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In short, the factory model affected the design of curriculum, instruction, and assessment in schools. Today, students need to understand the current state of their knowledge and to build on it, improve it, and make decisions in the face of uncertainty Talbert and McLaughlin, Doing history involves the construction and evaluation of historical documents see, e. Doing science includes such activities as testing theories. Colonists were literate enough if they could sign their name, or even an X, on deeds. That literacy was the ability to hold a book and reel off memorized portions of basic American texts such as the opening paragraph of the Declaration of Independence, a part of the Gettysburg address, or some Bryant or Longfellow.
With the coming of World War I, and the prospect of large numbers of men handling new equipment in foreign countries, Army testers redefined reading. Suddenly, to the dismay of men used to reading familiar passages, passing the army reading test meant being able to make sense, on the spot, of never-before-seen text. To achieve this vision requires rethinking what is taught, how teachers teach, and how what students learn is assessed. The remainder of this chapter is organized around Figure 6. Although we discuss these perspectives separately, they need to be conceptualized as a system of interconnected components that mutually support one another e.
This term includes teaching practices that. Teachers who are learner centered recognize the importance of building on the conceptual and cultural knowledge that students bring with them to the classroom see Chapters 3 and 4. The information on which to base a diagnosis may be acquired through observation, questioning and conversation, and reflection on the products of student activity.
A key strategy is to prompt children to explain and develop their knowledge structures by asking them to make predictions about various situations and explain the reasons for their predictions. By selecting critical tasks that embody known misconceptions, teachers can help students test their thinking and see how and why various ideas might need to change Bell, a, b, ; Bell et al. The model is one of engaging students in cognitive conflict and then having discussions about conflicting viewpoints see Piaget, ; Festinger, Learner-centered instruction also includes a sensitivity to the cultural practices of students and the effect of those practices on classroom learning.
Learner-centered teachers also respect the language practices of their students because they provide a basis for further learning. In science, one standard way of talking in both school and professional science is impersonal and expository, without any reference to personal or social intentions or experiences Lemke, ; Wertsch, In their narratives and arguments, students express both scientific and social intentions: If the responses of other students and the teacher to these multivoiced narratives are always keyed to the scientific point, it helps to shape the meaning that is taken from them and relates them back to the context of the unfolding scientific argument Ballenger, In standard science lessons, the scientific point in the talk of many students, particularly those whose discourse is not mainstream, is often missed, and the social intention is often devalued Lemke, ; Michaels and Bruce, ; Wertsch, ; see Chapter 7.
In another example of connecting everyday talk and school talk, African American high school students were shown that many of their forms of everyday speech were examples of a very high form of literacy that was taught in school, but never before connected with their everyday experience Lee, , Like Proust who discovered he had been speaking prose all of his life, the students discovered that they were fluent in a set of competencies that were considered academically advanced.
Overall, learner-centered environments include teachers who are aware that learners construct their own meanings, beginning with the beliefs, understandings, and cultural practices they bring to the classroom. If teaching is conceived as constructing a bridge between the subject matter and the student, learner-centered teachers keep a constant eye on both ends of the bridge. The teachers attempt to get a sense of what students know and can do as well as their interests and passions—what each student knows, cares about, is able to do, and wants to do.
Chapter 7 illustrates how these bridges can be built. Environments that are solely learner centered would not necessarily help students acquire the knowledge and skills necessary to function effectively in society. Knowledge-centered environments take seriously the need to help students become knowledgeable Bruner, by learning in ways that lead to understanding and subsequent transfer. Current knowledge on learning and transfer Chapter 3 and development Chapter 4 provide important guidelines for achieving these goals.
Standards in areas such as mathematics and science help define the knowledge and competencies that students need to acquire e. The story Fish Is Fish Chapter 1 illustrates how people construct new knowledge based on their current knowledge. Knowledge-centered environments also focus on the kinds of information and activities that help students develop an understanding of disciplines e.
This focus requires a critical examination of existing curricula. In history, a widely used history text on the American Revolution left out crucial information necessary to understand rather than merely memorize Beck et al. A concern with sense-making raises questions about many existing curricula. For example, it has been argued that many mathematics curricula emphasize. The process of calculation or computation only involves the deployment of a set routine with no room for ingenuity or flair, no place for guess work or surprise, no chance for discovery, no need for the human being, in fact Scheffler, The argument here is not that students should never learn to compute, but that they should also learn other things about mathematics, especially the fact that it is possible for them to make sense of mathematics and to think mathematically e.
