Components of Coherent Mathematics and Science Education Curriculum Programs

A curriculum program should contain goals, content standards, a common vision, a curriculum framework, and instructional materials.8 These components communicate the structure, organization, balance, and delivery of the content that students are expected to learn and, when effectively employed by teachers, that have the most direct impact on student learning in mathematics and science. These components constitute the instructional blueprint for the school district. This blueprint enables school system stakeholders — students, teachers, administrators, school board members, parents, representatives of colleges and universities, and others — to have a clear understanding of what students are expected to learn and the instructional opportunities they will have to learn it.

GOALS OF K-12 MATHEMATICS AND SCIENCE CURRICULUM PROGRAMS

Effective curriculum programs have goals that serve several important and interrelated functions. These goals should be written to communicate the overall purposes of the program to many audiences, including staff, parents, and policy makers, such as school board members. Goals also should be used to guide the actions and decisions of teachers, administrators, and support staff as these personnel develop, implement, and support activities to improve the quality of mathematics and science education in the district.

Goals serve to avoid the confusion between ends and means. For example, goals — and the standards that are

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The term "framework" refers to the "skeleton" or frame that guides and organizes the placement of the instructional materials. It does not refer to the comprehensive documents that many states have developed to describe all aspects of a mathematics or science program. Further, neither "assessment" nor "vision" is included as a component here. Assessments used by schools, districts, or states, although essential in the total scheme of improvement (see Fig. 3), are outside the definition of curriculum program and the scope of this report. Because high-quality instructional materials should contain a variety of assessments for use by classroom teachers, the presence of aligned assessments will be an important criterion in evaluating instructional materials. While a common ''vision" is a critical starting point for the design of a coherent curriculum program, it is not often considered to be a part of the actual program blueprint.



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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards Components of Coherent Mathematics and Science Education Curriculum Programs A curriculum program should contain goals, content standards, a common vision, a curriculum framework, and instructional materials.8 These components communicate the structure, organization, balance, and delivery of the content that students are expected to learn and, when effectively employed by teachers, that have the most direct impact on student learning in mathematics and science. These components constitute the instructional blueprint for the school district. This blueprint enables school system stakeholders — students, teachers, administrators, school board members, parents, representatives of colleges and universities, and others — to have a clear understanding of what students are expected to learn and the instructional opportunities they will have to learn it. GOALS OF K-12 MATHEMATICS AND SCIENCE CURRICULUM PROGRAMS Effective curriculum programs have goals that serve several important and interrelated functions. These goals should be written to communicate the overall purposes of the program to many audiences, including staff, parents, and policy makers, such as school board members. Goals also should be used to guide the actions and decisions of teachers, administrators, and support staff as these personnel develop, implement, and support activities to improve the quality of mathematics and science education in the district. Goals serve to avoid the confusion between ends and means. For example, goals — and the standards that are 8   The term "framework" refers to the "skeleton" or frame that guides and organizes the placement of the instructional materials. It does not refer to the comprehensive documents that many states have developed to describe all aspects of a mathematics or science program. Further, neither "assessment" nor "vision" is included as a component here. Assessments used by schools, districts, or states, although essential in the total scheme of improvement (see Fig. 3), are outside the definition of curriculum program and the scope of this report. Because high-quality instructional materials should contain a variety of assessments for use by classroom teachers, the presence of aligned assessments will be an important criterion in evaluating instructional materials. While a common ''vision" is a critical starting point for the design of a coherent curriculum program, it is not often considered to be a part of the actual program blueprint.

