6Learning with Understanding: Seven PrinciplesDuring the last four decades, scientists have engaged in research that has increased our understanding of human cognition, providing greater insight into how knowledge is organized, how experience shapes understanding, how people monitor their own understanding, how learners differ from one another, and how people acquire expertise. From this emerging body of research, scientists and others have been able to synthesize a number of underlying principles of human learning. This growing understanding of how people learn has the potential to influence significantly the nature of education and its outcomes.The committee’s appraisal of advanced study is organized around this research on how people learn (see, for example, Greeno, Collins, and Resnick, 1996; National Research Council NRC, 2000b; 2001a; Shepard, 2000). Our appraisal also takes into account a growing understanding of how people develop expertise in a subject area (see, for example, Chi, Feltovich, and Glaser, 1981; NRC, 2000b). Understanding the nature of expertise can shed light on what successful learning might look like and help guide the development of curricula, pedagogy, and assessments that can move students toward more expert-like practices and understandings in a subject area.

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To make real differences in students’ skill, it is necessary both to understand the nature of expert practice and to devise methods that are appropriate to learning that practice.The design of educational programs is always guided by beliefs about how students learn in an academic discipline. Whether explicit or implicit, these ideas affect what students in a program will be taught, how they will be taught, and how their learning will be assessed. Thus, educational program designers who believe students learn best through memorization and repeated practice will design their programs differently from those who hold that students learn best through active inquiry and investigation.The model for advanced study proposed by the committee is supported by research on human learning and is organized around the goal of fostering. Learning with deep conceptual understanding or, more simply, learning with understanding. Learning with understanding is strongly advocated by leading mathematics and science educators and researchers for all students, and also is reflected in the national goals and standards for mathematics and science curricula and teaching (American Association for Advancement of Science AAAS, 1989, 1993; National Council of Teachers of Mathematics NCTM, 1989, 1991, 2000; NRC, 1996). The committee sees as the goal for advanced study in mathematics and science an even deeper level of conceptual understanding and integration than would typically be expected in introductory courses.Guidance on how to achieve learning with understanding is grounded in seven research-based principles of human learning that are presented below (see ).

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In, these principles are used as the framework for the design of curricula, instruction, and assessments for advanced study—three facets of classroom activity that, when skillfully orchestrated by the teacher, jointly promote learning with understanding. These principles also serve as the foundation for the design of professional development, for it, too, is a form of advanced learning.The design principles for curriculum, instruction, assessment, and professional development provide one of the organizing frameworks of the committee’s analysis of the AP and IB programs (see Chapters and, this volume). While it could be argued that all components of the educational system (e.g., preservice training and leadership) should be included (and we believe they should), our analysis was limited to these four facets. Although this framework was developed to assess current programs of advanced study, it also can serve as a guide or framework for those involved in developing, implementing, or evaluating new educational programs. Learners use what they already know to construct new understandings.When students come to advanced study, they already possess knowledge, skills, beliefs, concepts, conceptions, and misconceptions that can significantly influence how they think about the world, approach new learning, and go about solving unfamiliar problems (Wandersee, Mintzes, and Novak, 1994). People construct meaning for a new idea or process by relating it to ideas or processes they already understand.

This prior knowledge can produce mistakes, but it can also produce correct insights. Some of this knowledge base is discipline specific, while some may be related to but not explicitly within a discipline.

Research on cognition has shown that successful learning involves linking new knowledge to what is already known. These links can take different forms, such as adding to, modifying, or reorganizing knowledge or skills. How these links are made may vary in different subject areas and among students with varying talents, interests, and abilities (Paris and Ayers, 1994). Learning with understanding, however, involves more than appending new concepts and processes to existing knowledge; it also involves conceptual change and the creation of rich, integrated knowledge structures.If students’ existing knowledge is not engaged, the understandings they develop through instruction can be very different from what their teacher may have intended; learners are more likely to construct interpretations that agree with their own prior knowledge even when those interpretations are in conflict with the teacher’s viewpoint. Thus, lecturing to students is often an ineffective tool for producing conceptual change.

