiplied by the number of gallons that were required to fill the tank in the car. Conversely, element b does not describe a commonly used skill. It is difficult to imagine many day-to-day situations that would demand an ability to recognize and appreciate geometry in the world. This element rather describes a goal of the curriculum, that is, a perspective or disposition that students might acquire as a result of the successful completion of studies in mathematics. Thus, it should not be identified as knowledge or skill. Similarly, element c does not describe student knowledge or skill but might be interpreted as a recommendation as to how to design other areas of the curriculum to work in concert with mathematics instruction. Evidence for this comes from the fact that element c appears in NCTM's Standard 4, Mathematical Connections. The first four standards in the NCTM guide (the other three being Mathematics as Problem Solving, Mathematics as Communication, Mathematics as Reasoning) were first designated as principles, not standards. For reasons of accommodation, since regretted by the chair of the NCTM Commission on Standards, the first four principles were also given the name standards, and confusion has resulted ever since (T.A. Romberg, personal communication, June 24, 1997). The most recent edition of standards from NCTM (2000) categorizes standards of this type as process, as opposed to content standards.
It is our belief that curriculum goals and principles should not be part of a description of content standards. Content standards describe the knowledge and skills that students should attain. Curriculum standards, on the other hand, can describe overarching goals, or ways in which the curriculum should be orchestrated to achieve a desired result. In either case, curriculum standards do not explicitly describe student knowledge and skills as do content standards. Mixing both types of standards as if there were no significant difference creates unnecessary confusion.
Differing Types of Content Description
All organisms are composed of cells - the fundamental unit of life. Most organisms are single cells; other organisms, including humans, are multicellular. (p. 156)This is a fairly straightforward description of what a student should know.
A contrasting approach is to present the content in the form of an activity or performance indicator. For example, the following, identified as a performance indicator, is provided by the Joint Committee on National Health Education Standards (NCHES):
As a result of health instruction in Grades 5-8, students will explain how health is influenced by the interaction of body systems (p. 17)In this case, information that the student should know is not directly described as in the previous example. Presumably, the student who successfully completes this activity has acquired the requisite information and/or skills for this topic within the specified grade range.
Finally, another common format for communicating the content of a standard is the performance task. A performance task, in comparison with an activity, can be thought of as providing a greater level of detail and specificity, both in terms of the context of the task and the information or skill that might be required to complete the task successfully. For example, the following task appears in the National History Standards (National Center for History in the Schools, 1994c):
Analyze pictures of hunter-gatherer sites in places such as Danube fishing villages, the Lascaux caves in France, and hunter sites in northern regions. Contrast these with agricultural sites such as those found in Jericho, Çatal Hüyük, Banpo village in North China, and the TehuacánValley in Mexico. How do hunter-gatherer sites differ from agricultural sites? (p. 48)This task describes a specific focus of study-the differences between hunter-gatherer sites and agricultural sites-and the context within which the student acquires and demonstrates this knowledge, that is, through the comparison and contrast of pictures or drawings of the sites. Thus, it differs from the simpler activity approach to content description.
There are, then, a number of different ways in which content has been described in the national reports. Our goal, to provide a synthesis of content from differing documents within each of the subject areas, requires a consistent description of content. We have chosen to describe content in the information and skills format. There are several reasons for this. First, the information and skills description, as opposed to the activity or task description, does not require the reader to make inferences from the activity or task to the information and skills that would be required for successful demonstration of that task; rather, student information and skills are described in a straightforward manner. Second, the activity or task description tends to be narrowly prescriptive in that it characterizes not only what the student should know and be able to do, but how the student should demonstrate this knowledge. Thus, the content described is likewise narrowed; users might erroneously believe that the skill or information required by the activity or task is a complete description of the information or skill the student should acquire. Finally, although the added information provided in a task or activity might be useful for teachers as a guide for instruction or classroom assessment, it is not useful for teachers as a guide to what information and skills are essential for students to learn. Such activity descriptions confound the issue of how students are to demonstrate competence with the logically prior and equally significant issue of what should comprise the content of the curriculum. Once the content has been determined, of course, delineating various ways knowledge might be presented and demonstrated is appropriate. Until and unless that content is identified, however, we believe it is best to keep the two kinds of description separate.