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards derived from them — help to maintain a focus on significant ends or outcomes but do not dictate a single means as "the way" to approach instruction. A number of suitable and effective instructional strategies can be used to help students learn the mathematics and science content. Goals for mathematics and science curriculum programs rarely stand alone. Often, they are derived from a broader set of educational goals already in place for the state or district. Groups designing curriculum programs may decide that their local goals should reflect the goals of the NCTM Standards (NCTM, 1989) and/or the NSES (NRC, 1996b). The NSES begin with a "Call to Action." The first sentence of this call is an important and broad goal: "The nation has established as a goal that all students should achieve scientific literacy" (NRC, 1996b). That overarching goal clearly and unambiguously frames the other goals by stating that the standards are to achieve scientific literacy for ALL students. The document then sets out four learning goals that describe students who are able "to experience the richness and excitement of knowing about and understanding the natural world; to use appropriate scientific processes and principles in making personal decisions; to engage intelligently in public discourse and debate about matters of scientific and technological concern; and to increase their economic productivity through the use of the knowledge, understanding, and skills of the scientifically literate person in their careers." The NCTM Standards state that ". . . today's society expects schools to insure that all students have an opportunity to become mathematically literate, are capable of extending their learning, have an equal opportunity to learn, and become informed citizens capable of understanding issues in a technological society" (NCTM, 1989). Following that opening charge, five goals for ALL students are given: that they learn to value mathematics; that they become competent and confident in their ability to do mathematics; that they become mathematical problem solvers; that they learn to communicate mathematically; and that they learn to reason mathematically." Criteria for Goals The target audience should be clearly specified. The NSES and NCTM

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards Standards make it clear that their goals and standards are intended for all students. If the audience for a set of goals is not all students, this should be clearly stated. The absence of such a declaration creates uncertainty when subsequent decisions are made about standards, instructional materials, instructional grouping, assessment, budget allocations, and so on. Although the goals in the national standards are for all students, it should be recognized that different students will proceed at different rates and, therefore, will have some common and some individualized experiences. Any student willing to work hard and persistently should be able to have access to all aspects of the curriculum with no disadvantage due to race, ethnicity, religion, socio-economic class, gender, or other non-relevant feature. Goals should communicate broad outcomes and values. Usually goals convey the essence of intended student behavior, ability, and knowledge. Generally, goals are not measured directly but are transformed into progressively more specific and measurable outcomes that can be used to develop assessments. Several levels of specificity can be derived from the goals. Typically, the next higher level of specificity consists of content standards, often followed by performance standards that describe the level of expectations called for in content standards. Yet another level of specificity would be objectives that are more specific and unique to student activities; these are usually found in instructional materials. Goals should provide guidance. Although general in nature, goals should provide guidance for the decisions that shape the curriculum program. They should not be written in such broad terms or so ambiguously that they could be interpreted in almost any manner. For example, both the NCTM Standards and the NSES make the target of "all students" very clear. The mathematics standards call for students to become "mathematical problem solvers," an outcome that moves beyond the traditional goal of getting correct answers to arithmetic exercises. The NSES add personal decision making, engaging in public discourse, and economic productivity to the traditional ''understanding the natural world" outcome. If used as guidance, goals such as these can significantly affect the nature of curriculum programs. Goals should describe student outcomes, not system outcomes. In this era of standards, emphasis on student learning, and use of student learning outcomes, goals should be written

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards with students as the focus. At present, goals often are written to describe outcomes for the district or school, such as expecting the scores on a standardized norm-referenced test to improve during the next year. Goals should be widely accepted. As with any policy document, goals will be of little value if they are not widely accepted. For maximum acceptance, goals should be free of jargon and highly technical language so that the public can understand them. To the degree possible, the development process should be initiated and led by the science and mathematics staff, but it should also involve extensive input, hearings, public and staff discussion, and review to achieve as high a level of agreement for the goals as possible. Avoid frequent modification of goals. After the goals are accepted, they guide the next steps in the process. The flow of this development process is in one direction. Once the total curriculum program has been implemented and is in place, modification of the goals should be undertaken with care, as unexamined changes could create inconsistencies throughout the program. CONTENT STANDARDS A comprehensive set of content standards that defines what students are to understand or be able to do is the key component in the design of an effective curriculum program. These content standards should be in place, along with goals, before development of the other components begins. The case for using standards to improve the quality of mathematics and science education and the achievement of students has been made by a number of groups (Gandal, 1997; Education Commission of the States [ECS], 1996; The Business Roundtable, 1996; McLaughlin & Shepard, 1995). The history of educational standards also has been well documented (Bybee, 1997; ECS, 1996). Although the initial development of content standards in mathematics and science was conducted at the national level (NCTM, 1989; AAAS, 1993; NRC, 1996b), virtually every state has developed its own mathematics and science education standards modeled in various degrees after the national standards (CCSSO, 1997). In some local-control states, each district is responsible for the development of content standards, although model state standards often are available as a default alternative. The National Science Education Standards define the content standards