For example, Vosniadou and Brewer (1992) describe how learners who believed the world is flat perceived the earth as a three-dimensional pancake after being taught that the world is a sphere.Moreover, when prior knowledge is not engaged, students are likely to fail to understand or even to separate knowledge learned in school from their beliefs and observations about the world outside the classroom. Example, despite instruction to the contrary, students of all ages (including college graduates) often persist in their belief that seasons are caused by the earth’s distance from the sun, rather than the inclination of the earth’s axis relative to the plane of its orbit around the sun, which affects the amount of solar energy striking the northern and southern regions of the earth as it orbits the sun (Harvard-Smithsonian Center for Astrophysics, Science Education Department, 1987). Roth (1986) similarly found that students continued to believe plants obtain food from the soil, rather than making it in their leaves, even after they had been taught about photosynthesis; this belief persisted since many failed to recognize that the carbon dioxide extracted from the air has weight and makes up most of a plant’s mass.Effective teaching involves gauging what learners already know about a subject and finding ways to build on that knowledge. When prior knowledge contains misconceptions, there is a need to reconstruct a whole relevant framework of concepts, not simply to correct the misconception or faulty idea. Effective instruction entails detecting those misconceptions and addressing them, sometimes by challenging them directly (Caravita and Hallden, 1994; Novak, 2002).The central role played by prior knowledge in the ability to gain new knowledge and understanding has important implications for the preparation of students in the years preceding advanced study. To be successful in advanced study in science or mathematics, students must have acquired a sufficient knowledge base that includes concepts, factual content, and relevant procedures on which to build.

This in turn implies that they must have had the opportunity to learn these things. Many students, however, particularly those who attend urban and rural schools, those who are members of certain ethnic or racial groups (African American, Hispanic, and Native American), and those who are poor, are significantly less likely to have equitable access to early opportunities for building this prerequisite knowledge base (Doran, Dugan, and Weffer, 1998; see also, this volume). Learning is facilitated through the use of metacognitive strategies that identify, monitor, and regulate cognitive processes.To be effective problem solvers and learners, students need to determine what they already know and what else they need to know in any given situation. They must consider both factual knowledge—about the task, their goals, and their abilities—and strategic knowledge about how and when to use a specific procedure to solve the problem at hand (Ferrari and Sternberg, 1998). In other words, to be effective problem solvers, students must be metacognitive. Empirical studies show that students who are metacognitively aware perform better than those who are not (Garner and Alexander, 1989; Schoenfeld, 1987).Metacognition is an important aspect of students’ intellectual development that enables them to benefit from instruction (Carr, Kurtz, Schneider, Turner, and Borkowski, 1989; Flavell, 1979; Garner, 1987; Novak, 1985; Van Zile-Tamsen, 1996) and helps them know what to do when things are not going as expected (Schoenfeld, 1983; Skemp, 1978, 1979).

For example, research demonstrates that students with better-developed metacognitive strategies will abandon an unproductive problem-solving strategy very quickly and substitute a more productive one, whereas students with less effective metacognitive skills will continue to use the same strategy long after it has failed to produce results (Gobert and Clement, 1999). The basic metacognitive strategies include (1) connecting new information to former knowledge; (2) selecting thinking strategies deliberately; and (3) planning, monitoring, and evaluating thinking processes (Dirkes, 1985).Experts have highly developed metacognitive skills related to their specific area of expertise. If students in a subject area are to develop problem-solving strategies consistent with the ways in which experts in the discipline approach problems, one important goal of advanced study should be to help students become more metacognitive. Fortunately, research indicates that students’ metacognitive abilities can be developed through explicit instruction and through opportunities to observe teachers or other content experts as they solve problems and consider ideas while making their thinking visible to those observing (Collins and Smith, 1982; Lester et al., 1994. Schoenfeld, 1983, 1985). Having students construct concept maps for a topic of study can also provide powerful metacognitive insights, especially when students work in teams of three or more (see for a discussion of concept maps). It is important to note that the teaching of metacognitive skills is often best accomplished in specific content areas since the ability to monitor one’s understanding is closely tied to the activities and questions that are central to domain-specific knowledge and expertise (NRC, 2000b).