There are interesting new approaches to the development of curricula that support learning with understanding and encourage sense making. Instructional units encourage students to build on their informal ideas in a gradual but structured manner so that they acquire the concepts and procedures of a discipline. The idea of progressive formalization is exemplified by the algebra strand for middle school students using Mathematics in Context National Center for Research in Mathematical Sciences Education and Freudenthal Institute, It begins by having students use their own words, pictures, or diagrams to describe mathematical situations to organize their own knowledge and work and to explain their strategies.
In later units, students gradually begin to use symbols to describe situations, organize their mathematical work, or express their strategies. At this level, students devise their own symbols or learn some nonconventional notation. Their representations of problem situations and explanations of their work are a mixture of words and symbols.
Later, students learn and use standard conventional algebraic notation for writing expressions and equations, for manipulating algebraic expressions and solving equations, and for graphing equations. Movement along this continuum is not necessarily smooth, nor all in one direction. Although students are actually doing algebra less formally in the earlier grades, they are not forced to generalize their knowledge to a more formal level, nor to operate at a more formal level, before they have had sufficient experience with the underlying concepts.
Thus, students may move back and forth among levels of formality depending on the problem situation or on the mathematics involved. Such questions represent another example of overlap between learnercentered and knowledge-centered perspectives. Older views that young children are incapable of complex reasoning have been replaced by evidence that children are capable of sophisticated levels of thinking and reasoning when they have the knowledge necessary to support these activities see Chapter 4.
An impressive body of research shows the potential benefit of early access by students to important conceptual ideas. Young children have also demonstrated powerful forms of early algebraic generalization Lehrer and Chazan, Forms of generalization in science, such as experimentation, can be introduced before the secondary school years through a developmental approach to important mathematical and scientific ideas Schauble et al. Attempts to create environments that are knowledge centered also raise important questions about how to foster an integrated understanding of a discipline.
Many models of curriculum design seem to produce knowledge and skills that are disconnected rather than organized into coherent wholes. The National Research Council Vast numbers of learning objectives, each associated with pedagogical strategies, serve as mile posts along the trail mapped by texts from kindergarten to twelfth grade….
Problems are solved not by observing and responding to the natural landscape through which the mathematics curriculum passes, but by mastering time tested routines, conveniently placed along the path National Research Council, In this metaphor, learning is analogous to learning. The progressive formalization framework discussed above is consistent with this metaphor. The curricula include the familiar scope and sequence charts that specify procedural objectives to be mastered by students at each grade: Yet it is the network, the connections among objectives, that is important.
This is the kind of knowledge that characterizes expertise see Chapter 2. Stress on isolated parts can train students in a series of routines without educating them to understand an overall picture that will ensure the development of integrated knowledge structures and information about conditions of applicability. An alternative to simply progressing through a series of exercises that derive from a scope and sequence chart is to expose students to the major features of a subject domain as they arise naturally in problem situations.
Activities can be structured so that students are able to explore, explain, extend, and evaluate their progress. Ideas are best introduced when students see a need or a reason for their use—this helps them see relevant uses of knowledge to make sense of what they are learning.
Problem situations used to engage students may include the historic reasons for the development of the domain, the relationship of that domain to other domains, or the uses of ideas in that domain see Webb and Romberg, In Chapter 7 we present examples from history, science, and mathematics instruction that emphasize the importance of introducing ideas and concepts in ways that promote deep understanding.
A challenge for the design of knowledge-centered environments is to strike the appropriate balance between activities designed to promote understanding and those designed to promote the automaticity of skills necessary to function effectively without being overwhelmed by attentional requirements. Students for whom it is effortful to read, write, and calculate can encounter serious difficulties learning.
Shape cut-outs are included. Thanks so much for including my tree sensory play and painting with nature posts! The argument here is not that students should never learn to compute, but that they should also learn other things about mathematics, especially the fact that it is possible for them to make sense of mathematics and to think mathematically e. It is important to distinguish between two major uses of assessment. Gus is a Tree. The model is one of engaging students in cognitive conflict and then having discussions about conflicting viewpoints see Piaget, ; Festinger, Alignment is as important for schools as for organizations in general e.
The importance of automaticity has been demonstrated in a number of areas e. In addition to being learner centered and knowledge centered, effectively designed learning environments must also be assessment centered. The key principles of assessment are that they should provide opportunities.
It is important to distinguish between two major uses of assessment. The first, formative assessment, involves the use of assessments usually administered in the context of the classroom as sources of feedback to improve teaching and learning. The second, summative assessment, measures what students have learned at the end of some set of learning activities. Examples of summative assessments include teacher-made tests given at the end of a unit of study and state and national achievement tests that students take at the end of a year. Issues of summative assessment for purposes of national, state, and district accountability are beyond the scope of this volume; our discussion focuses on classroom-based formative and summative assessments.