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards as "what students should know, understand and be able to do in natural science" (NRC, 1996b). The National Academy of Education has defined both content and performance standards, as follows: "Content standards are broad descriptions of the knowledge and skills students should acquire and be able to do in a particular subject area" and "Performance standards are the more specific, concrete examples and explicit definitions of what students must know and be able to do to demonstrate that they have attained the content standards. Performance standards should include multiple benchmarks that lead to higher standards of proficiency, making it possible to demonstrate progress for students at all levels of achievement. To the extent that content standards include examples of assessment tasks and of various levels of real student performance in response to these tasks, they can better provide teachers and the public with the insights into the concrete meaning of the standards and specific expectations for student learning" (McLaughlin & Shepard, 1995). Although states and schools districts rarely develop both types of standards initially, understanding the purposes of both types and the distinctions between them is important before standards are written for curriculum programs. Content standards describe "what" is to be learned, and performance standards describe "how" it will be assessed. The mistake that many writers make is to attempt to make content standards serve both purposes by using words of action such as "describe," "explain," or ''apply" to help describe content. Verbs such as these, if followed by detailed performance expectations, can be used as one means of assessing student knowledge and understanding, but they immediately eliminate other possible means of assessment and often obscure the important content or skill that should have been described in the content standard. The issue of the language used in the standards is visited again in the next section, "Criteria for Content Standards." Criteria for Content Standards Many groups faced with the task of designing curriculum programs will be expected to use a set of pre-existing content standards. Others may have the opportunity to create their own standards based on national or state standards. In this latter case, a few basic criteria or guidelines for writing standards will be useful. A clearly specified audience. The NSES, NCTM Standards, and most state standards make clear that they are intended for all students. Without a clear identification of audience,

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards subsequent decisions about instructional materials, assessment, and budget allocations are made more difficult. Fundamental content. One of the important purposes of standards is to focus instruction and student learning on a deep understanding of fundamental content. In science, the NSES (NRC, 1996b) considers content to be fundamental if it "represents a central event or phenomena in the natural world; represents a central scientific idea and organizing principle; has rich explanatory power; guides fruitful investigations; applies to situations and contexts common to everyday experiences; can be linked to meaningful learning experiences; and is developmentally appropriate for students at the grade level specified." In the national mathematics curriculum standards, content is considered fundamental if it meets the following criteria (NCTM, 1989): "Knowing mathematics is doing mathematics. Informational knowledge has value in the extent to which it is useful in the course of some purposeful activity. All students should have the opportunity to develop an understanding of mathematical models, structures, and simulations applicable to many disciplines. Students should have a balanced approach to calculation, be able to use appropriate procedures (including mental arithmetic, paper-and-pencil procedures, and calculators or computers), find answers, and judge the validity of those answers. The content of the curriculum should be appropriate for all students. All students should have an opportunity to learn the important ideas of the standards." Scientific and mathematical accuracy. All content standards should be reviewed carefully for scientific and mathematical accuracy. Understandable vocabulary. The general public should be able to read and understand the content standards. The terminology used should be similar to or reflect terminology used by the general public. The vocabulary for the lower grades should be adjusted to "signal the nature and sophistication of the understanding sought" (AAAS, 1993). Appropriate grain size. Many writers of standards are tempted to craft statements that contain several related ideas in an effort to present a coherent view