Learners have different strategies, approaches, patterns of abilities, and learning styles that are a function of the interaction between their heredity and their prior experiences.Individuals are born with potential that develops through their interaction with their environment to produce their current capabilities and talents. Thus among learners of the same age, there are important differences in cognitive abilities, such as linguistic and spatial aptitudes or the ability to work with symbolic quantities representing properties of the natural world, as well as in emotional, cultural, and motivational characteristics.Additionally, by the time students reach high school, they have acquired their own preferences regarding how they like to learn and at what pace. Thus, some students will respond favorably to one kind of instruction, whereas others will benefit more from a different approach. Educators need to be sensitive to such differences so that instruction and curricular materials will be suitably matched to students’ developing abilities, knowledge base, preferences, and styles. ( illustrates some of the ways in which curriculum and instruction might be modified to meet the learning needs of high-ability learners.)Appreciation of differences among learners also has implications for the design of appropriate assessments and evaluations of student learning.

Students with different learning styles need a range of opportunities to demonstrate their knowledge and skills. For example, some students work well.

2Concept maps are two-dimensional, hierarchical representations of concepts and relationships between concepts that model the structure of knowledge possessed by a learner or expert. The theory of learning that underlies concept mapping recognizes that all meaningful learning builds on the learner’s existing relevant knowledge and the quality of its organization. The constructivist epistemology underlying concept maps recognizes that all knowledge consists of concepts, defined as perceived regularities in events or objects or their representation, designated by a label, and propositions that are two or more concepts linked semantically to form a statement about some event or object. Free software that aids in the construction of concept maps is available at.

Under pressure, while the performance of others is significantly diminished by time constraints. Some excel at recalling information, while others are more adept at performance-based tasks. Some express themselves well in writing, while others do not. Thus using one form of assessment will work to the advantage of some students and to the disadvantage of others (Mintzes, Wandersee, and Novak, 2001; O’Neil and Brown, 1997; Shavelson, Baxter, and Pine, 1992; Sugrue, Valdes, Schlackman, and Webb, 1996). A learner’s motivation to learn and sense of self affects what is learned, how much is learned, and how much effort will be put into the learning process.Humans are motivated to learn and to develop competence (Stipek, 1998; White, 1959). Motivation can be extrinsic (performance oriented), for example to get a good grade on a test or to be accepted by a good college, or intrinsic (learning oriented), for example to satisfy curiosity or to master challenging material.

Regardless of the source, learners’ level of motivation strongly affects their willingness to persist in the face of difficulty. Intrinsic motivation is enhanced when learning tasks are perceived as being interesting and personally meaningful and are presented at the proper level of difficulty. A task that is too difficult can create frustration; one that is too easy can lead to boredom.Research has revealed strong connections between learners’ beliefs about their own abilities in a subject area and their success in learning about that domain (Eccles, 1987, 1994; Garcia and Pintrich, 1994; Graham and Weiner, 1996; Markus and Wurf, 1987; Marsh, 1990; Weiner, 1985). Some beliefs about learning are quite general. For example, some students believe their ability to learn a particular subject or skill is predetermined, whereas others believe their ability to learn is substantially a function of effort (Dweck, 1989). Believing that abilities are developed through effort is most beneficial to the learner, and teachers and others should cultivate that belief (Graham and Weiner, 1996; Weiner, 1985).

The use of instructional strategies that encourage conceptual understanding is an effective way to increase students’ interest and enhance their confidence about their abilities to learn a particular subject (Alaiyemola, Jegede, and Okebukola, 1990; Cavallo, 1996).Cultivating the belief among a broad range of students that the ability to learn advanced science and mathematics is, for the most part, a function of effort rather than inherited talent, ability, and/or intelligence has other benefits as well. For example, the belief that successful learning in advanced study is a matter of effort fosters risk taking in course selection and promotes students’ motivation to succeed in challenging situations (Novak. Gowin, 1984).

A belief in the value of effort is especially important for students who are traditionally underrepresented in advanced study. The practices and activities in which people engage while learning to shape what is learned.Research on the situated nature of cognition indicates that the way people learn a particular domain of knowledge and skills and the context in which they learn it become a fundamental part of what is learned (Greeno, 1993; Lave, 1991). When students learn, they learn both information and a set of practices, and the two are inextricably related. McLellan (1996, p. Countered in real life, in other classes, or in other disciplines. It is only by encountering the same concept at work in multiple contexts that students can develop a deep understanding of the concept and how it can be used, as well as the ability to transfer what has been learned in one context to others (Anderson, Greeno, Reder, and Simon, 1997).If the goal of education is to allow learners to apply what they learn in real situations, learning must involve applications and take place in the context of authentic activities (Brown et al., 1989).