Studies of adaptive expertise, learning, transfer, and early development show that feedback is extremely important see Chapters 2 , 3 , and 4. Given the goal of learning with understanding, assessments and feedback must focus on understanding, and not only on memory for procedures or facts although these can be valuable, too. Assessments that emphasize understanding do not necessarily require elaborate or complicated assessment procedures. Even multiple-choice tests can be organized in ways that assess understanding see below.
Opportunities for feedback should occur continuously, but not intrusively, as a part of instruction. The feedback they give to students can be formal or informal. Effective teachers also help students build skills of self-assessment. Students learn to assess their own work, as well as the work of their peers, in order to help everyone learn more effectively see, e.
Such self-assessment is an important part of the metacognitive approach to instruction discussed in Chapters 3 , 4 , and 7.
In many classrooms, opportunities for feedback appear to occur relatively infrequently. Most teacher feedback—grades on tests, papers,. After receiving grades, students typically move on to a new topic and work for another set of grades. Feedback is most valuable when students have the opportunity to use it to revise their thinking as they are working on a unit or project. Opportunities to work collaboratively in groups can also increase the quality of the feedback available to students Barron, ; Bereiter and Scardamalia, ; Fuchs et al.
New technologies provide opportunities to increase feedback by allowing students, teachers, and content experts to interact both synchronously and asynchronously see Chapter 9. Many assessments developed by teachers overly emphasize memory for procedures and facts Porter et al. In addition, many standardized tests that are used for accountability still overemphasize memory for isolated facts and procedures, yet teachers are often judged by how well their students do on such tests. One mathematics teacher consistently produced students who scored high on statewide examinations by helping students memorize a number of mathematical procedures e.
Appropriately designed assessments can help teachers realize the need to rethink their teaching practices. Even without technology, however, advances have been made in devising simple assessments that measure understanding rather than memorization. In the area of physics, assessments like those used in Chapter 2 to compare experts and novices have been revised for use in classrooms. One task presents students with two problems and asks them to state whether both would be solved using a similar approach and state the reason for the decision:.
How much work was done by friction? The ball travels on a horizontal surface and eventually rolls without slipping. Novices typically state that these two problems are solved similarly because they match on surface features—both involve a ball sliding and rolling on a horizontal surface. Students who are learning with understanding state that the problems are solved differently: These kinds of assessment items can be used during the course of instruction to monitor the depth of conceptual understanding.
Portfolio assessments are another method of formative assessment.
They take time to implement and they are often implemented poorly—portfolios often become simply another place to store student work but no discussion of the work takes place— but used properly, they provide students and others with valuable information about their learning progress over time. A challenge for the learning sciences is to provide a theoretical framework that links assessment practices to learning theory. An important step in this direction is represented by the work of Baxter and Glaser , who. A 1-kilogram stick that is 2 meters long is placed on a frictionless surface and is free to rotate about a vertical pivot through one end.
A gram lump of putty is attached 80 centimeters from the pivot. Performance on this item was near random for students finishing an introductory calculus-based physics course. Data such as these are important for helping teachers guide students toward the development of fluid, transferable knowledge Leonard et al. In their report, performance is described in terms of the content and process task demands of the subject matter and the nature and extent of cognitive activity likely to be observed in a particular assessment situation.
The kind and quality of cognitive activities in an assessment is a function of the content and process demands of the task involved. For example, consider the content-process framework for science assessment shown in Figure 6. In this figure, task demands for content. At one extreme are knowledge-rich tasks, tasks that require in-depth understanding of subject matter for their completion. At the other extreme are tasks that are not dependent on prior knowledge or related experiences; rather, performance is primarily dependent on the information given in the assessment situation.
The task demands for process skills are conceptualized as a continuum from constrained to open x axis. In open situations, explicit directions are minimized; students are expected to generate and carry out appropriate process skills for problem solution. In process-constrained situations, directions can be of two types: In this situation, students are asked to generate explanations, an activity that does not require using the process skills.
Assessment tasks can involve many possible combinations of content knowledge and process skills; Table 6. New developments in the science of learning suggest that the degree to which environments are community centered is also important for learning. Especially important are norms for people learning from one another and continually attempting to improve. We use the term community centered to refer to several aspects of community, including the classroom as a commu-. At the level of classrooms and schools, learning seems to be enhanced by social norms that value the search for understanding and allow students and teachers the freedom to make mistakes in order to learn e.