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards of the topic at hand. Other writers do the opposite and write several statements that parse ideas into their smallest parts. Both approaches have advantages and disadvantages. A collection of ideas may communicate how the components of the collection are related but also may require very large amounts (many weeks) of instructional time and the assessment of many different concepts or skills. On the other hand, confining one idea to one standard may make writing performance standards and assessments much easier, but one idea often cannot be evaluated alone; it must also be evaluated in light of student understanding of other ideas and their relationship or connections with one another. Use of verbs to describe the outcomes.9 The language used to describe what students should know or be able to do should do just that. If the outcome is knowledge or understanding, the standard should contain the verbs "know" or "understand." If the outcome is a skill, language related to that skill (such as "measure," "communicate," or "design'') should be used. The NSES developers settled on "understand" and "develop the abilities of" to communicate knowledge and skills, respectively, and the Benchmarks developers chose "know" and "know how." Both groups address the qualities of effective instruction in other ways: the NSES included "Science Teaching Standards," and Project 2061 included chapters on teaching in Benchmarks as well as in Blueprints for Reform: Science, Mathematics, and Technology Education (NRC, 1996b; AAAS, 1993 and 1998). In mathematics, the NCTM communicated its emphasis on instruction by developing a separate document, Professional Standards for Teaching Mathematics (NCTM, 1991c). Verbs that describe instruction, such as "investigate," "explore," or "research," should be avoided. These action verbs are often used to convey a message about the desirability of "hands-on" teaching, but, in so doing, they can limit instruction to a single strategy. Allowing standards to imply instruction also results in statements that communicate the "means" of learning rather than the "end" or outcomes of instruction. The writers of many state and local standards have used a variety of action verbs to describe different 9   Benchmarks for Science Literacy's chapter on "Characterizing Knowledge" has an excellent discussion of this topic (pg. 312).

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards observable behaviors as well as levels of sophistication or understanding as a way to guide the assessment of student understanding of the content of the standard. The problem with this is that the choices of action and level are arbitrary and limit the performance that can be used in the assessment to the ones specified. A much more satisfactory solution is to write the content standards as statements of knowledge or understanding and skill and to develop a separate set of performance standards to guide the assessment process. (See the earlier discussion of performance standards on pg. 21.) CURRICULUM FRAMEWORK A framework is the listing of outcomes (usually content standards or benchmarks) by grade level that guides the development of the curriculum and the selection and placement of instructional materials. Ideally, the framework also includes the performance standards associated with the content standards. It is a key component of a coherent curriculum program. In some ways, a framework is like an elaboration of the scope-and-sequence documents that have traditionally served as a basis for many district programs. In this report, though, use of the term "framework" is meant to highlight the critical need for attention to coherence — to the way the content that students learn builds within a year and over a span of years. Designing Frameworks to Facilitate Growth of Understanding. An important function of the framework is to identify and locate the standards or benchmarks that will facilitate the growth of understanding of ideas and skills, an important characteristic of coherence, during a year and from year to year. For example, in science, students should understand by the end of high school that, "The physical properties of [a] compound reflect the nature of the interactions among its molecules" (NRC, 1996b). Students could memorize this statement fairly quickly; however, they might understand the concept better if they first experiment with a variety of properties, know about the existence and properties of atoms, and understand that everything is made up of atoms. They also need to understand the relationship between atoms and molecules and realize that molecules vary in shape and size. Designs for Science Literacy describes such a sequence as follows: ". . . what is learned now should be based on what was learned earlier, what is capable of being learned now, and what needs to be learned next (AAAS, at press)." In short, in science, the more complex,