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Brown and colleagues (1989, p. 34) define authentic activities as “ordinary practices of a culture”—activities that are similar to what actual practitioners do in real contexts. Brown and colleagues (1993) offer a somewhat different definition: given that the goal of education is to prepare students to be lifelong learners, activities are authentic if they foster the kinds of thinking that are important for learning in out-of-school settings, whether or not those activities mirror what practitioners do.

Regardless of which definition is adopted, the importance of situating learning in authentic activities is clear. Munities of practice, have opportunities to test their own ideas, and learn by observing others. Research demonstrates that opportunities for students to articulate their ideas to peers and to hear and discuss others’ ideas in the context of the classroom is particularly effective in bringing about conceptual change (Alexopoulou and Driver, 1996; Carpenter and Lehrer, 1999; Cobb, Wood, and Yackel, 1993; Kobayashi, 1994; Towns and Grant, 1997; Wood, Cobb, and Yackel, 1991). Social interaction also is important for the development of expertise, metacognitive skills, and formation of the learner’s sense of self.The social nature of learning has important implications for the consequences of the ways in which students are grouped for instruction. For example, students who are placed in low-track classes often have less time to collaborate and interact around instructional tasks. Research indicates that teachers in low-track science and mathematics classes spend more time than teachers in higher-track classes on routines, and more frequently provide seatwork and worksheet activities that are designed to be completed independently (Oakes, 1990).

Additionally, teachers in higher-track classes often orchestrate more frequent and varied opportunities for students to participate in small-group problem-solving activities than are provided by teachers in lower-track classes, who tend to focus on behavior management and on maintaining control during learning activities. Some might contend that teachers in both types of classes are responding to the needs of their students. However, teachers must strike a balance between providing the structure that is often appropriate for low-ability students and the active engagement that allows these students to learn at deeper levels.Newmann and Wehlage (1995) identify teaching strategies that promote intellectual quality and authenticity. One of the most powerful strategies is the “substantive conversation,” in which students engage in extended conversational exchanges with the teacher and/or peers about subject matter in a way that builds an improved or shared understanding of ideas or topics. The authors stress that such subject matter conversations go far beyond reporting facts, procedures, or definitions; they focus on making distinctions, applying ideas, forming generalizations, and raising questions. According to the results of research by Gamoran and Nystrand (1990), the opportunities for such substantive engagement are far fewer in low-track than in higher-track classes.

ANNEX 6-1 CHARACTERISTICS OF HIGH-ABILITY LEARNERS AND IMPLICATIONS FOR CURRICULUM AND INSTRUCTIONDifferences among learners have implications for how curriculum and instruction should be structured. Provided below is an example of how a better understanding of learning can assist teachers in structuring their curricula and instruction more appropriately to meet the needs of a particular group of students. Different strategies would most likely be used to meet the needs of other students, although there might be some overlap.Characteristic: High-ability learners display an exceptionally rich knowledge base in their specific talent domain. Within that domain, they tend to achieve formal operational thought earlier than other students and to display advanced problem-solving strategies.

High-ability learners are also able to work with abstract and complex ideas in their talent domain at an earlier age.Implication: High-ability learners are ready to access the high school mathematics and science curriculum earlier than other students. Thus the high school mathematics and science sequence should be offered to them beginning in middle school.Characteristic: High-ability students pick up informally much of the content knowledge taught in school, and as a result, that knowledge tends to be idiosyncratic and not necessarily organized around the central concepts of the discipline.Implication: Assessment of what the learner has already mastered through diagnostic testing is critical. Instruction needs to build on what is already known and on previous experiences, filling in the gaps and correct. Ing misconceptions. It also must help the student organize his or her knowledge around the central ideas of the discipline. A full course in a content area often is not needed; either it could be skipped, with gaps being filled in as needed, or the curriculum compacted.