The documents consulted for this project differ considerably in the ways in which content is described; some presented unique challenges of interpretation. The introductory pages for each subject-area section in this report provide a brief summary of the type of analysis that was required given the documents that were used.
As a consequence of the method of standards description adopted for this project, the material identified in this report has some noteworthy characteristics. Specifically, the information that comprises standards identified within this report generally falls into one of three broad categories representing three general types of knowledge. Such distinctions have proved useful in descriptions of learning (Anderson, 1990). At a basic level, knowledge within any domain can be organized into the categories exemplified in Table 3.1.
The first column contains examples of knowledge that involves processes. These processes may or may not be performed in a linear fashion. For example, performing long division is a process: you perform one step, then another, and so on. Reading a map also involves certain steps, but these steps, unlike those in long division, do not have to be performed in any set order. You might read the name of the map first, then look at the legend, or you might just as effectively perform these steps in reverse order. Knowledge of this sort is usually called procedural knowledge. One might think of such knowledge as composed of the skills and processes important to a given content area.
The examples in the second column do not involve a process or a set of steps. Acquiring this type of knowledge involves understanding the component parts. For example, knowledge of the concept of "a geographic region" includes understanding the characteristics of a variety of regions, knowing criteria that give a region identity and how regional boundaries can change, and so on. This type of knowledge is commonly called declarative knowledge. One might think of such knowledge as composed of the information important to a given content area.
The last column contains items that are not simply declarative or procedural but that specify knowledge acquired in a unique context. One might think of contextual knowledge as information acquired only during the execution of some process, or a kind of process that gains special meaning only when applied to certain kinds of information. Column three contains examples of information and/or skills that are in part defined by the conditions under which they are learned. For example, "to classify" is a skill or procedure; to understand the characteristics of organisms is declarative knowledge, or information; but knowledge constructed while classifying organisms is a special type of knowledge, also known as taxonomy. Students learn how structure, function, biochemistry, and behavior can be used to classify organisms; they also know how a taxonomy can describe the degree of relatedness between organisms. Another example of contextual knowledge can be found in the following example from English language arts:
Represents key ideas and supporting details in outline or graph formThis describes not simply a skill the student must acquire-using an outline or a graph-but a knowledge of key ideas and supporting details and how they can be represented in such formats.
This report, then, identifies all content as belonging to one of the three categories described above. The reader is referred to "How the Subject Area Sections Are Structured", for a description of how the category of each item can be identified. Generally speaking, however, content that is declarative in nature usually begins with the stem "understands that . . ." or "knows that . . .". Content that is procedural in nature begins with verbs, such as "uses", "solves," and "predicts." Content that is contextual in nature also begins with verbs or verb phrases but tends to look more like activities in that a particular skill is described in terms of the information or knowledge about or upon which the skill is applied.
It is of interest to note that some subject areas are more heavily declarative or procedural in nature. Contextual knowledge, which is a special case, is not common. Table 3.2 displays the distribution of the types of knowledge across the subject areas in this report:
Differing grade ranges
Understands basic concepts about the structure and properties of matterAt the 12th-grade level, the benchmark, or expected level of understanding, might be described in the following way:
At the 8th-grade level, the benchmark or expected level of understanding might be
Theoretically, these benchmarks, or subcomponents of a standard, could be identified at all grade levels. However, the trend seems to be to develop benchmarks at a few key levels. For example, the National Assessment of Educational Progress (NAEP) identifies benchmarks at grades 4, 8, and 12. The American Association for the Advancement of Science (Project 2061) identifies benchmarks at grades 2, 5, 8, and 12.
In this model, benchmarks identify expected understanding or skill at various grade levels, with a preference for articulating benchmarks at primary, upper elementary, middle, and high school within each standard. However, these levels of identification may be different in some content areas, depending on the availability of source materials. The reader is referred to the introductory sections of each content area to determine what levels have been identified for that area.