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards higher level idea is understood best when it is built on a comprehension of earlier knowledge. Figure 4 on pg. 26 illustrates in more detailed fashion this growth of understanding from the NSES. In mathematics, a similar observation about growth of understanding has been made by researchers involved in an in-depth NSF-funded study of how young children develop computational understanding based on their informal background knowledge (Carpenter et al., 1992). The NCTM "Probability Standard" for grades 9-12 illustrates this. The goal within the standard is for students to "describe, in general terms, the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed" (NCTM, 1989). This outcome builds on many experiences from earlier grades. These include constructing and interpreting a variety of graphs, including line graphs, and making connections among a data set, a graph, and numerical statistical representations, such as mean and standard deviation. To use the normal curve in the ways described, a student should understand what a normal distribution is and should have had experiences using data to test the validity of hypotheses. It also is best if students have learned about rational numbers and their applications in a variety of situations. Yet another expectation is understanding and skill in computation with rational numbers. Figure 5 on pg. 27 illustrates in a more detailed fashion the growth of understanding from the NCTM "Statistics Standard." The treatment of the science and mathematics standards represented in Figures 4 and 5 represent only the "big idea" parts of these standards. It should be noted that the framework allows considerable flexibility for the design of the sequence of learning activities in the instructional materials. For example, in Figure 5, specific graphing forms, such as bar graphs, are not named at any of the levels. The grade levels at which such forms are introduced vary from one program or location to another. Some programs might wait until second grade and precede the introduction with student-invented graphing forms. The examples provided in Figures 4 and 5 do not indicate the precise placement of the standards. They are offered as an illustration of one thread through the curriculum program that can facilitate the growth in understanding of a fundamental concept. The national mathematics and science standards and the Benchmarks contain many such threads that are not obvious without developing the "growth of understanding" figures. These in turn facilitate the placement of the standards in the framework in a coherent manner.

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards By the end of grade 4, students will understand that Objects have many observable properties, including size, weight, shape, color, temperature, and the ability to react with other substances. Those properties can be measured using tools, such as rulers, balances, and thermometers. Objects are made of one or more materials, such as paper, wood, and metal. Objects can be described by the properties of the materials from which they are made, and those properties can be used to separate or sort a group of objects or materials. Materials can exist in different states — solid, liquid, and gas. Heating or cooling can change some common materials, such as water, from one state to another. By the end of grade 8, students will understand that A substance has characteristic properties, such as density, a boiling point, and solubility, all of which are independent of the amount of the sample. A mixture of substances often can be separated into the original substances using one or more of the characteristic properties. Substances react chemically in characteristic ways with other substances to form new substances (compounds) with different characteristic properties. In chemical reactions, the total mass is conserved. Substances often are placed in categories or groups if they react in similar ways; metal is an example of such a group. Chemical elements do not break down during normal laboratory reactions involving such treatments as heating, exposure to electric current, or reaction with acids. There are more than 100 known elements that combine in a multitude of ways to produce compounds, which account for the living and non-living substances that we encounter. By the end of grade 12, students will understand that Matter is made of minute particles called atoms, and atoms are composed of even smaller components. These components have measurable properties, such as mass and electrical charge. Each atom has a positively charged nucleus surrounded by negatively charged electrons. The electric force between the nucleus and electrons holds the atom together. Atoms interact with one another by transferring or sharing electrons that are farthest from the nucleus. These outer electrons govern the chemical properties of the element. An element is composed of a single type of atom. When elements are listed in order according to the number of protons (called the atomic number), repeating patterns of physical and chemical properties identify families of elements with similar properties. This "Periodic Table" is a consequence of the repeating pattern of outermost electrons and their permitted energies. Bonds between atoms are created when electrons are paired up by being transferred or shared. A substance composed of a single kind of atom is called an element. The atoms may be bonded together into molecules or crystalline solids. A compound is formed when two or more kinds of atoms bind together chemically. The physical properties of a compound reflect the nature of the interactions among its molecules. These interactions are determined by the structure of the molecule, including the constituent atoms and the distances and angles between them. Figure 4. Growth in Understanding the Structure of Matter: An Illustration of How Understanding Can Progress Over Many Years Based on the  National Science Education Standards