“The proper psychology of talent is one that tries to be reasonably specific in defining competencies as manifested in the world, with instruction aimed at developing the very competencies so defined” (Wallach, 1978, p. 617).Characteristic: High-ability learners learn at a more rapid rate than other students and can engage in simultaneous rather than only linear processing of ideas in their talent domain.Implication: The pace at which the curriculum is offered must be adjusted for these learners. The curriculum also must be at a more complex level, making interdisciplinary connections whenever possible. That is, the curriculum should allow for faster pacing of well-organized, compressed, and appropriate learning experiences that are, in the end, enriching and accelerative.Characteristic: Many high-ability students will have mastered the content of high school mathematics and science courses before formally taking the courses, either on their own, through special programs, or through Web-based courses.Implication: Opportunities for testing out of prerequisites should be provided. Achievement motivation and self-efficacy arises out of challenge and satisfaction in mastering tasks that appropriately match capabilities.Characteristic: The capacity for learning of high-ability students is underestimated and thus becomes underdeveloped, especially if learning criteria lack sufficient challenge, and curriculum is not adequately knowledge rich and rigorous.Implication: Curriculum must be targeted at developing especially deep and well-organized knowledge structures that with time will begin to approximate those of experts. Doing so will foster cognitive development, higher-level thinking skills, and creativity.

The depth of the curriculum should allow gifted learners to continue exploring an area of special interest to the expert level. Curricula for these students should enable them to explore constantly changing knowledge and information and develop the attitude that knowledge is worth pursuing in a global society.Characteristic: High-ability children are advanced in their critical and creative thinking skills. They tend to spend much more time up front (i.e., metacognitively) than in the execution phase of problem solving.Implication: The basic thinking skills to be developed in high-ability students are critical thinking, creative thinking, problem finding and solving, research, and decision making.

Those skills should be mastered within each content domain.Characteristic: High-ability students prefer unstructured problems in which the task is less well defined. They also like to structure their own learning experiences. They do not require careful scaffolding of material or step-by-step learning experiences to master new material or concepts; in fact, they become frustrated with such approaches.Implication: Opportunities to identify and solve problems should be provided. Interdisciplinarity, greater in-depth exploration of areas of interest, and autonomous learning should be encouraged. Meaningful project work in content areas, in which real-world products are generated, is appropriate as it allows students the opportunity to create on their own and to apply and expand ideas learned in class.

To facilitate such work, curricula should encourage exposure to, selection of, and use of specialized and appropriate resources.Characteristic: High-ability students have the capacity to make connections easily among disparate bodies of knowledge and to deal effectively with abstractions and complexity of thought.Implication: Curricula ought to emphasize providing students with a deep understanding of the important concepts of a discipline and how they. Are organized, as well as identify important pathways between disciplines so that separate facets of knowledge are understood as being integrated. Curricula should allow for the development and application of productive thinking skills to instill in students the capacity to reconceptualize existing knowledge and generate new knowledge.Characteristic: Eminent persons tend to have been profoundly influenced by a single individual, such as an educator. Students in the top mathematical/science graduate programs have reported research experiences during high school at unusually high levels. Those who are precocious in creative production tend to exhibit outstanding achievement in adult life.Implication: Mentorships, internships, or long-term research opportunities should be provided for advanced students.Characteristic: High-ability students who become productive adults in a domain have passed through that domain’s specific stages.

Exporting to a PDF File (Report Builder and SSRS). 5 minutes to read.In this articleThe PDF rendering extension renders Reporting Services paginated reports to files that can be opened in Adobe Acrobat and other third-party PDF viewers that support PDF 1.3. Although PDF 1.3 is compatible with Adobe Acrobat 4.0 and later versions, Reporting Services supports Adobe Acrobat 11.0 or later. The rendering extension does not require Adobe software to render the report. However, PDF viewers such as Adobe Acrobat are required to view or print a report in PDF format.The PDF rendering extension supports ANSI characters and can translate Unicode characters from Japanese, Korean, Traditional Chinese, Simplified Chinese, Cyrillic, Hebrew, and Arabic with certain limitations. For more information about the limitations, see.The PDF renderer is a physical page renderer and, therefore, has pagination behavior that differs from other renderers such as HTML and Excel. This topic provides PDF renderer-specific information and describes exceptions to the rules.