Differing Levels of Generality
From our observations, a benchmark seems to have a lower and an upper limit. As to the lower limit, in no case does it appear to describe specifics of information or specific skills that an average student could master quickly, assuming that the benchmark has been placed at the appropriate grade level. This lower limit means that a declarative benchmark would never be equivalent to a short list of facts, for example; nor would a two-step algorithm be identified as a procedural benchmark at the 4th-grade level. This provides a rough starting point for the lower level of a benchmark.
A useful reference point for a benchmark, particularly at the lower end of the interval, is the behavioral objective. A benchmark is "larger" than a behavioral objective. Measurement expert Robert Mager (1962), described what came to be called a behavioral objective as consisting of three key elements: a target behavior, a description of conditions under which the behavior is demonstrated, and criteria for acceptable performance. By limiting the description of information and skill to a behavior and to the conditions under which that behavior is demonstrated, this approach necessarily required many, many thousands of behavioral objectives to describe the knowledge within a given content domain. Benchmarks, by contrast, do not describe the behavior of students who meet an objective, nor do they narrow the description of information and skills to a particular set of conditions. (A contextual benchmark, discussed above, is a special case. It describes a general context for knowledge use rather than the specific conditions under which that knowledge could or should be demonstrated).
Thus, a single behavioral objective could not address all of the content described within a benchmark, but a single benchmark could be the source of a number of instructional objectives. This characteristic of benchmarks, at least as they appear in this report, is in part explained by the fact that the articulation of standards and benchmarks is not an attempt to organize learning or learning activities within a model for instruction. Rather, this approach uses a cognitive theory of knowledge types to assist in the analysis and identification of information and skills1. At the lower limit, then, a benchmark does not prescribe instructional objectives. That is, as said of the NCTM standards in a report from the National Academy of Education Panel (Shepard, 1993), they "do not delineate specific instructional activities, [but] they do set the direction for what should be taught" (p. 3).
In summary, a benchmark can be described as an "interval" of levels of generality in the description of information and skills. In this section, we have attempted to describe some of the characteristics of the lower end of that interval. Benchmarks do not describe trivial or "easy" information and skills for the developmental level at which they are found. They are not descriptions of information and skill that have been narrowed through behavioral objectives or by being translated into an instructional activity.
Where the lower bounds of a benchmark have some identifiable characteristics, the characteristics of the upper bound are much more vague. That is, within this study it became difficult to determine the point at which the component of a standard seemed too broad in scope or too generally stated to be characterized as a benchmark. In fact, at the next broader level of generality, we found that depending upon the document we analyzed, this level was either treated as a topic organizer or identified as a complete standard. The national history standards documents from NCHS were found to have at least four tiers of organization. In the design for the world history standards, for example, historical eras provided the most general structure. The level just beneath eras was identified as the standard level. Beneath the standard level there was no detailed information, but three or four more specific statements were given, under which benchmark-level information was provided.
The subject area of science offers a convenient example of the variance in approaches to levels of generality, inasmuch as two organizations have put considerable effort into the development of science standards, each using a different organizational scheme. Project 2061's Benchmarks for Science Literacy (1993) articulates most standards (termed literacy goals) across K-12. In practice, this means that a standard is described at a level that is broad enough to be articulated with benchmarks at each of four developmental levels: K-2, 3-5, 6-8, and 9-12. For example, one standard, or literacy goal, is on "the structure of matter." This idea is expressed at the earliest developmental level in terms such as the following:
By the end of the 2nd grade, students should know thatAt the upper level, 9-12, a sample benchmark under the same overarching idea is
By the end of the 12th grade, students should know thatContrasting material comes from the National Research Council (NRC), which was funded by the Department of Education to develop standards for science. If we search for an idea similar to the one found at the early grades in the Benchmarks, we find it in the following, which is identified as a content standard:
As a result of the activities in grades K-4, all students should develop an understanding ofConcepts related to these topics, or subcomponents, are elaborated under the heading "fundamental ideas that underlie this standard." At that level, the following description is found for "properties of objects and materials":
This demonstrates a dramatically different way of organizing very similar information. In this document, the standard has several organizing topics, each of which is defined at a greater level of detail. These details describe information and skills at about the same level as found in the benchmarks from Project 2061's Benchmarks. The benchmark information differs essentially in two ways: In the NRC document, benchmarks appear in a standard that is complete at grade level, rather than articulated across grades; and these benchmarks also appear arranged under topic headings.