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards By the end of kindergarten, students will understand that Objects and data can be sorted and displayed so that population characteristics are seen and comparisons can be made between populations (e.g., Did more students wear shoes with laces, shoes with Velcro, or slip-on shoes? Was it a lot more or just a little more?). By the end of grade 2, students will understand that Data are organized and displayed in a variety of ways to communicate information about groups or events (e.g., tables, charts, graphs, etc.). By the end of grade 4, students will understand that Graphic displays of data are interpreted to describe the characteristics of things such as populations and events. The general shape of the data as seen in the display can often be used to get a general sense of the story the data are telling. Information from a graphic data display can be used to solve problems, to make interpretations, or to generate questions (e.g., Do you think that next month's weather graph will show the same patterns as this month's? How is this month's weather graph different from last month's? Why do you think that is so?). By the end of grade 6, students will understand that Graphic displays of data can be used to make inferences and predictions and to support arguments about people and events. Looking at where the data cluster, the center, and how the data spread out can help with interpreting the story that the data tell. The way data are displayed has a significant effect on the ease of reading the display, as well as on the quality and accuracy of interpretations made by observers (e.g., If we group the data in intervals of 10, how is the display changed?). By the end of grade 8, students will understand that Decisions about data collection and display should be based on the questions that are to be addressed by the data. Data displays can be constructed to communicate information accurately and clearly. They can also be designed to distort communication and encourage wrong interpretations. By the end of grade 10, students will understand that Statistical methods provide powerful means of influencing people and making decisions based upon information. By the end of grade 12, students will understand that Statistical methods are used to test a wide variety of hypotheses about populations and events. If appropriate, data can be transformed to facilitate their interpretation and the making of predictions based upon the data. Statistical measures of central tendency, variability and correlation are used to describe and make decisions about populations and events. Large populations can be sampled to gather data to describe the population and/or to make predictions. The sample size and sampling method affect the confidence that one has in the interpretations and predictions that are made about the population. Figure 5. Growth in Understanding of Statistics: An Illustration of How Understanding Can Progress Over Many Years Based on the NCTM  Standards

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards It also should be noted that, at the district and school levels, standards that span more than one grade level can be too broad to be useful. Because most schools are organized around one-year grade levels, standards may need to be specified further to fit one-year blocks. In some cases, even shorter increments may be needed. To accommodate these needs, the concepts in the content standards (state and/or local) that span several grade levels can be "unpacked" and assigned to particular grade levels. At times, adding intermediate standards or benchmarks will be desirable because the conceptual or procedural gap between standards is so great. This is particularly true at the earliest level (grade 4 for the NCTM Standards and the NSES; grade 2 for the Benchmarks). Because of the large grade span and even larger difference in cognitive growth, informal standards for kindergarten or the early primary grades may be useful, also. For similar reasons, it may be useful to find intermediate "standards" to fill intervals that may exist in state or national standards, especially at the higher-grade levels. Although Figures 4 and 5 are linear, both contain a number of interconnected story lines. Anyone familiar with the concepts and processes of mathematics and science is aware of the multiple connections that exist among ideas within each discipline. The national mathematics and science standards describe some aspects of this type of connection, both within the text of the standards and in elaborations of the standards. Maps of the content standards across the grade levels, as illustrated by Appendixes B and C, can make even more apparent the comprehensive and interconnected nature of subject matter (Ahlgren & Kesidou, 1995). Such maps, whether they are simple or complex, represent the next possible phase in the development of a framework. This phase requires considerable time and effort. Project 2061 is planning to produce a series of maps based on the Benchmarks that illustrate such connections graphically (AAAS, 1999a). Criteria for a Curriculum Framework Concepts in the framework should be assigned to grade levels based on what students are capable of learning. The framework should indicate development of processes/skills/abilities over several years. The framework should clearly indicate what standards are prerequisites for other standards. The assignment of content across grade levels should be appropriately balanced or concentrated. (For example, do those who have been tasked to design the curriculum program want to emphasize geometry at the tenth