NoteYou can create and modify paginated report definition (.rdl) files in Report Builder and in Report Designer in SQL Server Data Tools. Each authoring environment provides different ways to create, open, and save reports and related items. Font EmbeddingWhen possible, the PDF rendering extension embeds the subset of each font that is needed to display the report in the PDF file. Fonts that are used in the report must be installed on the report server. When the report server generates a report in PDF format, it uses the information stored in the font referenced by the report to create character mappings within the PDF file. If the referenced font is not installed on the report server, the resulting PDF file might not contain the correct mappings and might not display correctly when viewed.Fonts are embedded in the PDF file when the following conditions apply:.Font embedding privileges are granted by the font author. Installed fonts include a property that indicates whether the font author intends to allow embedding a font in a document.

If the property value is EMBEDNOEMBEDDING, the font is not embedded in the PDF file. For more information, see 'TTGetEmbeddingType' on msdn.microsoft.com.The Font is TrueType.Fonts are referenced by visible items in a report.

If a font is referenced by an item that has the Hidden property set to True, the font is not needed to display rendered data and will not be included in the file. Fonts are embedded only when they are needed to display the rendered report data.If all of these conditions are met for a font, the font is embedded in the PDF file. If one or more of these conditions is not met, the font is not embedded in the PDF file. NoteAlthough the conditions are met, there is one circumstance under which fonts are not embedded in the PDF file. If the fonts used are the ones in the PDF specification that are commonly known as standard type 1 fonts or the base fourteen fonts, then fonts are not embedded for ANSI content. Fonts on the Client ComputerWhen a font is embedded in the PDF file, the computer that is used to view the report (the client computer) does not need to have the font installed for the report to display correctly.When a font is not embedded in the PDF file, the client computer must have the correct font installed for the report to display correctly. If the font is not installed on the client computer, the PDF file displays a question mark character (?) for unsupported characters.

Verifying Fonts in a PDF FileDifferences in PDF output occur most often when a font that does not support non-Latin characters is used in a report and then non-Latin characters are added to the report. You should test the PDF rendering output on both the report server and the client computers to verify that the report renders correctly.Do not rely on viewing the report in Preview or exporting to HTML because the report will look correct due to automatic font substitution performed by the graphical design interface or by Microsoft Internet Explorer, respectively.

If there are Unicode Glyphs missing on the server, you may see characters replaced with a question mark (?). If there is a font missing on the client, you may see characters replaced with boxes (□).The fonts that are embedded in the PDF file are included in the Fonts property that is saved with the file, as metadata. MetadataIn addition to the report layout, the PDF rendering extension writes the following metadata to the PDF Document Information Dictionary. PDF propertyCreated fromTitleThe Name attribute of the Report RDL element.AuthorThe Author RDL element.SubjectThe Description RDL element.CreatorReporting Services product name and version.ProducerRendering extension name and version.CreationDateReport execution time in PDF datetime format.InteractivitySome interactive elements are supported in PDF. The following is a description of specific behaviors. Show and HideDynamic show and hide elements are not supported in PDF. The PDF document is rendered to match the current state of any items in the report.

For example, if the item is displayed when the report is run initially, then the item is rendered. Images that can be toggled are not rendered, if they are hidden when the report is exported. Document MapIf there are any document map labels present in the report, a document outline is added to the PDF file. Each document map label appears as an entry in the document outline in the order that it appears in the report. In Acrobat, a target bookmark is added to the document outline only if the page it is on is rendered.If only a single page is rendered, no document outline is added. The document map is arranged hierarchically to reflect the level of nesting in the report. The document outline is accessible in Acrobat under the Bookmarks tab.

Clicking an entry within the document outline causes the document to go to the bookmarked location. BookmarksBookmarks are not supported in PDF rendering. Drillthrough LinksDrillthrough links are not supported in PDF rendering. The drillthrough links are not rendered as clickable links and drillthrough reports cannot connect to the target of the drillthrough. HyperlinksHyperlinks in reports are rendered as clickable links in the PDF file.

When clicked, Acrobat will open the default client browser and navigate to the hyperlink URL. CompressionImage compression is based on the original file type of the image. The PDF rendering extension compresses PDF files by default.To preserve any compression for images included in the PDF file when possible, JPEG images are stored as JPEG and all other image types are stored as BMP.