Although the categories in these two documents differ, the same or very similar material is covered. For example, the corollary to the 12th-grade benchmark from Project 2061 on the structure of molecules (see example above) can be found in the NRC document as part of a different standard, which has six organizing subcomponents (p. 176), under one of which ("structure and properties of matter") the following information can be found:
In short, NRC has determined that standards should be categories of information not so broad as to encompass a common set of information across K-12. This articulation does appear, however, at the next larger level of organization. That is, all the benchmark information presented in the examples above from the NRC document is organized under the category Physical Science.
In this study, wherever possible, we describe standards at a level of generality that is broad enough to allow the articulation of benchmarks across K-12. Sometimes this approach required the reorganization of material from the subject-area documents. However, this organization was considered advantageous in that it organized information and skills systematically across subject areas without any apparent loss of critical information. In addition, as mentioned at the outset (see Purpose of this work) this consistency of format provides a clearer system-wide picture for those who wish to integrate benchmarks from different subject areas but who also need to keep track of how and what curriculum they have addressed.
Standards, as found in the documents analyzed for this study, appeared at different levels of organization and structure. Standards provide a way of organizing information, that is, the benchmarks that identify important declarative, procedural, and contextual knowledge. This organization itself may provide information on how "pieces" of knowledge can be logically sequenced for students' ease of learning. For example, a study of research findings by the authors of Benchmarks for Science Literacy (1993) led them to the following kinds of adjustments for writing benchmarks:
1) Stating less-sophisticated precursors of an idea. For example, research suggests that the notion of a "fair comparison" can be understood in lower grades as a preliminary form of the later concept of a controlled experiment.It should be noted that the approach to benchmark writing discussed here-that is, the sequencing of information based upon the idea that learning occurs in a step-by-step fashion, leading to the understanding of more complex concepts or principles-may not be an approach that works well for all types of knowledge. Science is a nomothetic discipline, that is, it has as its focus universal laws or principles. Thus, it may be possible to arrange benchmarks to serve overarching ideas, for example, benchmarks that build toward the understanding of a general principle. The discipline of history provides a counter-example. History is an idiographic discipline, that is, one that has as its primary interest the nonabstract (e.g., specific individuals and concrete events). The discipline of history does not seek to extract universal ideas or laws from the stream of people and occurrences that it studies. Thus, with respect to this discipline, benchmark writing may not involve a step-by-step approach to larger generalizations but, rather, may simply entail the description of important facts, events, and episodes. Therefore, one would expect to find benchmarks organized by historical eras, rather than by ideas or principles.
In this report, the standards we have developed reflect both the character of the materials available to us and the model we have developed for identifying knowledge. There are other ways that benchmarks can be grouped, however, and except for the caution that developmentally sequenced information, when available, should not be lost, there appears to be no compelling reason that districts or schools should not feel free to organize benchmarks in whatever way they find most useful.
Although some variations exist in the manner in which standards from different domains were addressed, a general process was followed to identify the standards in this report.
Identify Significant Reports
In addition to these areas, documents were also reviewed for the domain of the workplace. Workplace standards, were developed to meet the growing demand for a smoother transition from school to the workplace, as made evident from recent Skills Standards efforts funded by the Departments of Education and Labor.
It is important to note that a number of documents used were in draft form. All relevant documents are discussed in the appropriate subject sections.
Select Reference Documents
Integrate Information from the Other Documents
Organize Standards into Categories