Different classrooms and schools reflect different sets of norms and expectations. For example, an unwritten norm that operates in some classrooms is never to get caught making a mistake or not knowing an answer see, e. Some norms and expectations are more subject specific. For example, the norms in a mathematics class may be that mathematics is knowing how to compute answers; a much better norm would be that the goal of inquiry is mathematical understanding.
Different norms and practices have major effects on what is taught and how it is assessed e. Sometimes there are different sets of expectations for different students. Teachers may convey expectations for school success to some students and expectations for school failure to others MacCorquodale, For example, girls are sometimes discouraged from participating in higher level mathematics and science.
Students, too, may share and convey cultural expectations that proscribe the participation of girls in some classes Schofield et al. A speech-language pathologist working in an Inuit school in northern Canada asked a principal—who was not an Inuit—to compile a list of children who had speech and language problems in the school.
They should be learning by looking. When the speech-language pathologist asked that teacher about one toddler she was studying who was very talkative and seemed to the non-Inuit researcher to be very bright, the teacher said: Classroom norms can also encourage modes of participation that may be unfamiliar to some students. For example, some groups rely on learning by observation and listening and then becoming involved in ongoing activities; school-like forms of talking may be unfamiliar for the children whose community has only recently included schools Rogoff et al.
The sense of community in classrooms is also affected by grading practices, and these can have positive or negative effects depending on the students. For example, Navajo high school students do not treat tests and grades as competitive events the way that Anglo students do Deyhle and Margonis, More broadly, competition among students for teacher attention, approval, and grades is a commonly used motivator in U.
And in some situations, competition may create situations that impede learning. An emphasis on community is also imortant when attempting to borrow successful educational practices from other countries. For example, Japanese teachers spend considerable time working with the whole class, and they frequently ask students who have made errors to share their thinking with the rest of the class. This can be very valuable because it leads to discussions that deepen the understanding of everyone in the class.
However, this practice works only because Japanese teachers have developed a classroom culture in which students are skilled at learning from one another and respect the fact that an analysis of errors is fruitful for learning Hatano and Inagaki, Japanese students value listening, so they learn from large class discussions even if they do not have many chances to participate.
The culture of American classrooms is often very different—many emphasize the importance of being right and contributing by talking. Teaching and learning must be viewed from the perspective of the overall culture of the society and its relationship to the norms of the classrooms. To simply attempt to import one or two Japanese teaching techniques into American classrooms may not produce the desired results. The sense of community in a school also appears to be strongly affected by the adults who work in that environment. As Barth states:.
The relationship among adults who live in a school has more to do with the character and quality of the school and with the accomplishments of the students than any other factor. Studies by Bray and Talbert and McLaughlin emphasize the importance of teacher learning communities.
We say more about this in Chapter 8. An analysis of learning environments from the perspective of community also includes a concern for connections between the school environment and the broader community, including homes, community centers, after-school programs, and businesses.
Cut out the shapes at the end of this lesson, one six-page set per child. You can print the sheets on colored paper or allow the child to color the shapes for easier identification. You will also be using these shapes in later lessons. Call the shape out before each verse.
Show the student images of Kandinsky paintings on the Internet. Here are a few examples. Have the student lay the shapes out on the floor or a table in order of most used. After the shape walk, reflect on the shapes that were easiest to find and those that were hardest to find, using questions such as:. If desired, have the student create a new drawing that reflects the shapes as found on the walk. If lots of circles were found, have lots of circles in the drawing.
Now you both have a visual representation of the shape walk results. Since this is a Kindergarten-level activity, this assessment is skills-based, rather than grade-based.
This series of lessons was designed to meet the needs of gifted children for extension beyond the standard curriculum with the greatest ease of use for the educator. The lessons may be given to the students for individual self-guided work, or they may be taught in a classroom or a home-school setting. Assessment strategies and rubrics are included at the end of each section. The rubrics often include a column for "scholar points," which are invitations for students to extend their efforts beyond that which is required, incorporating creativity or higher level technical skills.
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Nulla cursus dui id nunc ullamcorper sed semper nisl lobortis. Phasellus arcu ante, imperdiet in ornare sed, laoreet eu massa. Introduction The ability to accurately identify shapes is a foundational mathematical skill, and it is quite rewarding for children because their world is full of shapes. Guiding Questions What are some basic shapes? Where are these shapes found? Learning Objectives After completing the lessons in this unit, students will be able to: Recognize shapes in the environment.
Create original works of art using the shapes. Preparation Read through each of the mini-lessons.
Find the suggested materials you want to use.