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards grade or earth science at the eighth-grade? Or is a coordinated or integrated selection of content desired at each level?) Concepts in the framework should be grouped to form the basis of units or courses, with logical connections shown both within a grouping and across grades. The framework should account for all standards. In a well-designed curriculum program, the sequence is cumulative, with each subsequent level applying, extending, and building on previously obtained knowledge. The main purpose is to build coherence into the program by describing a reasonable flow of these ideas across the grade levels. It should be clear that neither the standards nor the framework constitute a curriculum program. Standards and frameworks identify the concepts that are to be learned and the order in which they are to be addressed. They do not specify how the content is to be taught. This is addressed by the fourth — and final — component of the curriculum program to be addressed in this report — instructional materials. INSTRUCTIONAL MATERIALS THAT SUPPORT THE K-12 STANDARDS There is broad consensus in both the mathematics and science education communities that use of instructional materials aligned with the content and teaching standards in national standards documents is a critical component of effective curriculum programs. With funding from the NSF, developers have designed instructional materials to address the standards, have tested them in classrooms, and have made available evidence of their effectiveness. The use of exemplary instructional materials to support the student learning identified in the K-12 instructional framework increases the likelihood that all students will have an opportunity to attain the level of understanding called for in the standards. In recent years, several groups have developed objective criteria that can be used to identify exemplary instructional materials. Various review instruments have been produced that can be used by a school or district to select high-quality instructional materials. While the review instruments vary in format and some criteria, they all address two important dimensions of materials: 1) the degree of alignment between the content of the materials with that specified in the standards; and 2) the quality of the suggested instructional strategies. Many of the instruments also include a review of the assessments that are used in the materials and their degree of alignment with the specified learning outcomes (AAAS, 1997; NCTM, 1995; NRC, 1999c;

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards National Science Resources Center (NSRC), 1998a; U.S. Department of Education [DoEd], 1997; NSF, 1997; National Association of Biology Teachers (NABT) [year of publication not available]; Kahle & Rogg, 1996). Both the materials review process developed by Project 2061 (AAAS, 1997) and the process and instrument developed by the Center for Science, Mathematics, and Engineering Education at the NRC link the review of instructional strategies to specific learning outcomes (AAAS, 1997; NRC, 1999c). Although the two tools differ in many ways, both of them first examine the match between the materials under review and the learning outcomes of the Benchmarks, the NSES, or other relevant local standards. If materials do not match standards to a reasonable degree, they are dropped from further consideration for selection. If there is a reasonable match between the materials and content standards, the materials are examined more closely to judge whether or not the teaching strategies in the materials provide adequate opportunities for students to learn what is called for in the content standards. An instructional materials review and selection process from the U.S. Department of Education differs from those discussed above in that it asks reviewers to ascertain empirical evidence that student learning can be attributed to use of the materials (DoEd, 1997). Criteria for the Selection of Instructional Materials The following broad criteria have been gleaned from the procedures for analyzing and selecting instructional materials described above. The content of the instructional material should be mathematically and scientifically accurate, consistent with the outcomes in standards, and targeted at the level called for in the framework. The instructional strategies consistently used by the material should be supported by learning research and make it possible for students to attain the specific outcomes identified in the first criterion, above. The assessments that accompany the material should be aligned with the content in the standards and the level of understanding or skill expected by the standard. The support for the teacher in the teacher's guide and ancillary materials should be adequate. There should be evidence from field trials that students can learn the specified content and skills if the materials are used as intended. With these components and criteria in mind, a process for developing a complete curriculum program is discussed in the next section, "Process for Designing a Curriculum Program."